Author Archives: Anand Sarwate

an upcoming concert

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The concert mentioned earlier now has a website with useful information on it. Hooray for useful information. In case you’re too lazy to click the link:

The Haydn Singers
dir. Paul Flight

a concert in honor of Mozart’s 250th birthday, featuring his Misericordias Domini (K222) and Missa Brevis in F (K192) as well as Haydn’s Partsongs and other music.

Fri., March 10, 8 p.m.
First Presbyterian Church of Palo Alto
1140 Cowper Street Palo Alto, CA

Sat., March 11, 8 p.m.
Church of St. Mary Magdalen in Berkeley
2005 Berryman Street (at Milvia), Berkeley

Tickets at the door: $15 general, $12 seniors, $10 students

6 degrees

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1403 Solano (in Albany). This is a new vaguely European small-plates restaurant near the Albany/Berkeley border. I went there with my research group after reading about it on Chowhound. The menu is still a little in flux and the wheels of the operation haven’t yet been oiled, but I’m pretty confident that they could work out the kinks by the end of February when they officially open. At the moment, however, the restaurant leaves a lot to be desired.

I ordered the Roman Manhattan, which was Maker’s and Cinzano and was a bit watery. This might have been due to the 10 minutes they spent making it — it had that left-in-the-shaker-to-melt taste to it. For a restaurant that was so empty, it was a little disappointing.

There were a lot of things missing from the menu — the venison was absent to lack of availability, and the Holland crepes were also out, which was surprising since as far as I could tell they are like Dutch quesadillas. The menu also had some pretty glaring typos; not something you expect in such a high-end place. It was especially bad if you knew French. It was hard to tell what was vegetarian and what was not. Lots of the things had ham or something hidden in them.

We ended up getting the pommes frites, saffron rice croquettes with pancetta, breaded olives stuffed with ricotta, ham, marjoram, “amalfi grilled vegetables,” crostini with various spreads, mussels cooked in white wine and garlic, and the vegetarian grill, which was an entree with lots of veggies and some vegetarian croquettes. The bread that came initially was clearly not that fresh, which was a real downer, especially since the Acme bakery is so close by. Of the dishes we ordered, the saffron rice was a clear winner — lightly fried and the saffron was clear but not overpowering. The wine from the mussels was overpowered by the intense brine flavor and the garlic was mostly absent. The vegetarian grill had some sauce on it that was a little sour but absolutely delicious. The olives kept losing their breading but the ricotta was surprisingly good as a stuffing. I didn’t really get to try the crostini so I can’t comment.

Dessert was cheese and fruit and a creme brulée. The latter didn’t have a crunchy enough top — certain movie characters would have been sorely disappointed. On a different day I would have chosen something more chocolate-oriented — there were some other tasty options on there that may have been more exciting.

All in all it seemed like the whole place was getting into the rhythm of things, and I think they have a lot going for them. I’ll definitely try it out again sometime.

Afterwards, we went bowling, and I managed to bowl a 151, which is shockingly good for me. I attribute the score to the white Russians.

more singing

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I just signed up to sing a concert with Paul Flight (venue TBA):

Mozart – Misericordias Domini
Haydn – Salve Regina
Haydn – Six Partsongs
Beethoven – Elegy
Gasparini – Adoramus Te

With the Babi Yar rehearsal coming up on Monday and more Mahler than I can shake a stick at, I’m certainly going to be kept busy!

contradiction injunction

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I came across the following in Royden’s Real Analysis:

All students are enjoined in the strongest possible terms to eschew proofs by contradiction!  There are two reasons for this prohibition : First, such proofs are very often fallacious, the contradiction on the final page arising from an erroneous deduction on an earlier page… Second, even when correct, such a proof gives little insight into the connection between A and B, whereas both the direct proof and the proof by contraposition construct a chain of argument connecting A with B.  One reason that mistakes are so much more likely in proofs by contradiction than in direct proofs or proofs by contraposition is that in a direct proof (assuming the hypothesis is not always false) all deductions from the hypothesis are true in those cases where the hypothesis holds, and similarly for proofs by contraposition (if the conclusion is not always true), the deductions from the negation of the conclusion are true in those cases where the conclusion is false.  Either way, one is dealing with true statements, and one’s intuition and knowledge about what is true help to keep one from making erroneous statements.  In proofs by contradiction, however, you are (assuming the theorem is true) in the unreal world where any statement can be derived, and so the falsity of a statement is no indication of an erroneous deduction.

This impassioned attack reminds me of Ionesco’s The Lesson or Stoppard’s Jumpers.  It’s tempting to psychoanalyze Royden and say that he must have an irrational fear of an unreal “make-believe” world or an overwhelming need to have certainty and truth.  But that’s just silly, isn’t it?

paper a day : exponential error bounds for AVCs

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Exponential Error Bounds for Random Codes in the Arbitrarily Varying Channel
Thomas Ericson
IEEE Transactions on Information Theory, 31(1) : 42–48

I really wish I had read this paper fully before writing my ISIT submission, because the vocabulary and terminology is less confusing here. The title is pretty self-explanatory, as long as you know information theory. An arbitrarily varying channel (AVC) is a probabilistic/mathematical model for a communication scenario in which there is a sender, receiver, and jammer. The jammer wants to minimize the communication rate between the sender and receiver. Assuming there exists some nonzero communication rate that is achievable over all possible strategies of the jammer, Ericson wants to find how the probability of making a decoding error decays as a function of the blocklength of the code. In a heuristic sense, if we make the packets of data larger and larger, how does the error probability scale?

AVCs have a lot of technical junk around them, but one important thing is the distinction between random and deterministic codes. A deterministic code C is a fixed mapping from messages {1, 2, 3, … N} into codewords {x1,x2, …, xN }. The jammer knows this mapping and so can tailor its strategy to be as bad as possible for this codebook. A random code is a random variable C taking values in the set of deterministic codes. If the values that C can take on is exp(n Rz), Ericson calls Rz the key rate of the code. That is, for a blocklength of n, we have nRz bits securely shared between the sender and receiver in order to choose a codebook without the jammer’s knowledge.

Ericson wants to find the largest attainable E such that the probability of decoding error is upper bounded by exp(-n (E – d)) for some small d. This is called the reliability function of the channel. Clearly it will depend on the code rate Rx = n-1 log N and the key rate Rz . Let F(Rx) is the reliability function when Rz is infinite. The first result is that E(Rx, Rz) >= min[ F(Rx), Rz].

In some cases the AVC capacity for deterministic codes is zero. This happens intuitively when the jammer can “pretend” to be the sender, so that the receiver can’t tell how to decode the message. In this case we say the channel is symmetrizable. If the channel is symmetrizable, then in fact E(Rx, Rz) = min[ F(Rx), Rz]. This basically says that the best decay in the error probability is limited by the key rate.

Interestingly enough, this is a similar result to the one that I proved in my ISIT paper, only in my case I did it for the Gaussian channel and I only have an upper bound on the error decay. Strict equality is a bit of a bear to prove.

Anyway, this paper is highly relevant to my current research and probably of interest to about 15 people in the world.

cambridge and coffee

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I spent the morning reading and working in the 1369 Coffeehouse in Central Square. It was like the good old days except that this time I had a laptop. Perhaps it’s just me being wistful and reminiscing, but I find the coffeehouses in Cambridge/Somerville significantly better than the ones in Berkeley. Maybe it’s because the weather makes you appreciate them more.

The music was perfect — Gotan Project, Tosca, and Django Reinhardt. I feel like I’m home.