https://reu.cs.mu.edu/api.php?action=feedcontributions&user=Babcock&feedformat=atomREU@MU - User contributions [en]2024-03-28T19:58:17ZUser contributionsMediaWiki 1.23.13https://reu.cs.mu.edu/index.php/REUCarissaBabcockPaper.pdfREUCarissaBabcockPaper.pdf2017-09-08T00:07:54Z<p>Babcock: Created page with "File:Competition_and_(1,2)-step_Competition_Numbers_in_4-Cycle_Graph_Variations_Paper.pdf"</p>
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<div>[[File:Competition_and_(1,2)-step_Competition_Numbers_in_4-Cycle_Graph_Variations_Paper.pdf]]</div>Babcockhttps://reu.cs.mu.edu/index.php/File:Competition_and_(1,2)-step_Competition_Numbers_in_4-Cycle_Graph_Variations_Paper.pdfFile:Competition and (1,2)-step Competition Numbers in 4-Cycle Graph Variations Paper.pdf2017-09-08T00:06:35Z<p>Babcock: </p>
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<div></div>Babcockhttps://reu.cs.mu.edu/index.php/REUCarissaBabcockPoster.pdfREUCarissaBabcockPoster.pdf2017-08-04T21:53:28Z<p>Babcock: Created page with "File:REU_Poster_Carissa_Babcock.pdf"</p>
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<div>[[File:REU_Poster_Carissa_Babcock.pdf]]</div>Babcockhttps://reu.cs.mu.edu/index.php/File:REU_Poster_Carissa_Babcock.pdfFile:REU Poster Carissa Babcock.pdf2017-08-04T21:52:08Z<p>Babcock: </p>
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<div></div>Babcockhttps://reu.cs.mu.edu/index.php/REUCarissaBabcockPresentation.pdfREUCarissaBabcockPresentation.pdf2017-08-04T21:47:19Z<p>Babcock: Created page with "File:Observing_Patterns_in_4-Cycle_Graphs.pdf"</p>
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<div>[[File:Observing_Patterns_in_4-Cycle_Graphs.pdf]]</div>Babcockhttps://reu.cs.mu.edu/index.php/File:Observing_Patterns_in_4-Cycle_Graphs.pdfFile:Observing Patterns in 4-Cycle Graphs.pdf2017-08-04T21:46:03Z<p>Babcock: Babcock uploaded a new version of &quot;File:Observing Patterns in 4-Cycle Graphs.pdf&quot;</p>
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<div></div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-08-04T21:44:29Z<p>Babcock: /* Artifacts */</p>
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<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
*Typed up findings to give to Dr. Factor (one hour)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Worked on paper outline (one hour)<br />
*Continued competition number research (four hours)<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
*Finished working on outline for paper and emailed it to Dr. Factor (one hour)<br />
*Continued competition number research (seven hours)<br />
<br />
==='''Reflection: End of Week 7'''===<br />
This week was very successful. I made a lot of progress in my research. In addition, I completed my goals of meeting with my mentor and presenting her with my outline for my paper. I am prepared to get started on my paper and to start working on writing up proofs for my research findings. I will work on those in the weeks to come.<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
*Begin work on proof for research findings (8 hours)<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
*Finalize proof write-up (8 hours)<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
*Work on poster draft (four hours)<br />
*Write up findings for meeting (four hours)<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
*Finish poster draft (two hours)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Work on fixing proof (four hours)<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
*Work on fixing proofs (four hours)<br />
*Work on fixing poster (four hours)<br />
<br />
==='''Reflection: End of Week 8'''===<br />
This was another successful week. I was able to get the draft of my poster done and submitted. I also worked on writing up a proof for one of my research findings (this was pretty exciting for me). I have a lot of changes to make on both, but I will be able to fix them in the upcoming week.<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
*Worked on editing poster (four hours) <br />
*Worked on starting paper (four hours)<br />
==='''Day 2 (7/25/17)'''===<br />
*Worked on editing poster (four hours)<br />
*worked on research (four hours)<br />
==='''Day 3 (7/26/17)'''===<br />
*Edited and submitted poster (two hours)<br />
*Worked on research (six hours)<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
*Attended working lunch (two hours)<br />
*Worked on paper (two hours)<br />
*Worked on research (four hours)<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
*Worked on proof/paper/research (eight hours)<br />
<br />
==='''Reflection: End of Week 9'''===<br />
This week was spent preparing to wrap everything up for the REU. I was able to submit my poster (on time) and begin to finalize all of my findings. Next week I will be finalizing my paper and preparing a presentation.<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
*Work on presentation (eight hours)<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
*Attend poster session (two hours)<br />
*Meet with Dr. Factor (one hour)<br />
*Edit/finalize presentation (five hours)<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
*Practice presentation (two hours)<br />
*Attend presentations (four hours)<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
*Attend presentations (two hours)<br />
*Work on paper (two hours)<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
*Finalize and submit paper (eight hours)<br />
<br />
==='''Reflection: End of Week 10'''===<br />
This is the last week of the REU. I was able to accomplish a lot in the short ten weeks. I was able to partially answer a research question by finding two graphs in which the competition number was greater than the (1,2)-step competition number. This week was very busy since I had to present my poster in the poster session, give a presentation, and finish my paper. I was able to successfully get everything done, though.<br />
<br />
='''Artifacts'''=<br />
*[http://reu.mscs.mu.edu/index.php/REUCarissaBabcockPaper.pdf Paper]<br />
*[http://reu.mscs.mu.edu/index.php/REUCarissaBabcockPresentation.pdf Presentation]<br />
*[http://reu.mscs.mu.edu/index.php/REUCarissaBabcockPoster.pdf Poster]</div>Babcockhttps://reu.cs.mu.edu/index.php/File:Observing_Patterns_in_4-Cycle_Graphs.pdfFile:Observing Patterns in 4-Cycle Graphs.pdf2017-08-04T21:42:40Z<p>Babcock: </p>
<hr />
<div></div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-08-04T21:38:36Z<p>Babcock: </p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
*Typed up findings to give to Dr. Factor (one hour)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Worked on paper outline (one hour)<br />
*Continued competition number research (four hours)<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
*Finished working on outline for paper and emailed it to Dr. Factor (one hour)<br />
*Continued competition number research (seven hours)<br />
<br />
==='''Reflection: End of Week 7'''===<br />
This week was very successful. I made a lot of progress in my research. In addition, I completed my goals of meeting with my mentor and presenting her with my outline for my paper. I am prepared to get started on my paper and to start working on writing up proofs for my research findings. I will work on those in the weeks to come.<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
*Begin work on proof for research findings (8 hours)<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
*Finalize proof write-up (8 hours)<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
*Work on poster draft (four hours)<br />
*Write up findings for meeting (four hours)<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
*Finish poster draft (two hours)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Work on fixing proof (four hours)<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
*Work on fixing proofs (four hours)<br />
*Work on fixing poster (four hours)<br />
<br />
==='''Reflection: End of Week 8'''===<br />
This was another successful week. I was able to get the draft of my poster done and submitted. I also worked on writing up a proof for one of my research findings (this was pretty exciting for me). I have a lot of changes to make on both, but I will be able to fix them in the upcoming week.<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
*Worked on editing poster (four hours) <br />
*Worked on starting paper (four hours)<br />
==='''Day 2 (7/25/17)'''===<br />
*Worked on editing poster (four hours)<br />
*worked on research (four hours)<br />
==='''Day 3 (7/26/17)'''===<br />
*Edited and submitted poster (two hours)<br />
*Worked on research (six hours)<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
*Attended working lunch (two hours)<br />
*Worked on paper (two hours)<br />
*Worked on research (four hours)<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
*Worked on proof/paper/research (eight hours)<br />
<br />
==='''Reflection: End of Week 9'''===<br />
This week was spent preparing to wrap everything up for the REU. I was able to submit my poster (on time) and begin to finalize all of my findings. Next week I will be finalizing my paper and preparing a presentation.<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
*Work on presentation (eight hours)<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
*Attend poster session (two hours)<br />
*Meet with Dr. Factor (one hour)<br />
*Edit/finalize presentation (five hours)<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
*Practice presentation (two hours)<br />
*Attend presentations (four hours)<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
*Attend presentations (two hours)<br />
*Work on paper (two hours)<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
*Finalize and submit paper (eight hours)<br />
<br />
==='''Reflection: End of Week 10'''===<br />
This is the last week of the REU. I was able to accomplish a lot in the short ten weeks. I was able to partially answer a research question by finding two graphs in which the competition number was greater than the (1,2)-step competition number. This week was very busy since I had to present my poster in the poster session, give a presentation, and finish my paper. I was able to successfully get everything done, though.<br />
<br />
='''Artifacts'''=<br />
*[http://reu.mscs.mu.edu/index.php/REUMaxBlackPaper.pdf Paper]<br />
*[http://reu.mscs.mu.edu/index.php/REUMaxBlackPresentation.pdf Presentation]<br />
*[http://reu.mscs.mu.edu/images/4/45/REUMaxBlackPoster.pdf Poster]</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-08-04T21:33:56Z<p>Babcock: /* Week 10 (7/31/17-8/4/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
*Typed up findings to give to Dr. Factor (one hour)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Worked on paper outline (one hour)<br />
*Continued competition number research (four hours)<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
*Finished working on outline for paper and emailed it to Dr. Factor (one hour)<br />
*Continued competition number research (seven hours)<br />
<br />
==='''Reflection: End of Week 7'''===<br />
This week was very successful. I made a lot of progress in my research. In addition, I completed my goals of meeting with my mentor and presenting her with my outline for my paper. I am prepared to get started on my paper and to start working on writing up proofs for my research findings. I will work on those in the weeks to come.<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
*Begin work on proof for research findings (8 hours)<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
*Finalize proof write-up (8 hours)<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
*Work on poster draft (four hours)<br />
*Write up findings for meeting (four hours)<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
*Finish poster draft (two hours)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Work on fixing proof (four hours)<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
*Work on fixing proofs (four hours)<br />
