6/27/2008
primal scream
i'm just so fucking frustrated. i put in a shift mondays to fridays and all i fucking want is a nice stretch of time to practise guitar. as usual i catch some stupid illness on thursday, it gets worse on friday and on friday night i'm incapacitated.
"portmanteau of the day"
following up on my fetish for these words
backronym
a phrase constructed after the fact to fit a certain abbreviation, usually an urban legend, folk etymology
backronym
a phrase constructed after the fact to fit a certain abbreviation, usually an urban legend, folk etymology
have low eq? need a fix?
Check this out: social-emotional recognition software/robotics project
http://affect.media.mit.edu/projectpages/esp/
Gotta love MIT. Go science!
http://affect.media.mit.edu/projectpages/esp/
Gotta love MIT. Go science!
6/25/2008
bouncebackability <>
Iain Dowie, manager of Crystal Palace once famously talked of bouncebackability. His team showed great bouncebackability to snatch a draw against Arsenal.
I had a bad day, and I'm not one to be happy when things aren't going well. But I must be careful not to let unhappiness turn into cynicism at the way things are. when people look at me, maybe the word "zest for life" doesn't immediately spring to mind. but unhappiness is not pessimism.
but if only to recalibrate the tiny (moral?) compass which we have to navigate the seas of life (couldn't resist that), let's end with something that sounds like a jobism (i.e. something steve jobs would say and every goes waaaah). complain less, do more. the adjective bad doesn't change to good in a day, but bad is a state of affairs, and not an inherent property of anything.
jobism. job. job is the chapter of the bible you read when you want strength against adversity anyway. he got royally screwed over a number of times, complained maybe once but everything turned out fine in the end. fitting name, huh?
I had a bad day, and I'm not one to be happy when things aren't going well. But I must be careful not to let unhappiness turn into cynicism at the way things are. when people look at me, maybe the word "zest for life" doesn't immediately spring to mind. but unhappiness is not pessimism.
but if only to recalibrate the tiny (moral?) compass which we have to navigate the seas of life (couldn't resist that), let's end with something that sounds like a jobism (i.e. something steve jobs would say and every goes waaaah). complain less, do more. the adjective bad doesn't change to good in a day, but bad is a state of affairs, and not an inherent property of anything.
jobism. job. job is the chapter of the bible you read when you want strength against adversity anyway. he got royally screwed over a number of times, complained maybe once but everything turned out fine in the end. fitting name, huh?
6/13/2008
Euro 2008 season
Fabio Capello impresses me. He's not the best speaker of English (although some would say better than the vast majority of Englishmen), but it always amazes me how charismatic he is in a language which is essentially his second language, as well as how quickly he was able to pick it up. He puts himself about too, giving interviews although they aren't the most comfortable for him or the interviewer. I guess there are universal football jokes like jokes about 9-1 formations and playing only 4-4-2.
I've been messing about on betfair.com, although I've recently stopped because I know that the inevitable forces of randomness will bring me down to banker's ruin, so I had to withdraw while I was ahead. The ability to bet as well as lay was very useful, and I like the way they had good reserves of data. I managed to make a few trades which covered themselves regardless of the outcome, but later i learnt that this was not exactly arbitrage, but subject to market timing risk. Basically, on Asian Handicap, a bet on the outcome is like a binary option which goes into the money, while a lay is a put option. So if you were to bet for odds of £2.14, and 12 hours later the odds have fallen to £2.00, then you could lay at that price and lock in your profit before the event. Of course, there's always the risk that the odds will rise further from £2.14, leaving you with an unhedged bet (which is still worth it's expected value). So, you still need to identify fair value. Arbitrage is also difficult to find across markets (e.g. a bet on the no goals market and correct score 0-0 is almost always identical, as is arbitrage between -0.5 AH and straight win markets.) To find arbitrage which clears the 5% commission is even harder.
Interestingly, there has been a jump in expectatations that the Fed will raise interest rates next month.
This is the Fed Funds implied probability chart lipjin sent me 2 weeks ago? Notice how there wasn't even a probability for an increase priced in. Ridiculous. You would have got a very good price.
