# User:Lenzi.Cram

## Contents

## REU - Summer 2015

### Personal Information

My name is Lenzi Cram. I am originally from Las Vegas, NV. I am pursuing a B.S. degree in Mathematics at Marquette University, where I am expected to graduate in May of 2016.

### Research Topic

I am working with Dr. Factor researching Graph Theory with an application of (1,2)-step competition graphs. Specifically, I am working with an application of digraphs, competition graphs, and (1,2)-step competition graphs to model global crude oil trading networks. In addition, I am working on maximizing the number of arcs in digraphs while maximizing the number of edges in (1,2)-step competition graphs, with only one edge missing.

### Goals and Milestones

**Week 1:**

- Complete the education module “The Biology and Mathematics of Food Webs”
- Enter the title, description, and milestones/goals into the Wiki
- Search for current papers on graph theory and economics or competition graphs and economics
- Prepare initial findings for meeting with Dr. Factor on Monday, 6/8
- Combine the abstracts of the papers that have been found and come up with talking points about how to narrow down my topic and proceed efficiently with my research

**Week 2:**

* Meetings/Important Dates:*

- Meet with Dr. Factor on Monday, 6/8, to discuss initial findings
- Participate in talk and luncheon on Thursday, 6/11
- Discuss accomplishments and difficulties so far
- Ask general questions about “how” to do things, “where” to find things, etc.

- Meet with Dr. Factor Thursday, 6/11, to discuss questions and comments on Katie’s paper and competition graph paper

* Research:*

- Begin reading Kaitlyn Ryan’s master’s thesis
- Understand the biological background, mathematical background, and some statistical information for this topic
- Take notes to prepare for Thursday’s meeting

- Begin reading “A Characterization of Competition Graphs”
- Start learning LaTeX
- Update the wiki

**Week 3:**

* Meetings/Important Dates:*

- Meet with Dr. Factor on Tuesday, 6/16
- Attend talk Tuesday, 6/16,
- Discuss good presentations, good technical writing, and the difference between them

- Attend Workshop Thursday, 6/18
- Responsible Conduct of Research Workshop

- Meet with Dr. Factor after the Workshop

* Research:*

- Begin to read paper “The (1,2)-step Competition Graph of a Tournament”
- Start to compare the competition graphs and (1,2)-step competition graphs by using some small food webs from the initial food web packet, and by creating your own small food web examples.
- Try to use LaTeX to write up some findings
- Find a way to draw a small food web on the computer and find a way to import it into the LaTeX manuscript
- Update the wiki

**Week 4:**

* Meetings/Important Dates:*

- Meet with Dr. Factor on Monday, 6/22
- Luncheon Thursday, 6/25
- Meet with Dr. Factor Thursday, 6/25

* Research:*

- Begin to look at competition graphs and (1,2)-step competition graphs for each focus area
- Develop questions that can be asked in focus area regarding the graphs
- Continue to write up findings in LaTeX and create figures
- Prepare for the 8-10 minute talk that is due on Monday
- Update the wiki

**Week 5:**

* Meetings/Important Dates:*

- Present 8-10 minute presentation to peers and mentors on Thursday, 7/2 regarding what has been learned so far
- Meet with Dr. Factor after the presentation

* Research:*

- Have a draft of 8-10 minute talk prepared on what has been learned so far by 11 AM Monday, 6/29
- Show it to Dr. Factor

- Look at competition graphs and (1,2)-step competition graphs for each focus area
- Develop questions that can be asked in focus area regarding the graphs
- Update wiki

**Week 6:**

* Meetings/Important Dates:*

- Meet with Dr. Factor on Monday, 7/6
- Evaluate status of research and make plans for the remainder of the research period

- Go to the talk on Tuesday, 7/7
- Meet with Dr. Factor on Thursday, 7/9
- Attend lunch on Thursday, 7/9

* Research:*

- Look at competition graphs and (1,2)-step competition graphs for each focus area
- LaTeX updates
- Update wiki

**Week 7:**

* Meetings/Important Dates:*

- Meet with Dr. Factor on Monday, 7/13
- Attend lunch on Thursday, 7/16
- Paper outline due by email of Friday, 7/16 by 5 PM

* Research:*

- Determine how to approach a solution to the conjectures that have been made
- Create a brief paper outline
- Update wiki

**Week 8:**

* Meetings/Important Dates:*

- Participate in the luncheon on Thursday, 7/23
- Initialize poster draft and email it to Dr. Factor by Friday, 7/24

