Just a link to Vazirani's guest post on Noam Nisan's blog Algorithmic Game Theory, which seems to relate to my interest in convex sets with beautiful structure.  (Homogeneous self-dual cones, like the positive semidefinite matrices (semidefinite programming) or the positive orthant (linear programming);  just plain homogeneous cones; hyperbolicity cones...; just plain self-dual cones; weakly self-dual cones (ones isomorphic to their dual, but for which no inner product on the space can make the dual (defined according to said inner product) equal to the cone itself), etc...).  And a thought, perhaps misguided:  isn't a crucial ingredient of an efficient algorithm for a convex program usually something like an efficient algorithm for something like: determining membership in the convex set, or calculating a nice barrier function for the set?  And doesn't the ability to do that usually depend on the set (and/or the cone it generates) having a "nice" structure?  Perhaps the detailed properties of this structure bears some relation to the "combinatorial" structure of algorithms like the Ford-Fulkerson algorithm for max-flow?  Or perhaps particular problems have additional structure that isn't being captured in a typical convex formulation.  I'm no expert here (and have indeed forgotten what the Ford-Fulkerson algorithm is, though I think I once read about it in a book by Vazirani).  This post is primarily to remind myself to look at this more closely---and to link to Vazirani's, which seems worth of attention.

The horns and cheers are sounding in my house a block off the main street (King street) of uptown Waterloo.  I watched the end of the US-Canada hockey game in a pub, the Fox and Fiddle, on King street and it was a hard-fought thriller.  I'm happy for Canada, and they're sure as heck happy! The US team fought hard and has nothing to be ashamed of---but you could see the disappointment in their faces afterward, though they were absolutely sportsmanlike about it.

King street near the major pubs is lined with people hugging each other, high-fiving, waving canadian flags, and stopping passing motorists to high-five them as well.  After a Candian lead of 2-1 held for a long time, the US, which had been playing strongly and getting plenty of time with the puck, made a tieing goal with about 20 seconds left.  In a really hard-fought overtime, Canada sunk a sudden-death goal for the gold.  With that medal, they now have the most gold medals any country has won in a single winter olympics, said the commentators on CBC TV.

There was a lot of spirit in the pub, and I realized I was dressed in black, grey and blue from head to toe---not a spot of red except on my red, grey, and blue hat.  (Or should that be tuque?)  No issues, though---I am not a hugely vocal sports fan and don't normally watch hockey---though somehow the guy who was going 'round hugging everyone in the pub took a look and gave me a miss.  I walked up and down King street to check out the scene, and ended up having to high-five a few people and clap one person on the back, all with a "Congratulations!" which presumably marked me as not Canadian.    (A Canadian would yell "Canada, yeeeaaaaaaaah!!!"., as about five hundred are doing a block or two away right now.)

I did see one ambulance turn the corner onto King, lights flashing.  Keep it safe out there, guys and gals.  Don't drink and drive, don't get into fast traffic, etc...  (Fifteen minutes after the victory, after the medal ceremony, a group in the pub raised a chant of "Let's get wasted!".)

I had a pint of Molson's Canadian Lager during the overtime.  The drink of the Canadian women's hockey team, it was clear, smooth, and tasty, and really hit the spot.  No cigars today, though---although I suppose up here you can get real Cubans.  (Now there would be a provocative way to celebrate a US win!)

I'm glad it was a really hard-fought game, with everyone playing their best, and I don't think anybody should feel bad about their performance.   Great job all around, and a smashing finish for the Canadians to a great olympics!

It's getting louder out there.  Hopefully I can find my camera and post some pics of the celebration.

Edit:  didn't find my camera, but Youtubers provide more than enough flavor of the scene:

Interesting-looking bit of political economy research.  They propose that sectors employing lower-earning workers more intensively are receive relatively more trade protection, based on research in the US and China, and apparently attempt to differentiate between the contributions of envy and altruism to this effect.  Also, presumably, compare it to theories where amount of protection depends primarily on the resources available to an industry to help secure it.  NBER charges five bucks (OK, that beats Springer journals hands-down, but still) to download, so unless PI gets a subscription, looks like I'm not reading it.  What is with charging money for working papers!?  Can't we get these economists on the arXiv???

