User ohai - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T04:29:40Z http://mathoverflow.net/feeds/user/9501 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/41141/should-i-not-cite-an-arxiv-org-paper Should I not cite an arxiv.org paper? ohai 2010-10-05T12:55:28Z 2011-05-24T07:52:08Z <p>I want to cite a paper which is on arxiv.org but is not published or reviewed anywhere, and no publication or review seems to be in the pipeline. Would citing this arxiv.org paper be bad? Should I wait for a paper to be peer reviewed before I cite it?</p> <p>Added: I don't actually know whether a 'real' publication is in the pipeline. The alternative to citing the paper would probably be to ignore it; I have a way to extend the results in the paper if the paper's results are true, but I don't have the skill or time to verify that the arxiv.org paper is correct.</p> http://mathoverflow.net/questions/44136/what-is-the-average-center-of-six-points-in-space/44145#44145 Answer by ohai for What is the average center of six points in space ohai 2010-10-29T15:28:29Z 2010-10-29T15:28:29Z <p>You want mini ball.</p> <p><a href="http://www.inf.ethz.ch/personal/gaertner/miniball.html" rel="nofollow">http://www.inf.ethz.ch/personal/gaertner/miniball.html</a></p> http://mathoverflow.net/questions/43848/two-sequences-whose-difference-converges-to-zero two sequences whose difference converges to zero ohai 2010-10-27T18:46:07Z 2010-10-28T03:26:34Z <p>Is there a name for the relationship between sequences $A_n$ and $B_n$ which means that the sequence $A_n - B_n$ converges to zero? I want to say something like "sequence $A$ converges to sequence $B$" which might not mean the right thing, or something like "sequences $A$ and $B$ converge" which certainly doesn't mean what I want it to. Sorry if this question is too noob.</p> http://mathoverflow.net/questions/43864/describe-subsets-of-the-integers-closed-under-the-binary-operation-axby/43866#43866 Answer by ohai for describe subsets of the integers closed under the binary operation Ax+By ohai 2010-10-27T20:21:50Z 2010-10-27T20:21:50Z <p>All sets of integers are closed under this binary operation when A=1 and B=0.</p> http://mathoverflow.net/questions/43849/how-to-ensure-the-non-negativity-of-kullback-leibler-divergence-kld-metric-relat/43851#43851 Answer by ohai for How to ensure the non-negativity of Kullback-Leibler Divergence KLD Metric (Relative Entropy)? ohai 2010-10-27T19:00:21Z 2010-10-27T19:00:21Z <p>"The K-L divergence is only defined if P and Q both sum to 1 and if Q(i) > 0 for any i such that P(i) > 0."</p> <p>I suspect that the second condition is your problem. Say that you have x which appears in P but not Q -- in this case you're probably adding zero contribution to the sum in your code so that you don't have to divide by zero or take the logarithm of zero, but this is effectively throwing out mass from P and you get a negative number for the divergence.</p> <p><a href="http://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence" rel="nofollow">http://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence</a></p> http://mathoverflow.net/questions/43815/leading-eigenvalues/43817#43817 Answer by ohai for Leading eigenvalues ohai 2010-10-27T15:49:57Z 2010-10-27T16:00:31Z <p>I would guess that the magnitude of the leading eigenvalue of the sum is at most the sum of the magnitudes of the leading eigenvalues of the two operators, because the size of the leading eigenvalue is like a norm and the norms have the triangle inequality.</p> <p>Added: I guess this assumes the operators are self adjoint.</p> http://mathoverflow.net/questions/43690/whats-a-mathematician-to-do/43692#43692 Answer by ohai for What's a mathematician to do? ohai 2010-10-26T17:00:23Z 2010-10-26T17:00:23Z <p>I suspect that most interesting mathematical results raise more questions than they settle, so in this case you would not have anything to worry about.