Author Archives: Anand Sarwate

Concert Bleg : Bach Collegium San Diego presents all 6 Bach Motets

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Six Bach Motets BWV 225-230 & Gala Reception

Ruben Valenzuela, Music Director

Vocalists of the Bach Collegium San Diego
Daniel Zuluaga, Lute
Shanon Zusman, Violone
Michael Sponseller, organ

Saturday, 20 February
St James by-the-Sea Episcopal Church
743 Prospect Street, La Jolla CA 92037
(Gala Reception to immediately follow in Van Schaick Room)

Sunday, 21 February
Loyola Marymount University (Murphy Recital Hall)
1 LMU Drive, Los Angeles CA 90045

Concerts at 7pm

$35 Reserved Patron
$25 General Admission
$15 Student/Senior

For tickets or other inquiries: online or (619) 341.1726

Since its founding in 2003, the Six Bach Motets have been at the core of the BCSD’s repertoire, but never ALL SIX! The motets will be performed with vocal ensembles ranging from 4-16 voices.

The San Diego concert will be immediately followed by our annual Gala Benefit Reception in the Van Schaick Room of St. James by-the-Sea. Plan now to attend both!

For combination ticket packages are available for both concert and gala. Please refer to our website for details.

McGill’s policy on “harmful consequences”

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McGill University is contemplating ending “a requirement that any professor receiving research support from the military indicate whether the research could have ‘direct harmful consequences.'” The proponents of striking the measure say that all research should be scrutinized for harmful consequences, whereas the opponents say that it opens the gates for the US defense industry to shift the Canadian (Canadien?) research agenda.

I’m surprised they even had such a provision in the first place, given the existing injunctions against secret/classified research.

This reminds me a discussion last night at dinner, where my friend told us about a book by UCSD professor Chandra Mukerji called A Fragile Power: Scientists and the State, which talks a bit about science is dependent on state (and military funding) and how the state views scientists as a kind of “reserve force” of experts whose knowledge may become crucial later.

From Polya urns to the OK Corral

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A new postdoc here, Punyaslok Purkayastha, pointed out to me a Probability Surveys paper by Robin Pemantle on random processes with reinforcement, and I’ve been reading through it in spare moments (usually on the bus). I have had a problem knocking about my head that is related (Ram Rajagopal and I thought we could do in our spare time but we never managed to find enough time to work on it). All this stuff is pretty well-known already, but I thought it was a nice story.

A Polya urn process starts by taking an urn with R_0 = a red balls and B_0 = b black balls at time 0. For each time t \ge 1, draw a ball uniformly from the balls in the urn and then replace it together with another ball of the same color. Let X_n be the sequence of colors that you draw, where red is 0 and black is 1. So with probability R_n / (R_n + B_n) we have X_n = 0. The urn is updated according to R_{n+1} = R_n + 1(X_n = 0) and B_{n+1} = B_n + 1(X_n = 1).`

To figure out the asymptotic behavior of this process, just note that the sequence of colors is exchangeable. If x_1^n has k 1’s in it, then

\mathbb{P}(X_0^{n} = x_0^n) = \frac{ \prod_{i = 0}^{k-1} (a + i) \prod_{i=0}^{n-k-1} (b + i)}{ \prod_{i=0}^{n-1} (a + b + i) }

From this it is clear that the probability of seeing $x_1^n$ only depends on its type (empirical distribution, for non-information theorists). Since the sequence is exchangeable, de Finetti’s Theorem shows that the fraction of red balls W_n = R_n/(R_n + B_n) converges almost surely to a random variable W, and the limit of the formula above shows that the limit is a beta distribution with parameters (a,b):

f_W(w) = \frac{\Gamma(a+b)}{\Gamma(a) \Gamma(b)} w^{a-1} (1 - w)^{b-1}

A more general process is the Friedman urn process, in which you add \alpha balls of the same color you drew and \beta balls of the opposite color. If \alpha > \beta > 0 then Freedman (different spelling, different guy) showed that the proportion of red balls tends almost surely to 1/2. This happens because the evolution ends up looking like a symmetric two-state Markov chain, which has (1/2, 1/2) as its stationary distribution. Note here that the limiting fraction is almost surely constant, as opposed to there being a limiting distribution, as in the Polya process.

Let’s look at a special case where instead of adding a ball of the same color that you drew, you only add a ball of the opposite color (which is a Friedman process with parameters (0,1)). Freedman’s result doesn’t apply here, but Kingman has a nice paper (which I am reading now) relating this process to a third process: the OK Corral process.

