# User:Kenny

## Contents

## Personal Information

My name is Kehinde Faronbi. I am a student at Alverno college. My Major is Mathematics and my minors are Computer Information Technology and Elective studies. My research title is "Calculating the Effect of Competition on Survivability on an Ecosystem Using a Weighted (1,2)-step Competition Graph Model" with Andria and Dr. Factor. I will be focusing my research on Lake Tanganyika Ecosystem.

## Goals and Milestones

**Week 1:**

- Complete the education module, “The Biology and Mathematics of Food Webs”, by
**Friday, 6/3/2011** - Enter the title, description and milestones/goals into the Wiki by
**Friday, 6/3/2011**, midnight - Update Wiki at end of week or during week to reflect what has been accomplished

**Week 2:**

- Determine the specific ecosystem from which the community food web will be obtained by
**Monday, 6/6** - Go over basic graph theory material in textbooks, do problems, and have questions ready for meeting with mentor by
**11:00 AM Tuesday, 6/7** - Read the selected material from the text by Cohen by
**Wednesday, 6/8** - Read paper #1 (
*Competition Graphs of Strongly Connected and Hamiltonian Digraphs*) and be prepared to present examples of some of the results by**10:30 AM Thursday, 6/9** - Participate in the luncheon at
**11:30 on 6/9** - Update Wiki at end of week or during week to reflect what has been accomplished

**Week 3:**

- Create food web (predator/prey model) and competition graph of the chosen ecosystem by
**Monday, 6/13**, and determine any “special” vertices that may represent vulnerable species or dominant species - Read paper #2 (either
*“A Characterization of Competition Graphs”*or “*The (1,2)-step Competition Graph of a Tournament*”) by**11:00 AM Tuesday, 6/14**and have examples worked out that explain some of the results in the paper - Attend the talk at
**1:00 PM on Tuesday, 6/14** - Read paper #3 (the opposite of the previous one) by
**10:30 AM Thursday, 6/16**, and have examples worked out that explain some of the results in the paper - Attend the luncheon at
**11:30 AM on Thursday, 6/16** - Create the (1,2)-step competition graph of the model made on Monday by
**Friday, 6/17** - Write up a draft synopsis of the background material studies to date—portions of this will be used as the introduction in the formal paper and in the mini-presentations—by
**Friday, 6/17**, and email a copy to the mentor - Update Wiki at end of week or during week to reflect what has been accomplished

**Week 4**:

- Read paper #4 (either “Weighted Competition Graphs” or “A Class of Acyclic Digraphs with Interval Competition Graphs”) by
**11:00 AM Tuesday, 6/21**, and have examples worked out that explain some of the results in the paper (Note that only a portion of the former paper will be needed for this project) - Read paper #5 (the opposite of the previous one) by
**10:30 AM Thursday, 6/23**, and have examples worked out that explain some of the results in the paper - Attend the luncheon at
**11:30 AM on Thursday, 6/23** - Begin to look at the (1,2)-step competition graph of the food web and see if there are any characteristics that may correspond to the vulnerability of a species; experiment with removing a vertex to see what effect it has on the food web and the graph
- Update Wiki at end of week or during week to reflect what has been accomplished

**Week 5:**• Have a draft 8 – 10 minute talk prepared on what has been learned so far by **11:00 AM Tuesday, 6/28**, and be prepared to practice it

- Begin looking at (1,2)-step competition graphs of an acyclic digraph family (perhaps unipathic digraphs) and try to find results toward characterization
- Present 8 – 10 informal talk to peers and mentors on
**Thursday, 6/30** - Update Wiki at end of week or during week to reflect what has been accomplished

**Week 6:**• Develop a draft definition for a weighted (1,2)-step competition graph by 11:00 AM Tuesday, 7/5

- Go to the talk on Tuesday, 7/5
- Continue working on the (1,2)-step competition graphs of the acyclic digraph family
- Determine possible measures to use for weights on the arcs of the food web or the edges of the (1,2)-step competition graph; use the definition of the weighted (1,2)-step competition graph to test measures and ascertain if any meaningful outcome can be obtained—discuss with mentor on Thursday, 7/7
- Go to the luncheon and possible talk on Thursday, 7/7
- Update Wiki at end of week or during week to reflect what has been accomplished

**Week 7:**• Begin to write up results for the (1,2)-step competition graphs of the acyclic digraph family—include conjectures if not proven; rough draft due Tuesday, 7/12

- Continue to experiment with weights on the (1,2)-step competition graphs and isolate at least one characteristic that this model may help identify or predict changes in given a change in the ecosystem; present current state of findings to mentor at 10:30 AM Thursday, 7/14
- Go to luncheon on Thursday, 7/14
- Update Wiki at end of week or during week to reflect what has been accomplished