</p> http://mathoverflow.net/questions/43514/how-do-eigenvectors-and-eigenvalues-change-when-we-remove-a-row-column-pair-of-a/43520#43520 Answer by ohai for How do eigenvectors and eigenvalues change when we remove a row/column pair of a matrix? ohai 2010-10-25T14:09:18Z 2010-10-25T14:09:18Z <p>Removing a paired row/column from a symmetric matrix is kind of like setting the corresponding entries to zero. This reformulation would allow you to consider a perturbed matrix of the same dimensions.</p> http://mathoverflow.net/questions/43081/number-of-spanning-trees-bounds-from-structural-parameters/43082#43082 Answer by ohai for Number of spanning trees: bounds from structural parameters ohai 2010-10-21T18:01:40Z 2010-10-21T18:01:40Z <p>kirchhoff's theorem gives both a lower and upper bound</p> http://mathoverflow.net/questions/42818/stable-orthogonalization-procedure/42824#42824 Answer by ohai for Stable orthogonalization procedure ohai 2010-10-19T19:40:04Z 2010-10-20T13:53:06Z <p>Use a Procrustes rotation of the standard basis vectors onto your vectors. This gives the set of orthogonal vectors with the smallest sum of squares of distances to your vectors.</p> <p><a href="http://en.wikipedia.org/wiki/Orthogonal_Procrustes_problem" rel="nofollow">http://en.wikipedia.org/wiki/Orthogonal_Procrustes_problem</a></p> <p>"The orthogonal Procrustes problem is a matrix approximation problem in linear algebra. In its classical form, one is given two matrices A and B and asked to find an orthogonal matrix R which most closely maps A to B."</p> <p>In your case you want to find the orthogonal matrix R which most closely maps the standard basis to your matrix. Something like the columns of R should then be the set of orthogonal vectors which are nearest to your vectors, where 'nearest' is in the sense of sum of squares.</p> http://mathoverflow.net/questions/42791/quadratic-optimization-without-non-negativity-restriction/42793#42793 Answer by ohai for Quadratic optimization without non-negativity restriction ohai 2010-10-19T14:24:50Z 2010-10-19T14:24:50Z <p>You could replace each unrestricted variable x by (y-z) where y and z are each restricted to be positive.</p> http://mathoverflow.net/questions/42667/two-reference-requests-pinskers-inequality-and-pontryagin-duality/42669#42669 Answer by ohai for Two reference requests: Pinsker's inequality and Pontryagin duality ohai 2010-10-18T17:09:54Z 2010-10-18T17:09:54Z <p>proof of pinkser's inequality: <a href="http://www.clsp.jhu.edu/~sanjeev/520.674/notes/I-divergence-properties.pdf" rel="nofollow">http://www.clsp.jhu.edu/~sanjeev/520.674/notes/I-divergence-properties.pdf</a></p> http://mathoverflow.net/questions/42153/which-rights-do-mathematicians-usually-have-on-their-published-works-and-how-do-t/42155#42155 Answer by ohai for Which rights do mathematicians usually have on their published works and how do they use them? ohai 2010-10-14T14:25:04Z 2010-10-14T14:25:04Z <p>Some journals are public access. Some journals make articles publicly available after some time period, for example a year. Others are complete paywalls.</p> <p>There is a distinction between the document you submit and the edited document which is published; your freedom to distribute the edited document may be more limited, although you will typically be able to share on an individual basis with colleagues.</p> <p>Also there is arxiv. I would bet that you would be allowed to keep your preprint on arxiv as long as it is untouched by an editor of a journal, but I'm not positive about this and I would like to know more myself.