User:Aheaton

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Alex Heaton

My name is Alex and I am working with Bridget St. Peter (User:Bstpeter07), Anna Mohr (User:07amohr), and Dr. Kim Factor on exploring different ways to find dominating sets and dominating set approximations. These dominating sets and approximations will be useful in many different applications, in particular, finding possible testing solutions and prevention strategies for containing outbreaks of foot and mouth disease in dairy cattle, sheep, and pigs. I am a math major.

May 18-22, 2009: (Week 1)

May 18, 2009:

May 19, 2009:

  • Research: Testing methods, testing schedules, and economic impacts
    • Created word documents with thoughts, links, and considerations to organize thoughts on each topic
  • Reading: "Economic Impacts of Foreign Animal Diseases," published by the USDA Economic Research Service
  • Time: 3.5 hours

May 20, 2009:

  • Reading: "Application of GIS in Animal Disease Control - Possibilities and Limits,"
    • Note to my group: Read especially, or actually read first page 11-12, starting at the heading "Animal Disease Information Systems"
    • Here is a link to the EpiMAN-FMD decision support system publication abstract referenced in the above paper. Read the abstract. "EpiMAN-FMD Abstract,"
  • Reading: "Models of Foot and Mouth Disease," by Matt J. Keeling, gives a good overview of FMD modeling efforts in the 2001 UK Outbreak, as well as past models and future possibilities for modifications and improvements
    • Note: Keeling, the author, also wrote the paper we used most extensively in our original project for Math 91.
  • Time: 4.5 hours

May 21, 2009:

May 22, 2009:

  • Meeting with Dr. Factor
  • Meeting with group discussing research options
  • Time: 2 hours

May 26-31, 2009: (Week 2)

May 26, 2009:

  • Read articles on Bridget's page
  • Formulated a general project outline
  • Met with group and finished project outline
  • Scheduled dairy farm tour for Friday morning
  • Split up farms to enter into Anna's program
  • Read from Applied Combinatorics textbook
  • Time 4.5 hours

May 27, 2009:

  • Read Applied Combinatorics Textbook
  • Finished my txt file for Anna's program
  • Time: 3 hours

May 28, 2009:

  • Met with group talked about project
  • Came up with possible ways to find the analog of dominating sets for weighted graphs
  • Came up with possible way to determine "goodness" of a dominating set
  • Time: 5 hours

May 29, 2009:

  • Tour of diary farm in Sheboygan
  • Time: 4 hours

May 30-31, 2009:

  • Read Applied Combinatorics
  • Worked on ideas for approximating minimum dominating sets
  • Time: 3 hours

June 1-7, 2009: (Week 3)

June 1, 2009:

June 2, 2009:

  • Met with group, worked on ideas for appoximating minimum dominating sets
  • Reading: Applied Combinatorics
  • Time: 5 hours

June 3, 2009:

  • Reading: Graphs as Mathematical Models, Chartrand 1977
  • Worked on ideas for approximating dominating sets
  • Typed up formal explanation of above ideas
  • Time: updated 7 hours

June 4, 2009:

  • Worked on dominating set ideas
  • Read books on graph theory
  • Time: 4.5 hours

June 5, 2009:

  • Dominating sets ideas
  • Time: 2 hours

June 6, 2009:

  • Typed up formal explanations of ideas so far on dominating sets
  • Time: 5 hours

June 7, 2009:

  • Time: 1 hour

June 8-14, 2009: (Week 4)

June 8, 2009:

  • Typed up explanations of ideas for dominating sets and "goodness" tests
  • Time: 3 hours so far

June 9, 2009:

  • Met with Dr. Factor
  • Typed up explanations
  • Time: 5 hours

June 10, 2009:

  • Typed up spanning tree method to find dom. set
  • Worked on other explanations and methods
  • Time: 4 hours

June 11, 2009:

  • Worked on way to see if a set is truly dominating
  • Met with group, talked about ideas and goals
  • Reading: "Graph Theory With Applications to Algorithms and Computer Science" 1985
  • TIme: 4 hours plus another 3 hours

June 12, 2009:

  • Time: 4 hours

June 13, 2009:

  • Worked on dominating set ideas. Came up with possibilities to assign a "value" to each vertex in the graph based on a bunch of different factors. Possibly giving options about how to weight each factor, yielding specified and individually chosen dominating set approximation results, tailored to what is important in different situations.
  • Time: 2.5 hours

June 14, 2009:

  • Worked with Anna on how our first program works. Anna fixed some issues with it.
  • Time: 2 hours