I've been messing about on betfair.com, although I've recently stopped because I know that the inevitable forces of randomness will bring me down to banker's ruin, so I had to withdraw while I was ahead. The ability to bet as well as lay was very useful, and I like the way they had good reserves of data. I managed to make a few trades which covered themselves regardless of the outcome, but later i learnt that this was not exactly arbitrage, but subject to market timing risk. Basically, on Asian Handicap, a bet on the outcome is like a binary option which goes into the money, while a lay is a put option. So if you were to bet for odds of £2.14, and 12 hours later the odds have fallen to £2.00, then you could lay at that price and lock in your profit before the event. Of course, there's always the risk that the odds will rise further from £2.14, leaving you with an unhedged bet (which is still worth it's expected value). So, you still need to identify fair value. Arbitrage is also difficult to find across markets (e.g. a bet on the no goals market and correct score 0-0 is almost always identical, as is arbitrage between -0.5 AH and straight win markets.) To find arbitrage which clears the 5% commission is even harder.
Interestingly, there has been a jump in expectatations that the Fed will raise interest rates next month.
This is the Fed Funds implied probability chart lipjin sent me 2 weeks ago? Notice how there wasn't even a probability for an increase priced in. Ridiculous. You would have got a very good price.
adverts are pretty. just look at vegas.
will work on slowly, and belatedly improving this blog with all the technology i've managed to miss out on in the intervening years. i figured a lazy layout served well enough for someone who just wished to have somewhere to store his quarterlife angst, but in a valiant attempt to transcend that, jesse is commencing the battle for ideas by making sure his ideas are surrounded by prettier pictures.
i will keep you posted on the interesting post (and during) exam activities which i have managed to fool around with soon!
will work on slowly, and belatedly improving this blog with all the technology i've managed to miss out on in the intervening years. i figured a lazy layout served well enough for someone who just wished to have somewhere to store his quarterlife angst, but in a valiant attempt to transcend that, jesse is commencing the battle for ideas by making sure his ideas are surrounded by prettier pictures.
i will keep you posted on the interesting post (and during) exam activities which i have managed to fool around with soon!
6/08/2008
federer and the french open
sadly i think frankly i've run out of stamina for this exam season. usually that means you've been giving it your full tilt, but with the last one on tomorrow i'm approaching it somewhat like roger federer did his last set against nadal. towards the end i felt that he knew that nothing he could throw at nadal could hurt him. and he sort of gave up and got spanked 6-0. to be fair i don't think if he ran any harder he could have made a difference. i think he acknowledged that tactically he didn't have the correct game or technique to begin with, and nadal wasn't making any errors. so mentally he just gave up and was probably thinking what he could work on this year to beat him next year.
which he says he'll do. i'll be waiting roger.
which he says he'll do. i'll be waiting roger.
6/07/2008
notice that in the previous post, c is in between 0 and 1, but not 0 or 1. Therefore you know that c, c^2, c^3, c^4... are distinct roots, and so the equation has n-1 roots in total. So you can confirm this by doing (2002b)
Suppose that f: R --> R is a differentiable function with k real roots a(1) < a(2) < ... a(n), and thus f(a(i)) = 0 for each i. Show that f'(x) has at least k-1 real roots.
Again, apply Rolle's theorem n-1 times on each of the intervals a(i), a(i+1), since f(a(i)) are all equal to 0. This implies that there is a c in each of the n-1 intervals such that f'(c) = 0. So this implies that it has at least n-1 real roots.
Now the next part stumps me.
Show that f'(x)sin(x) + f(x)cos(x) has infinitely many real roots, whenever f:R--->R is differentiable.
Ok I notice that this is the derivative of f(x)sin(x), by the product rule. So, surprise, surprise, use Rolle's theorem on each of the intervals ((n-1)*pi, n*pi). So we know that there is a c in between (n-1)*pi and n*pi such that f(c) which is the function in question is a root. So because sin(x) has an infinite number of real roots space at intervals of pi, the function has an infinite number of roots as well.
sin(x) has an infinite number of real roots, but i'm not sure if i'm supposed to take this as given or prove it. I am not sure if the fundamental theorem of algebra applies, but anyway, since it can be expanded as an infinite series with polynomial up to infinite power, does the FTA imply that sin(x) has an infinite number of roots? well, we know this from intuition anyway.