*Work on fixing poster (four hours)<br />
<br />
==='''Reflection: End of Week 8'''===<br />
This was another successful week. I was able to get the draft of my poster done and submitted. I also worked on writing up a proof for one of my research findings (this was pretty exciting for me). I have a lot of changes to make on both, but I will be able to fix them in the upcoming week.<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
*Worked on editing poster (four hours) <br />
*Worked on starting paper (four hours)<br />
==='''Day 2 (7/25/17)'''===<br />
*Worked on editing poster (four hours)<br />
*worked on research (four hours)<br />
==='''Day 3 (7/26/17)'''===<br />
*Edited and submitted poster (two hours)<br />
*Worked on research (six hours)<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
*Attended working lunch (two hours)<br />
*Worked on paper (two hours)<br />
*Worked on research (four hours)<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
*Worked on proof/paper/research (eight hours)<br />
<br />
==='''Reflection: End of Week 9'''===<br />
This week was spent preparing to wrap everything up for the REU. I was able to submit my poster (on time) and begin to finalize all of my findings. Next week I will be finalizing my paper and preparing a presentation.<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
*Work on presentation (eight hours)<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
*Attend poster session (two hours)<br />
*Meet with Dr. Factor (one hour)<br />
*Edit/finalize presentation (five hours)<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
*Practice presentation (two hours)<br />
*Attend presentations (four hours)<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
*Attend presentations (two hours)<br />
*Work on paper (two hours)<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
*Finalize and submit paper (eight hours)<br />
<br />
==='''Reflection: End of Week 10'''===<br />
This is the last week of the REU. I was able to accomplish a lot in the short ten weeks. I was able to partially answer a research question by finding two graphs in which the competition number was greater than the (1,2)-step competition number. This week was very busy since I had to present my poster in the poster session, give a presentation, and finish my paper. I was able to successfully get everything done, though.</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-08-04T21:30:13Z<p>Babcock: /* Week 9 (7/24/17-7/28/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
*Typed up findings to give to Dr. Factor (one hour)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Worked on paper outline (one hour)<br />
*Continued competition number research (four hours)<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
*Finished working on outline for paper and emailed it to Dr. Factor (one hour)<br />
*Continued competition number research (seven hours)<br />
<br />
==='''Reflection: End of Week 7'''===<br />
This week was very successful. I made a lot of progress in my research. In addition, I completed my goals of meeting with my mentor and presenting her with my outline for my paper. I am prepared to get started on my paper and to start working on writing up proofs for my research findings. I will work on those in the weeks to come.<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
*Begin work on proof for research findings (8 hours)<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
*Finalize proof write-up (8 hours)<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
*Work on poster draft (four hours)<br />
*Write up findings for meeting (four hours)<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
*Finish poster draft (two hours)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Work on fixing proof (four hours)<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
*Work on fixing proofs (four hours)<br />
*Work on fixing poster (four hours)<br />
<br />
==='''Reflection: End of Week 8'''===<br />
This was another successful week. I was able to get the draft of my poster done and submitted. I also worked on writing up a proof for one of my research findings (this was pretty exciting for me). I have a lot of changes to make on both, but I will be able to fix them in the upcoming week.<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
*Worked on editing poster (four hours) <br />
*Worked on starting paper (four hours)<br />
==='''Day 2 (7/25/17)'''===<br />
*Worked on editing poster (four hours)<br />
*worked on research (four hours)<br />
==='''Day 3 (7/26/17)'''===<br />
*Edited and submitted poster (two hours)<br />
*Worked on research (six hours)<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
*Attended working lunch (two hours)<br />
*Worked on paper (two hours)<br />
*Worked on research (four hours)<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
*Worked on proof/paper/research (eight hours)<br />
<br />
==='''Reflection: End of Week 9'''===<br />
This week was spent preparing to wrap everything up for the REU. I was able to submit my poster (on time) and begin to finalize all of my findings. Next week I will be finalizing my paper and preparing a presentation.<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-08-04T21:25:11Z<p>Babcock: /* Week 8 (7/17/17-7/21/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
*Typed up findings to give to Dr. Factor (one hour)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Worked on paper outline (one hour)<br />
*Continued competition number research (four hours)<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
*Finished working on outline for paper and emailed it to Dr. Factor (one hour)<br />
*Continued competition number research (seven hours)<br />
<br />
==='''Reflection: End of Week 7'''===<br />
This week was very successful. I made a lot of progress in my research. In addition, I completed my goals of meeting with my mentor and presenting her with my outline for my paper. I am prepared to get started on my paper and to start working on writing up proofs for my research findings. I will work on those in the weeks to come.<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
*Begin work on proof for research findings (8 hours)<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
*Finalize proof write-up (8 hours)<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
*Work on poster draft (four hours)<br />
*Write up findings for meeting (four hours)<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
*Finish poster draft (two hours)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Work on fixing proof (four hours)<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
*Work on fixing proofs (four hours)<br />
*Work on fixing poster (four hours)<br />
<br />
==='''Reflection: End of Week 8'''===<br />
This was another successful week. I was able to get the draft of my poster done and submitted. I also worked on writing up a proof for one of my research findings (this was pretty exciting for me). I have a lot of changes to make on both, but I will be able to fix them in the upcoming week.<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-08-04T21:17:16Z<p>Babcock: /* Reflection: End of Week 7 */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
*Typed up findings to give to Dr. Factor (one hour)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Worked on paper outline (one hour)<br />
*Continued competition number research (four hours)<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
*Finished working on outline for paper and emailed it to Dr. Factor (one hour)<br />
*Continued competition number research (seven hours)<br />
<br />
==='''Reflection: End of Week 7'''===<br />
This week was very successful. I made a lot of progress in my research. In addition, I completed my goals of meeting with my mentor and presenting her with my outline for my paper. I am prepared to get started on my paper and to start working on writing up proofs for my research findings. I will work on those in the weeks to come.<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
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==='''Day 2 (7/18/17)'''===<br />
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==='''Day 3 (7/19/17)'''===<br />
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==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
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<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
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<br />
==='''Day 1 (7/24/17)'''===<br />
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==='''Day 2 (7/25/17)'''===<br />
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==='''Day 3 (7/26/17)'''===<br />
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==='''Day 4 (7/27/17)'''===<br />
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==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
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<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
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<br />
==='''Day 1 (7/31/17)'''===<br />
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==='''Day 2 (8/1/17)'''===<br />
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==='''Day 3 (8/2/17)'''===<br />
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==='''Day 4 (8/3/17)'''===<br />
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==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-08-04T21:15:46Z<p>Babcock: /* Day 5 (7/14/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
*Typed up findings to give to Dr. Factor (one hour)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Worked on paper outline (one hour)<br />
*Continued competition number research (four hours)<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
*Finished working on outline for paper and emailed it to Dr. Factor (one hour)<br />
*Continued competition number research (seven hours)<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-08-04T21:15:06Z<p>Babcock: /* Day 4 (7/13/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
*Typed up findings to give to Dr. Factor (one hour)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
*Worked on paper outline (one hour)<br />
*Continued competition number research (four hours)<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-08-04T21:12:56Z<p>Babcock: /* Project Description */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. I am focusing on answering a previous research question proposed by Drs. Factor, Merz, and Sano in their paper The (1,2)-step competition number of a graph. I am working on finding other graphs in which the competition number is greater than the (1,2)-step competition number. My focus will be on unions of 4-cycle graphs and 4-cycle graphs with pendants. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
*Typed up findings to give to Dr. Factor (one hour)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-07-13T16:10:42Z<p>Babcock: /* Day 4 (7/13/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
*Typed up findings to give to Dr. Factor (one hour)<br />
*Met with Dr. Factor (one hour)<br />
*Working lunch (one hour)<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-07-13T16:09:19Z<p>Babcock: /* Day 2 (7/11/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
*Worked on creating paper outline (one hour)<br />
*Worked on C4 graph research (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-07-13T16:08:34Z<p>Babcock: /* Day 3 (7/12/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
*Finished up abstract and submitted application for conference (one hour) <br />
*Worked on C4 graph research (six hours)<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
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==='''Day 2 (7/25/17)'''===<br />
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==='''Day 3 (7/26/17)'''===<br />
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==='''Day 4 (7/27/17)'''===<br />
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==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
