Douglas Zare
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 Nov 8 comment Generalization of asymptotic notations like big O or little o notation So, your $R_O(a_n)$ means $a_n = O(1)?$ It's common to use $O(1)$ and $o(1)$. Sep 25 comment Build polynomial orthogonal to set of other pre-defined polynomials Is the problem that the number of predefined functions is much larger than the number of functions you want to orthogonalize, so orthogonalizing the predefined functions takes too long? If not, why not use Gram-Schmidt on the union of the predefined functions and the ones you want to orthogonalize? Also, why is this tagged orthogonal-groups? Sep 25 comment Build polynomial orthogonal to set of other pre-defined polynomials How is this research? Is your predefined set infinite? Jul 21 awarded Enlightened Jul 21 awarded Nice Answer Jun 19 comment Calculate the maximum probability of a result of rolling n dice of varying number of faces This isn't research-level mathematics without some indication that straightforward approaches are not adequate. You can use dynamic programming: Let a[i,j] be the probability that the first j dice have a sum of i. The simple approach to calculating this takes $O(n^2k^2)$ because you calculate nk values n times, and each sum is over k terms. You can speed that up by using the fast Fourier transform, or by using the binomial theorem if dice are repeated. You could estimate the maximum values using a normal approximation instead. Apr 27 comment Runs of consecutive numbers all of which are rebel numbers I usually applaud when other people have broad interests, but I don't think this qualifies as on-topic. I don't think it counts as "the sorts of questions you come across when you're writing or reading articles or graduate-level books." Does anyone else study "rebel numbers?" Quick Google searches turned up pages on civil wars. Your definition seems unmotivated and unnatural to me, like studying not the largest eigenvalue but the one that is alphabetically first in Tagalog. What fields of mathematics other than elementary number theory do you expect would be helpful for studying these numbers? Apr 27 comment Runs of consecutive numbers all of which are rebel numbers Why do you care about the digits base 10? Usually, this indicates that the problem is recreational mathematics and unlikely to be connected to anything rather than what research mathematicians study. Mar 16 awarded Yearling Dec 16 awarded Caucus Nov 19 comment What is the Vapnik-Chervonenkis dimension of sigmoidal functions? Whatever threshold you use gives half-spaces. It doesn't matter how complicated the sigmoid function is because it is monotone. This is an exercise. It is not research level. Mar 16 awarded Yearling Feb 2 comment maybe this sum have approximation $\sum_{k=0}^{n}\binom{n}{k}^3\approx\frac{2}{\pi\sqrt{3}n}\cdot 8^n,n\to\infty$ Dec 30 comment A lemma on the growth of the number of certain edge paths for a given train track This lemma is at the bottom of page 22: www-bcf.usc.edu/~fbonahon/Research/Preprints/Bouquin.pdf The proof is on page 23. What's the problem? The basic idea is that because the arcs are embedded, you only get a polynomial number of choices on each piece (each switch of the train track). Apr 20 comment Simple probability question, balls and bins @Zev Chonoles: I'm not upset with you, but it's odd that you responded within minutes to my response to whuber, while his nasty comment was left for weeks. Apr 15 comment Simple probability question, balls and bins @Zev Chonoles: I think you missed whuber's snarky comment. I'm glad he had the decency to delete it after I responded; too bad it was up for weeks before I noticed, and that he doesn't have the decency to apologize. I reserve the right to defend myself from additional attacks. Would that you were so eager to delete his comment when he made it. Apr 12 comment Simple probability question, balls and bins Here you might have missed the context of the comments on the deleted answer, where multiple people were repeating that I was wrong when I pointed out simple cases which my answer handles correctly, but which were not enumerated correctly by the then-accepted answer. The pattern is that I don't like it when I post something correct, and then multiple people say something clearly incorrect is better. I'm not always right, but I value correctness, and having a club of people praising each other's incorrect answers and voting down my correct answers is intolerable to me. Apr 12 comment Simple probability question, balls and bins @whuber: I spent hours showing that the accepted answer was incorrect. You made a stupid comment on my correct answer, objecting to my use of a prior on a problem tagged Bayesian, where everyone else uses priors, and where optimization with no prior does not make sense. You had no objection to the incorrect, accepted answer which used the same prior. You refused to apologize or communicate with me other than questionable uses of your moderator powers. This is unacceptable to me, so I will no longer contribute to CV. I do not understand your rudeness or disrespectful attitude. Mar 16 awarded Yearling Oct 4 comment Mountain Number Probability This is not probability, this is combinatorics. Also, please use the homework tag for any exercise like this.