Last week I attended a conference at the Perimeter Institute for Theoretical Physics, titled “Hopf Algebras in Kitaev’s Quantum Double Models: Mathematical Connections from Gauge Theory to Topological Quantum Computing and Categorical Quantum Mechanics”. My flight from LAX (Los Angeles) to YYZ (Pearson-Toronto) was delayed due to a maintenance issue, leaving me sitting in the plane on the tarmac for about an hour and a half before takeoff, right close to midnight. My flight to Oxford for the QPL conference (Quantum Physics and Logic) two years ago had a similarly long delay… Hmmmn. Despite this conference being fairly small—40 people on the list of participants—there were several people present that I met at that QPL conference (Ross Duncan, Stefano Gogioso, and Pawel Sobocinski), and a couple more that I met while I was a grad student at Riverside (Tobias Fritz and Derek Wise). It turns out Ross and Stefano are sharing an apartment on the floor above my room. Continue reading
It has been nearly two years since my last post here, and several things of note have occurred or are about to occur. My Ph.D was conferred last December. My dissertation, Categories in Control: Applied PROPs, is available on the arXiv and via eScholarship. In the meantime I have been teaching as adjunct faculty at Victor Valley College in the Mathematics and Physics departments, keeping an eye on conferences of interest and postdoc positions.
Since I last wrote, there are two new countries’ stamps on my passport, and in a few days I’ll finally be adding one from a country that shares a land border with the U.S. Less cryptically, I will be spending next week in Canada, attending a conference on Hopf Algebras and other things in a title that is longer than this description at the Perimeter Institute. I would like to take this opportunity to thank Tobias Fritz for bringing the conference to my attention and Daniel Gottesman for providing the Perimeter Institute invitation. Saying the invitation covers practically all the expenses is putting it mildly.
I have been in courtship with a postdoc position since about the beginning of June with the Air Force Research Laboratory in Dayton, Ohio. There is a close connection there with a group at Penn led by Daniel Koditschek. I have been invited to give a talk and spend a couple of days at Penn in early September so we can get to know each other better, both personally and mathematically.
A little bit farther in the future, I am looking with interest at the upcoming AMS sectional meeting in November at UC Riverside and the upcoming Joint Math Meeting in January in San Diego. I still need to submit an abstract for the Applied Category Theory session at the sectional meeting. I plan to simply attend the JMM—it will be 14 years since the last time I went to a JMM, when it was last in Phoenix. It will be nice to have a fresh look from a more mathematically mature perspective.
About two months ago I gave a talk at the AMS Fall Western Sectional Meeting. While I could have safely rehashed my QPL talk, I decided to push forward instead. That may or may not have been the best idea – the results were certainly less polished. On the other hand, I was able to describe controllability and observability of a control system in terms of string diagrams. This is something that was painfully missing from my QPL talk’s results in July. Seeing the nontrivial constants in the string diagrams the quantum folk were using provided the key insight, and I wanted to capitalize on it as soon as possible.
The punchline of the AMS talk is that the duality between controllability and observability noticed by Kalman in the late 50s and early 60s can be expressed in terms of a PROP, which is a kind of symmetric monoidal category. In particular, this PROP includes a subPROP of finite-dimensional vector spaces and linear relations, which is basically what Paweł Sobociński deals with here under the name of Interacting Hopf monoids. Okay, so the actual punchline is that the duality Kalman noticed six and a half decades ago between controllability and observability? it’s simply time-reversed bizarro duality.
Bizarro is Sobociński’s term (seen in episode 7 of his blog), but I’m kind of partial to it.
Exams are some of the most time-consuming parts of being an instructor. They have to be written, proctored, and finally graded. Given a class of students, it seems reasonable to expect that writing a free-response exam would be a time commitment, proctoring would also be a time commitment, while grading would be a time commitment. Maybe grading speeds up as you get familiar with the particular set of mistakes your class makes, so I might believe something like instead of . In any case, asymptotically, grading takes a much greater share of time consumed than the other portions of the process combined.