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==='''Day 2 (8/1/17)'''===<br />
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==='''Day 3 (8/2/17)'''===<br />
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==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-07-11T18:04:18Z<p>Babcock: /* Week 7 (7/10/17-7/14/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (three hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-07-11T17:44:44Z<p>Babcock: /* Week 7 (7/10/17-7/14/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
* Continued research on competition numbers (two hours)<br />
*Worked on editing abstract (one hour)<br />
*Worked on finishing the type ups of my findings (four hours)<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
*Typed up abstract in latex and edited it more (two hours)<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-07-11T17:42:57Z<p>Babcock: /* Reflection: End of Week 6 */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
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==='''Day 1 (7/10/17)'''===<br />
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==='''Day 2 (7/11/17)'''===<br />
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==='''Day 3 (7/12/17)'''===<br />
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==='''Day 4 (7/13/17)'''===<br />
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==='''Day 5 (7/14/17)'''===<br />
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==='''Reflection: End of Week 7'''===<br />
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=='''Week 8 (7/17/17-7/21/17)'''==<br />
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==='''Day 1 (7/17/17)'''===<br />
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==='''Day 2 (7/18/17)'''===<br />
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==='''Day 3 (7/19/17)'''===<br />
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==='''Day 4 (7/20/17)'''===<br />
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==='''Day 5 (7/21/17)'''===<br />
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==='''Reflection: End of Week 8'''===<br />
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=='''Week 9 (7/24/17-7/28/17)'''==<br />
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==='''Day 1 (7/24/17)'''===<br />
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==='''Day 2 (7/25/17)'''===<br />
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==='''Day 3 (7/26/17)'''===<br />
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==='''Day 4 (7/27/17)'''===<br />
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==='''Day 5 (7/28/17)'''===<br />
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==='''Reflection: End of Week 9'''===<br />
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=='''Week 10 (7/31/17-8/4/17)'''==<br />
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==='''Day 1 (7/31/17)'''===<br />
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==='''Day 2 (8/1/17)'''===<br />
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==='''Day 3 (8/2/17)'''===<br />
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==='''Day 4 (8/3/17)'''===<br />
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==='''Day 5 (8/4/17)'''===<br />
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==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-07-11T17:42:32Z<p>Babcock: /* Week 6 (7/3/17-7/7/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
*Worked on typing up findings with the competition numbers (about four hours)<br />
*Continued research with competition numbers (about six hours)<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
*Met with Dr. Factor and went over my findings (about an hour)<br />
*Attended working lunch and attended presentation about having a good poster (about two hours)<br />
*Worked on competition number research (about five hours)<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
*Worked on abstract for conference (about an hour)<br />
*Worked on competition number research (about five hours)<br />
*Worked on typing up findings (about three hours)<br />
<br />
==='''Worked over Weekend (7/9/17)'''===<br />
*Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)<br />
<br />
==='''Reflection: End of Week 6'''===<br />
*This week I feel that I completed my goals. I started applying for the conference, and am coming to a place where I can start writing proofs for my findings. I realized that what I was working on had to be changed since there were smaller competition numbers than what I was finding, but I was able to improve my work and can go on to writing proofs from there. In the next few weeks, I will be working on exploring other graph families, writing proofs, and preparing my presentations for the upcoming weeks.<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
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==='''Day 1 (7/10/17)'''===<br />
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==='''Day 2 (7/11/17)'''===<br />
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==='''Day 3 (7/12/17)'''===<br />
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==='''Day 4 (7/13/17)'''===<br />
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==='''Day 5 (7/14/17)'''===<br />
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==='''Reflection: End of Week 7'''===<br />
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<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
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==='''Day 1 (7/17/17)'''===<br />
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==='''Day 2 (7/18/17)'''===<br />
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==='''Day 3 (7/19/17)'''===<br />
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==='''Day 4 (7/20/17)'''===<br />
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==='''Day 5 (7/21/17)'''===<br />
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==='''Reflection: End of Week 8'''===<br />
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<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
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==='''Day 1 (7/24/17)'''===<br />
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==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-07-11T17:34:40Z<p>Babcock: /* Week 5 (6/26/17-6/30/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
*Continued work on Competition numbers for about eight hours (worked from home)<br />
<br />
==='''Reflection: End of Week 5'''===<br />
During this week I completed many goals. I feel that I did well on my mini presentation. I know I still need improvement, but I don't think it went horribly. I have also completed a lot with my research involving the competition numbers. I have been figuring out a lot with the competition numbers, and I am excited to see what else I figure out. I am hoping to continue to learn more about this topic and improve what I already know in the upcoming weeks.<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-29T19:42:10Z<p>Babcock: /* Day 4 (6/29/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
*Practiced mini presentation at home for about an hour<br />
*Practiced mini presentation on campus for about two hours<br />
*Attended mini presentations for about 2.5 hours<br />
*Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-29T19:40:51Z<p>Babcock: /* Day 3 (6/28/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
* Worked on mini presentation for about eight hours<br />
* Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-29T19:39:56Z<p>Babcock: /* Day 2 (6/27/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
*Practiced mini presentation at home for about an hour<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-27T21:15:45Z<p>Babcock: /* Day 2 (6/27/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
*Worked on mini presentation for about eight hours<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-26T21:03:58Z<p>Babcock: /* Day 1 (6/26/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours)<br />
*Attended talk on giving a good research presentation (about two hours)<br />
*Worked on mini presentation (about two hours)<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-26T16:47:42Z<p>Babcock: /* Week 5 (6/26/17-6/30/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
*Worked on Competition Number Practice (about three hours) <br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-26T16:41:54Z<p>Babcock: /* Week 4 (6/19/17-6/23/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
Worked from home.<br />
*Worked on Competition Numbers practice (about eight hours)<br />
<br />
==='''Reflection: End of Week 4'''===<br />
I feel that I am starting to get an idea of where I will be taking this research. I am working on actual applications instead of just reading, which I enjoy. This week I worked on exploring different topics where I looked at food webs and competition numbers. This was a struggle at first since I wasn't sure where to start with the competition number, but after working with Dr. Factor, I feel much more confident with that I am working on. I am looking forward to continuing my work with this idea and presenting my findings in the mini presentations next week. I feel that I met all of my goals for the week, and this seemed to be a successful week.<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-22T20:56:10Z<p>Babcock: /* Day 4 (6/22/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
* Worked on Competition Numbers practice (about six hours (split between morning and afternoon))<br />
* Met with Dr. Factor (about 30 minutes)<br />
* (Working Lunch (about an hour)<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-21T21:08:56Z<p>Babcock: /* Day 3 (6/21/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
* Continued work with Food Webs (about two hours)<br />
* Worked on answering question about competition number (about five hours)<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-20T20:38:06Z<p>Babcock: /* Day 2 (6/20/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about an hour)<br />
* Fixed work with food webs (about four hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-20T17:14:42Z<p>Babcock: /* Day 2 (6/20/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
* Met with Dr. Factor. (about thirty minutes)<br />
* Continued with working on the graph exploration (about an hour and a half)<br />
* Fixed work with food webs (about two hours hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-20T15:14:33Z<p>Babcock: /* Day 2 (6/20/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-20T15:14:22Z<p>Babcock: /* Day 1 (6/19/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours) <br />
* Continued work on Food Web work (about four hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-19T21:14:38Z<p>Babcock: /* Day 1 (6/19/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about two hours) <br />
* Continued work on Food Web work (about three hours)<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-19T19:49:33Z<p>Babcock: /* Day 1 (6/19/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about two hours) <br />
* Continued work on Food Web work (about three hours)<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about hours)<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-19T16:58:11Z<p>Babcock: /* Week 4 (6/19/17-6/23/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
* Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about two hours) <br />
* Continued work on Food Web work (about hours)<br />
* Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about hours) <br />
<br />
==='''Day 2 (6/20/17)'''===<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-19T16:29:16Z<p>Babcock: /* Week 3 (6/12/17-6/16/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
* Worked on background research to try to find a topic to study (about five hours)<br />
* Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