June 15-21, 2009: (Week 5)

June 15, 2009:

  • Typed up an introduction to our methods section. Useful for the presentation we will be giving soon.
  • Time: 3.5 hours

June 16, 2009:

  • Typed up Spanning Tree procedure for finding a dominating set.
  • Revised previous explanations and compiled them together.
  • Time: 6.5 hours updated from notebook

June 17, 2009:

  • Worked on new method of assigning value to each vertex in the graph
  • Revised Spanning Tree procedure to make more sense hopefully for Anna
  • Time: 6 hours updated from notebook

June 18, 2009:

  • Printed out final copies to give to Dr. Factor
  • Met with Dr. Factor and our group
  • Worked on finalizing new value weighted method of finding dominating set approximations
  • Time: 4 hours so far

June 19, 2009:

  • Worked at Cudahy on the "probability chopping graph into sections method" to find dominating set approximations
  • Also worked on trying to explain the "customized vertex value method" for finding a dom set approx. because it is really confusing to explain clearly, even though it is simple
  • Time: 6 hours updated from notebook

June 20, 2009:

  • Revised dominating set descriptions to hopefully make the more clear and well-written
  • Worked on variations for the "customized vertex value method" of finding a dom. set approx.
  • 3 hours

June 22-28, 2009: (Week 6)

June 22, 2009:

  • Time: 3.5 hours
  • Made diagrams for explanations, made example graph for explanation

June 23, 2009:

  • Time: SO FAR... 5 hours

June 24, 2009:

  • Came up with another method for finding dominating sets, hopefully this can replace one of my worse methods, like the spanning tree one
  • Worked on explanation for this method
  • Read articles about applications of minimum dominating sets
  • Time: 7 hours updated from rec center notebook

June 25, 2009:

  • Time: 1 hour

June 26, 2009:

  • Time: 1 hour so far

June 27-28, 2009:

  • Time: 4 hours

June 29-July 5, 2009: (Week 7)

June 29, 2009:

  • Time: 4 hours

June 30, 2009:

  • Time: 2 horus

July 1, 2009:

  • Worked with Anna on programming some methods, then worked on finding errors
  • Time: 6 hours

July 2, 2009:

  • Worked on comparing IEWVM inputs, created tables to compare values
  • Group Presentation for REU
  • Time: 4.5 hours

July 3, 2009:

  • Time: 2 hours, made up some graphs comparing results of IEWVM inputs, definitely needs more work

July 4-5, 2009:

July 6-12, 2009: (Week 8)

July 6, 2009:

  • Worked on making excel graphs comparing IEWVM inputs legible, readable, and useful
  • Talked to and worked with Anna about programming the next comparison test, which starts a random infection and then spreads that infection until a dominating set element is hit.
  • Time: 5 hours

July 7-14, 2009: In Calfornia visiting my aunts and uncles with my mom and sister, read Applied Combinatorics, Chapter 2, including sections on Permutations, Complexity of Computation, r-Permutations, Combinations, Probability, and Sampling with Replacement. Read Applied Combinatorics Chapter 13, on Minimum Spanning Trees, the Shortest Route Problem, which are optimization problems for graphs.

  • Time: 5.5 hours

July 13-19, 2009: (Week 9)

July 15, 2009:

  • Worked on Random Path Infection Test, worked on "Things to Consider When Comparing Graphs," figured out how to use the new program that does a bunch of calculations for us when comparing inputs on different methods
  • Time: 4 hours

July 16, 2009:

  • Working on how to generate graphs with certain properties, so that we can run the tests on multiple graphs, and hopefully find out how certain properties of the graphs affect the results of our methods for finding dominating sets
  • Working on programming the Random Path Infection Test with Anna
  • Reading old paper
  • Time: 7 hours

July 17, 2009:

  • Worked on programming with Anna for doing bulk run results for our now totalling two tests of dom sets
  • Modified the excel file outputs so that they make more sense for the bulk run programs
  • Worked on paper organization and content
  • Learned some programming
  • Time: 6 hours

July 18-19, 2009:

  • Worked on introduction to paper
  • Listed questions for Anna to make sure that the programs are running correctly
  • Thought about properties of graphs and how to characterize them so that we can compare results
  • Time: 6 hours

July 20-26, 2009: (Week 10)

July 20, 2009:

  • Started comparing OWN with Random Path Infection Test, made excel files, compared results to Min Dist Test results
  • Anna came to work on programming with me
  • Worked on RandomPathInfectionTest program troubleshooting... forever
  • Fixed it, then worked on other method, called Probabilities, and got that to work
  • Started programming the PathLengthTwo method
  • Time: 6 hours

July 21, 2009:

  • Worked on figuring out how to characterize graphs by properties, sort of like metric spaces
  • Time: 4 hours

July 22, 2009:

  • Took OWN Method for finding dom sets, and compared the "Best" results based on 1) the Min Dist Test, 2) the average path length from the Random Path Infection Test, and 3) the # of infected farms from the Random Path Infection Test
  • Compiled results and trends in an excel file and graphed it, showed that Min Dist Test results actually DISAGREED with the Random Path Infection Test as far as the best inputs to put into OWN, to get the "closest" dominating set
  • Time: 6.5 hours

July 23, 2009:

  • Working on extracting trends and insights from the bulk run data
  • Graphing things in excel
  • Created excel sheet to compare PLT vs. OWN in terms of the minimum distance test => negligible difference
  • Created excel file to compare PLT vs. OWN in terms of Random Path Infection Test, not done yet, have all the data though
  • Time: 7 hours

July 24, 2009:

  • Finishing excel file to compare PLT vs. OWN by Rand. Path Inf. Test
  • Found diminishing returns of adding elements to OWN, compared OWN inputs and graphed the trends
  • Worked with Anna to fix PLT program, meaning PLT vs. OWN will have to battle again, because PLT apparently cheated/was injured
  • Time: 7 hours

July 25-26, 2009:

  • Worked on writing up OWN evaluation for paper, in final form. Incorporated graphs from excel file on OWN-MDT.
  • Time: 5 hours

July 27-August 2, 2009: (Week 11)

July 27, 2009:

  • Continued working on writing up OWN for paper.
  • Finished OWN write-up, except for very last part
  • Time: 7.5 hours

July 28, 2009:

  • Working on editing OWN write-up, grammar, sentence structure, clarity.
  • Working on the last part of OWN write-up
  • Working on writeup of MDT write-up
  • Working on computing error of MDT for differing numbers of trials, incorporating this into MDT write-up
  • Time: 7 hours

July 29, 2009:

  • Error excel files for MDT
  • Found what I thought was problem in MDT, but after a long time of trying to figure it out, Anna showed me that as long as you pick that first vertex near the middle of the graph, every other vertex is at least 0.76 close to it, so that's the minimum you will ever get as a result of MDT
  • Finished PLT vs. OWN, the epic battle
  • Started on PLT vs. OWN write-up
  • Time: 7 hours

July 30, 2009:

  • Continued working on PLT vs. OWN write-up
  • Also will edit the "we's" out of OWN write-up, because apparently it's not cool
  • Time: 7 hours

August 2, 2009:

  • Working on write-ups
  • Finished RPIT explanation write-up, started the evaluation portion as well
  • Time: 3 hours

August 3-9, 2009: (Week 12)

August 3, 2009:

  • Finished MDT and RPIT write-ups completely, started working on OWN explanation write-up
  • Finished OWN write-up completely, including editing it for passive tense
  • Finished PLT explanation
  • Time: 8 hours

August 4, 2009:

  • Finished PLT evaluation
  • Finished PROBS explanation
  • Discussed PROBS problems with Anna for programming
  • Discussed need for a PROBS bulk run
  • Time: 7 hours

August 5, 2009:

  • Trying to finish PROBS and CVVM, explanations, evaluations, and comparisons to OWN if possible
  • Found problem in PROBS programming, told anna about it, she's gonna work on it
  • Also suggested we implement a "cut-off" value before PROBS, like in PLT, but slightly different in that we either change the edge to zero or leave it how it is, not change it to 1.
  • Time: 5 hours

August 6, 2009:

  • MSCS decided to update all its computers, so I couldn't access my Z drive, making it very difficult to work on writing up the paper
  • Wrote explanations and evaluations of CVVM and PROBS
  • Planned out what thigns to run for CVVM and PROBS and what graphs to make, made predictions
  • Did some things on Anna's computer too
  • Time: 7 hours

August 7, 2009:

  • Finished writing the CVVM and PROBS things
  • Finsihed evaluating them
  • Ran like 10 computers at once to get some PROBS graphs and use them to evaluate PROBS
  • Just need to type that PROBS up
  • Typed up a "final thoughts" section
  • Finished typing up all things PROBS and CVVM, sent everything to Anna, who compiled it and sent it to Dr. Factor
  • Time: 7 hours
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