With this in mind, I propose the following as a way of reducing the amount of necessary time spent in the grading process, while still giving a reasonable estimate of student understanding. At least for a game theory class.
Game theory final exam (proposed)
(1) (100 points) Your score on this exam will be based entirely on this one question. If is your answer and no one in this class answers with a greater number, will be your score. Otherwise, will be your score.
It is interesting to think about the possible strategies one may devise, which, for the student taking the exam, may depend on the class size and/or the student’s grade going into the final exam. While it is fun to ponder, I will leave that as food for thought for the time being save that discussion for the comments. Hopefully it will be clear that this isn’t entirely a serious proposal for an actual basis for grading a class, as forcing the entire class into a final exam that somewhat resembles the prisoner’s dilemma would be somewhat cruel. There are some variations that may or may not be as evil:
Variation 1 (Unlimited collaboration)
The students are told in advance what the exam problem will be. Thus, they are free to collaborate with as many of their classmates as they would like in order to come up with a strategy. However, they cannot see what answers are actually submitted by their classmates. This variation might be more evil.
Variation 2 (Limited collaboration)
The students are paired up and are allowed to discuss strategy only with their partner. They may be able to see what their partner submits, but they have no information about what anyone else does.
Variation 3 (Multitrack)
The students are given the option to take one of two exams. The first choice is the proposed exam above. The wording could be modified slightly to restrict from the entire class to the subset of the class that chooses that choice. The second choice is a standard final exam. For the student who thinks, “I just need 50% on the exam to get the grade I want.”, it seems plausible for that student to take the first choice and write for a guaranteed score and a personal 3 hour savings.
I thought about this game while grading some calc exams. It turned out there were quite a few people who incorrectly solved the problem I was grading, yet according to my rubric, their score was exactly the answer they wrote down. Purely a coincidence, but it sparked the thought that led me to this game. I showed this game to a few people yesterday, and the first two variations directly came from some of those discussions. One person I showed immediately declared, “I don’t want to play this game!”. Between the game and the variations, the multitrack variation seems the most reasonable to even consider actually giving. Concerning the title of this post – computer printouts (in some contexts) used to display ^H when the user hit the backspace key. Thus, it is meant to indicate the previous characters are being stricken out.
After finding out I could take advantage of public transportation to get to and from school, I decided to enroll in Alternative Transportation, a program offered by Transportation & Parking Services (TAPS) that provides incentives for people to substitute alternate means of transport over driving. I ran into a few glitches along the way, but ultimately I succeeded at obtaining a night/weekend parking permit free of charge. There are other incentives available, some of which depend on what mode of transportation you opt to use. For instance, people who walk or ride their bicycles to school can take advantage of locker and shower facilities; people who carpool or vanpool can get an emergency ride home when an emergency prevents them from going home on the carpool/vanpool.
Since I had just started riding the bus to school, I decided to apply for Alternative Transportation as a public transportation commuter. This choice ended up causing me a bit of grief. TAPS accepts this kind of application for people who have had at least five rides on the bus. However, TAPS only receives monthly reports from Riverside Transit Agency (RTA). I had already made twenty trips to/from school by bus when my application was denied — when TAPS got the September report in mid-October, only two of those twenty rides would have appeared.
Instead of waiting until mid-November to reapply, I asked about applying as a walker. By then I had already walked home from school twice, so I knew it was not an implausible option. That application was accepted in about four hours.
Another choice I made that caused some grief was the method of delivery of the award: I asked to pick it up instead of just having it mailed to me. In the application approval e-mail, TAPS told me they would send another e-mail when the permit was available for pick up. I waited weeks and never received that e-mail. Finally, on Monday (ereyesterday) I sent TAPS an e-mail asking when I could pick up my permit. The response was almost immediate. With half an hour to my next class, I walked to the TAPS building and picked up my night/weekend parking permit.