* Worked on completing the ethics training quizzes and readings (about six hours)<br />
*Wasn't feeling well, so left early at about 3:30. <br />
<br />
==='''Day 4 (6/15/17'''===<br />
*Worked from home- was home sick<br />
*Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)<br />
*Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)<br />
<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
*Worked from home- was home sick<br />
*Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)<br />
*Worked on reading background information to find a topic to research (about two hours) <br />
*Continued work on Food Webs (about an hour) <br />
<br />
==='''Reflection: End of Week 3'''===<br />
I feel that this a difficult week. I have been struggling to try to find a topic to research since I'm not really sure what I'm interested yet. It was also difficult since I was sick, so I was doing most of my work from home. I accomplished my goals of completing a presentation with Max that showed definitions and examples from the (1,2)-step competition number of a graph (Factor, et al.) paper. After the presentation, Dr. Factor told me to start exploring Food Webs and find their (1,2)-step competition graph. I was successful in this, and I feel that it was good practice for me to complete this work. I was also given the task to look at the question found in the paper that asks if there exists a graph ''G'', other than ''C<sub>4</sub>'', such that ''k(G)> k<sub>(1,2)</sub>(G)''. I have been having issues going about answering that question. I'm not sure how to start, so I haven't gotten too far. I will make sure to work on it next week before I meet with Dr. Factor. <br />
<br />
I am nervous about not knowing what I'm doing yet, but after meeting with Dr. Factor on Tuesday, she informed me that this is normal. I will make sure to continue to explore various readings to try to figure out what I would like to do for the rest of the REU. I am hoping to have a topic chosen soon. Since I was unable to meet with Dr. Factor on Thursday (due to me being home sick), I am hoping to meet with her early next week to go over my work so far and future work.<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-12T20:32:31Z<p>Babcock: /* Day 1 (6/12/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about four hours)<br />
* Revised hand out for presentation with Dr. Factor tomorrow (one hour)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
<br />
==='''Day 4 (6/15/17'''===<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
<br />
==='''Reflection: End of Week 3'''===<br />
<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
<br />
==='''Day 3 (7/12/17)'''===<br />
<br />
==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-12T20:31:40Z<p>Babcock: /* Day 1 (6/12/17) */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
<br />
<br />
==='''Day 1 (6/12/17)'''===<br />
* Finished up presentation for Dr. Factor (about fives hours)<br />
* Worked on finishing up readings (about two hours)<br />
<br />
==='''Day 2 (6/13/17)'''===<br />
<br />
==='''Day 3 (6/14/17)'''===<br />
<br />
==='''Day 4 (6/15/17'''===<br />
<br />
==='''Day 5 (6/16/17)'''===<br />
<br />
==='''Reflection: End of Week 3'''===<br />
<br />
<br />
=='''Week 4 (6/19/17-6/23/17)'''==<br />
<br />
<br />
==='''Day 1 (6/19/17)'''===<br />
<br />
==='''Day 2 (6/20/17)'''===<br />
<br />
==='''Day 3 (6/21/17)'''===<br />
<br />
==='''Day 4 (6/22/17)'''===<br />
<br />
==='''Day 5 (6/23/17)'''===<br />
<br />
==='''Reflection: End of Week 4'''===<br />
<br />
<br />
<br />
=='''Week 5 (6/26/17-6/30/17)'''==<br />
<br />
<br />
==='''Day 1 (6/26/17)'''===<br />
<br />
==='''Day 2 (6/27/17)'''===<br />
<br />
==='''Day 3 (6/28/17)'''===<br />
<br />
==='''Day 4 (6/29/17)'''===<br />
<br />
==='''Day 5 (6/30/17)'''===<br />
<br />
==='''Reflection: End of Week 5'''===<br />
<br />
<br />
<br />
=='''Week 6 (7/3/17-7/7/17)'''==<br />
<br />
<br />
==='''Day 1 (7/3/17)'''===<br />
<br />
==='''Day 2 (7/4/17)'''===<br />
<br />
==='''Day 3 (7/5/17)'''===<br />
<br />
==='''Day 4 (7/6/17)'''===<br />
<br />
==='''Day 5 (7/7/17)'''===<br />
<br />
==='''Reflection: End of Week 6'''===<br />
<br />
<br />
=='''Week 7 (7/10/17-7/14/17)'''==<br />
<br />
<br />
==='''Day 1 (7/10/17)'''===<br />
<br />
==='''Day 2 (7/11/17)'''===<br />
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==='''Day 3 (7/12/17)'''===<br />
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==='''Day 4 (7/13/17)'''===<br />
<br />
==='''Day 5 (7/14/17)'''===<br />
<br />
==='''Reflection: End of Week 7'''===<br />
<br />
<br />
=='''Week 8 (7/17/17-7/21/17)'''==<br />
<br />
<br />
==='''Day 1 (7/17/17)'''===<br />
<br />
==='''Day 2 (7/18/17)'''===<br />
<br />
==='''Day 3 (7/19/17)'''===<br />
<br />
==='''Day 4 (7/20/17)'''===<br />
<br />
==='''Day 5 (7/21/17)'''===<br />
<br />
==='''Reflection: End of Week 8'''===<br />
<br />
<br />
<br />
=='''Week 9 (7/24/17-7/28/17)'''==<br />
<br />
<br />
==='''Day 1 (7/24/17)'''===<br />
<br />
==='''Day 2 (7/25/17)'''===<br />
<br />
==='''Day 3 (7/26/17)'''===<br />
<br />
==='''Day 4 (7/27/17)'''===<br />
<br />
==='''Day 5 (7/28/17)'''===<br />
<br />
==='''Reflection: End of Week 9'''===<br />
<br />
<br />
=='''Week 10 (7/31/17-8/4/17)'''==<br />
<br />
<br />
==='''Day 1 (7/31/17)'''===<br />
<br />
==='''Day 2 (8/1/17)'''===<br />
<br />
==='''Day 3 (8/2/17)'''===<br />
<br />
==='''Day 4 (8/3/17)'''===<br />
<br />
==='''Day 5 (8/4/17)'''===<br />
<br />
==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-09T21:14:18Z<p>Babcock: /* Reflection: End of Week 2 */</p>
<hr />
<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
<br />
='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
<br />
==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
<br />
=='''Week 2 (6/5/17-6/9/17)'''==<br />
<br />
<br />
==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
<br />
==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
<br />
==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
<br />
==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
<br />
==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
<br />
==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out. Next week I am hoping to figure out a research question with Dr. Factor so I know where to focus my research, but until then, I am continuing to do the necessary background research in preparation. <br />
<br />
I accomplished many goals this week including attending ethics training, the Thursday during lunch meeting, and a meeting with Dr. Factor. I also became familiar with the campus, Overleaf (and using Tex language), and (1,2)-step competition graphs.<br />
<br />
=='''Week 3 (6/12/17-6/16/17)'''==<br />
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=='''Week 4 (6/19/17-6/23/17)'''==<br />
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=='''Week 5 (6/26/17-6/30/17)'''==<br />
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=='''Week 6 (7/3/17-7/7/17)'''==<br />
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=='''Week 7 (7/10/17-7/14/17)'''==<br />
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=='''Week 8 (7/17/17-7/21/17)'''==<br />
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=='''Week 9 (7/24/17-7/28/17)'''==<br />
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=='''Week 10 (7/31/17-8/4/17)'''==<br />
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==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/User:BabcockUser:Babcock2017-06-09T21:10:40Z<p>Babcock: /* Week 2 (6/5/17-6/9/17) */</p>
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<div>='''Project Description'''=<br />
I am conducting research on [http://reu.mscs.mu.edu/index.php/(i,j)-step_competition_graphs ''(i,j)-step competition graphs''] in the ten week long Marquette MSCS REU. The mentor that I am working with is [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]. For the beginning part of this REU, I will be doing background research with Max Black and then I will work on my own research. The work I do each week can be seen below.<br />
<br />
='''Background Readings'''=<br />
There were some background readings given to Max and I to build an understanding on the topics we will be working on. Note: if a link is missing, the reading is either from a textbook or I could not find a link.<br />
<br />
*''BioMath: The Biology and Mathematics of Food Webs'' by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood<br />
*Chapter 3 from ''Applied Combinatorics'' by Fred S. Roberts<br />
*[https://pdfs.semanticscholar.org/84cd/7fb860483f6ab2699ca8118de30bd20f2eb7.pdf ''(i,j) Competition Graphs''] by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.<br />
*[http://www.sciencedirect.com/science/article/pii/S0166218X10003501 ''The (1,2)-step competition graph of a tournament''] by Kim A.S. Factor and Sarah K. Merz<br />
*[https://www.researchgate.net/publication/266069208_An_introduction_to_12-domination_graphs ''An Introduction to (1,2)-Domination Graphs''] by Kim A.S. Factor<br />
*[http://ac.els-cdn.com/S0166218X05001009/1-s2.0-S0166218X05001009-main.pdf?_tid=36995176-4701-11e7-b81d-00000aacb35e&acdnat=1496345799_24933243dc1d7943d7669b01ba4dcb39 ''The m-step, same-step, and any-step competition graphs''] by Wei ho<br />
*[http://ac.els-cdn.com/S0166218X04002008/1-s2.0-S0166218X04002008-main.pdf?_tid=4db26550-4701-11e7-9a29-00000aab0f02&acdnat=1496345838_0602db3093f1b3c7a0137620eb428303 ''Connected triangle-free m-step competition graphs''] by Geir T. Helleloid<br />
*[http://ac.els-cdn.com/S0166218X00002146/1-s2.0-S0166218X00002146-main.pdf?_tid=8948cf6a-4700-11e7-af12-00000aab0f26&acdnat=1496345508_3370ea3bf71913b7bf5f67101e12bad1 ''The m-step competition graph of a digraph''] by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam<br />
*[http://www.sciencedirect.com/science/article/pii/0166218X83900859 ''A Characterization of Competition Graphs''] by R.D. Dutton and R.C. Brigham<br />
*[http://lab.rockefeller.edu/cohenje/assets/file/014.1CohenIntervalGraphsFoodWebsRAND1968.pdf ''Interval Graphs and Food Webs: A finding and a Problem''] by Joel E. Cohen<br />
*''Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions'' by Kaitlin A. Ryan (a master's thesis)<br />
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='''Project Log'''=<br />
<br />
=='''Week 1 (5/30/17-6/2/17)'''==<br />
* Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time. <br />
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==='''Reflection: End of Week 1'''===<br />
Since I was not present, there wasn't much work that I completed this week, but I made sure to complete any readings and introduction work that I could on my own. <br />
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=='''Week 2 (6/5/17-6/9/17)'''==<br />
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==='''Day 1 (6/5/17)'''===<br />
* Finished BioMath packet.<br />
*Printed readings and materials that were emailed to me. <br />
*Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.<br />
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==='''Day 2 (6/6/17)'''===<br />
*Attended meeting with Max at 8:00AM<br />
* Attended meeting with Petra at 8:30AM to complete paperwork.<br />
*Attended ethical research training at 9:00AM until about 3:00PM. <br />
*Began reviewing ''The (1,2)-step competition graph'' with Max at 3:15PM for about 3 hours.<br />
*Made note to include approximate total number of hours in end-of-week reflection<br />
*Estimated work for the day is about ten hours.<br />
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==='''Day 3 (6/7/17)'''===<br />
* Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.<br />
* Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour. <br />
* Set up WIKI page for about half an hour. <br />
* Continued to read and go through ''The (1,2)-step competition graph'' with Max for about an hour.<br />
* Practiced Overleaf/ TeX for about half an hour<br />
* Meeting with Dr. Factor and Max for about an hour.<br />
* Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.<br />
