Tuesday, April 29, 2008
"Still don't believe things even out? Try this simple test: Flip a coin, over and over again, calling out 'Heads!' or 'Tails!' after each flip. Half the time people will ask you to please stop."
10 miles to go...
Song: 10 Miles To Go On A 9 Mile Road
Artist: Jim White
Disc: No Such Place
Monday, April 28, 2008
The physics Arxiv:
"The hunt for superheavy elements has focused banging various heavy nuclei together and hoping they’ll stick. In this way, physicists have extended the periodic table by manufacturing elements 111, 112, 114, 116 and 118, albeit for vanishingly small instants. Although none of these elements is particularly long lived, they don’t have progressively shorter lives and this is taken as evidence that islands of nuclear stability exist out there and that someday we’ll find stable superheavy elements.
But if these superheavy nuclei are stable, why don’t we find them already on Earth? Turns out we do; they’ve been here all along. The news today is that a group led by Amnon Marinov at the Hebrew University of Jerusalem has found the first naturally occuring superheavy nuclei by sifting through a large pile of the heavy metal thorium."
Update: Chemistry Blog is skeptical.
Life on Mars
Tuesday, April 22, 2008
I see a different you
Song: I see a different you
Disc: Koop Islands
"Koop, the duo of Oscar Simonsson and Magnus Zingmark, seem to grasp what many other trip-hop production units never did -- that, no matter which instruments are used in your productions, digital or acoustic or electric, a sense of place is what should never be lost." - All Music Guide
Saturday, April 19, 2008
From a design perspective, what can we learn from nature? A longtime subject of interest, National Geographic recently published a new piece, Biomimetics.
Is a longevity pill just around the corner? Technology Review: Longevity Pill Tested in Humans.
National Geographic chronicles discoveries of strange and bizarre critters in Antarctica. (Men without Hats sing Antarctica.)
Rising commodity prices... Krugman: Deja vu all over again. Soros says a commodity bubble is still in the growth phase as noted at The Big Picture.
None of the standard platinum-iridium cylinders defining the kilogram weigh the same anymore, The International Kilogram Conundrum.
Since plants absorb energy in sunlight, I've often wondered why plants aren't black. What's the point of rejecting green? SciAm: The Color of Plants on Other Worlds.
You know when you hang out with a friend, have a few drinks, take the bus home, have a snack, take a nap and your wife wakes you up because you have a knife sticking out of your back? I hate when that happens! BBC News: Drunk Russian sleeps off knifing.
This Flash game is addicting: Bloxorz
Tuesday, April 15, 2008
Saturday, April 12, 2008
Friday, April 11, 2008
Wednesday, April 09, 2008
Same Old Drag
Tuesday, April 08, 2008
Pulitzer: Editorial Writing
"For distinguished editorial writing, the test of excellence being clearness of style, moral purpose, sound reasoning, and power to influence public opinion in what the writer conceives to be the right direction, in print or in print and online, Ten thousand dollars ($10,000).
Sunday, April 06, 2008
Song: Breathe (mp3)
Disc: Genetic World
Saturday, April 05, 2008
SVD for the Vertically Challenged
Today, I found an obvious bug in my applet and fixed it. In the process, I discovered a number of people querying the Net about the issue leading to the bug. The problem was that the JAMA code only calculated the SVD in cases where m >= n; i.e., it could only calculate the SVD on matrices with more rows (m) than columns (n).
This is easily fixed, if you consider the matrix transpose and corresponding transpose of its SVD.
AT = (U*S*VT)T
The basic rule of matrix algebra to consider: The transpose of a matrix product is equal to the reverse product of the individual matrix transposes (cf. The Matrix Cookbook).
In other words:
(U*S*VT)T = V*ST*UT
Bottom line: If you can only calculate the SVD of A where m >= n, all you need to do is calculate the SVD of AT and swap the resulting U and V matrices.
Wednesday, April 02, 2008
Advice for the Thirsty Triangle
A picture is worth a thousand words, but when it comes to comprehending algorithms, I think a decent visualization applet is worth even more--maybe ten thousand words--but I'll be happy if the following helps elucidate a concept for a single curious soul.
The applet du jour demonstrates the Nelder-Mead method, also called the downhill simplex method, the simplex method or the amoeba algorithm.
Suppose you're a triangle and you're thirsty. Knowing water runs downhill, you seek the lowest point you can, but what rules will you apply in finding this thirst-quenching minimum?
Let's refer to your two lowest vertices as your feet and your highest vertex as your head. Here are some of your possible power moves:
1. Stretch to twice your height and flip on your feet.
2. Flip on your feet.
3. Shrink to half your height.
4. Shrink to half your size.
Try each each move in order. If a move puts your head in a lower position, start over and keep doing it until you've shrunk yourself down to a point. Note: which vertex is your head may change after each round.
Try it here: Nelder-Mead applet
This simple algorithm is useful in finding minimums of functions when you have no information about derivatives (i.e., the slope of the surface at a given point). The value of the function at each point is all that's required. The triangle is easily extended to a simplex in higher dimensions (in 4D, it's a flipping tetrahedron, etc.), and the algorithm can be applied to find minimums in n-dimensional space.
In practice, I've used Nelder-Mead to simultaneously optimize the weighted sum of a collection of polynomial models. Because the algorithm finds local minimums, it's best to run a number of trials from random starting points--especially when the underlying space contains a lot of hills and valleys.
A competing method that is said to converge faster is Powell's method. I may see if I can come up with an applet for it in the future, but I had to do Nelder-Mead first, because I think it makes for a much more interesting animation.
Tuesday, April 01, 2008
The New Frontier
Artist: Donald Fagen
Song: New Frontier
Disc: The Nightfly
The Tax Break Fairy Strikes Again
"NEW YORK (CNNMoney.com) -- Lawmakers grilled executives from the world's five largest publicly traded oil companies Tuesday, criticizing them for taking tax subsidies and not investing in renewable resources amid record prices for oil and gasoline."
*How else could those oil companies have gotten all those tax breaks and subsidies?