EMS

1,139 reputation

313

bio	website	suitdummy.blogspot.com
	location	Cambridge, MA
	age
visits	member for	1 year, 2 months
	seen	yesterday
stats	profile views	298

I once launched swi-prolog and asked it a question:

ely:~/home$ prolog
Welcome to SWI-Prolog (Multi-threaded, 64 bits, Version 5.10.1)
Copyright (c) 1990-2010 University of Amsterdam, VU Amsterdam
SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
and you are welcome to redistribute it under certain conditions.
Please visit http://www.swi-prolog.org for details.

For help, use ?- help(Topic). or ?- apropos(Word).

?- love(math) is unrequited.
true.

	1,139 reputation	bio	website	suitdummy.blogspot.com	visits	member for	1 year, 2 months
313 badges		location	Cambridge, MA		seen	yesterday

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125 Comments

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Mar 1	comment	How can Radon-Nikodym and Borel-Cantelli be used to calculate Probability distribution? @Did I apologize for trying to be helpful. Since you would rather win the argument than understand the paragraph, I will not bother you about it further.
Mar 1	comment	How can Radon-Nikodym and Borel-Cantelli be used to calculate Probability distribution? @Did The random variable induces a probability measure via is cumulative distribution function. This is standard in any probability theory textbook. If that measure is absolutely continuous w.r.t. the Lebesgue measure, then the random variable admits a probability density function (unfortunately often just called a 'distribution' function).
Feb 28	comment	How can Radon-Nikodym and Borel-Cantelli be used to calculate Probability distribution? @Did For instance, have you considered the Wikipedia article on the Radon-Nikodym Theorem? There it says: "... Specifically, the probability density function of a random variable is the Radon–Nikodym derivative of the induced measure with respect to some base measure (usually the Lebesgue measure for continuous random variables)."
Feb 28	comment	How can Radon-Nikodym and Borel-Cantelli be used to calculate Probability distribution? @Did I'm sorry that you don't understand the paragraph. It is a very nice way of explaining absolute continuity in the context of probability distributions here. Perhaps if you explain why you don't understand it, we can work together to provide a better explanation for you.
Jan 25	comment	How to study math to really understand it and have a healthy lifestyle with free time? Some of it is. But the linked articles on the lack of a wage premium for PhD holders in computer science and math over Master's degree holders, and also the rise of post-docs as principal investigators (hence more concentration of academic employment at the lower levels and less at associate or tenured professor positions) are from outside sources that derive from peer-reviewed research. Other observations such as having a limited time budget and needing to do something economically productive are more or less default attributes of nature. So if a person cares about these, it's less anecdotal.
Jul 21	comment	Fastest numeric method for ODE Also, FYI this question is probably better suited for either SciComp or Stack Overflow. It's not clear that this is due to your chosen algorithm. It could easily be due to an inefficient C implementation. If you post some code along with the question at either of those other sites, you'll almost surely get better help... and folks on those sites will also be able to suggest other mathematical algorithms to try if indeed that is the right way to solve the problem.
Jul 21	comment	Fastest numeric method for ODE Are you sure it is Euler's method that is slowing you down, and not the implementation? What language are you using? Is it a built-in or library function? What is your data set like? What sort of machine are you performing the calculation on, and with how much RAM? When you say it is 4-8 times too slow, what is this relative to and what timing benchmarks have led you to this conclusion?
Jul 4	comment	Can I use the geometric mean instead of the arithmetic mean to calculate the covariance between yields of different stocks? Normally what you are calling "yield" is called price return (in this case, daily price return). Also make sure you're computing the price of the later day minus the prior day, not vice versa (that is, subtracting 1 after dividing is equivalent to subtracting the prices, then normalizing to the prior day's price).
May 11	comment	Does a random action have probability? Probability is in the mind!
Apr 29	comment	Probability and Axiom of Choice Cox's Theorem prevents you from distributing "indifference" among infinitely many things. That's not a state of knowledge one can possibly have, and probability is in the mind
Apr 29	comment	Probability and Axiom of Choice You should read this paper and the Freiling paper mentioned in it.
Apr 25	comment	Fourier transform probability distribution It does seem from Box-Muller that you'd be computing a weighted combination of normal components, and so the result ought to be normal.
Apr 24	comment	Undergrad Student Trying to Figure Out What to Study I don't understand your numbers. How can the question get 0.0328 votes per view while any single answer gets 0.4251 votes per view. Any view of an answer is a view of a question...
Apr 24	comment	Undergrad Student Trying to Figure Out What to Study It is also fun for me to note that this question has been viewed 97 times so far, and my answer has received only 3 upvotes. So to (very crude) first approximation, this idea has about a 3% popularity rating. I love to contrast this with the 50% drop-out rate among Ph.D. students... Smoking gun evidence of overconfidence bias and planning fallacy if there ever was any...
Apr 24	comment	Undergrad Student Trying to Figure Out What to Study Of course you should give weight to your preferences. I am merely suggesting that most people give too much weight to what they currently enjoy doing, and not enough weight to the real externalities involved. Obviously, do not do something you don't enjoy. But surely most people enjoy more than one thing. I mostly think that when someone says, "I do what I love", they haven't thought about it very much. Surely you don't love just one vocation. It's a fallacy that is unique to high standard-of-living countries that we teach our young to focus almost exclusively on imagined preferences.
Apr 22	comment	Efficient principal pivots You definitely want to ask at scicomp.stackexchange.com. Since this is mostly an implementational / speed issue, they can probably help a lot more.
Apr 22	comment	Weird conclusion about variance/covariance from differentiating In the sense that it minimized portfolio volatility.
Apr 21	comment	Cluster Analysis Terminology question In the applied machine learning literature, 'hypergraph' is the appropriate term for most applications, and it is meant in the full mathematical sense. You see that in everything from stats papers to computer vision to social networks. See my answer below.
Apr 21	comment	Weird conclusion about variance/covariance from differentiating I think something is being lost in translation in the OP. The question should be asking: suppose $a$ is chosen to optimize portfolio risk between $X$ and $Y$, and is chosen such that $\text{COV}(X,Y) = a\text{Var}(X)$. Then show that $a$ must be 1.
Apr 18	comment	Can't see how $e^{\operatorname{Log}(z)} = z$ in these notes What is $Re[z]$ and $Im[z]$ in terms of $\|z\|$ and the angle $z$ makes with the positive real axis? It's just polar coordinates, basically.