User tergi - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T13:28:39Z http://mathoverflow.net/feeds/user/24848 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/105425/finding-the-smallest-eigenvalues-of-a-large-but-structured-matrix/105434#105434 Answer by tergi for Finding the smallest eigenvalues of a large, but structured, matrix tergi 2012-08-25T00:36:11Z 2012-08-25T00:36:11Z <p>If it is a Laplacian then you not only know the smallest eigenvalue is zero, but you also know its corresponding eigenvector. You can use this information by essentially adding a single step to your procedure, it's something like adding back the mean of v to each element of Mv. Then use arnoldi to find the smallest (instead of second smallest) eigenpair.</p> http://mathoverflow.net/questions/104948/distribution-of-maximum-of-a-uniform-multinomial-distribution/104954#104954 Answer by tergi for Distribution of Maximum of a uniform multinomial distribution tergi 2012-08-17T23:08:59Z 2012-08-17T23:08:59Z <p>This is addressed by Bruce Levin, 1983, "On Calculations Involving the Maximum Cell Frequency."</p> <p>Also in <a href="http://www.jstor.org/stable/2347220" rel="nofollow">http://www.jstor.org/stable/2347220</a> .</p> http://mathoverflow.net/questions/104573/open-problems-in-sub-riemannian-geometry/104574#104574 Answer by tergi for Open problems in sub-Riemannian geometry tergi 2012-08-12T19:24:30Z 2012-08-12T19:24:30Z <p>Chapter 10 of "A Tour of Subriemannian Geometries, Their Geodesics and Applications" describes four open problems.</p> http://mathoverflow.net/questions/104442/find-both-maximum-and-minimum-values-in-linear-programming-problem/104443#104443 Answer by tergi for Find both maximum and minimum values in linear programming problem tergi 2012-08-10T22:13:10Z 2012-08-10T22:13:10Z <p>Probably not much more efficient than finding the max and min solutions separately.</p> http://mathoverflow.net/questions/104413/tail-bound-for-poisson-random-variable/104425#104425 Answer by tergi for Tail bound for Poisson random variable tergi 2012-08-10T17:33:49Z 2012-08-10T18:34:38Z <p>This is not a full answer, but according to <a href="http://en.wikipedia.org/wiki/Incomplete_gamma_function#Regularized_Gamma_functions_and_Poisson_random_variables" rel="nofollow">this explanation</a> I think the question asks whether $\Gamma(k, k \lambda) \geq e^{-\lambda} \Gamma(k)$ when $k \in Z^+$, and $\lambda \in (0, 1)$.</p> <p>Edit: Some answers to <a href="http://math.stackexchange.com/questions/129170/are-there-well-known-lower-bounds-for-the-upper-incomplete-gamma-function" rel="nofollow">this math.se question</a> have lower bounds for the upper incomplete gamma function.</p> http://mathoverflow.net/questions/73538/surface-fitting-with-convexity-requirement/104376#104376 Answer by tergi for Surface fitting with convexity requirement tergi 2012-08-09T21:15:27Z 2012-08-09T21:15:27Z <p>You should use an ellipsoid.</p> http://mathoverflow.net/questions/104309/how-to-find-the-minimum-string-length-to-produce-a-set-of-a-given-size-with-a-min/104313#104313 Answer by tergi for How to find the minimum string length to produce a set of a given size with a minimum pairwise Hamming distance tergi 2012-08-08T22:41:53Z 2012-08-08T23:05:12Z <p>According to my interpretation of Table I of <a href="http://neilsloane.com/doc/Me54.pdf" rel="nofollow">http://neilsloane.com/doc/Me54.pdf</a> it was not known at the time whether you needed bit ($q=2$) strings of length $n=23$, $n=22$, or possibly only of length $n=21$, to construct a set of $x=50$ codewords that are separated from each other by at least Hamming distance $d=10$. This particular example may or may not still be an open question, but there is probably not a known general formula for $n$ in terms of $q$, $x$, and $d$.</p> <p>Edit: The bounds update at <a href="http://webfiles.portal.chalmers.se/s2/research/kit/bounds/unr.html" rel="nofollow">http://webfiles.portal.chalmers.se/s2/research/kit/bounds/unr.html</a> shows that $n$ is now known to be $22$ for the example above, but you can still see that a nice way to compute the function you want has not been discovered.</p> http://mathoverflow.net/questions/104160/eigenvector-update-formula/104163#104163 Answer by tergi for eigenvector update formula tergi 2012-08-06T23:24:10Z 2012-08-06T23:32:28Z <p>By $A$ do you mean $B$?</p> <p>Edit: You will probably also want to know quantitatively how `simple' $\lambda$ is, for example something like the distance to its nearest eigenvalue neighbor.</p> http://mathoverflow.net/questions/104137/can-the-friendship-graph-be-determind-by-its-adjacency-spectrum/104159#104159 Answer by tergi for Can the friendship graph be determind by its adjacency spectrum? tergi 2012-08-06T22:56:06Z 2012-08-06T22:56:06Z <p>This isn't a real answer, but wolfram-alpha says that $F_n$ is determined by its (adjacency) spectrum for $n \in \lbrace 2,3,4 \rbrace$. It doesn't say anything about $n=5$.</p> <p><a href="http://www.wolframalpha.com/input/?i=%285%2C3%29-windmill+graph" rel="nofollow">http://www.wolframalpha.com/input/?i=%285%2C3%29-windmill+graph</a></p> http://mathoverflow.net/questions/102652/given-a-grothendieck-topos-what-does-its-localic-groupoid-look-like/102679#102679 Answer by tergi for Given a Grothendieck topos, what does its localic groupoid look like? tergi 2012-07-19T15:56:47Z 2012-07-19T15:56:47Z <p>Starting from a topos $T$, construct a locale $L$ and a surjection $L \to T$ 'nice enough' (like a proper surjection). Then $(L, L \times TL,L \times TL \times TL)$ is a truncated simplicial locale, which can be seen as a localic groupoid. There is a canonical geometric morphism from the topos of sheaves on this groupoid to $T$, and if the surjection $L \to T$ was nice enough it's an isomorphism.