</p> http://mathoverflow.net/questions/41808/what-is-this-decomposition-called What is this decomposition called? ohai 2010-10-11T16:34:04Z 2010-10-11T18:59:21Z <p>Let $M$ be a positive semi-definite matrix, symmetric with real entries. Then $M$ can be written as $X X^T$. One way is by a Cholesky decomposition (unique for positive definite but not necessarily for positive semi-definite $M$). Also note that for any $X X^T$ decomposition, $Y Y^T$ is also a decomposition where $Y = X R$ with $R$ orthogonal.</p> <p>I was wondering about the (possibly non-unique) factorization where $X$ is $U D^\frac{1}{2}$ and columns of $U$ are orthonormal eigenvectors of $M$ and $D$ is the diagonal matrix of sorted eigenvalues of $M$. Is this called something? I've been informally calling this $X$ the 'square root' of $M$ but I know that this is wrong and I would like to know if there is a correct word for it.</p> http://mathoverflow.net/questions/41771/pdes-as-a-tool-in-other-domains-in-mathematics/41810#41810 Answer by ohai for PDEs as a tool in other domains in mathematics ohai 2010-10-11T17:12:03Z 2010-10-11T17:12:03Z <p>Graph theory, e.g. <a href="http://arxiv.org/abs/math/0009120" rel="nofollow">http://arxiv.org/abs/math/0009120</a></p> http://mathoverflow.net/questions/41774/what-is-this-probability-distribution/41787#41787 Answer by ohai for What is this probability distribution? ohai 2010-10-11T14:13:57Z 2010-10-11T14:33:02Z <p>It is a finite distribution over numbers which aren't necessarily integers. I wouldn't expect it to have a name.</p> http://mathoverflow.net/questions/41059/generating-unique-combinations-from-a-list-of-possible-repeated-characters/41066#41066 Answer by ohai for Generating Unique Combinations from a list of possible repeated characters ohai 2010-10-04T20:59:12Z 2010-10-04T20:59:12Z <p>...what about aa</p> http://mathoverflow.net/questions/40514/measuring-the-randomness-in-random-numbers/40516#40516 Answer by ohai for Measuring the randomness in random numbers ohai 2010-09-29T19:15:49Z 2010-09-29T19:15:49Z <p><a href="http://www.phy.duke.edu/~rgb/General/dieharder.php" rel="nofollow">http://www.phy.duke.edu/~rgb/General/dieharder.php</a></p> http://mathoverflow.net/questions/40475/what-the-the-probability-distribution-of-a-mean/40477#40477 Answer by ohai for What the the probability distribution of a mean? ohai 2010-09-29T14:38:01Z 2010-09-29T15:01:35Z <p>"Based on the known random subset, what is the probability distribution of the mean of the unknown larger set?" With this question you've entered Bayesian land.</p> <p>Added: Use an uniformative prior. This way you can still talk about the 'probability distribution of the mean of the unknown larger set' without frequentists getting on your case because you are presuming to know too much about the prior distribution.</p> http://mathoverflow.net/questions/40351/edges-minus-vertices edges minus vertices ohai 2010-09-28T17:38:12Z 2010-09-28T21:39:11Z <p>Is there a more interesting name for this graph invariant? It seems to have been called 'complexity' here <a href="http://arxiv.org/abs/math/0502579" rel="nofollow">http://arxiv.org/abs/math/0502579</a> and here <a href="http://www.mathunion.org/ICM/ICM1994.2/Main/icm1994.2.1375.1383.ocr.pdf" rel="nofollow">http://www.mathunion.org/ICM/ICM1994.2/Main/icm1994.2.1375.1383.ocr.pdf</a> .</p> <p>The motivation is that we want to talk about a quantity that is preserved under the graph transformation of collapsing two distinct vertices connected by an edge to a single vertex (thereby removing one edge and one vertex, preserving 'edges minus vertices'). So for example if the quantity 'edges minus vertices plus one' is more natural for some reason and has a name, then this would also be helpful. The concept should not be restricted to e.g. planar graphs.</p> http://mathoverflow.net/questions/39879/how-to-get-nonzero-eigenvalues-of-a-large-symmetric-matrix-with-lots-of-duplicate how to get nonzero eigenvalues of a large symmetric matrix with lots of duplicate rows ohai 2010-09-24T17:59:38Z 2010-09-24T22:25:59Z <p>Is there a nice trick for this? I would like to compute the eigenvalues more efficiently.