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Latest revision as of 06:25, 12 June 2015
Contents
Personal Information
My name is Andria Barraza. I am a senior at the University of the Pacific in Stockton, California majoring in Pure Math. I will be graduating next year and plan to continue on to get my masters degree in math.
Week 1(May 31stJune 3)
Tuesday May 31
 Met my mentor finally!
 Welcome/ Introductions to the program
 Tour of the campus
 Lunch with the mentors and grad students
 Paperwork
 How to use the wiki
Wednesday June 1
 Met with Dr. Factor to set up description and title for program
 Worked on Biomath Module packet completed packet up to pg. 35
Read about food webs Mathematical modeling Basic Graph Theory Definition Trophic levels/Energy Levels/Energy Transfer (Interesting!!) Species importance and vulnerability Redundancy and resiliency
Thursday June 2
 Worked on Module packet with Kenny in the morning
Weighted arcs in food webs Trophic status
 Had lunch with Dr. Factor, Kenny and Zac to discuss our goals and milestones for our research project
 Dr. Factor gave us a quick intro to graph theory and some basic definitions
 Went to talk "Good Research Practices, and the Art of Keeping Logs"
 Attended library orientation
Friday June 3
 Met with Kenny early in the morning to work on Graph Theory assignment
 Began working through the problem set in "Applied Combinatorics" by Alan Tucker
Graph models  Basic definitions needed to begin working through the problem set
 Kenny and I worked through most of the set from this book. So far there have been few application to ecology but I am beginning to see how we will model the food webs using directed graphs
 Posted project name, milestones, and weekly log on the wiki today
Week 2 (June 6  June 10)
Monday June 6
 Worked through problems from various graph theory books
 Working on familiarizing myslef with definitions so that I can read through the graph theory papers I will begin looking through next week
Tuesday June 7
 Worked on the section about Isomorphisms. I underestimated how long it would take me to get through this section!
 Picked out the ecostytem I will be working with over the summer. The Sahara
 Met with Dr. Factor to discuss the graph theory Kenny and I have been studying so far
 Read through some of the Cohen material Dr. Factor assigned
Wednesday June 8
 Finished the last of the Isomorphism problems from one of the text books. I finally found a more efficient method I can use to identify isomorphic graphs.
 Continued reading the Cohen material
 Began reading the first paper on competition graphs
Thursday June 9
 Met with Dr. Factor to discuss the paper (Competition Graphs of Strongly Connected and Hamiltonian Digraphs)
 Participated in the luncheon
 Continued reading through the Cohen material paying special attention to the Cascade Model he uses to work with food webs
 Met with Zac and worked on going through the proofs from the paper we read this week
Friday June 10
 Began reading the second paper Dr. Factor assigned ( A Characterization of Competition Graphs)
 Finished reading through the Cohen material in the book
 I have been looking for information on the species found in the Sahara so that I can put together the food web and have not been able to find anything yet
Week 3 (June 13June 18)
Monday June 13
 Read through " A Characterization of Competition Graphs" and then met with Zac and Kenny to discuss and work through some of the theorems in the paper together
 Read various articles concerning food webs
 Picked the ecoregion I will be working on
 Found list of species in this region and began to do research to see what predator/prey relations there are among the species from the list
Tuesday June 14
 Finished going through the list of mammals.I have been listing what each animal preys on. I worked through 29 bird species out of 51 but then decided to leave them as one since group.
 Met with Dr. Factor to discuss how our research is going so far.
 Attended talk by Dr. Brylow. Learned about what makes a good research paper and what makes a good research talk.
 Finished going through the list of species. I wrote down what each one preys on.
Wednesday June 15
 Read through various encyclopedia entries to find out more about trophic levels, ecological communities, and food web theory.
 Put together entire food web. I grouped various animals together and my food web now includes 25 species.
 Updated wiki
Thursday June 15
 Finished compiling food web. When I looked over it again I realized I had missed some arcs.
 Met with Dr. Factor to discuss a paper we read through this week and to show her the food web.