* Research:*

- Finalize results
- Enter results into LaTeX and create needed figures
- Create poster draft
- Update wiki

**Week 9:**

* Meetings/Important Dates:*

- Meet with Dr. Factor on Tuesday, 7/28
- Discuss finalizing poster, prepare for final talk, and get pointers on the final paper

- Have updated poster emailed to Dr. Factor Tuesday, 7/28
- Submit final electronic poster version to Dr. Brylow on Wednesday, 7/29
- Attend luncheon on Thursday, 7/30

* Research:*

- Finalize poster
- Finalize results
- Construct a “future research” list that will go into the paper
- Begin to turn LaTeX writings into a formal paper
- Update wiki

**Week 10:**

*Meetings/Important Dates:*

- Draft of formal talk due to Dr. Factor Monday, 8/3
- Draft of paper due to Dr. Factor Monday, 8/3
- Poster Session Tuesday, 8/4
- Formal Presentations
- Wednesday, 8/5
- Thursday, 8/6

- Final meeting Friday, 8/7
- Paper due Friday, 8/7
- Update wiki

### Log

**Week 1:**

*Monday, June 1st*

- Orientation
- Met with Dr. Factor and discussed the general concepts of graph theory over lunch

*Tuesday, June 2nd*

- Tour of campus
- Finished up handing in paperwork
- Attended a library presentation on the resources available to Marquette students/employees
- This included, more specifically, the databases that would be beneficial to locate journals for our research

*Wednesday, June 3rd*

- Worked on the education module “The Biology and Mathematics of Food Webs”
- Looked up articles that helped elaborate on Graph Theory
- Looked up articles that explained typical applications of Graph Theory
- Looked up articles that elaborated on the field of economics and where Graph Theory has been applied

*Thursday, June 4th*

- Finished the education module “The Biology and Mathematics of Food Webs”
- Collected a list of talking points to discuss with Dr. Factor about Graph Theory, the expectations for my research, and the milestones for the summer
- Met with Dr. Factor to discuss the plan for the summer
- We discussed where I can start, how I can start narrowing down a topic, and where to go from there

- Attended the talk – Dr. Factor discussed the complexity of the problems we will be dealing with, and how we can use our previous knowledge as well as the help from our mentor to come up with a strategic approach to tackling the question we intend to research
- Spent the remainder of the afternoon looking up more journal articles
- The searches were centered around finding a network in the economy that can be represented by a competition graph

*Friday, June 5th*

- Read the abstracts of the articles obtained and compiling them to prepare to meet with Dr. Factor on Monday
- Completed Goals and Milestones for the summer
- Found more articles that will be good talking points for the meeting with Dr. Factor on Monday

**Week 2:**

*Monday, June 8th*

- Prepared to meet with Dr. Factor to discuss material she has found as well as the results of my literature search
- Met with Dr. Factor to discuss literary findings and get a feel for the math I will be working with
- We discussed (1,2) step competition graphs and their use in providing additional information
- I decided to narrow my search to a direct-trade network.

- Began reading Kaitlyn Ryan’s master’s thesis
- It focuses on food webs, so I am getting a more thorough understanding of how food webs demonstrate the math we are working with

- Took a look at “A Characterization of Competition Graphs”
- Downloaded LaTeX

*Tuesday, June 9th*

- Continued reading Kaitlyn Ryan’s master’s thesis
- Continued reading “A Characterization of Competition Graphs”
- Worked to understand competition graphs more thoroughly
- Started to apply thoughts from the reading to maybe a potential topic

*Wednesday, June 10th*

- Finished final thoughts with the two readings
- Met with Ben to discuss the readings
- Continued to work to apply this to a topic

*Thursday, June 11th*

- Completed readings
- Attended luncheon
- Discussed readings with Dr. Factor
- Looked into the global petroleum market to see if that could be a network to research
- Began defining vertices and arcs

*Friday, June 12th*

- Uploaded Goals and Milestones, Log, and other information to the Wiki
- Learned how to appropriately format the Wiki
- Continued looking into the petroleum market as a potential topic
- Worked on the problem Dr. Factor assigned in order to further understand the reading on “A Characterization of Competition Graphs”

**Week 3:**

*Monday, June 15th*

- Finished the problem Dr. Factor gave based on "A Characterization of Competition Graphs"
- Continued practicing competition graphs
- Continued looking up data to determine potential vertices for the petroleum market