</p> http://mathoverflow.net/questions/45424/is-this-sequence-of-polynomials-well-known Comment by ohai ohai 2010-11-09T14:56:14Z 2010-11-09T14:56:14Z Is there a polynomial sequence search web thingy? I'm thinking like OEIS or ISC (inverse symbolic calculator)? http://mathoverflow.net/questions/45350/application-of-partial-derivatives/45353#45353 Comment by ohai ohai 2010-11-08T21:00:32Z 2010-11-08T21:00:32Z If this is such a clearly inappropriate question, then maybe the mods can just nuke it somehow? http://mathoverflow.net/questions/44957/what-is-the-simplest-way-to-fathom-the-monster-group Comment by ohai ohai 2010-11-05T15:23:50Z 2010-11-05T15:23:50Z Here's an animated visualization of the Monster Group and how it is so relevant and big, and why it exists: <a href="http://www.youtube.com/watch?v=azEvfD4C6ow" rel="nofollow">youtube.com/watch?v=azEvfD4C6ow</a> http://mathoverflow.net/questions/44871/equation-i-dont-know-how-solve-it Comment by ohai ohai 2010-11-04T21:52:39Z 2010-11-04T21:52:39Z <a href="http://www.wolframalpha.com/input/?i=-2x" rel="nofollow">wolframalpha.com/input/?i=-2x</a>^3+%2B10x^2+-17x+%2B8%3D%282x^2%29%285x+-x^3%29^1%2F3 http://mathoverflow.net/questions/43982/dishonest-article Comment by ohai ohai 2010-10-28T15:10:35Z 2010-10-28T15:10:35Z This is why Asia is winning, by the way. http://mathoverflow.net/questions/43815/leading-eigenvalues Comment by ohai ohai 2010-10-27T20:56:50Z 2010-10-27T20:56:50Z ask this as a separate question? http://mathoverflow.net/questions/43812/when-is-it-possible-to-construct-a-joint-law-from-its-two-dimensional-marginals Comment by ohai ohai 2010-10-27T16:08:41Z 2010-10-27T16:08:41Z Do you have an example of such a sequence for a non-decomposable joint distribution? http://mathoverflow.net/questions/42046/efficiently-getting-bits-of-n Comment by ohai ohai 2010-10-13T20:34:47Z 2010-10-13T20:34:47Z there is also a theoretical computer science stackexchange http://mathoverflow.net/questions/41837/1-n-game-how-to-analyze Comment by ohai ohai 2010-10-12T16:33:45Z 2010-10-12T16:33:45Z Both players know the permutation before the game begins. You can't make a bid that would tie. If you are out of money then you have to either bid 0 or lose the bid. http://mathoverflow.net/questions/41904/weighted-adjacency-matrix-in-matlab/41905#41905 Comment by ohai ohai 2010-10-12T14:14:08Z 2010-10-12T14:14:08Z what format is your input graph http://mathoverflow.net/questions/41310/any-sum-of-2-dice-with-equal-probability/41312#41312 Comment by ohai ohai 2010-10-06T20:06:52Z 2010-10-06T20:06:52Z Yeah i get only link|edit|flag|cite. I would flag it, but this needs me to use an openid or something. http://mathoverflow.net/questions/41310/any-sum-of-2-dice-with-equal-probability/41312#41312 Comment by ohai ohai 2010-10-06T19:58:21Z 2010-10-06T19:58:21Z Maybe I need to collect more mathoverflow trinkets before I am allowed to delete my answers. http://mathoverflow.net/questions/41310/any-sum-of-2-dice-with-equal-probability/41312#41312 Comment by ohai ohai 2010-10-06T19:36:22Z 2010-10-06T19:36:22Z i don't see a delete button http://mathoverflow.net/questions/41310/any-sum-of-2-dice-with-equal-probability/41312#41312 Comment by ohai ohai 2010-10-06T18:53:54Z 2010-10-06T18:53:54Z Right. This answer is worthless so can I delete it, or does it have to just get downvoted to oblivion instead? http://mathoverflow.net/questions/40475/what-the-the-probability-distribution-of-a-mean/40477#40477 Comment by ohai ohai 2010-09-29T14:58:41Z 2010-09-29T14:58:41Z I would have made it a comment except that I'm only allowed to comment in my own answer threads because I don't have enough mathoverflow badges or achievements or whatever.