Infinite series, the Basel problem is at the bottom of the page. Also, apparently an open question is the sum of inverse cubes.
http://plus.maths.org/issue19/features/infseries/index.html
Suppose that f: R --> R is a differentiable function with k real roots a(1) < a(2) < ... a(n), and thus f(a(i)) = 0 for each i. Show that f'(x) has at least k-1 real roots.
Again, apply Rolle's theorem n-1 times on each of the intervals a(i), a(i+1), since f(a(i)) are all equal to 0. This implies that there is a c in each of the n-1 intervals such that f'(c) = 0. So this implies that it has at least n-1 real roots.
Now the next part stumps me.
Show that f'(x)sin(x) + f(x)cos(x) has infinitely many real roots, whenever f:R--->R is differentiable.
Ok I notice that this is the derivative of f(x)sin(x), by the product rule. So, surprise, surprise, use Rolle's theorem on each of the intervals ((n-1)*pi, n*pi). So we know that there is a c in between (n-1)*pi and n*pi such that f(c) which is the function in question is a root. So because sin(x) has an infinite number of real roots space at intervals of pi, the function has an infinite number of roots as well.
sin(x) has an infinite number of real roots, but i'm not sure if i'm supposed to take this as given or prove it. I am not sure if the fundamental theorem of algebra applies, but anyway, since it can be expanded as an infinite series with polynomial up to infinite power, does the FTA imply that sin(x) has an infinite number of roots? well, we know this from intuition anyway.
Infinite series, the Basel problem is at the bottom of the page. Also, apparently an open question is the sum of inverse cubes.
http://plus.maths.org/issue19/features/infseries/index.html
Real Analysis
2003 3a.) Nice question on use of Rolle's Theorem. No answers provided, this is my candidate. Ignoring the bombastic definition of the theorem, the second part of the question is secondary school math.
Rolle's Theorem. Let a function f R---> R be defined on an interval [a,b]. Then if f(a) = f(b), and f is continuous and differentiable on (a,b), there is a point c in (a,b) such that f'(c) = 0
Suppose that the numbers a(1), a(2).... a(n) satisfy
a(1) + a(2)/2 + a(3)/3 +..... a(n)/n = 0
Prove that there is a a c in (0,1) such that
a(1)c + a(2)c + a(3)c^2 +.... a(n)c^(n-1) = 0
The trick is to see that the first equation can be seen as f(1), where f is the infinite series expansion:
a(1)x + a(2)/2 x^2 + a(3)/3 x^3 +.... a(n)/n x^n
Putting x = 1 into this expansion yields exactly the first equation.
Putting x=0 into this expansion yields 0 = 0.
So we know that f(0) = f(1), and f is an infinite series expansion, hence it is continuous and differentiable as it is the sum of polynomials. So Rolle's Theorem applies, and you can differentiate f with respect to x and notice that all the divisors cancel out nicely, and that f'(c) = 0, where c is in (0,1)
f'(c) = a(1) + a(2)x + a(3) c^2 + .... a(n)c^n = 0
as required.
wah, how to think of this in the pressure of an exam? ok this seems irrelevant now, but it seems to be related to a question in 2002 which I haven't solved yet. But looking at the question it seems like the preliminary of Euler's sine product expansion, which he used to prove that the sum of the inverse squares 1 + 1/2 + 1/4 +1/9 + 1/16 + ... = pi^2/6, which is pretty stunning.
but then again, of course you would think pi is involved, because it's a curve so the area under the curve surely has something to do with a circle. so i will follow this up when i've done that.
Rolle's Theorem. Let a function f R---> R be defined on an interval [a,b]. Then if f(a) = f(b), and f is continuous and differentiable on (a,b), there is a point c in (a,b) such that f'(c) = 0
Suppose that the numbers a(1), a(2).... a(n) satisfy
a(1) + a(2)/2 + a(3)/3 +..... a(n)/n = 0
Prove that there is a a c in (0,1) such that
a(1)c + a(2)c + a(3)c^2 +.... a(n)c^(n-1) = 0
The trick is to see that the first equation can be seen as f(1), where f is the infinite series expansion:
a(1)x + a(2)/2 x^2 + a(3)/3 x^3 +.... a(n)/n x^n
Putting x = 1 into this expansion yields exactly the first equation.
Putting x=0 into this expansion yields 0 = 0.
