It feels funny to think that I've only been working at this job for a week and a half. I'm happy with the progress I've made. At the moment I'm thinking about the distinguishability of signals when transmitted through a granular material. I have three different areas of attack at the moment:
1) Make some simulations to see what happens in cases with and without spatial structure as the systems get bigger. Tom's previous work suggested that, although for a system made of a bunch of rigid rods, you can transmit more and more signals through as the system gets bigger, this doesn't work for a granular material. This isn't what he was hoping to find, and my suggestion was that removing spatial structure would help. So far, it doesn't seem to.
2) Have a look at how distinguishability is affected by four-element covariance in the matrix. What I'm saying is that if A and C are close, and B and C are close, and A and D are close, then if we can assume that B and D are close, it will be bad for distinguishability. A simple calculation suggests this is the case, though I want to make it more rigorous by chasing around expectation values.
3) Find a theorem regarding distinguishability if the matrix describing the transmission of signals is completely random. This gives a yardstick against which to measure specific systems. So far I've found (but not proven) that the relevant amplitudes are uniformly distributed between zero and a maximum. This is good distinguishability, though not as good as the ideal case where they are all at the maximum. I think I will be able to provide a good quantitative argument (the outline I have at the moment would not quite be a proof), but I will need to think carefully about measure when choosing perpendicular vectors.
I've also been reasonably social, especially with new friends from church. On Wednesday evening I went to the monthly Holy Hour. That wasn't a social occasion, but it was a good chance to pray and reflect on how to live the best life I can in a new city and new job.
On Thursday I went to Sarita's place for games night. It was nice both to meet some grad students (I always want to write "fellow" grad students - I've been a grad student for longer than I've had this blog), and to do so in a setting that was so familiar. Extremely familiar: we played Seven Wonders, one of my favourite games back at PPP Junction. It was a new game to the group, so I was able to explain how it works. I like it because although there are many things to do, it feels more like you have many opportunities to succeed, rather than many different ways to fail as in a game like Agricola (I have an earned reputation for banning Agricola at games nights I attend: we have enough games that there's no point playing any attendee's least favourite). And it showed: I think we did well on the whole and the final scores were very close (I came second, behind the only other person to have played the game before).
One thing I noticed was how funny it is to spend time with PhD students in the arts! I had almost forgotten that such creatures exist. The research methods are so different: one classicist was talking about how it can be difficult to find new material in works that have been studied for so many generations. Science never has that problem! I was also amused when a different classicist (apparently UC is famous for classics) was talking about dropping a class because it would have required her to go to campus four days a week! And at 9:30 in the morning!!
On Friday evening I went to a wine and cheese evening hosted by Lumen Christi, an group that organises seminars of interest to Catholic UC students and others. Once again, I met some friendly people. I think I might be at the top of the age group I consider my peer group (undergrads, grad students and postdocs: certainly I notice differences between the three groups but smaller than between grad students and faculty). I was talking to some people who turned out to be ten years younger than me, and discussing the really old 24-year-old they knew. OK, he is a first year undergrad, so he is old for his situation, but it made me feel ancient!
I worked hard for much of Saturday, getting the second MIT paper ready for a final round of reading by all the coauthors. I achieved almost all I set out to before a long chat with Mum and Dad in the afternoon. By the time I had finished talking with them, the NFL playoff game was in full swing (I ended happy, though I was worried for much of the game).
Usually I don't have many activities schedule for Sunday, but this was an exception. I talked to Enrico about the paper before Mass. After Mass an lunch, I went to a faith and science discussion group, talking about the ideas of Thomas Kuhn's famous book, The Structure of Scientific Revolutions. We hadn't all read the book (I had not): the main ideas are easily summarised. The group had a different feeling to the MIT Monday night discussion. I would say it was more speculative and philosophical: discussing ideas rather than trying to understand truths. And it stayed more on topic, though I was told that that was unusual.
I then went to help my officemate and new friend Arvind by listening to a practice talk. Today he had an interview here for a faculty position. It was a good talk and I think my comments might have helped make it better.
Yesterday evening I did some planning for Tom's visit in summer. I'm already getting excited on his behalf!
No comments:
Post a Comment