(i,j)-step competition graphs

Researchers: Max Black and Carissa Babcock

Mentor: Dr. Kim A.S. Factor

Background

Cohen, in 1968, began modeling ecosystems with competition graphs. Consequently, mathematicians began developing the theory of competition graphs. Competition graphs are, essentially, graphs

Objectives

During this project, we will examine and explore the following:

1. Previous research regarding competition graphs and (1,2)-step competition graphs of food webs
2. Competition graphs and (1,2)-step competition graphs of a specific food web

Additionally, we will further previous research by doing the following:

1. Furthering research on (i,j)-step competition graphs by exploring new theory and computation
2. Applying competition graphs and (i,j)-step competition graphs in new areas

A brief overview of our goals for this 10 week process are listed below. For a complete list of our goals, click here.

Week	Description
Week 1 (5/30/17-6/2/17): Orientation and Introductions	Complete the education mdule, The Biology and Mathematics of Food Webs, by Thursday, 6/1/17 Attend the talk at 11:00PM in CU 401 Enter the title, description and milestones/goals into the wiki by Friday, 6/2/2017, by midnight Update Wiki at end of week or during week to reflect on what has been accomplished Read (1,2)-step competition graph of a tournament and have questions ready for Wednesday, 6/7/2017
Week 2 (6/5/17-6/9/17): Experiment with (1,2)-Step Competition Graphs Using Specific Examples	Meeting Wednesday, 6/7, with Dr. Factor Discuss the paper from last week--prepare to answer questions and/or ask them 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 Begin reading A Characterization of Competition Graphs Attend Ethics training at 9:00AM on 6/6 in CU 401 Participate in the talk and luncheon at 11:30AM on 6/8, CU 401 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 Learn LaTex (Carissa--Max can tutor) Update Wiki at end of week or during week to reflect on what has been accomplished
Week 3 (6/12/17-6/16/17): Formulating Research Questions	Meeting with Dr. Factor on Tuesday, 6/13 Meeting with Dr. Factor on Thursday, 6/15 Attend working lunch on Thursday, 6/15, where lunch will be provided Begin thinking about individual research questions. Discuss these during the Tuesday and Thursday meetings Write up findings in LaTeX Experiment with creating small food webs and competition graphs in LaTeX Update Wiki at end of week or during week to reflect on what has been accomplished
Week 4 (6/19/17-6/23/17): Refine Research	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 Continue writing up finding in LaTeX and creating figures Optional: meet with Dr. Factor on Tuesday, 6/20 Attend the luncheon at 11:30 AM on Thursday, 6/22 Meet with Dr. Factor on Thursday, 6/22, focus will be on what to put on slides for next week's mini-presentations Update Wiki at end of week or during week to reflect what has been accomplished
Week 5 (6/26/17-6/30/17): Mini Presentations	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. Continue, as time allows, working on the research and placing in document Present mini-presentation to peers and mentors on Thursday, 6/29 Short meeting with mentor after mini-presentations Update Wiki at end of week or during week to reflect what has been accomplished
Week 6 (7/3/17-7/7/17): Continue Individual research	Continue working on research and LaTeX updates Meet with mentor on Thursday, 7/6 to give research updates and discuss research direction Atend working lunch at 11:30 AM on Thursday, 7/6; includes talk on making an effective poster Update Wiki at end of week or during week to reflect what has been accomplished
Week 7 (7/10/17-7/14/17): Resolve Conjectures	Should have conjectures in individual areas, determine an approach to a solution or support for conjectures As needed: mentor meeting on Monday, 7/10 Go to working lunch on Thursday, 7/13 Meet with Dr. Factor on Thursday, 7/13 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 Update Wiki at end of week or during week to reflect what has been accomplished
Week 8 (7/17/17-7/21/17): Begin Finalizing Paper
Week 9 (7/24/17-7/28/17): Posters and Future Research (Dr. Factor Out of Town)
Week 10 (7/31/17-8/4/17): Formal Talks, Posters, Papers, and Goodbyes