* Estimated work for the day is about eight hours.<br />
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==='''Day 4 (6/8/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for about an hour. <br />
* Read (1,2)-step competition graph article in detail. (about five hours).<br />
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==='''Day 5 (6/9/17)'''===<br />
* Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)<br />
* Worked on adding a picture to the background section.<br />
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==='''Reflection: End of Week 2'''===<br />
I feel that my first week was very successful. I am learning a lot, and I am enjoying the work I do. I know that I have a lot more to learn, but I am continuing to try to figure out as much as I can with Max. I am nervous that I'm still not sure what I want to research on, but I know this is something I can work out with Dr. Factor. All of this is very new to me, but I know with enough hard work and time, I will be able to figure things out.<br />
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=='''Week 3 (6/12/17-6/16/17)'''==<br />
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=='''Week 10 (7/31/17-8/4/17)'''==<br />
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==='''Reflection: End of Week 10'''===</div>Babcockhttps://reu.cs.mu.edu/index.php/(i,j)-step_competition_graphs(i,j)-step competition graphs2017-06-09T21:05:45Z<p>Babcock: /* Background */</p>
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<div>'''Researchers:''' [[User:Babcock|Carissa Babcock]] and [[User:Maxblack45|Max Black]]<br />
<br />
'''Mentor:''' [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]<br />
<br />
=='''Background'''==<br />
[[File:Graphs.jpg|500px|thumb|right|Here are some tournaments (top row) and their corresponding (''1,2'')-step competition graphs (bottom row) found in the (''1,2'')-step competition graph of a tournament paper by Factor and Merz.]]<br />
<br />
Joel E. Cohen, in 1968, began modeling ecosystems with competition graphs; consequently, mathematicians began developing his new mathematical object. Informally, competition graphs are collections of dots and lines representing some "competitive" relationship between two species, players, companies, etc. Formally, if we let "let ''D'' be a directed graph having no multiple edges, the competition graph of ''D'' is an undirected graph G on the same node set as ''D'' and having an undirected edge ''{u<sub>i</sub>, v<sub>j</sub>}'' if and only if there exists a third node ''u''<sub>k</sub> such that ''{v<sub>i</sub>, v<sub>k</sub>}'' and ''{v<sub>j</sub>, u<sub>k</sub>}'' are directed edges in the edge set of ''D'' "[http://reu.mscs.mu.edu/images/3/38/CharacterizingCompetitionGraphs.pdf (Dutton et al)]. Competition graphs, when applied to ecosystems, illuminate previously mysterious properties regarding a community through portraying relationships between species. The relationships they portray help identify primary and secondary extinctions between species, when exploring them. <br />
<br />
(''1,2'')-step competition graphs expand on competition graphs. We know from Dr. Factor and Dr. Merz's paper, ''The (1,2)-step competition graph of a tournament'', that the competition graph of a digraph ''D'' is contained in (a subgraph of) the (''1,2'')-step competition graph on D. Specifically, (''1,2'')-step competition graphs clearly display direct and indirect relationships between vertices; in the language of ecosystems, they display the direct and indirect relationships (up to length 2) between various species within a community. Our formal definition for these graphs comes from Factor and Merz's paper: "the (''1,2'')-step competition graph of a digraph ''D'', denoted ''C<sub>1,2</sub>(D)'', is a graph on ''V(D)'' where ''{x,y}'' in ''E(C<sub>1,2</sub>(D))'' if and only if there exists a vertex ''z'' not equal to ''x,y'', such that either ''d<sub>D-y</sub>''(x,z) less than or equal to 1 and ''d<sub>D-x</sub>''(y,z) is less than or equal to 2 [or vice versa]." The (''1,2'')-step competition graph is generalized by the (''i,j'')-step graph.<br />
<br />
(''i,j'')-step graphs display relationships between vertices of an arbitrary length. That is, since they generalize (''1,2'')-step competition graphs, our formal definition comes, again, from Factor and Merz's paper: "the (''i,j'')-step competition graph of a digraph ''D'', denoted ''C<sub>i,j</sub>(D)'', is a graph on ''V(D)'' where ''{x,y}'' in ''E(C<sub>i,j</sub>(D))'' if and only if there exists a vertex ''z'' not equal to ''x,y'', such that either ''d<sub>D-y</sub>''(x,z) less than or equal to ''i'' and ''d<sub>D-x</sub>''(y,z) is less than or equal to ''j'' [or vice versa]". In the (''1,2'')-step competition graph, we saw indirect relationships up to 2; with the (''i,j'')-step competition graph, we can identify indirect relationships up to '' i'' and ''j''. For instance, we could let ''i'' = 1, preserving direct relationships, and let ''j'' be the value of ''how'' indirect of relationships we want to observe. Thus, with the (''i,j'')-step graph, we control the relationships we want to see. <br />
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This project has two main goals: expanding the theory for (''i,j'')-step graphs and exploring their applications. For expanding their theory, this project may explore generalizations, applications to various families of graphs, or explorations with hypergraphs. Concerning their applications, this project may examine and implement various (1,2)-step competition graphs directed towards explaining various relations between species, explaining primary and secondary extinctions, or explaining potential for extinctions within various communities. Throughout the summer, the researchers will take this project in the directions they see fit.<br />
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=='''Objectives'''==<br />
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During this project, we will examine and explore the following:<br />
<br />
<ol style="margin-left: 5em;"><br />
<li>Previous research regarding competition graphs and (1,2)-step competition graphs of food webs</li><br />
<li>Competition graphs and (1,2)-step competition graphs of a specific food web</li><br />
</ol><br />
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Additionally, we will further previous research by doing the following:<br />
<br />
<ol style="margin-left: 5em;"><br />
<li>Furthering research on (i,j)-step competition graphs by exploring new theory and computation</li><br />
<li>Applying competition graphs and (i,j)-step competition graphs in new areas</li><br />
</ol><br />
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A brief overview of our goals for this 10 week process are listed below. For a complete list of our goals, click [http://reu.mscs.mu.edu/images/2/2a/Milestones.pdf here].<br />
<br />
{| class="wikitable"<br />
|-<br />
|'''Week''' || '''Description'''<br />
|-<br />
!Week 1 (5/30/17-6/2/17): Orientation and Introductions<br />
| <br />
*Complete the education mdule, ''The Biology and Mathematics of Food Webs'', by '''Thursday, 6/1/17'''<br />
*Attend the talk at '''11:00PM in CU 401'''<br />
*Enter the title, description and milestones/goals into the wiki by '''Friday, 6/2''', by midnight<br />
*Read ''(1,2)-step competition graph of a tournament'' and have questions ready for Wednesday, 6/7/2017<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 2 (6/5/17-6/9/17): Experiment with (1,2)-Step Competition Graphs Using Specific Examples<br />
| <br />
*'''Meeting Wednesday, 6/7,''' with Dr. Factor<br />
*Discuss the paper from last week--prepare to answer questions and/or ask them<br />
*Begin reading Kaitlyn Ryan's master's thesis to explore biological background, mathematical background, and statistical information for the topic. Make notes and questions for Thursday's meeting<br />
*Begin reading ''A Characterization of Competition Graphs''<br />
*Attend Ethics training at '''9:00AM on 6/6 in CU 401'''<br />
*Participate in the talk and luncheon at '''11:30AM on 6/8, CU 401'''<br />
*Start comparing competition graphs and (1,2)-step competition graphs by using some small food webs from the initial food web packet, and by creating our own small food web examples<br />
*Learn LaTex (Carissa--Max can tutor)<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 3 (6/12/17-6/16/17): Formulating Research Questions<br />
| <br />
*Meeting with Dr. Factor on '''Tuesday, 6/13'''<br />
*Meeting with Dr. Factor on '''Thursday, 6/15'''<br />
*Attend working lunch on '''Thursday, 6/15,''' where lunch will be provided<br />
*Begin thinking about individual research questions. Discuss these during the Tuesday and Thursday meetings<br />
*Write up findings in LaTeX<br />
**Experiment with creating small food webs and competition graphs in LaTeX<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 4 (6/19/17-6/23/17): Refine Research<br />
|<br />
* Begin looking at competition graphs and (1,2)-step (alternately some (i,k)-step) competition graphs for focus areas. Start refining the direction of research<br />
*Continue writing up finding in LaTeX and creating figures<br />
*Optional: meet with Dr. Factor on '''Tuesday, 6/20'''<br />
*Attend the luncheon at '''11:30 AM on Thursday, 6/22'''<br />
*Meet with Dr. Factor on '''Thursday, 6/22,''' focus will be on what to put on slides for next week's mini-presentations<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 5 (6/26/17-6/30/17): Mini Presentations<br />
|<br />
*Draft an 8 or so minute talk discussing what has been learned so far by '''11:00AM Tuesday, 6/27''', and be prepared to show it to Dr. Factor, should have some things to use already in LaTeX.<br />
*Continue, as time allows, working on the research and placing in document<br />
*Present mini-presentation to peers and mentors on '''Thursday, 6/29'''<br />
*Short meeting with mentor after mini-presentations<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 6 (7/3/17-7/7/17): Continue Individual research<br />
|<br />
*Continue working on research and LaTeX updates<br />
*Meet with mentor on '''Thursday, 7/6''' to give research updates and discuss research direction<br />
*Atend working lunch at '''11:30 AM on Thursday, 7/6'''; includes talk on making an effective poster<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 7 (7/10/17-7/14/17): Resolve Conjectures<br />
|<br />
*Should have conjectures in individual areas, determine an approach to a solution or support for conjectures<br />
*As needed: mentor meeting on '''Monday, 7/10'''<br />
*Go to working lunch on '''Thursday, 7/13'''<br />
*Meet with Dr. Factor on '''Thursday, 7/13'''<br />
*Paper outline (brief) based on last week and this week's meetings, submit to Dr. Factor via email by '''Friday, 7/14''' by '''5:00 PM'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 8 (7/17/17-7/21/17): Begin Finalizing Paper<br />
|<br />
*Meeting with Dr. Factor: '''Monday, 7/17'''; start discussing how to finalize paper and poster<br />
*Begin finalizing results; enter theorems, figures, explanations, etc. into LaTeX and create needed Figures<br />
*Initialize poster draft and email to Dr. Factor by '''Thursday, 7/20''' in time for mentor meeting<br />
*Participate in working luncheon on '''Thursday, 7/20'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|<br />
|- <br />
!Week 9 (7/24/17-7/28/17): Posters and Future Research (Dr. Factor Out of Town)<br />
|<br />
*Have updated poster emailed to Dr. Factor by '''8 PM Tuesday, 7/25'''; comments from Dr. Factor will be back by '''10 AM Wednesday'''<br />
*Make any last minute changes and submit electronic version of poster to Dr. Brylow by '''12:00 PM on Wednesday, 7/26'''<br />
*Finalize any results<br />
*Construct a list regarding future research for paper<br />
*Begin turning LaTeX writing into formal paper<br />
*Go to luncheon on '''Thursday, 7/30'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 10 (7/31/17-8/4/17): Formal Talks, Posters, Papers, and Goodbyes<br />
|<br />