Proving that Proving is Hard.  Computer scientist Dick Lipton gives a beautiful introduction to work by Fischer and Rabin on the computational complexity of the formal first-order theory of the real numbers.  As Lipton explains, Alfred Tarski showed that this theory is complete---that every well-formed statement in the language of the theory can either be proved, or be disproved, from the axioms of the theory. Fischer and Rabin investigated how hard it can be to prove statements in the theory.   According to Lipton, they showed that it's (worst-case) exponentially hard:  there is a positive constant such that there are true sentences of the theory, of length shorter than , whose shortest proof has length at least .  (I'd guess what's meant is that they show this holds for all large enough , or at least for an infinite set of .)

Quantifier elimination---the method of deciding statements in the theory of the reals, used by Tarski in his decidability proof---has, at least theoretically, applications in optimization, which I hope to delve into in a future post.

A nice, probably not-too-easy (for me) and not-too-hard problem in group theory from my colleague Alberto Montina: is a subgroup of of maximal dimension (as a manifold) and are there any others.

Paul Halmos, How to Write Mathematics.

Amazing interview with Eugene Fama who doesn't believe the present crisis is due to the bursting of a bubble in housing:  "That’s where economics has always broken down. We don’t know what causes recessions. Now, I’m not a macroeconomist so I don’t feel bad about that. (Laughs again.) We’ve never known. Debates go on to this day about what caused the Great Depression. Economics is not very good at explaining swings in economic activity."  (Link found on Paul Krugman's blog. )

And an interesting bit about consumption and healthcare from something called Left Business Observer (link found on Brad Delong's blog).  The basic point is that of the six percentage point rise in what the national-income accounts categorize as consumption, as a share of GDP (from around 64 in the 80's to around 70% in 2007 and 2008), about four percentage points are in health care.

More wine from Perimeter Institute's bistro:  at today's wine and cheese, a Slowine Syrah from South Africa (didn't catch the vintage, maybe 2008?) was quite nice, smooth and tasty.  The 2007 Closson Chase South Clos Chardonnay was remarkable...obviously unfiltered, deeply colored for a chardonnay, and tasting unfiltered as well.  Their chardonnays are some of bistro manager Dan Lynch's favorite wines, and this was a chance to taste a little of something quite special.  The winery, and I believe also the vineyard for this wine, is in Prince Edward County, a large peninsula that's nearly an island, in a relatively sparsely populated part of the North shore of Lake Ontario, about two-thirds of the way from Toronto to Kingston.  The wine is barrel fermented (in 25% new oak, 75% old, in a typical  year, according to their website), and as a result noticeably oaky.  It's also not so high in acid or racy as one might expect from a high-end chardonnay (then again 2007 yielded exceptionally ripe grapes most places in Ontario, I think) but very "natural-tasting"--grapey, slightly sweet but not in a cloying way, with deep flavor underlying the oak.  I don't really feel like doing the tutti frutti thing with the flavors---it tasted mostly like ripe chardonnay grapes.  I guess someone might say it had hints of fruitcake.  The wine, that is, the wine.  This will be interesting to watch over the years as the flavors integrate with the oak in the bottle.  Really made the case for unfiltered chardonnay, for me---even the appearance in the glass is so much more interesting than just a clear liquid.  Slight question marks perhaps, on whether there is a tad too much oak, and whether it has enough acid to age gracefully, but I think the strong fruit and relaxed, natural style render these questions moot.  Bottom line: I want more, and will take steps to secure some if possible.

Incidentally, yesterday at PI's pub night  I had the Pillitteri standard (i.e. non-reserve) 2007 Merlot again, and liked it better this time.  It was served in one of the tall, big-bowled Riedel restaurant glasses, and seemed more elegant and velvety.  Perhaps a case of the glass influencing perception, or maybe it was the extra room in the glass for the aromas to develop  (and the schnozz to dip into them), or maybe it was just a different bottle or an extra month's age.  Still not earthshaking, but a solid, enjoyable drink.

