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| | =='''Background'''== | | =='''Background'''== |
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| − | Cohen, in 1968, began modeling ecosystems with competition graphs. Consequently, mathematicians began developing the theory of competition graphs. Competition graphs are, essentially, graphs | + | Cohen, in 1968, began modeling ecosystems with competition graphs. Consequently, mathematicians began developing the theory of competition graphs. Informally, competition graphs are collections of dots and lines representing some "competitive" relationship between two species, player, companies, etc. Formally, if we "let <math> D </math> 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 <math> \{ u_i, v_j \} </math> if and only if there exists a third node <math> u_k </math> such that <math> \{ v_i, v_k \} </math> and <math> \{v_j, u_k \} </math> are directed edges in the edge set of <math> D </math>" [http://reu.mscs.mu.edu/images/3/38/CharacterizingCompetitionGraphs.pdf (Dutton et al)]. |
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| | =='''Objectives'''== | | =='''Objectives'''== |
Revision as of 02:58, 3 June 2017
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. Informally, competition graphs are collections of dots and lines representing some "competitive" relationship between two species, player, companies, etc. Formally, if we "let <math> D </math> 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 <math> \{ u_i, v_j \} </math> if and only if there exists a third node <math> u_k </math> such that <math> \{ v_i, v_k \} </math> and <math> \{v_j, u_k \} </math> are directed edges in the edge set of <math> D </math>" (Dutton et al).
Objectives
During this project, we will examine and explore the following:
- Previous research regarding competition graphs and (1,2)-step competition graphs of food webs
- Competition graphs and (1,2)-step competition graphs of a specific food web
Additionally, we will further previous research by doing the following:
- Furthering research on (i,j)-step competition graphs by exploring new theory and computation
- 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
- Read (1,2)-step competition graph of a tournament and have questions ready for Wednesday, 6/7/2017
- Update Wiki at end of week or during week to reflect on what has been accomplished
|
| 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
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| Week 4 (6/19/17-6/23/17): Refine Research
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- 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 on what has been accomplished
|
| Week 5 (6/26/17-6/30/17): Mini Presentations
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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.
- 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 on what has been accomplished
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| Week 6 (7/3/17-7/7/17): Continue Individual research
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- 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 on 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 on what has been accomplished
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| Week 8 (7/17/17-7/21/17): Begin Finalizing Paper
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- Meeting with Dr. Factor: Monday, 7/17; start discussing how to finalize paper and poster
- Begin finalizing results; enter theorems, figures, explanations, etc. into LaTeX and create needed Figures
- Initialize poster draft and email to Dr. Factor by Thursday, 7/20 in time for mentor meeting
- Participate in working luncheon on Thursday, 7/20
- Update Wiki at end of week or during week to reflect on what has been accomplished
|
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| Week 9 (7/24/17-7/28/17): Posters and Future Research (Dr. Factor Out of Town)
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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
- Make any last minute changes and submit electronic version of poster to Dr. Brylow by 12:00 PM on Wednesday, 7/26
- Finalize any results
- Construct a list regarding future research for paper
- Begin turning LaTeX writing into formal paper
- Go to luncheon on Thursday, 7/30
- Update Wiki at end of week or during week to reflect on what has been accomplished
|
| Week 10 (7/31/17-8/4/17): Formal Talks, Posters, Papers, and Goodbyes
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- Draft formal talk, which is due to Dr. Factor bu 11:00 AM Monday, 7/31
- Draft paper, which is due to Dr. Factor by 11:00 AM Thursday, 8/3
- Attend poster session 1:00 PM - 3:00 PM on Tuesday, 8/1
- Formal presentations
- Wednesday, 8/5, 10:00-2:00, CU 401
- Thursday, 8/6, 10:00-12:00, CU 401
- Paper due electronically Friday, 8/4 by midnight, sent to Dr. Brylow
- Update Wiki at end of week or during week to reflect on what has been accomplished
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