So we know that f(0) = f(1), and f is an infinite series expansion, hence it is continuous and differentiable as it is the sum of polynomials. So Rolle's Theorem applies, and you can differentiate f with respect to x and notice that all the divisors cancel out nicely, and that f'(c) = 0, where c is in (0,1)
f'(c) = a(1) + a(2)x + a(3) c^2 + .... a(n)c^n = 0
as required.
wah, how to think of this in the pressure of an exam? ok this seems irrelevant now, but it seems to be related to a question in 2002 which I haven't solved yet. But looking at the question it seems like the preliminary of Euler's sine product expansion, which he used to prove that the sum of the inverse squares 1 + 1/2 + 1/4 +1/9 + 1/16 + ... = pi^2/6, which is pretty stunning.
but then again, of course you would think pi is involved, because it's a curve so the area under the curve surely has something to do with a circle. so i will follow this up when i've done that.
6/05/2008
No information arbitrage?
First, read this article, fascinating article about how seeing where people put their money where their mouth is is a more accurate forecaster than opinion polling.
http://ftalphaville.ft.com/blog/2008/05/14/13029/prediction-markets-101/
I was looking at US political futures today on 2 sites, 1 being based in the UK, betfair.com (and thus theoretically open to UK residents), and another based in the US, intrade.com. Barack Obama is roughly a 60-40 favourite to be the president. I was struck by how close the percentages quoted were on both sites. I had made a few assumptions:
That many people would go onto these sites just for a rough punt. So there should be no logical reason why the prices should equalize over the 2 markets.
Second, the markets are artificially segmented by residence, so even if they do accurately reflect expectations one should expect that british expectations should differ from american ones (due to different media coverage, biases, etc). So it was quite eye-opening to read this article.
So it occurs that some form of no-arbitrage does hold in predictions markets. ok, next step, figure out how the markets aggregate information. Is the market driven by insiders who make big bets when price diverge from what seems obvious to them (e.g, insiders working on the campaign who have a very good sense of how it's going through evaluating poll data and on-the ground knowledge). Then the small stakers are simply price takers, or look at already existing prices as markers. So in a sense, the stronger the knowledge is, the more it contributes to the price. This seems to fit with the liquidity patterns of the markets. The alternative explanation would be that people who place a parlay actively search for information by aggregating all the polls into a "super-average" poll. This is how theoretically stock markets work but I suspect that even the former hypothesis holds for stock markets.
anyway, it's amazing that these things exist nowadays. there's no reason they should. ever need to hedge against a democrat winning? buy democrat futures. perhaps you're dependent on republican trade policy. so yes, the world which kenneth arrow dreamed off is becoming a little more perfect everyday. one arrow security for every state of the world. vulnerable to instability in the middle east? Got to get one of those futures against the US and Israel bombing Iran (15% chance of that happening)
my favourite quote of the day, on probability, on the european poker tour.
table was showing quad 4's to Player A, and 3 pair to another (Player B) with the river card to come, Player B was thus drawing dead (nothing the last card could do to make her win). So the probabilities were quoted at (100%-0%). the commentator replied : "i don't understand how they can be so sure. there's always a risk the chandelier will fall through the table and nobody can remember what the cards were."
well of course, they're quoted to the nearest whole number, so i'm sure infinitesimal chance of that happening isn't quoted. in the words of what i unfortunately, have to go back to studying now, the limit of the probability that player A will win is 1.
ok, i need to concentrate on analysis now.
http://ftalphaville.ft.com/blog/2008/05/14/13029/prediction-markets-101/
I was looking at US political futures today on 2 sites, 1 being based in the UK, betfair.com (and thus theoretically open to UK residents), and another based in the US, intrade.com. Barack Obama is roughly a 60-40 favourite to be the president. I was struck by how close the percentages quoted were on both sites. I had made a few assumptions:
That many people would go onto these sites just for a rough punt. So there should be no logical reason why the prices should equalize over the 2 markets.
Second, the markets are artificially segmented by residence, so even if they do accurately reflect expectations one should expect that british expectations should differ from american ones (due to different media coverage, biases, etc). So it was quite eye-opening to read this article.