**Week 8:** (Mentor out of town)

- Continue to work on conjectures for the (1,2)-step competition graphs of the acyclic digraph family—both by finding new ones and trying to prove (or disprove) existing ones
- Consider weighting the edges of the acyclic digraph family; apply the measure being developed for the food web to this; try to isolate some results
- Begin to write up results of the food web and weighted (1,2)-step competition graph; find or create figures that will be needed in the poster and/or presentation and/or paper
- Participate in the luncheon on Thursday, 7/21
- Update Wiki at end of week or during week to reflect what has been accomplished

**Week 9:**• Draft of the poster due to mentor by 5 PM Monday, 7/25

- Meet with mentor at 11:00 AM Tuesday, 7/26, to receive feedback on poster, give current state of research, and talk about finishing the paper and creating the final presentation
- Poster (in electronic form) to be submitted by noon on Wednesday, 7/27
- Very rough draft of final paper due to mentor at 10:30 on Thursday, 7/28—go over papers at that time and receive recommendations—there may still be blank or incomplete areas
- Go to luncheon on Thursday, 7/28
- Update Wiki at end of week or during week to reflect what has been accomplished

**Week 10:**• Draft of formal talk due 11:00 AM Monday, 8/1—meet with mentor and practice

- Poster session 1:00 – 3:00 PM on Tuesday, 8/2
- Formal presentations 11:00 – 1:30 Wednesday, 8/3, and Thursday, 8/4
- Paper due Friday, 8/5 by midnight
- Last update of Wiki due Friday, 8/5

**week 1**

**Tuesday, May 31**

- Orientation
- Campus tour
- paper works and Pre survey

**Wednesday, June 1**

- Meeting with Dr. Factor
- Studying “The Biology and Mathematics of Food Webs” with Andria

**Thursday, June 2**

- Complete “The Biology and Mathematics of Food Webs” with Andria
- Lunch with Dr. Factor, Zac and Andria while setting goals and milestone
- Introduction to Competion Graph by Dr Factor.
- Attended Talk on good research practice
- Library Orientation

**Friday, June 3**

- Studing
*Applied Combinatorics*by Alan Tucker and solving assigned problems with Andria. - Updating Wiki
- continued solving assigned Exercise in
*Applied Combinatorics*over the weekend

**week 2**

**Monday, June 6**

- Choose Ecosystem
- Complete Exercises in
*Applied Combinatorics*by Alan Tucker. - Read and solve assigned exercises in chapter 10.3
*Discrete Math and Graph Thoery*by Goodaire and Parmenter - Started Chapter 3 of
*Applied Combinatorics*by Fred Roberts.

**Tuesday, June 7**

- Finished
*Applied Combinatorics*by Fred Roberts - Meeting with Dr Factor.

**Wednesday, June 8**

- Decided to study in the Computer Lab reserved room (at Alverno College)
- studied assigned chapters in Cohen's biomath book.
- read
*Competition Graphs of Strongly Connected and Hamiltonian Digraphs*(intersting, but some terms and proof were not so clear)

**Thursday, June 9**

- Meeting with Dr Factor. She reviewed and explained some terminologies (clique, partion, optimize etc).
- Working lunch with other REU student.
- Meeting with Zac. He gave a detailed explanation of proposition 2.1 and other reviews.
- Finished reading Cohen's biomath, but still need to go over it again.

**Friday, June 10**

- Decided to stay in the Computer Lab Reserved room (Alverno College)
- Read
*A Characteristics of Competition Graph*by R.D Dutton and R.C Brigham - Read
*Littoral Fish Communities in Lake Tanganyika: Irreplaceable Diversity Supported by Intricate Interaction among species*by Hori et al. It contains food web of fish species (using their botanical names) and aggression among fishes. However, It doesn't include other classes of living organisms like amphibians, reptiles and the likes. - Searching other sources that include different classes of living organism.

**Week 3**

**Monday, June 13**

- Draw food web, competion graph and adjacency matrix
- Meeting with Zacc.

**Tuesday, June 14**

- Meeting with Dr Factor
- Attended
*Good Presentations, Good Technical writing, and the Difference Between Them*by Dr Brylow.

**Wednesday, June 15**

- Trip to Skyline Technology

**Thursday, June 16**

- Read
*The (1,2)-Step Competition Graph of a Tournament* - Meeting with Dr Factor
- Working Lunch with other REU student
- Attend Seminar on
*Responsible Conduct of Research*. - Read Food Web Pattern and their Consequence
- Reviewing drawn food web and competition graph.

**Friday, June 17**

- Reviewing all background materials
- and writing draft synopsis
- Finished and submit draft over the weekend.