*Tuesday, June 16th*

- Worked on inputting information into LaTeX
- Met with Dr. Factor to discuss “A Characterization of Competition Graphs”
- Began reading “The (1,2)-step Competition Graph of a Tournament”

*Wednesday, June 17th*

- Collected data
- Continued reading/understanding “The (1,2)-step Competition Graph of a Tournament”

*Thursday, June 18th*

- Attended RCR training
- Met with Dr. Factor
- Watched the assigned videos to complete RCR training

*Friday, June 19th*

- Continued reading/understanding “The (1,2)-step Competition Graph of a Tournament”
- Practiced inputting findings into LaTeX
- Began building graphs in GeoGebra 5 for findings

**Week 4:**

*Monday, June 22th*

- Continued building graphs in GeoGebra
- Practiced LaTeX
- Met with Dr. Factor

*Tuesday, June 23rd*

- Worked on applying the concept of (1,2)-step Competition Graphs to my digraph
- Practiced inputting the graphs into LaTeX
- Looked into having more vertices

*Wednesday, June 24th*

- Finished inputting graphs into GeoGebra
- Continued working with LaTeX
- Began thinking about the affects of moving a vertex out of the network and what that would do to the digraph, the competition graph, and the (1,2)-step competition graph

*Thursday, June 25th*

- Continued working with LaTeX
- Continued thinking about the vertices and their functions in the crude oil market
- Working lunch
- Met with Dr. Factor

*Friday, June 26th*

- Began preparing for presentation run-through with Dr. Factor
- Looked into background information that would help with the presentation
- Began attempting to navigate GraphTea and fix my digraph

**Week 5:**

*Monday, June 29th*

- Finished up presentation in preparation for Thursday's scheduled mini presentation
- Met with Dr. Factor to run through my presentation
- Finished fixing digraph
- Continued thinking about the vertices and their functions
- Continued thinking about what would happen if a vertex were removed

*Tuesday, June 30th*

- Continued working on presentation
- Worked on details of research

*Wednesday, July 1st*

- Finished presentation
- Fixed figures for PowerPoint
- Fixed definitions of each graph

*Thursday, July 2nd*

- Prepared for presentation
- Gave presentation and attended all other presentations

**Week 6:**

*Monday, July 6th*

- Met with Dr. Factor to discuss further steps with research
- Dr. Factor gave me pure math questions to look at
- Decided to return to the crude oil market upon further findings

*Tuesday, July 7th*

- Worked on pure math questions

*Wednesday, July 8th*

- Worked on pure math questions

*Thursday, July 9th*

- Worked on pure math questions
- Working lunch

*Friday, July 10th*

- Worked on pure math questions

**Week 7:**

*Monday, July 13th*

- Worked on pure math questions
- phone meeting with Dr. Factor

*Tuesday, July 14th*

- Worked on pure math questions

*Wednesday, July 15th*

- Worked on pure math questions

*Thursday, July 16th*

- Worked on pure math questions

*Friday, July 17th*

- Worked on pure math questions

**Week 8:**

*Monday, July 20th*

- Worked on pure math questions
- Began working on poster
- Began working to produce theorems from findings pertaining to pure math questions

*Tuesday, July 21st*

- Worked on pure math questions
- Continued working on poster
- Continued working to produce theorems from findings pertaining to pure math questions

*Wednesday, July 22nd*

- Worked on pure math questions
- Continued working on poster
- Continued working to produce theorems from findings pertaining to pure math questions

*Thursday, July 23rd*

- Worked on pure math questions
- Continued working on poster
- Continued working to produce theorems from findings pertaining to pure math questions
- Attended working lunch

*Friday, July 24th*

- Continued working on poster
- Continued working to produce theorems from findings pertaining to pure math questions
- Began outlining paper

**Week 9:**

*Monday, July 27th*

- Continued working on poster
- Continued working to produce theorems from findings pertaining to pure math questions
- Continued outlining paper

*Tuesday, July 28th*

- Continued working on poster
- Continued working to produce theorems from findings pertaining to pure math questions
- Continued outlining paper

*Wednesday, July 29th*

- Turned in poster
- Continued working to produce theorems from findings pertaining to pure math questions
- Continued outlining paper
- Met with Dr. Factor

*Thursday, July 30th*

- Outlined paper and began typing content into LaTeX
- Finished abstract for talk
- Began working on PowerPoint for next week's talk
- Met with Dr. Factor

*Friday, July 31st*