My expectation was a permit for the quarter, but my expectations were exceeded. The permit is a full year permit, valid from 1 July 2015 to 30 June 2016. Long story short, Alternative Transportation seems to be a decent program when it works. Getting it to work was a little bit of a headache for me, though the delays were at least as much from me waiting to deal with minor hassles as from TAPS’ side of the process.
I’ve been holding onto these jokes for a little while now — one a variation on a well-worn theme, the other something I don’t think I’ve quite seen before. Naturally, if you’ve seen something similar to the second one before, I would appreciate comments that can point to previous incarnations.
1. A variation on a theme
There are 10 types of people in the world:
• Those who think this is a binary joke.
• Those who think this is a ternary joke.
• Those who think this is a quaternary joke.
• Those who realize this is a base 10 joke.
• Those who just don’t get this joke.
2. Something else
I have discovered a truly marvelous punchline, which this joke is too small to contain.
… to get on the bus that takes me to U…CR.
It looks like my schedule this quarter will allow for me to take public transportation to and from school. That means I can avoid purchasing a parking permit. While it is nice to be making a step towards `going green’, my motivations for taking this step are admittedly more financial than environmental. As a student at UCR, I can ride on the RTA busses free, so I can save a bit more than 2% of my net income by not buying a parking permit (almost 3%, counting the little bit of gas I save).
It may not be much, but with the uncertainty of what happens after the end of this quarter, I’m happy to be able to cut corners financially, especially since it does not stress my schedule. I might even be able to take advantage of routes other than the home ⇒ school ⇒ home circuit at some point. の_の
On July 17 I gave a talk at Oxford in the Quantum Physics and Logic 2015 conference. It was recently released on the Oxford Quantum Group youtube channel. There were a bunch of other really cool talks that week. In my talk I refer to Pawel Sobocinski’s Graphical Linear Algebra tutorial on Monday and Tuesday, as well as Sean Tull’s talk on Categories of relations as models of quantum theory. There are benefits to speaking near the end of the conference.
I’m giving a talk tomorrow afternoon at the CSUSB Mathematics department. I will explain some of the stuff I’ve been working on, then shift gears to show how the general machinery can be applied to another mathematical landscape: knots. Sticking purely with knots is a bit restrictive, so I almost immediately skip ahead to the open version of knots, i.e. tangles. Luckily John Armstrong posted an article on arXiv in 2005, where he showed (among other very nice things) that tangle groups really are tangle invariants.
While I probably will not mention it tomorrow, another landscape that is being opened up (in the same sense that tangles open up knots) is Markov processes. Blake Pollard is doing exciting work on this front, and the same general machinery I’ll be talking about should have some interesting things to say about Markov processes as well.
Out on the road today I saw some things that made me think. While none of those things were Deadhead stickers on Cadillacs, one thing I did see was a license plate, 4GIV2##. I think it was 258 at the end, but that was not the part I was focused on. I thought, “How cool to have an ID plate in the 4GIV series. And how even more cool would it be to have the plate 4GIV490.” (Matt. 18:21-22). Actually, I thought 4GIV539 would be cool because I misremembered the quote as seventy seven times seven. I’m glad I looked up the reference before writing this. * whistles *
Another thing I saw was a truck for a company called Shipping Experts Consumer Handling Transportation (SECH Transportation). Unfortunately I do not read Hangul, so I can’t really tell what their website says, but you’ve gotta appreciate their enthusiasm. Not having the benefit of seeing their website while on the road, my mind naturally went to the obvious mathematical connection – hyperbolic secant, the reciprocal to a perhaps more familiar shape: hyperbolic cosine, a.k.a. catenary. The catenary is the shape a chain or cord will naturally fall into if its ends are held fixed in a constant gravitational field. It is also the shape (inverted) of a famous US landmark.