**Week 4**

**Monday, June 20**

- Read
*Weighted Competition Graph* - met with Zacc

**Tuesday, June 21**

- Finished
*Weighted Competition graph* - Created (1,2) Step competition graph
- Met with Dr Factor

**Wednesday, June 22**

- Put weight on competition graph
- Created (1,2) step competition in food web (using created algorithm).
- Reread
*Weighted Competition Graph*

**Thursday, June 23**

- Recreated (1,2) step competition graph
- Met with Dr. Factor.
- Working lunch with other REU students
- Met with Zacc
- Created Weight(1,2) step competition graph.

**Friday, June 24**

- Tried out matlab
- Checked for charcterization of weighted and unweighted (1,2) step competition graph.

**Week 5**

**Monday, June 27**

- Started mini presentation preparation
- Discovered a mistake in competition graph constructed
- Reconstructed and fixed adjacency matrices

**Tuesday, June 28**

- prepared Mini presentation Power point.
- Met with Dr Factor.

**Wednesday, June 29**

- presentation preparation
- worked on % weighted competition graph, but resulted in digraph
- powerpoint revision

**Thursday, June 30**

- Mini presentation
- Got familiarized with matlab and puting adjacency matrix in matlab

**Friday, July 1**

- created competition, weighted competition,(1,2)-step competition and weight(1,2)-step competition graph for Cochin back water, India in order to work with a smaller ecosystem.
- Made some obervations about completeness (using determinant,degree and partition) and forwarded to Andria for checking.

**Week 6**

**Monday, July 4**

- Holiday

**Tuesday, July 5**

- Searching and forming Lemmas
- Met with Dr. Factor
- Met with Zac
- Continued working of Characterization

**Wednesday, July 6**

- Reviewed materials
- Read
*A class of acyclic digraph with interval competition graphs* - Checked matrices, but nothing is coming out.
- Wrote theorems and proofs on relationship between (1,2)-step completeness and weighted C(D).

**Thursday, July 7**

- Met with Dr Factor
- Working lunch and talk on MSCS application in fetal diagnostics in the health care industry by Dr. Craig Struble.
- Studied section 3
*Species Importance and vulnerability*of Biomath packet. - Came up with deductions on survivalbility using Pw C(D).

**Friday, July 8**

- Reviewed conclusion about Pw C(D).
- checked anotheer foodweb from biomath packet.

**Week 7**

**Monday, July 11**

- Redefined Pw C(D).
- Met with Zacc
- Applied refined definitions to foodweb
- Made draft.

**Tuesday, July 12**

- Made and edit draft
- Met with Dr Factor
- Made corrections in draft
- Extended definition of Pw C(D) to (1,2)-step competition.

**Wednesday, July 13**

- Applied definition of Pw C1,2(D) but there were challenges
- Redefined and applied defintion.
- Finally came up with one. I think this will work for all cases.

**Thurday, July 14**

- Had to redefine Pw C1,2(D) a couple more times
- working lunch with other REU student and discussion on posters
- Applied new definition to some of the food web.

**Friday, July 15**

- worked on paper
- Checked poster templates

**Week 8**

**Monday, July 18**

- Applied definition to Lake Tanganyika food web.
- worked on Paper
- Downloaded Latex and checking tutorials on how to use Latex
- Stared editing paper in LaTex

**Tuesday, July 19**

- Continued working on paper in Latex
- Worked on electronic poster.

**Wednesday, July 20**

- Prepared electronic poster
- Worked on research paper in Latex
- Found a contradiction to a theorem
- Reread
*Weighted Competition Graph*

**Thursday, July 21**

- Came up with a theorem and application of Percentage-weighted C(D)
- Created and insert sugraphs and other pictures into posters
- Working lunch with other REU students
- Met with Zac.

**Friday, July 22**

- Edited research paper and poster.
- Created pictures and insert into posters and paper.But, the research paper pictures are coming out too large.
- Checked for other ways of inserting pictures in Latex.
- Finally came up with using photoshop to resize picture before inserting in Latex. However, the jpg format are a little blurr.

**Week 9**

**Monday, July 25**

- Edit poster and paper
- Met with Zac
- Edit poster and email to mentor.

**Tuesday, July 26**

- Met with mentor
- Revise poster and resubmit.

**Wednesday, July 27**

- Poster Revision and submission of final draft.

**Thursday, July 28**

- Reviewed research paper

**Friday, July 29**

- Powerpoint preparation and created diagrams.

**Week 10**

**Monday, August 1**

- Revised and submit powerpoint presentation.

**Tuesday, August 2**

- Poster Presentation.

**Wednesday, August 3**

- Attended Formal presentation and prepared for mine

**Thursday, August 4**

- Gave formal research talk.
- Worked on my research paper.

**Friday, August 5**

- Editted and submited Research paper
- Survey and Research.