*Draft formal talk, which is due to Dr. Factor bu '''11:00 AM Monday, 7/31'''<br />
*Draft paper, which is due to Dr. Factor by '''11:00 AM Thursday, 8/3'''<br />
*Attend poster session '''1:00 PM - 3:00 PM on Tuesday, 8/1'''<br />
*Formal presentations<br />
**'''Wednesday, 8/5, 10:00-2:00, CU 401'''<br />
**'''Thursday, 8/6, 10:00-12:00, CU 401'''<br />
*Paper due electronically '''Friday, 8/4''' by '''midnight''', sent to Dr. Brylow<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
|}<br />
<br />
=='''Research Logs'''==<br />
<br />
Each researcher keeps a log of the entire process, including reflections at the end of the week. These logs demonstrate the researcher's actual progress on their respective projects. Specifically, this determines whether or not they are actually reaching their milestones and completing their goals. If you would like to read them, click the researcher's name: [[User:Babcock|Carissa Babcock]] or [[User:maxblack45|Max Black]].</div>Babcockhttps://reu.cs.mu.edu/index.php/(i,j)-step_competition_graphs(i,j)-step competition graphs2017-06-09T21:04:47Z<p>Babcock: /* Background */</p>
<hr />
<div>'''Researchers:''' [[User:Babcock|Carissa Babcock]] and [[User:Maxblack45|Max Black]]<br />
<br />
'''Mentor:''' [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]<br />
<br />
=='''Background'''==<br />
<br />
[[File:Graphs.jpg|500px|thumb|right|Here are some tournaments (top row) and their corresponding (''1,2'')-step competition graphs (bottom row) found in the (''1,2'')-step competition graph of a tournament paper by Factor and Merz.]]<br />
<br />
Joel E. Cohen, in 1968, began modeling ecosystems with competition graphs; consequently, mathematicians began developing his new mathematical object. Informally, competition graphs are collections of dots and lines representing some "competitive" relationship between two species, players, companies, etc. Formally, if we let "let ''D'' be a directed graph having no multiple edges, the competition graph of ''D'' is an undirected graph G on the same node set as ''D'' and having an undirected edge ''{u<sub>i</sub>, v<sub>j</sub>}'' if and only if there exists a third node ''u''<sub>k</sub> such that ''{v<sub>i</sub>, v<sub>k</sub>}'' and ''{v<sub>j</sub>, u<sub>k</sub>}'' are directed edges in the edge set of ''D'' "[http://reu.mscs.mu.edu/images/3/38/CharacterizingCompetitionGraphs.pdf (Dutton et al)]. Competition graphs, when applied to ecosystems, illuminate previously mysterious properties regarding a community through portraying relationships between species. The relationships they portray help identify primary and secondary extinctions between species, when exploring them. <br />
<br />
(''1,2'')-step competition graphs expand on competition graphs. We know from Dr. Factor and Dr. Merz's paper, ''The (1,2)-step competition graph of a tournament'', that the competition graph of a digraph ''D'' is contained in (a subgraph of) the (''1,2'')-step competition graph on D. Specifically, (''1,2'')-step competition graphs clearly display direct and indirect relationships between vertices; in the language of ecosystems, they display the direct and indirect relationships (up to length 2) between various species within a community. Our formal definition for these graphs comes from Factor and Merz's paper: "the (''1,2'')-step competition graph of a digraph ''D'', denoted ''C<sub>1,2</sub>(D)'', is a graph on ''V(D)'' where ''{x,y}'' in ''E(C<sub>1,2</sub>(D))'' if and only if there exists a vertex ''z'' not equal to ''x,y'', such that either ''d<sub>D-y</sub>''(x,z) less than or equal to 1 and ''d<sub>D-x</sub>''(y,z) is less than or equal to 2 [or vice versa]." The (''1,2'')-step competition graph is generalized by the (''i,j'')-step graph.<br />
<br />
(''i,j'')-step graphs display relationships between vertices of an arbitrary length. That is, since they generalize (''1,2'')-step competition graphs, our formal definition comes, again, from Factor and Merz's paper: "the (''i,j'')-step competition graph of a digraph ''D'', denoted ''C<sub>i,j</sub>(D)'', is a graph on ''V(D)'' where ''{x,y}'' in ''E(C<sub>i,j</sub>(D))'' if and only if there exists a vertex ''z'' not equal to ''x,y'', such that either ''d<sub>D-y</sub>''(x,z) less than or equal to ''i'' and ''d<sub>D-x</sub>''(y,z) is less than or equal to ''j'' [or vice versa]". In the (''1,2'')-step competition graph, we saw indirect relationships up to 2; with the (''i,j'')-step competition graph, we can identify indirect relationships up to '' i'' and ''j''. For instance, we could let ''i'' = 1, preserving direct relationships, and let ''j'' be the value of ''how'' indirect of relationships we want to observe. Thus, with the (''i,j'')-step graph, we control the relationships we want to see. <br />
<br />
This project has two main goals: expanding the theory for (''i,j'')-step graphs and exploring their applications. For expanding their theory, this project may explore generalizations, applications to various families of graphs, or explorations with hypergraphs. Concerning their applications, this project may examine and implement various (1,2)-step competition graphs directed towards explaining various relations between species, explaining primary and secondary extinctions, or explaining potential for extinctions within various communities. Throughout the summer, the researchers will take this project in the directions they see fit.<br />
<br />
=='''Objectives'''==<br />
<br />
During this project, we will examine and explore the following:<br />
<br />
<ol style="margin-left: 5em;"><br />
<li>Previous research regarding competition graphs and (1,2)-step competition graphs of food webs</li><br />
<li>Competition graphs and (1,2)-step competition graphs of a specific food web</li><br />
</ol><br />
<br />
Additionally, we will further previous research by doing the following:<br />
<br />
<ol style="margin-left: 5em;"><br />
<li>Furthering research on (i,j)-step competition graphs by exploring new theory and computation</li><br />
<li>Applying competition graphs and (i,j)-step competition graphs in new areas</li><br />
</ol><br />
<br />
A brief overview of our goals for this 10 week process are listed below. For a complete list of our goals, click [http://reu.mscs.mu.edu/images/2/2a/Milestones.pdf here].<br />
<br />
{| class="wikitable"<br />
|-<br />
|'''Week''' || '''Description'''<br />
|-<br />
!Week 1 (5/30/17-6/2/17): Orientation and Introductions<br />
| <br />
*Complete the education mdule, ''The Biology and Mathematics of Food Webs'', by '''Thursday, 6/1/17'''<br />
*Attend the talk at '''11:00PM in CU 401'''<br />
*Enter the title, description and milestones/goals into the wiki by '''Friday, 6/2''', by midnight<br />
*Read ''(1,2)-step competition graph of a tournament'' and have questions ready for Wednesday, 6/7/2017<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 2 (6/5/17-6/9/17): Experiment with (1,2)-Step Competition Graphs Using Specific Examples<br />
| <br />
*'''Meeting Wednesday, 6/7,''' with Dr. Factor<br />
*Discuss the paper from last week--prepare to answer questions and/or ask them<br />
*Begin reading Kaitlyn Ryan's master's thesis to explore biological background, mathematical background, and statistical information for the topic. Make notes and questions for Thursday's meeting<br />
*Begin reading ''A Characterization of Competition Graphs''<br />
*Attend Ethics training at '''9:00AM on 6/6 in CU 401'''<br />
*Participate in the talk and luncheon at '''11:30AM on 6/8, CU 401'''<br />
*Start comparing competition graphs and (1,2)-step competition graphs by using some small food webs from the initial food web packet, and by creating our own small food web examples<br />
*Learn LaTex (Carissa--Max can tutor)<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 3 (6/12/17-6/16/17): Formulating Research Questions<br />
| <br />
*Meeting with Dr. Factor on '''Tuesday, 6/13'''<br />
*Meeting with Dr. Factor on '''Thursday, 6/15'''<br />
*Attend working lunch on '''Thursday, 6/15,''' where lunch will be provided<br />
*Begin thinking about individual research questions. Discuss these during the Tuesday and Thursday meetings<br />
*Write up findings in LaTeX<br />
**Experiment with creating small food webs and competition graphs in LaTeX<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 4 (6/19/17-6/23/17): Refine Research<br />
|<br />
* Begin looking at competition graphs and (1,2)-step (alternately some (i,k)-step) competition graphs for focus areas. Start refining the direction of research<br />
*Continue writing up finding in LaTeX and creating figures<br />
*Optional: meet with Dr. Factor on '''Tuesday, 6/20'''<br />
*Attend the luncheon at '''11:30 AM on Thursday, 6/22'''<br />
*Meet with Dr. Factor on '''Thursday, 6/22,''' focus will be on what to put on slides for next week's mini-presentations<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 5 (6/26/17-6/30/17): Mini Presentations<br />
|<br />
*Draft an 8 or so minute talk discussing what has been learned so far by '''11:00AM Tuesday, 6/27''', and be prepared to show it to Dr. Factor, should have some things to use already in LaTeX.<br />
*Continue, as time allows, working on the research and placing in document<br />
*Present mini-presentation to peers and mentors on '''Thursday, 6/29'''<br />
*Short meeting with mentor after mini-presentations<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 6 (7/3/17-7/7/17): Continue Individual research<br />
|<br />
*Continue working on research and LaTeX updates<br />
*Meet with mentor on '''Thursday, 7/6''' to give research updates and discuss research direction<br />
*Atend working lunch at '''11:30 AM on Thursday, 7/6'''; includes talk on making an effective poster<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 7 (7/10/17-7/14/17): Resolve Conjectures<br />
|<br />
*Should have conjectures in individual areas, determine an approach to a solution or support for conjectures<br />
*As needed: mentor meeting on '''Monday, 7/10'''<br />
*Go to working lunch on '''Thursday, 7/13'''<br />
*Meet with Dr. Factor on '''Thursday, 7/13'''<br />
*Paper outline (brief) based on last week and this week's meetings, submit to Dr. Factor via email by '''Friday, 7/14''' by '''5:00 PM'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 8 (7/17/17-7/21/17): Begin Finalizing Paper<br />
|<br />
*Meeting with Dr. Factor: '''Monday, 7/17'''; start discussing how to finalize paper and poster<br />
*Begin finalizing results; enter theorems, figures, explanations, etc. into LaTeX and create needed Figures<br />
*Initialize poster draft and email to Dr. Factor by '''Thursday, 7/20''' in time for mentor meeting<br />
*Participate in working luncheon on '''Thursday, 7/20'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|<br />
|- <br />
!Week 9 (7/24/17-7/28/17): Posters and Future Research (Dr. Factor Out of Town)<br />
|<br />
*Have updated poster emailed to Dr. Factor by '''8 PM Tuesday, 7/25'''; comments from Dr. Factor will be back by '''10 AM Wednesday'''<br />
*Make any last minute changes and submit electronic version of poster to Dr. Brylow by '''12:00 PM on Wednesday, 7/26'''<br />
*Finalize any results<br />
*Construct a list regarding future research for paper<br />
*Begin turning LaTeX writing into formal paper<br />
*Go to luncheon on '''Thursday, 7/30'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 10 (7/31/17-8/4/17): Formal Talks, Posters, Papers, and Goodbyes<br />
|<br />
*Draft formal talk, which is due to Dr. Factor bu '''11:00 AM Monday, 7/31'''<br />
*Draft paper, which is due to Dr. Factor by '''11:00 AM Thursday, 8/3'''<br />
*Attend poster session '''1:00 PM - 3:00 PM on Tuesday, 8/1'''<br />
*Formal presentations<br />
**'''Wednesday, 8/5, 10:00-2:00, CU 401'''<br />
**'''Thursday, 8/6, 10:00-12:00, CU 401'''<br />
*Paper due electronically '''Friday, 8/4''' by '''midnight''', sent to Dr. Brylow<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
|}<br />
<br />
=='''Research Logs'''==<br />
<br />
