Revision as of 21:12, 4 August 2017

Project Description

I am conducting research on (i,j)-step competition graphs in the ten week long Marquette MSCS REU. The mentor that I am working with is 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.

Background Readings

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.

• BioMath: The Biology and Mathematics of Food Webs by Midge Cozzens, Nancy Crisler, Randi Rotjan, and Tom Fleetwood
• Chapter 3 from Applied Combinatorics by Fred S. Roberts
• (i,j) Competition Graphs by Kim A.S. Hefner, Kathryn F. Jones, Suh-ryung Kim, J. Richard Lundgren, and Fred S. Roberts.
• The (1,2)-step competition graph of a tournament by Kim A.S. Factor and Sarah K. Merz
• An Introduction to (1,2)-Domination Graphs by Kim A.S. Factor
• The m-step, same-step, and any-step competition graphs by Wei ho
• Connected triangle-free m-step competition graphs by Geir T. Helleloid
• The m-step competition graph of a digraph by Han Hyuk Cho, Suh-Ryun Kim, and Yunsun Nam
• A Characterization of Competition Graphs by R.D. Dutton and R.C. Brigham
• Interval Graphs and Food Webs: A finding and a Problem by Joel E. Cohen
• Using Food Webs In Order To Determine Possible Predictors of Primary and Secondary Extinctions by Kaitlin A. Ryan (a master's thesis)

Project Log

Week 1 (5/30/17-6/2/17)

• Note: I was not physically present during week 1 of the REU. I completed the BioMath packet during this time.

Reflection: End of Week 1

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.

Week 2 (6/5/17-6/9/17)

Day 1 (6/5/17)

• Finished BioMath packet.
• Printed readings and materials that were emailed to me.
• Confirmed a meeting with Max tomorrow, 6/6, for 8:00 AM before the ethics training to go over week 1.

Day 2 (6/6/17)

• Attended meeting with Max at 8:00AM
• Attended meeting with Petra at 8:30AM to complete paperwork.
• Attended ethical research training at 9:00AM until about 3:00PM.
• Began reviewing The (1,2)-step competition graph with Max at 3:15PM for about 3 hours.
• Made note to include approximate total number of hours in end-of-week reflection
• Estimated work for the day is about ten hours.

Day 3 (6/7/17)

• Started reading chapter 3 about graph theory in Applied Combinatorics. Read at home for about half an hour.
• Started to read thesis paper- Using Food Webs in Order to Determine... Read first 19 pages for about half an hour.
• Set up WIKI page for about half an hour.
• Continued to read and go through The (1,2)-step competition graph with Max for about an hour.
• Practiced Overleaf/ TeX for about half an hour
• Meeting with Dr. Factor and Max for about an hour.
• Worked with Max on new (1,2)-step competition graph article and added definitions to Overleaf for about four hours.
• Estimated work for the day is about eight hours.

Day 4 (6/8/17)

• Worked on presentation for Dr. Factor with Max for about an hour.
• Read (1,2)-step competition graph article in detail. (about five hours).

Day 5 (6/9/17)

• Worked on presentation for Dr. Factor with Max for most of the day. (About six hours)
• Worked on adding a picture to the background section.

Reflection: End of Week 2

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.

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.

Week 3 (6/12/17-6/16/17)

Day 1 (6/12/17)

• Finished up presentation for Dr. Factor (about four hours)
• Revised hand out for presentation with Dr. Factor tomorrow (one hour)
• Worked on finishing up readings (about two hours)

Day 2 (6/13/17)

• Worked on background research to try to find a topic to study (about five hours)
• Met with Dr. Factor and did presentation. Went over what I should be working on. (about an hour)

Day 3 (6/14/17)

• Worked on completing the ethics training quizzes and readings (about six hours)
• Wasn't feeling well, so left early at about 3:30.

Day 4 (6/15/17

• Worked from home- was home sick
• Worked on taking Food Webs and finding their (1,2)-step competition graph (about six hours)
• Wrote up information from the Food Webs with Tex and emailed to Dr. Factor (about two hours)

Day 5 (6/16/17)

• Worked from home- was home sick
• Read chapter 3 from Applied Combinatorics (Roberts) (about four hours)
• Worked on reading background information to find a topic to research (about two hours)
• Continued work on Food Webs (about an hour)

Reflection: End of Week 3

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 C₄, such that k(G)> k_(1,2)(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.

