Log of REACH activities

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30 total hours worked from 1/1/03 through 1/16/03
Log for week ending 1/16/03
  • I spent so much time on the diagrams earlier this month, I really need to fill out my grad school applications. But I did find a counter-example for the proof of lemma 2 (as stated): left operand is a vertex with a single vedge connected to an anti-vertex. This is connected by a hedge- empty vertex - hedge chain to the right operand, which is an anti-vertex with a single anti-vedge connected to a vertex (the conjugate graph of the left operand). This doesn't ruin the whole proof - I think it just means we need to make the lemma more defined (for example, the family of "natural" graphs where all the vertices to either side of the adjunction are either all anti or all regular, not mixed. Although I did some experimenting, and noticed that the counterexample's components (counted on their own, without the hedge-empty vertex - hedge) have a total of 0 signed matchings. Examples of "unnatural" or mixed components whose total signed matchings are not 0 so far seem to work under the lemma as is.
  • Attended both meetings.
  • Total hours ~10.
    • Log for week ending 1/9/03
  • Have created 4 diagrams for the article. They don't bear much discussing, but boy are they ever time consuming! I spent a tremendous amount of time trying to get them right.
  • Something is bothering me about the proof for lemma 2. It seems like it might not always be true if you have mixed vertices and the "box product" elements are not the same.
  • Attended both meetings.
  • Total hours ~20.
    • 113 total hours worked from 9/1/02 through 12/31/02
    Log for week ending 12/19/02
  • Finals this week kept me pretty busy. Went over the article some more. Made some more progress with the editor.
  • Attended both meetings.
  • Total hours ~10.
    • Log for week ending 12/12/02
  • We've started going over the article and discussing some modifications to the presentation. I've started trying to find an editor to create the diagrams for the article with.
  • Finished implementing empty vertices for the java applet. Cleaned up the code. that pretty much wraps up what I think I can accomplish with the applet this semester. Next semester perhaps I can implement multiple tabs, etc.
  • Attended both meetings.
  • Total hours ~14.
    • Log for week ending 12/5/02
  • Refactored the java applet. Didn't improve performance much - big O tells us that performance is going to be abysmal anyway. But it does set the stage for having more than one graph on different tabs, with the ability to merge them and demonstrate adjuction with our new model. Still need to implement empty vertices.
  • Attended both meetings.
  • Total hours ~10.
    • 79 total hours worked from 9/1/02 through 11/30/02
    Log for week ending 11/28/02
  • Things are a little busy right now. I'm working more on trying to understand how Speyer's matrix model for graph concatenation works. I also spent some time on the java applet - it needs to be significantly refactored. More than I originally anticipated. It still won't be very difficult, but it will take a little time and I haven't had much of that lately. I hope to have the applet working as a demonstration of our combinatorial model (complete with the correct properties for empty edges and verticies) by the end of the year with the paper. I think it would be neat to let people understand the paper better by experimenting with the applet.
  • Attended both meetings.
  • Total hours ~4.
    • Log for week ending 11/21/02
  • I spent some time going through Speyer's article on Matrix representations of these graphs and how Kyle and John are trying to apply them to our not-necessarily perfect matchings. I also thought some more about "hex" graphs (an example of which is in Speyer's article) - John had come up with an object that allows adjunction of two hex graphs that maintains reciprocity. I wanted to play with this some more to see if I could find an obvious relationship or rule explaining the difference between the adjunction object for the regular graphs and the adjunction object for the hex graphs. I didn't get very far with this - but I think it might be worth looking into some more. Perhaps next semester.
  • Attended both meetings.
  • Total hours ~6.
    • Log for week ending 11/14/02
  • Modified Rui's applet so the user can create custom edges. it counts perfect, not-necessarily perfect, and signed matchings. But it does all these separately, and it's really slow for anything but really small graphs. I think this will be easy to fix and hope to do that this weekend.
  • Updated log.
  • Attended both meetings.
  • Total hours ~10.
    • Log for week ending 11/07/02
    Not much this week. GREs, a big CS project, and some personal
    stuff I had to take care of kept me from putting much time in.
  • Attended both meetings.
  • Total hours ~4.
    • 55 total hours worked through 10/31/02
    Log for week ending 10/31/02
  • Read Speyer's "recip5" article on matricies for counting perfect matches.
  • Worked on pictorial adjunction model for 3xn case.
  • 2 hour meeting Tues, 10/29.
  • 2 hour meeting Thurs, 10/31.
  • Total hours ~ 6.
    • Log for week ending 10/27/02
  • Made 5 copies of class 192 DVDs.
  • Came up with recursion for 2xn "cylinder" strip.
  • Found, installed, and started learning PARI/GP freeware math software.
  • Implemented 2xn recursion with PARI/GP.
  • 2 hour meeting Tues, 10/22.
  • 2 hour meeting Thurs, 10/24.
  • Total hours ~ 15.
    • Log for week ending 10/20/02
  • Background reading, articles for possible research.
  • 2 hour meeting Tues, 10/15.
  • 2 hour meeting Thurs, 10/17.
  • Total hours ~ 8.
    • Log for week ending 10/13/02
  • Homework for Tues, 10/8.
  • Background reading: GeneratingFunctionology, Wilf.
  • Reading: Assigned articles.
  • 2 hour meeting Tues, 10/8.
  • 2 hour meeting Thurs, 10/10.
  • Total hours ~ 8.
    • Log for week ending 10/06/02
  • Homework for Tues, 10/2.
  • Background reading: GeneratingFunctionology, Wilf.
  • Homework for Tues, 10/8.
  • 2 hour meeting Tues, 10/2
  • 2 hour meeting Thurs, 10/4
  • Total hours ~ 8.
    • Log for week ending 9/29/02
  • Homework for Thurs, 9/26.
  • Background reading: The Carus Mathematical Monographs, #14, Combinatorial Mathematics, by Herbert John Ryser.
  • Background reading: article on Aztec diamonds.
  • Creation of web site.
  • Made inquiry about getting Maple at UMB.
  • Homework for Tues, 10/1.
  • 2 hour meeting Tues, 9/24
  • 2 hour meeting Thurs, 9/26
  • Total hours ~ 10.

    • Last updated: November 1, 2002
    njanzalo@cs.umb.edu