So it occurs that some form of no-arbitrage does hold in predictions markets. ok, next step, figure out how the markets aggregate information. Is the market driven by insiders who make big bets when price diverge from what seems obvious to them (e.g, insiders working on the campaign who have a very good sense of how it's going through evaluating poll data and on-the ground knowledge). Then the small stakers are simply price takers, or look at already existing prices as markers. So in a sense, the stronger the knowledge is, the more it contributes to the price. This seems to fit with the liquidity patterns of the markets. The alternative explanation would be that people who place a parlay actively search for information by aggregating all the polls into a "super-average" poll. This is how theoretically stock markets work but I suspect that even the former hypothesis holds for stock markets.
anyway, it's amazing that these things exist nowadays. there's no reason they should. ever need to hedge against a democrat winning? buy democrat futures. perhaps you're dependent on republican trade policy. so yes, the world which kenneth arrow dreamed off is becoming a little more perfect everyday. one arrow security for every state of the world. vulnerable to instability in the middle east? Got to get one of those futures against the US and Israel bombing Iran (15% chance of that happening)
my favourite quote of the day, on probability, on the european poker tour.
table was showing quad 4's to Player A, and 3 pair to another (Player B) with the river card to come, Player B was thus drawing dead (nothing the last card could do to make her win). So the probabilities were quoted at (100%-0%). the commentator replied : "i don't understand how they can be so sure. there's always a risk the chandelier will fall through the table and nobody can remember what the cards were."
well of course, they're quoted to the nearest whole number, so i'm sure infinitesimal chance of that happening isn't quoted. in the words of what i unfortunately, have to go back to studying now, the limit of the probability that player A will win is 1.
ok, i need to concentrate on analysis now.
remember all those crazy overdraft fees you received last year? well, the test case has finally been brought before the court involving the Financial Services Authority, the 6 major banks, and the Office for Fair Trading. It is proceeding at an excruciatingly slow rate, though, and what they have determine so far is that these overdraft fees are "not exempt from being assessible for fairness". i really do not get law. so what does happen? they look at something that goes on in the past to determine if it's right or wrong? well, i suppose in a certain superstitious kind of way that's better than having a judge decide on a whim.
anyway, i'm happy that the army of well paid lawyers the banks have paid for are the beneficiaries of our overdraft fees, which will keep the banks honest. i can only hope that the fees are refunded to both me AND the lawyers, which will make the banks net losers from this stunt. (by the way, these were unarranged, e.g. i was charged £50 for accidentally going to -5£ in my account, which is an unacceptable rate of interest). complaining works if it's based on principle and you don't expect your money back immediately. this is a classic example of political economy. people don't complain because the gains are diffuse (£50 each) while the banks have an intrinsic interest to protect themselves because their losses are huge, even though the sums involved are the same on both sides.
i am worried about being too harsh on banks though. i realized today that i am their pimp. i was walking around with my debit card trying to draw money at various atms. i couldn't draw any money out of any of the other banks atms so i thought maybe there was a glitch with the interbank clearing system. i walked a long while to find a hsbc machine to see it was out of service. a thought flashed into my mind: "oh no, bank run". this was in the context of bank shares sliding (AGAIN) amidst news that they may have to recapitalize AGAIN. (bear in mind that there was already a run here on Northern Rock before the government stepped in) but they have branches in singapore, so they can't fail! they're too big to fail. but i was relieve to find that their branch was open after another long walk although only one machine was open. part of me still suspects they were trying to limit withdrawals. still, it's a long time still before i put money under my pillow. i've never experienced a bank run before, and isn't it crazy that we're even talking about it now?
anyway, i'm happy that the army of well paid lawyers the banks have paid for are the beneficiaries of our overdraft fees, which will keep the banks honest. i can only hope that the fees are refunded to both me AND the lawyers, which will make the banks net losers from this stunt. (by the way, these were unarranged, e.g. i was charged £50 for accidentally going to -5£ in my account, which is an unacceptable rate of interest). complaining works if it's based on principle and you don't expect your money back immediately. this is a classic example of political economy. people don't complain because the gains are diffuse (£50 each) while the banks have an intrinsic interest to protect themselves because their losses are huge, even though the sums involved are the same on both sides.
i am worried about being too harsh on banks though. i realized today that i am their pimp. i was walking around with my debit card trying to draw money at various atms. i couldn't draw any money out of any of the other banks atms so i thought maybe there was a glitch with the interbank clearing system. i walked a long while to find a hsbc machine to see it was out of service. a thought flashed into my mind: "oh no, bank run". this was in the context of bank shares sliding (AGAIN) amidst news that they may have to recapitalize AGAIN. (bear in mind that there was already a run here on Northern Rock before the government stepped in) but they have branches in singapore, so they can't fail! they're too big to fail. but i was relieve to find that their branch was open after another long walk although only one machine was open. part of me still suspects they were trying to limit withdrawals. still, it's a long time still before i put money under my pillow. i've never experienced a bank run before, and isn't it crazy that we're even talking about it now?