Each researcher keeps a log of the entire process, including reflections at the end of the week. These logs demonstrate the researcher's actual progress on their respective projects. Specifically, this determines whether or not they are actually reaching their milestones and completing their goals. If you would like to read them, click the researcher's name: [[User:Babcock|Carissa Babcock]] or [[User:maxblack45|Max Black]].</div>Babcockhttps://reu.cs.mu.edu/index.php/(i,j)-step_competition_graphs(i,j)-step competition graphs2017-06-09T21:04:21Z<p>Babcock: /* Background */</p>
<hr />
<div>'''Researchers:''' [[User:Babcock|Carissa Babcock]] and [[User:Maxblack45|Max Black]]<br />
<br />
'''Mentor:''' [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]<br />
<br />
=='''Background'''==<br />
<br />
[[File:Graphs.jpg|500px|right|Here are some tournaments (top row) and their corresponding (''1,2'')-step competition graphs (bottom row) found in the (''1,2'')-step competition graph of a tournament paper by Factor and Merz.]]<br />
<br />
Joel E. Cohen, in 1968, began modeling ecosystems with competition graphs; consequently, mathematicians began developing his new mathematical object. Informally, competition graphs are collections of dots and lines representing some "competitive" relationship between two species, players, companies, etc. Formally, if we let "let ''D'' be a directed graph having no multiple edges, the competition graph of ''D'' is an undirected graph G on the same node set as ''D'' and having an undirected edge ''{u<sub>i</sub>, v<sub>j</sub>}'' if and only if there exists a third node ''u''<sub>k</sub> such that ''{v<sub>i</sub>, v<sub>k</sub>}'' and ''{v<sub>j</sub>, u<sub>k</sub>}'' are directed edges in the edge set of ''D'' "[http://reu.mscs.mu.edu/images/3/38/CharacterizingCompetitionGraphs.pdf (Dutton et al)]. Competition graphs, when applied to ecosystems, illuminate previously mysterious properties regarding a community through portraying relationships between species. The relationships they portray help identify primary and secondary extinctions between species, when exploring them. <br />
<br />
(''1,2'')-step competition graphs expand on competition graphs. We know from Dr. Factor and Dr. Merz's paper, ''The (1,2)-step competition graph of a tournament'', that the competition graph of a digraph ''D'' is contained in (a subgraph of) the (''1,2'')-step competition graph on D. Specifically, (''1,2'')-step competition graphs clearly display direct and indirect relationships between vertices; in the language of ecosystems, they display the direct and indirect relationships (up to length 2) between various species within a community. Our formal definition for these graphs comes from Factor and Merz's paper: "the (''1,2'')-step competition graph of a digraph ''D'', denoted ''C<sub>1,2</sub>(D)'', is a graph on ''V(D)'' where ''{x,y}'' in ''E(C<sub>1,2</sub>(D))'' if and only if there exists a vertex ''z'' not equal to ''x,y'', such that either ''d<sub>D-y</sub>''(x,z) less than or equal to 1 and ''d<sub>D-x</sub>''(y,z) is less than or equal to 2 [or vice versa]." The (''1,2'')-step competition graph is generalized by the (''i,j'')-step graph.<br />
<br />
(''i,j'')-step graphs display relationships between vertices of an arbitrary length. That is, since they generalize (''1,2'')-step competition graphs, our formal definition comes, again, from Factor and Merz's paper: "the (''i,j'')-step competition graph of a digraph ''D'', denoted ''C<sub>i,j</sub>(D)'', is a graph on ''V(D)'' where ''{x,y}'' in ''E(C<sub>i,j</sub>(D))'' if and only if there exists a vertex ''z'' not equal to ''x,y'', such that either ''d<sub>D-y</sub>''(x,z) less than or equal to ''i'' and ''d<sub>D-x</sub>''(y,z) is less than or equal to ''j'' [or vice versa]". In the (''1,2'')-step competition graph, we saw indirect relationships up to 2; with the (''i,j'')-step competition graph, we can identify indirect relationships up to '' i'' and ''j''. For instance, we could let ''i'' = 1, preserving direct relationships, and let ''j'' be the value of ''how'' indirect of relationships we want to observe. Thus, with the (''i,j'')-step graph, we control the relationships we want to see. <br />
<br />
This project has two main goals: expanding the theory for (''i,j'')-step graphs and exploring their applications. For expanding their theory, this project may explore generalizations, applications to various families of graphs, or explorations with hypergraphs. Concerning their applications, this project may examine and implement various (1,2)-step competition graphs directed towards explaining various relations between species, explaining primary and secondary extinctions, or explaining potential for extinctions within various communities. Throughout the summer, the researchers will take this project in the directions they see fit.<br />
<br />
=='''Objectives'''==<br />
<br />
During this project, we will examine and explore the following:<br />
<br />
<ol style="margin-left: 5em;"><br />
<li>Previous research regarding competition graphs and (1,2)-step competition graphs of food webs</li><br />
<li>Competition graphs and (1,2)-step competition graphs of a specific food web</li><br />
</ol><br />
<br />
Additionally, we will further previous research by doing the following:<br />
<br />
<ol style="margin-left: 5em;"><br />
<li>Furthering research on (i,j)-step competition graphs by exploring new theory and computation</li><br />
<li>Applying competition graphs and (i,j)-step competition graphs in new areas</li><br />
</ol><br />
<br />
A brief overview of our goals for this 10 week process are listed below. For a complete list of our goals, click [http://reu.mscs.mu.edu/images/2/2a/Milestones.pdf here].<br />
<br />
{| class="wikitable"<br />
|-<br />
|'''Week''' || '''Description'''<br />
|-<br />
!Week 1 (5/30/17-6/2/17): Orientation and Introductions<br />
| <br />
*Complete the education mdule, ''The Biology and Mathematics of Food Webs'', by '''Thursday, 6/1/17'''<br />
*Attend the talk at '''11:00PM in CU 401'''<br />
*Enter the title, description and milestones/goals into the wiki by '''Friday, 6/2''', by midnight<br />
*Read ''(1,2)-step competition graph of a tournament'' and have questions ready for Wednesday, 6/7/2017<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 2 (6/5/17-6/9/17): Experiment with (1,2)-Step Competition Graphs Using Specific Examples<br />
| <br />
*'''Meeting Wednesday, 6/7,''' with Dr. Factor<br />
*Discuss the paper from last week--prepare to answer questions and/or ask them<br />
*Begin reading Kaitlyn Ryan's master's thesis to explore biological background, mathematical background, and statistical information for the topic. Make notes and questions for Thursday's meeting<br />
*Begin reading ''A Characterization of Competition Graphs''<br />
*Attend Ethics training at '''9:00AM on 6/6 in CU 401'''<br />
*Participate in the talk and luncheon at '''11:30AM on 6/8, CU 401'''<br />
*Start comparing competition graphs and (1,2)-step competition graphs by using some small food webs from the initial food web packet, and by creating our own small food web examples<br />
*Learn LaTex (Carissa--Max can tutor)<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 3 (6/12/17-6/16/17): Formulating Research Questions<br />
| <br />
*Meeting with Dr. Factor on '''Tuesday, 6/13'''<br />
*Meeting with Dr. Factor on '''Thursday, 6/15'''<br />
*Attend working lunch on '''Thursday, 6/15,''' where lunch will be provided<br />
*Begin thinking about individual research questions. Discuss these during the Tuesday and Thursday meetings<br />
*Write up findings in LaTeX<br />
**Experiment with creating small food webs and competition graphs in LaTeX<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 4 (6/19/17-6/23/17): Refine Research<br />
|<br />
* Begin looking at competition graphs and (1,2)-step (alternately some (i,k)-step) competition graphs for focus areas. Start refining the direction of research<br />
*Continue writing up finding in LaTeX and creating figures<br />
*Optional: meet with Dr. Factor on '''Tuesday, 6/20'''<br />
*Attend the luncheon at '''11:30 AM on Thursday, 6/22'''<br />
*Meet with Dr. Factor on '''Thursday, 6/22,''' focus will be on what to put on slides for next week's mini-presentations<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 5 (6/26/17-6/30/17): Mini Presentations<br />
|<br />
*Draft an 8 or so minute talk discussing what has been learned so far by '''11:00AM Tuesday, 6/27''', and be prepared to show it to Dr. Factor, should have some things to use already in LaTeX.<br />
*Continue, as time allows, working on the research and placing in document<br />
*Present mini-presentation to peers and mentors on '''Thursday, 6/29'''<br />
*Short meeting with mentor after mini-presentations<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 6 (7/3/17-7/7/17): Continue Individual research<br />
|<br />
*Continue working on research and LaTeX updates<br />
*Meet with mentor on '''Thursday, 7/6''' to give research updates and discuss research direction<br />
*Atend working lunch at '''11:30 AM on Thursday, 7/6'''; includes talk on making an effective poster<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 7 (7/10/17-7/14/17): Resolve Conjectures<br />
|<br />
*Should have conjectures in individual areas, determine an approach to a solution or support for conjectures<br />
*As needed: mentor meeting on '''Monday, 7/10'''<br />
*Go to working lunch on '''Thursday, 7/13'''<br />
*Meet with Dr. Factor on '''Thursday, 7/13'''<br />
*Paper outline (brief) based on last week and this week's meetings, submit to Dr. Factor via email by '''Friday, 7/14''' by '''5:00 PM'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 8 (7/17/17-7/21/17): Begin Finalizing Paper<br />
|<br />
*Meeting with Dr. Factor: '''Monday, 7/17'''; start discussing how to finalize paper and poster<br />
*Begin finalizing results; enter theorems, figures, explanations, etc. into LaTeX and create needed Figures<br />
*Initialize poster draft and email to Dr. Factor by '''Thursday, 7/20''' in time for mentor meeting<br />
*Participate in working luncheon on '''Thursday, 7/20'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|<br />
|- <br />
!Week 9 (7/24/17-7/28/17): Posters and Future Research (Dr. Factor Out of Town)<br />
|<br />
*Have updated poster emailed to Dr. Factor by '''8 PM Tuesday, 7/25'''; comments from Dr. Factor will be back by '''10 AM Wednesday'''<br />
*Make any last minute changes and submit electronic version of poster to Dr. Brylow by '''12:00 PM on Wednesday, 7/26'''<br />
*Finalize any results<br />
*Construct a list regarding future research for paper<br />
*Begin turning LaTeX writing into formal paper<br />
*Go to luncheon on '''Thursday, 7/30'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 10 (7/31/17-8/4/17): Formal Talks, Posters, Papers, and Goodbyes<br />
|<br />
*Draft formal talk, which is due to Dr. Factor bu '''11:00 AM Monday, 7/31'''<br />
*Draft paper, which is due to Dr. Factor by '''11:00 AM Thursday, 8/3'''<br />
*Attend poster session '''1:00 PM - 3:00 PM on Tuesday, 8/1'''<br />
*Formal presentations<br />
**'''Wednesday, 8/5, 10:00-2:00, CU 401'''<br />
**'''Thursday, 8/6, 10:00-12:00, CU 401'''<br />
*Paper due electronically '''Friday, 8/4''' by '''midnight''', sent to Dr. Brylow<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
|}<br />
<br />
=='''Research Logs'''==<br />
<br />
Each researcher keeps a log of the entire process, including reflections at the end of the week. These logs demonstrate the researcher's actual progress on their respective projects. Specifically, this determines whether or not they are actually reaching their milestones and completing their goals. If you would like to read them, click the researcher's name: [[User:Babcock|Carissa Babcock]] or [[User:maxblack45|Max Black]].</div>Babcockhttps://reu.cs.mu.edu/index.php/File:Graphs.jpgFile:Graphs.jpg2017-06-09T20:58:51Z<p>Babcock: </p>
<hr />
<div></div>Babcockhttps://reu.cs.mu.edu/index.php/(i,j)-step_competition_graphs(i,j)-step competition graphs2017-06-09T20:58:37Z<p>Babcock: /* Background */</p>
<hr />