What with pub night and wine 'n cheese, I realize I'm making PI sound like a boozefest, but pub night mostly means inexpensive food (and beer, to be sure), and is very family-oriented---a welcome chance to socialize with non-physicists.  And, hey, after my two glasses at wine and cheese, I went back to my office and LaTeX'd up five pages or so on tensor products of JC algebras.  So we're not slacking off here, or anything.  The bistro and the science are synergetic...

On the recommendation of the guys at Cherries and Clay, who've made it one of their New Years resolutions to stage a Battle Royale between Rieslings from BC's Tantalus and Ontario's Cave Springs plus a few others, I tried the Cave Springs 2008 Riesling, VQA Beamsville Bench, from the Niagara peninsula.  Very, very, tasty.  Quite crisp, tannic, flavorful, with plenty of appley fruit and minerality, especially a certain slightly spicy dirt kind of thing that I associate with Niagara, and also noticed in the Clos Jordanne Pinot Noirs and Chardonnays (both wineries are located in Jordan, and Beamsville Bench is in the area), along with some chalkiness.  11.5% alchohol.  This struck me as a rather Alsatian Riesling.  Some sweetness, but basically dry and quite snappy and high in acid compared to, say, my memory of California Rieslings (from the 1980s though).  Though not cheap for a North American Riesling, this gets the thumbs-up for multiple-bottle buys.  Very distinctive, loads of Niagara Peninsula escarpment terroir, and just plain tasty.  Should probably age fine for a few years, maybe longer, but it's definitely delicious now.  Make yourself a choucroute garni, if you're up for it.  (I had it with broiled salmon, which was fine, but not really an outstanding wine-food pairing.)  Thanks for the recommendation, Kurtis and Jake at C&C.   (They also link to some videos about Cave Springs, here.)

Via Brad Delong, an interesting article (that is, however, likely to be somewhat obscure to a general audience) to consider when reading, say, Paul Krugman on  the Chinese renminbi / US dollar exchange rate.  (Note that in this article, Krugman doesn't actually say the Chinese currency is undervalued; he just says they'd be doing us a favor by appreciating it relative to the dollar (which they would do by lending us less money, notably by buying fewer US treasury bills and such)).  Helmut Reisen thinks the exchange rate is not as undervalued as some claim based on purchasing power parity; low-income countries tend to have a lower exchange rate due to the fact that nontraded goods in such countries are cheap, relative to traded ones whose prices are equalised internationally through trade, and even more, relative to similar nontraded goods in high-income countries.  Based on a linear regression, he estimates the RMB is only 12% undervalued.  The scatter plot of deviation of exchange rate from purchasing power parity versus log GDP per capita doesn't look linear to me (it looks convex downward), and if the apparent nonlinearity reflects some some relevant functional form in the dependence of one on the other, it might suggest the Chinese currency is even less undervalued.  Of course, comparison with such a cross-country regression shouldn't necessarily be decisive if more detailed China-specific analysis is available.  But I wonder what such analysis suggests.

Unsubstantiated rumors from anonymous sources department: "Jester", who claims to be a particle physicist formerly working at CERN and now in New Jersey, blogs that there may be indirect evidence that CDMS' announcement this coming Friday may contain evidence for dark matter having been detected in a mine in Minnesota.  But the real news is the purported email from a senior editor at Nature, in which a rumor that Nature was about to publish a paper from CDMS on this is shot down as containing "as much truth as the average Fox News story".  Of course Fox intermingles truth, falsehood, and opinion, so maybe he's leaving them some wiggle room...those Nature editors can be wily!

Caveat link-follower:

Resonaances is a particle theory blog from New Jersey. Here you find latest news and comments on developments in particle physics, spiced up with my legendary sense of humour. As my name tells, my primary objective is to make laugh. If you get more out of this blog, that's entirely on your own responsibility.

I was pointed to it by a particle physicist at PI, though.