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.

Week 4 (6/19/17-6/23/17)

Day 1 (6/19/17)

• Worked on finishing Chapter three in Applied Combinatorics (Roberts) (about three hours)
• Continued work on Food Web work (about four hours)

Day 2 (6/20/17)

• Explored question about graphs found in The (1,2)-step competition number of a graph (Factor, et al.) paper (about two hours)
• Met with Dr. Factor. (about an hour)
• Fixed work with food webs (about four hours)

Day 3 (6/21/17)

• Continued work with Food Webs (about two hours)
• Worked on answering question about competition number (about five hours)

Day 4 (6/22/17)

• Worked on Competition Numbers practice (about six hours (split between morning and afternoon))
• Met with Dr. Factor (about 30 minutes)
• (Working Lunch (about an hour)

Day 5 (6/23/17)

Worked from home.

• Worked on Competition Numbers practice (about eight hours)

Reflection: End of Week 4

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.

Week 5 (6/26/17-6/30/17)

Day 1 (6/26/17)

• Worked on Competition Number Practice (about three hours)
• Attended talk on giving a good research presentation (about two hours)
• Worked on mini presentation (about two hours)

Day 2 (6/27/17)

• Worked on mini presentation for about eight hours
• Practiced mini presentation at home for about an hour

Day 3 (6/28/17)

• Worked on mini presentation for about eight hours
• Practiced mini presentation at home for about an hour

Day 4 (6/29/17)

• Practiced mini presentation at home for about an hour
• Practiced mini presentation on campus for about two hours
• Attended mini presentations for about 2.5 hours
• Continued work on Competition Numbers (worked on C4 union C4 union C4) for about two hours

Day 5 (6/30/17)

• Continued work on Competition numbers for about eight hours (worked from home)

Reflection: End of Week 5

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.

Week 6 (7/3/17-7/7/17)

Day 1 (7/3/17)

Day 2 (7/4/17)

Day 3 (7/5/17)

• Worked on typing up findings with the competition numbers (about four hours)
• Continued research with competition numbers (about six hours)

Day 4 (7/6/17)

• Met with Dr. Factor and went over my findings (about an hour)
• Attended working lunch and attended presentation about having a good poster (about two hours)
• Worked on competition number research (about five hours)

Day 5 (7/7/17)

• Worked on abstract for conference (about an hour)
• Worked on competition number research (about five hours)
• Worked on typing up findings (about three hours)

Worked over Weekend (7/9/17)

• Worked on abstract for conference (researching how to do abstract/ typing it) (about three hours)

Reflection: End of Week 6

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.

Week 7 (7/10/17-7/14/17)

Day 1 (7/10/17)

• Continued research on competition numbers (two hours)
• Worked on editing abstract (one hour)
• Worked on finishing the type ups of my findings (four hours)

Day 2 (7/11/17)

• Typed up abstract in latex and edited it more (three hours)
• Worked on creating paper outline (one hour)
• Worked on C4 graph research (three hours)

Day 3 (7/12/17)

• Finished up abstract and submitted application for conference (one hour)
• Worked on C4 graph research (six hours)

Day 4 (7/13/17)

• Typed up findings to give to Dr. Factor (one hour)
• Met with Dr. Factor (one hour)
• Working lunch (one hour)

Day 5 (7/14/17)

Reflection: End of Week 7

Week 8 (7/17/17-7/21/17)

Day 1 (7/17/17)

Day 2 (7/18/17)

Day 3 (7/19/17)

Day 4 (7/20/17)

Day 5 (7/21/17)

Reflection: End of Week 8

Week 9 (7/24/17-7/28/17)

Day 1 (7/24/17)

Day 2 (7/25/17)

Day 3 (7/26/17)

Day 4 (7/27/17)

Day 5 (7/28/17)

Reflection: End of Week 9

Week 10 (7/31/17-8/4/17)

Day 1 (7/31/17)

Day 2 (8/1/17)

Day 3 (8/2/17)

Day 4 (8/3/17)

Day 5 (8/4/17)

Reflection: End of Week 10