<div>'''Researchers:''' [[User:Babcock|Carissa Babcock]] and [[User:Maxblack45|Max Black]]<br />
<br />
'''Mentor:''' [http://www.marquette.edu/mscs/facstaff-factor.shtml Dr. Kim A.S. Factor]<br />
<br />
=='''Background'''==<br />
<br />
[[File:Graphs.jpg|350px|thumb|right|Here are some tournaments and their (1,2)-step competition graphs found in the (1,2)-step competition graph of a tournament paper.]]<br />
<br />
Joel E. Cohen, in 1968, began modeling ecosystems with competition graphs; consequently, mathematicians began developing his new mathematical object. Informally, competition graphs are collections of dots and lines representing some "competitive" relationship between two species, players, companies, etc. Formally, if we let "let ''D'' be a directed graph having no multiple edges, the competition graph of ''D'' is an undirected graph G on the same node set as ''D'' and having an undirected edge ''{u<sub>i</sub>, v<sub>j</sub>}'' if and only if there exists a third node ''u''<sub>k</sub> such that ''{v<sub>i</sub>, v<sub>k</sub>}'' and ''{v<sub>j</sub>, u<sub>k</sub>}'' are directed edges in the edge set of ''D'' "[http://reu.mscs.mu.edu/images/3/38/CharacterizingCompetitionGraphs.pdf (Dutton et al)]. Competition graphs, when applied to ecosystems, illuminate previously mysterious properties regarding a community through portraying relationships between species. The relationships they portray help identify primary and secondary extinctions between species, when exploring them. <br />
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(1,2)-step competition graphs expand on competition graphs. We know from Dr. Factor and Dr. Merz's paper, ''The (1,2)-step competition graph of a tournament'', that the competition graph of a digraph ''D'' is contained in (a subgraph of) the (1,2)-step competition graph on D. Specifically, (1,2)-step competition graphs clearly display direct and indirect relationships between vertices; in the language of ecosystems, they display the direct and indirect relationships (up to length 2) between various species within a community. Our formal definition for these graphs comes from Factor and Merz's paper: "the (1,2)-step competition graph of a digraph ''D'', denoted ''C<sub>1,2</sub>(D)'', is a graph on ''V(D)'' where ''{x,y}'' in ''E(C<sub>1,2</sub>(D))'' if and only if there exists a vertex ''z'' not equal to ''x,y'', such that either ''d<sub>D-y</sub>''(x,z) less than or equal to 1 and ''d<sub>D-x</sub>''(y,z) is less than or equal to 2 [or vice versa]." The (1,2)-step competition graph is generalized by the (i,j)-step graph.<br />
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(i,j)-step graphs display relationships between vertices of an arbitrary length. That is, since they generalize (1,2)-step competition graphs, our formal definition comes, again, from Factor and Merz's paper: "the (i,j)-step competition graph of a digraph ''D'', denoted ''C<sub>i,j</sub>(D)'', is a graph on ''V(D)'' where ''{x,y}'' in ''E(C<sub>i,j</sub>(D))'' if and only if there exists a vertex ''z'' not equal to ''x,y'', such that either ''d<sub>D-y</sub>''(x,z) less than or equal to ''i'' and ''d<sub>D-x</sub>''(y,z) is less than or equal to ''j'' [or vice versa]". In the (''1,2'')-step competition graph, we saw indirect relationships up to 2; with the (''i,j'')-step competition graph, we can identify indirect relationships up to '' i'' and ''j''. For instance, we could let ''i' = 1, preserving direct relationships, and let ''j'' be the value of ''how'' indirect of relationships we want to observe. Thus, with the (''i,j'')-step graph, we control the relationships we want to see. <br />
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This project has two main goals: expanding the theory for (''i,j'')-step graphs and exploring their applications. For expanding their theory, this project may explore generalizations, applications to various families of graphs, or explorations with hypergraphs. Concerning their applications, this project may examine and implement various (1,2)-step competition graphs directed towards explaining various relations between species, explaining primary and secondary extinctions, or explaining potential for extinctions within various communities. Throughout the summer, the researchers will take this project in the directions they see fit.<br />
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=='''Objectives'''==<br />
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During this project, we will examine and explore the following:<br />
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<ol style="margin-left: 5em;"><br />
<li>Previous research regarding competition graphs and (1,2)-step competition graphs of food webs</li><br />
<li>Competition graphs and (1,2)-step competition graphs of a specific food web</li><br />
</ol><br />
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Additionally, we will further previous research by doing the following:<br />
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<ol style="margin-left: 5em;"><br />
<li>Furthering research on (i,j)-step competition graphs by exploring new theory and computation</li><br />
<li>Applying competition graphs and (i,j)-step competition graphs in new areas</li><br />
</ol><br />
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A brief overview of our goals for this 10 week process are listed below. For a complete list of our goals, click [http://reu.mscs.mu.edu/images/2/2a/Milestones.pdf here].<br />
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{| class="wikitable"<br />
|-<br />
|'''Week''' || '''Description'''<br />
|-<br />
!Week 1 (5/30/17-6/2/17): Orientation and Introductions<br />
| <br />
*Complete the education mdule, ''The Biology and Mathematics of Food Webs'', by '''Thursday, 6/1/17'''<br />
*Attend the talk at '''11:00PM in CU 401'''<br />
*Enter the title, description and milestones/goals into the wiki by '''Friday, 6/2''', by midnight<br />
*Read ''(1,2)-step competition graph of a tournament'' and have questions ready for Wednesday, 6/7/2017<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 2 (6/5/17-6/9/17): Experiment with (1,2)-Step Competition Graphs Using Specific Examples<br />
| <br />
*'''Meeting Wednesday, 6/7,''' with Dr. Factor<br />
*Discuss the paper from last week--prepare to answer questions and/or ask them<br />
*Begin reading Kaitlyn Ryan's master's thesis to explore biological background, mathematical background, and statistical information for the topic. Make notes and questions for Thursday's meeting<br />
*Begin reading ''A Characterization of Competition Graphs''<br />
*Attend Ethics training at '''9:00AM on 6/6 in CU 401'''<br />
*Participate in the talk and luncheon at '''11:30AM on 6/8, CU 401'''<br />
*Start comparing competition graphs and (1,2)-step competition graphs by using some small food webs from the initial food web packet, and by creating our own small food web examples<br />
*Learn LaTex (Carissa--Max can tutor)<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 3 (6/12/17-6/16/17): Formulating Research Questions<br />
| <br />
*Meeting with Dr. Factor on '''Tuesday, 6/13'''<br />
*Meeting with Dr. Factor on '''Thursday, 6/15'''<br />
*Attend working lunch on '''Thursday, 6/15,''' where lunch will be provided<br />
*Begin thinking about individual research questions. Discuss these during the Tuesday and Thursday meetings<br />
*Write up findings in LaTeX<br />
**Experiment with creating small food webs and competition graphs in LaTeX<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 4 (6/19/17-6/23/17): Refine Research<br />
|<br />
* Begin looking at competition graphs and (1,2)-step (alternately some (i,k)-step) competition graphs for focus areas. Start refining the direction of research<br />
*Continue writing up finding in LaTeX and creating figures<br />
*Optional: meet with Dr. Factor on '''Tuesday, 6/20'''<br />
*Attend the luncheon at '''11:30 AM on Thursday, 6/22'''<br />
*Meet with Dr. Factor on '''Thursday, 6/22,''' focus will be on what to put on slides for next week's mini-presentations<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
!Week 5 (6/26/17-6/30/17): Mini Presentations<br />
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*Draft an 8 or so minute talk discussing what has been learned so far by '''11:00AM Tuesday, 6/27''', and be prepared to show it to Dr. Factor, should have some things to use already in LaTeX.<br />
*Continue, as time allows, working on the research and placing in document<br />
*Present mini-presentation to peers and mentors on '''Thursday, 6/29'''<br />
*Short meeting with mentor after mini-presentations<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 6 (7/3/17-7/7/17): Continue Individual research<br />
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*Continue working on research and LaTeX updates<br />
*Meet with mentor on '''Thursday, 7/6''' to give research updates and discuss research direction<br />
*Atend working lunch at '''11:30 AM on Thursday, 7/6'''; includes talk on making an effective poster<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 7 (7/10/17-7/14/17): Resolve Conjectures<br />
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*Should have conjectures in individual areas, determine an approach to a solution or support for conjectures<br />
*As needed: mentor meeting on '''Monday, 7/10'''<br />
*Go to working lunch on '''Thursday, 7/13'''<br />
*Meet with Dr. Factor on '''Thursday, 7/13'''<br />
*Paper outline (brief) based on last week and this week's meetings, submit to Dr. Factor via email by '''Friday, 7/14''' by '''5:00 PM'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 8 (7/17/17-7/21/17): Begin Finalizing Paper<br />
|<br />
*Meeting with Dr. Factor: '''Monday, 7/17'''; start discussing how to finalize paper and poster<br />
*Begin finalizing results; enter theorems, figures, explanations, etc. into LaTeX and create needed Figures<br />
*Initialize poster draft and email to Dr. Factor by '''Thursday, 7/20''' in time for mentor meeting<br />
*Participate in working luncheon on '''Thursday, 7/20'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
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|- <br />
!Week 9 (7/24/17-7/28/17): Posters and Future Research (Dr. Factor Out of Town)<br />
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*Have updated poster emailed to Dr. Factor by '''8 PM Tuesday, 7/25'''; comments from Dr. Factor will be back by '''10 AM Wednesday'''<br />
*Make any last minute changes and submit electronic version of poster to Dr. Brylow by '''12:00 PM on Wednesday, 7/26'''<br />
*Finalize any results<br />
*Construct a list regarding future research for paper<br />
*Begin turning LaTeX writing into formal paper<br />
*Go to luncheon on '''Thursday, 7/30'''<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|- <br />
!Week 10 (7/31/17-8/4/17): Formal Talks, Posters, Papers, and Goodbyes<br />
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*Draft formal talk, which is due to Dr. Factor bu '''11:00 AM Monday, 7/31'''<br />
*Draft paper, which is due to Dr. Factor by '''11:00 AM Thursday, 8/3'''<br />
*Attend poster session '''1:00 PM - 3:00 PM on Tuesday, 8/1'''<br />
*Formal presentations<br />
**'''Wednesday, 8/5, 10:00-2:00, CU 401'''<br />
**'''Thursday, 8/6, 10:00-12:00, CU 401'''<br />
*Paper due electronically '''Friday, 8/4''' by '''midnight''', sent to Dr. Brylow<br />
*Update Wiki at end of week or during week to reflect on what has been accomplished<br />
|-<br />
|}<br />
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=='''Research Logs'''==<br />
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Each researcher keeps a log of the entire process, including reflections at the end of the week. These logs demonstrate the researcher's actual progress on their respective projects. Specifically, this determines whether or not they are actually reaching their milestones and completing their goals. If you would like to read them, click the researcher's name: [[User:Babcock|Carissa Babcock]] or [[User:maxblack45|Max Black]].</div>Babcock