6/01/2008
truckers did a mini-blockade on the highways leading in to london, gathering all the way up to marble arch... ties in with what i have been reading recently on government's policies towards oil. here are a few controversial points:
1. european governments, with a high tax on oil, effectively reduce their countries demand for oil... all very environmental... except that this tax is exclusively on european consumers. reduced demand for oil from the europeans simply leads to cheaper oil (then it would have been) for the rest of the world. european oil consumers are thus indirectly subsidizing oil to the rest of the world, allowing them to feed the habit. not very environmental.
2. this one from the comments on MR: the US, in invading iraq, has effectively knocked out a large marginal supply of oil from the world market, and thus has done much more to raise prices on a global scale and choke off demand than any european tax could have done. so, the war cannot have been about cheap oil, and bush has done more to slow global warming than any other european leader. i find this more doubtful because oil was never really plentiful coming out of iraq anyway, due to embargoes, so the war actually adds to secured, proven reserve counts.
do incentives work? marks and sparks started charging 5p per plastic bag. i got myself a bag for life (10p) and i bring it everytime i go shopping there. of course, while queuing up i realised not so many people do that... i can understand why not many people shop from home and remember to bring their bag along. so i don't see what the charging does but allow the supermarket to cover costs on their bags. although, perhaps, targeting the marginal consumer like me helps well enough.
however, i think they're channeling all this into becoming carbon neutral , planting trees etc. so while i said all along that the costs for covering your emissions are minute and should just be tagged onto flights, etc, i begin to see using the argument above why an international protocol is needed. any tax on carbon imposed only by a certain country merely shifts demand, and does not reduce the world demand at all. however, a domestic tax would work if the proceeds go directly to offsetting emissions (then you're effectively paying for a product), but not if the government uses it as a revenue generating mechanism as it is so often tempted to do.
so, reforestation or building carbon scrubbers? i find it amusing we would find it more convenient to try to build a carbon scrubber
1. european governments, with a high tax on oil, effectively reduce their countries demand for oil... all very environmental... except that this tax is exclusively on european consumers. reduced demand for oil from the europeans simply leads to cheaper oil (then it would have been) for the rest of the world. european oil consumers are thus indirectly subsidizing oil to the rest of the world, allowing them to feed the habit. not very environmental.
2. this one from the comments on MR: the US, in invading iraq, has effectively knocked out a large marginal supply of oil from the world market, and thus has done much more to raise prices on a global scale and choke off demand than any european tax could have done. so, the war cannot have been about cheap oil, and bush has done more to slow global warming than any other european leader. i find this more doubtful because oil was never really plentiful coming out of iraq anyway, due to embargoes, so the war actually adds to secured, proven reserve counts.
do incentives work? marks and sparks started charging 5p per plastic bag. i got myself a bag for life (10p) and i bring it everytime i go shopping there. of course, while queuing up i realised not so many people do that... i can understand why not many people shop from home and remember to bring their bag along. so i don't see what the charging does but allow the supermarket to cover costs on their bags. although, perhaps, targeting the marginal consumer like me helps well enough.
however, i think they're channeling all this into becoming carbon neutral , planting trees etc. so while i said all along that the costs for covering your emissions are minute and should just be tagged onto flights, etc, i begin to see using the argument above why an international protocol is needed. any tax on carbon imposed only by a certain country merely shifts demand, and does not reduce the world demand at all. however, a domestic tax would work if the proceeds go directly to offsetting emissions (then you're effectively paying for a product), but not if the government uses it as a revenue generating mechanism as it is so often tempted to do.
so, reforestation or building carbon scrubbers? i find it amusing we would find it more convenient to try to build a carbon scrubber
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