Carter and Complexity

This is not my active blog currently

Carter Schonwald — Thu, 30 Jun 2011 17:22:05 +0000

fyi

Test Post

Carter Schonwald — Sun, 19 Jun 2011 03:36:36 +0000

this is a test post!

\[\int f(x) dx = \sin(x)\]

\(\binom{x}{y}= \xi\)

Forthcoming Interesting stuff

Carter Schonwald — Sun, 21 Mar 2010 06:03:01 +0000

So it looks like I’ll be starting the Dartmouth CS PhD program next year, likely doing stuff that falls under the umbrella of theoretical computer science and related math (also known as the subset of math which people are willing to hire people to do yet still also be able to understand hard core theory in either of CS or Math :p)

I’m also finally going to finish writing up and gluing together my various results relating to social collaboration and flirting sometime in the next several months, I swear!

Also, I’m currently putting together a toy library for having computer algebra functionality within haskell in a pretty light weight way, we’ll see how that turns out soon, perhaps I’ll have it working and get funding via google summer of code to develop it further, that would make for a pretty cool summer.

Senior Thesis Will be available soon.

Carter Schonwald — Sun, 13 Dec 2009 18:20:45 +0000

Just need to clean up some proofs and expositions a smidge. As an interesting aside, certain really general results in my thesis needed algorithmic/mathematical machinery as developed in the work of Saugata Basu and others. I’ve several ideas for interesting/cute questions to play with next, including coming up with computationally plausible models for flocking of birds and the signaling processes for various types of flirtation.

The Research Program for the Fall 2009

Carter Schonwald — Sun, 27 Sep 2009 05:54:20 +0000

This fall is me finishing up the icing on the cake which is my project analyzing the complexity / tractability of solving various classes of models regarding social collaboration, as well as hopefully some results which identify which bits form the essential core of their respective tractability/hardness characters. This should be publicly available come early December in the form of a Technical Report/ my Senior Thesis!

At the same time, I’m also really excited because I’m beginning a project related in spirit (ie global properties arising from local interactions) over the fall over a class of problems which have a wee bit more mathematical structure, and I do hope I’ll have partial results by late fall too.

Hopefully with those powers of self directed research combined, I’ll be able to do something fun next year!

My Research Present and Future, Summer and Fall 09

Carter Schonwald — Fri, 21 Aug 2009 07:49:46 +0000

So I am literally within a week of completing a draft of the past year’s research that is suitable for external consumption! Before discussing that/anything, those of you who only care about math skip past the bump.

Ok, now that there aren’t any misanthropes reading, I’d like to make a few observations of varying utility and/or obviousness.

Avoidable or unjustifiable stress is bad, don’t let it crop up
Stress is bad, don’t have it
Sleep, at regular intervals after no more than 18 hours of being awake, is always good
Exercise is pleasant, if you’re not stressed.
For the dopamine addicts and their diametric opposites the novelty avoiding curmudgeons, if when you exercise regularly (which you should), it should be enough that you feel slightly sore, but assuredly less than that which causes any pain. Pain is bad, don’t do it, injuries tend to happen otherwise.
Eat healthy, or failing that exercise more. At least for me, I’ve found that exercising regularly and with reasonable intensity sensitives me to food tastes in a way that seemingly correlates with health. Ie more exercise means I enjoy (and am thence incentivized to follow through on) the consumption of healthy food
Did I mention that sleep is good? If you’re not well rested, the only things you can do are things whose thoughts have already been thought in your mind. Every single element of content in this article was not thought of as I was writing it, but was thunk [sic] a while ago, and it is only now amidst a bout of insomnia that I find myself with the time and lack of things to occupy my self that are safe to do when tired that I’m actually writing this blog entry. I was also going to include pictures of my cute aged 2 niece in this entry along with some mini cute thing about how family can be a fun break from whatever, but look, I got distracted!
Insomnia sucks, avoid having stress that may trigger it from all the worry.
having fun things to look forward to at regular intervals is great for snaity
Only if people really want shall I make cute niece/fam pictures available

Now for some quick thoughts about doing research and related intellectual tasks, then on to a capsule summary of the summer research and what might be going on this fall

having a notebook around at all times to scribble and write in for ideas… this is key, if you don’t have that, theres no way to keep track of complicated stuff even one at a time.
part of the opportunity cost in starting research in any new domain is figuring out the right habits of problem selection and problem solving. (ok and if it matters for professional reasons, interest of the relevant research community)
for any given problem type, there is a `right’ way of decomposing problems into tractable bits, and a `right’ way of attacking problems with a standard tool kit. The best crafts metaphor is carving a block of wood or clay into puzzle pieces, and then repeatedly trying to guess the right faces to color various colors so that each external face has the same color, and each adjacent interior face is a different color from its adjacent faces on the same block, and the same color as any face it touches on other blocks, and you want to find the minimum the minimum size coloring, but you deliberately choose to not recall how they were initially combined and you’re essentially guess / only doing local matching.
its a dangerously fun hobby
making up notation and vocab is fun, but make sure its not already been defined!

Now as for my research:

This past summer I came up with a very simple tight proof that what I call generalized social collaboration is np complete for even very simple matching matching graphs and utilities. I also worked out a bunch of tractable cases. This will all be detailed in the soon to be available paper. However, in the general case social collaboration, I can only deduce that this type of problem is NP hard. More importantly, I think I can show that certain related problems are actually complete for certain nontrivial classes within the Polynomial Hierarchy, in particular and . This latter bit and related problems are one element of my research efforts for the fall, though I do intend to work on several ideas that are completely unrelated as a pleasant cognitive contrast.

And at their heart lay equation solving…

Carter Schonwald — Mon, 06 Jul 2009 05:40:50 +0000

Wewf, taking an intensive language class while also doing mathy research is tiring.

I’ve starting to read up on how to apply linear programming style techniques to combinatorial optimization (this book) by a fellow named schrijver does a lovely job of talking about when they can be used to exactly solve problems, and I’m also perusing this book by vijay vazirani about what are similar techniques but applied to approximating intractable problems.

It’s already given me some nifty ideas, but first FINISHING my other work!

Cool stuff forthcoming

Carter Schonwald — Wed, 03 Jun 2009 23:19:03 +0000

Do you know or care about any of the following?

graphical nash games
combinatorial auctions
price of blah (where blah = anarchy, stability, etc)
robust computational modelling of multiagent economic or sociological phenomena
equation solving with a nonlinear twist and combinatorial pinch
interesting variations on maximum weight matching

then you’ll want to read the draft of my research that I’ll have available in a few weeks. If you’re more into abstract algebra or pure math, you’ll have to wait another month or so for more suitable fair.

-Carter

Almost there…

Carter Schonwald — Sun, 17 May 2009 17:28:17 +0000

I’ve been spending the past half month finishing up the last of my coursework, by hell or high water, I’ll be done by the 19th, and thence to resume my research and fun!
-carter

Combinatorics is at the root of everything

Carter Schonwald — Sat, 09 May 2009 23:46:52 +0000

So earlier this semester I was sitting in my painfully computational galois theory class that was poorly exposited in lecture (and in the text ) and I asked my instructor whether for every lattice there’s a group who’s subgroup structure is isomorphic to that lattice.

Her response wasn’t terribly helpful, but I was recently able to find a paper that talks about that and related matters. this paper by Michael Aschbacher (of classification of finite groups fame) talks about that and related questions, and provides some references that seem to indicate that this is a pretty important open problem! I think its pretty cool, so once i’ve finished up the semester and have appropriately rested and written up my social optimization work, I think i’ll play with this family of problem!

mwhahahaha