</p> http://mathoverflow.net/questions/102566/solving-a-system-of-linear-inequalities/102581#102581 Answer by tergi for Solving a system of linear inequalities tergi 2012-07-18T20:36:26Z 2012-07-18T20:36:26Z <p>From <a href="http://www.faqs.org/faqs/linear-programming-faq/" rel="nofollow">http://www.faqs.org/faqs/linear-programming-faq/</a></p> <p>Q6.4: "I just want to know whether or not a feasible solution <em>exists</em>."</p> <p>A: From the standpoint of computational complexity, finding out if an LP model has a feasible solution is essentially as hard as actually finding the optimal LP solution, within a factor of 2 on average, in terms of effort in the Simplex Method; plug your problem into a normal LP solver with any objective function you like, such as c=0. For MIP models, it's also difficult - if there exists no feasible solution, then you must go through the entire Branch and Bound procedure (or whatever algorithm you use) to prove this. There are no shortcuts in general, unless you know something useful about your model's structure (e.g., if you are solving some form of a transportation problem, you may be able to assure feasibility by checking that the sources add up to at least as great a number as the sum of the destinations).</p> http://mathoverflow.net/questions/41994/basic-software-libraries-for-numerical-analysis-using-modern-programming-language/102088#102088 Answer by tergi for Basic software libraries for numerical analysis using modern programming languages? tergi 2012-07-13T01:10:48Z 2012-07-13T01:10:48Z <p>You should use code from Numerical Recipes. If you do this, then when people ask you for your code you can tell them that you aren't allowed to give it to them because it would violate the licence. Then people will stop bugging you and you won't have to reveal how messy your code is.</p> http://mathoverflow.net/questions/101958/nearly-elliptic-equations/101960#101960 Answer by tergi for Nearly elliptic equations tergi 2012-07-11T16:05:01Z 2012-07-11T16:05:01Z <p>do you mean positive semi-definite</p> http://mathoverflow.net/questions/101600/how-to-enumerate-all-possible-k-connected-components-partition-of-a-two-dimension/101603#101603 Answer by tergi for How to enumerate all possible k-connected-components partition of a two dimensional 4-connected grid tergi 2012-07-07T21:17:41Z 2012-07-07T22:07:22Z <p>Constraining m=n and k=2, this is <a href="http://oeis.org/A068416" rel="nofollow">http://oeis.org/A068416</a>.</p> http://mathoverflow.net/questions/105977/reversing-the-carry-operation-in-multiplication Comment by tergi tergi 2012-08-30T17:59:29Z 2012-08-30T17:59:29Z Any question that begins &quot;Hello I'm not a mathematician&quot; is going to be closed. http://mathoverflow.net/questions/105087/nash-equilibrium-of-simple-betting-game Comment by tergi tergi 2012-08-20T14:35:32Z 2012-08-20T14:35:32Z I find the terminology counterintuitive. Folding is usually defined so that if one player folds and the other player does not fold, then the player that does not fold gets a larger reward. http://mathoverflow.net/questions/105087/nash-equilibrium-of-simple-betting-game Comment by tergi tergi 2012-08-20T13:40:38Z 2012-08-20T13:40:38Z If the result is correct then maybe it is &quot;highly counterintuitive&quot; because of the counterintuitive folding rule &quot;If either player folds, each player receives 0.&quot; http://mathoverflow.net/questions/104698/the-expected-minimum-hamming-distance-within-a-set-of-randomly-selected-binary-st Comment by tergi tergi 2012-08-14T15:14:59Z 2012-08-14T15:14:59Z possibly relevant --- <a href="http://mathoverflow.net/questions/16359/minimum-hamming-distance-distribution-in-a-random-subset-of-binary-vectors" rel="nofollow" title="minimum hamming distance distribution in a random subset of binary vectors">mathoverflow.net/questions/16359/&hellip;</a> http://mathoverflow.net/questions/104695/agostino-prastaro Comment by tergi tergi 2012-08-14T14:49:27Z 2012-08-14T14:49:27Z Is it cool to use mathoverflow for general discussion of an arxiv upload? If not, is there a forum for this specific purpose? http://mathoverflow.net/questions/104413/tail-bound-for-poisson-random-variable/104428#104428 Comment by tergi tergi 2012-08-10T18:21:56Z 2012-08-10T18:21:56Z @irchans: $\lambda$ is supposed to be in $(0,1)$. http://mathoverflow.net/questions/104309/how-to-find-the-minimum-string-length-to-produce-a-set-of-a-given-size-with-a-min Comment by tergi tergi 2012-08-08T21:52:05Z 2012-08-08T21:52:05Z This is close enough to sphere packing to probably be an open research question. http://mathoverflow.net/questions/104137/can-the-friendship-graph-be-determind-by-its-adjacency-spectrum/104159#104159 Comment by tergi tergi 2012-08-07T19:26:34Z 2012-08-07T19:26:34Z @Jernej: &quot;graph features&quot; of (2,3)-, (3,3), and (4,3)-windmill graphs include &quot;determined by spectrum&quot; (meaning adjacency spectrum) in wolfram alpha. The link in the answer above goes to a (5,3)-windmill graph which does not mention such a graph feature, probably because wolfram-alpha doesn't know the answer.