In the OK Corral process, say we start with (c,d) good and bad cowboys. We choose one cowboy uniformly at random and then he kills a cowboy on the opposite side. This process continues until one side has all been shot. This process is precisely the time reversal of the special Friedman urn process above. If we let S_N denote the number of surviving cowboys after the process terminates when we start with (N,N), Kingman proves that

V_N = \frac{3S_N^4}{2N^3}

converges to a gamma distribution with parameter 1/2:

f_V(v) = v^{-1/2} e^{-v}/\Gamma(1/2)

The weird thing about this is that the scaling is N^{3/4} to get an asymptotic distribution.

Kingman and Volkov extend the analysis by embedding the urns into birth processes, which is another technique for balls-into-bins with feedback of urns with reinforcement. But that’s another story for another time (but maybe not another blog post, this one took a bit longer than I expected).

ITA Workshop Aftermath

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The 2010 ITA Workshop is over, and now that I have almost caught up on sleep, I can give a short report. I think this year was the largest workshop so far, with over 300 speakers.

One of the additions this year was a poster session to give those students who didn’t get a chance to speak at the “Graduation Day” talks on Wednesday an opportunity to present their research. The posters went up on Monday and many stayed up most of the week. I am usually dubious of poster sessions for more theoretical topics; from past experience I have had a hard time conveying anything useful in the poster and they are poorly attended. However, this poster session seemed to be a rousing success, and I hope they continue to do it in future years.

The theme this year was “networks,” broadly construed, and although I didn’t end up going to a lot of the “pure” networking sessions, the variety of topics was nice to see, from learning in networks to network models. Jon Kleinberg gave a great plenary lecture on cascading phenomena. I particularly enjoyed Mor Harchol-Balter’s tutorial on job scheduling in server farms. I learned to re-adjust my intuition for what good scheduling policies might be. The tutorials should be online sometime and I’ll post links when that happens.

The “Senseless Decompression” session organized by Rudi Urbanke and Ubli Mitra should also be online sometime. Apparently 20+ schools contributed short videos on the theme of \frac{1}{2} \log(1 + \mathrm{SNR}). Maybe we can make a YouTube channel for them.

Perhaps later I’ll touch on specific talks that I went to, but this time around I didn’t take too many notes, probably because I was a little exhausted from the organizing. I may post a more technical thing on the talk I gave about my recent work on privacy-preserving machine learning, but that will have to wait a bit in the queue. Mor’s tutorial suggests I should use Shortest Remaining Processing Time (SRPT) to make sure things don’t wait too long, and I have some low-hanging tasks that I can dispatch first.

Anti-miscegenation laws

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I came across this tidbit about anti-miscegenation laws in the US as applied to groups other than blacks in Randall Kennedy’s Interracial Intimacies. In these states, the groups not allowed to marry whites were:

  • Arizona : Mongolians, Malayans, Hindus, Indians
  • California : Mongolians, Malayans
  • Georgia : Japanese, Chinese, Malayans, Asiatic Indians
  • Mississippi : Mongolians
  • Montana : Chinese, Japanese
  • Nebraska : Chinese, Japanese
  • Nevada : Ethiopians, Malays, Mongolians
  • Wyomimg : Malayans, Mongolians

Tips for writing

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As a postdoc at a school with a gigantic biosciences program and surrounded by other biomedical research institutes (Scripps, Burnham, etc), a lot of the professional development workshops offered here are not specifically helpful to me. For example, I went to a workshop on writing grants, but it was almost entirely focused on NIH grants; the speaker said he had never applied to the NSF for a grant. Still, I did pick up general tips and strategies about the process of writing a grant. In the same vein, I read an article in The Scientist (registration required) about improving scientific writing which offered ideas applicable to technical writing in general. One that stuck out for me was:

Write daily for 15 to 30 minutes
During your daily writing sessions, don’t think about your final manuscript. Just write journal entries, says Tara Gray, director of the teaching academy that provides training and support to New Mexico State University professors. “People think there’s two phases of a research project—doing the research and writing it up,” she says. Rather than setting aside large chunks of time for each activity, combine them to improve your writing and your research. The first time Gray encouraged a group of faculty members at New Mexico State to adhere to this schedule for three months, they wrote about twice as much as their normal output.

I think I’ll try doing this. I often complain that I live an “interrupt-driven” lifestyle, but sometimes flailing on some very involved epsilonics at the last minute to get something to work results in errors, tension, and woe.

US drones’ video feed was wiretapped

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From Bobak I saw that US drones in Iraq have been hacked because “the remotely flown planes have an unprotected communications link” but “there was no evidence that they [insurgents] were able to jam electronic signals from the aircraft.”

This illustrates nicely the difference between eavesdropping and jamming. However, a nice by-product of anti-jamming codes using shared encryption keys (here they can be easily agreed upon before the drone takes off) is that sometimes you can get both eavesdropping and jamming protection at the same time.