 Attended weekly luncheon
 Attended NSF talk about ethical research
Friday June 16
 Put together competition graph.
 Wrote a draft sysnopsis what the backgroud material I have studied to date.
 Began reading through "Weighted Competition Graphs"
Week 4 (June 20June 24)
Monday June 20
 Met with Zac to discuss the paper about weighted competition graphs.
 I spent a great deal of time today revising my food web.I am going to begin working on the (1,2)step competion graph so I want to make sure that I make all the necessary changes before I go on. I took out a few species after checking various sources and finding that they might not be a part of the ecoregion I am working with. I also divided the birds into two groups. Aves and birds, the Aves are omnivores.
Tuesday June 21
 Used sketchpad to draw my food web and competition graph.
 Met with Dr. Factor to show her what I have done in the past week. My synopsis was a little bit too short. Remember to go back and rewrite it!
 I began working on the (1,2)Step competition graph. I decided to look at what specices will not (1,2) compete since it seems that most species WILL (1,2) compete.
Wednesday June 22
 I drew out the (1,2) Step competition graph using sketch pad and I have to find a better way of grouping the species together. There are way too many edges, so many that the graph is basically useless.
 I decided to switch over to working with matrices. I made the adjacency matrix for the food web and put together the competition matrix. I began working on the (1,2)Step competition matrix. Basically I printed out the one used to represent the competition matrix but deleted all of the zeroes since they can potentially be ones in the (1,2) step graph.
Thursday June 23
 I finished working on the matrix the represents the (1,2) Step competition graph. Finally!! (on paper)
 Met with Dr. Factor to discuss what direction we would like to go with the research.
 Attended the luncheon.
Friday June 24
 Completed the matrix using excell so that. I went back and corrected a few errors in the other matrices.
 I spent the day compiling (1,2)Step competition graphs based on the foodwebs found in the back of the Cohen book "Community Food Webs:Data and Theory." I would like to find why there are edges missing since most of the graphs are complete. I am only using the commmunity webs that have 1013 species because anything bigger becomes hard to work with and extremely time consuming. It would be helpful if we could write a matlab program that will produce the matrix that corresponds to the competition graph and the (1,2)Step competiion graph.
Week 5 (June 27July 1)
Monday June 27
 Put together (1,2)Step competition graphs for a few more community webs from Cohen's book
 I came up with a few more propositions about the completeness of (1,2)Step competition graphs that I will present to Dr. Factor tomorrow
 Brainstormed ideas for which directon I would like my research to go in
Tuesday June 28
 Made outline for what my talk is going to be about this Thursday
 Met with Dr. Factor to discuss my work
 Continued preparing for my presentation.... took a long time to find some source of information that would help motivate the research area that we are working in. I finally found it in the Cohen book!!
Wednesday June 29
 Prepared powerpoint slides for presentation. Making the diagrams in sketchpad is very time consuming but Word is not much better.
 Sent it to Dr. Factor and had to make a lot of revisions, mostly I had to add background information and more diagrams.
Thursday June 30
 Practiced presentation a few times to work on the timing.
 Made final changes to slides
 Presentations Today!!!!
Friday July 1
 Continued trying to find what there must be in the digraph in order to have a (1,2)Step Competion graph that is NOT complete.... I'm thinking this may not be an idea worth pursuing because of the limited amount of time we have this summer.
 Some of the different aspects of the webs that I am looking at are the insets/ outsets, trophic levels, and chains in the food webs
Week 6 (July 4 July 8)
Tuesday July 5
 Met with Dr. Factor and discussed presentation I need to work on motivating problem but we decided that I will mention in the next presentation that we are working on developing a tool that can be applied we are not focused on applying it ourselves!!!
 Continued working on Characterizing digraphs of complete (1,2)Step Competition graphs.... Dr. Factor gave me some new idease to pursue.
Wednesday July 6
 COntinued my pursuit of characterizing the digraph
 Also put together a handout of the conjectures I have made so far, including diagrams and I also worked on proofs for these statements
Thursday July 7
 Finished handout this morning before meeting with Dr. Factor
 Met with Dr. Factor today to discuss progress
 Discussed new direction for my work. I will be looking at the connectedness of (1,2)Step Competition graphs and characterizing the corresponding digraphs. This will probably take up the remaining weeks of research that are left.
Friday July 8
 In attempting to characterize the digraphs I have found that there are too many variables to work with! There is the number of species in the foodweb, the number of basal species, top predators and the number of trophic levels.
 Spent most of the day looking at different combination of these variables and trying to find a systematic way of working with all of the different food webs we can consider.
 It seems that because of all of the variables that there are in this problem it is going to be very difficult to come up with definite conclusions.
Week 7 ( July 11July 15)
Monday July 11
 Inputted data for about 30 food webs from the Cohen web. My plan is to find what the average number of basal species are for a web as well as top predators so that there can be some constraints set on these variables.
 Found the average percentage of basal species and top predators in a foodweb
 Continued working on characterizing the digraphs using the percentages from the data
 Met with Zac and installed LaTeX on my laptop
Tuesday July 12
 Met with Dr. Factor and discussed my work with her
 Wrote out some background info that will be useful for my research paper
 It looks like I may not have to look at so many individual webs and that I only have to consider the trophic levels of the foodwebs!!
Wednesday July 13
 Came up with a few conjectures this morning but then I found that I was able to disprove almost every single one... disappointing.
 I finally came up with a few conjectures concerning the connectednes of species that are found in the 2nd and 3rd trophic level but I have yet to prove them
Thursday July 14
 I have continued working on coming up with a counterexample for the conjectures I have but I have not been able to produce one. I will probably begin working on proving them soon.
 I am working on digraphs with 1 trophic level and only varying the number of species in the first trophic level. Looking to see if any work has been done concerning the connectedness of the competition graphs for foodwebs, but I haven't been able to find anything yet.
Friday July 15
 I have decided to begin to look for specific cases where there is going to be an edge in the (1,2)Step comepetition graph and when it is going to be missing... smaller steps.
 Finally came up with a conjecture concerning the connectedness of the first trophic level! I had made things too complicated before.
Week 8(July 18July 22)
Monday July 18
 Wrote out a few proofs for some of the conjectures I had
 Continued working on what I can say about the connectedness of the (1,2)Step Competition graph
Tuesday July 19
 Met with Zac to go over the proofs I have
 Disscussed what other topics I may be able to look at this week
Wednesday July 20
 I worked on proving a statement that had many cases to consider....after spending hours working on it I was able to find a case that disproved the statement!
 Rewrote some of the proofs I had done before
Thursday July 21
 Met with Zac to go over proofs
 I continued working on characerizing the digraph that corresponds to the nearly connected (1,2)step competition graph
Friday July 22
 My intuition led me astray. I had a few statements I thought might be true but I was able to disprove all of them!
 Worked on my poster for the presentations
Week 9(July25July 29)
Monday July 25
 Met with Dr. Factor to show her my poster
 Edited my poster
 Coninued working on some proofs
Tuesday July 26
 Continued working/editing my poster
 Began to work on my presentation
Wednesday July 27
 Edited my poster some more and submitted the final copy to Dr. Factor
 Worked on identifying relationships between connected digraph and the nearly connected (1,2)step competition graph
Thursday July 28
 Attended Luncheon
 Met with Dr. Factor to disucss the plans for our last week of work
 Wrote out a rough draft of the research paper on Word
Friday July 29
 Worked on presentation
Week 10(August 15)
Monday August 1
 Met with Dr. Factor to show her my presentation
 Edited my presentation
 Began working on the graphics for my research paper
Tuesday August 2
 Poster presentation
 Worked on research paper...in Word
Wednesday August 3
 Mini presentations
 Continued working on paper
Thursday August 4
 Mini presentations
 Continued working on paper
 Submitted research paper to Dr. Factor
Friday August 5
 Edited research paper
 Attended final meeting....lots of surveys!
 Submitted final research paper