User optima - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T20:00:35Z http://mathoverflow.net/feeds/user/11853 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/50872/how-might-m-c-escher-have-designed-his-patterns/50874#50874 Answer by optima for How might M.C. Escher have designed his patterns? optima 2011-01-01T18:19:17Z 2011-01-01T18:31:02Z <p>'Around 1956, Escher explored the concept of representing infinity on a two-dimensional plane. Discussions with Canadian mathematician H.S.M. Coxeter inspired Escher's interest in hyperbolic tessellations, which are regular tilings of the hyperbolic plane. Escher's works Circle Limit I–IV demonstrate this concept. In 1995, Coxeter verified that Escher had achieved mathematical perfection in his etchings in a published paper. Coxeter wrote, "Escher got it absolutely right to the millimeter."'</p> <p><a href="http://en.wikipedia.org/wiki/M._C._Escher" rel="nofollow">http://en.wikipedia.org/wiki/M._C._Escher</a></p> <p>If Angels and Devils is a hyperbolic tessellation then it might have been inspired by Coxeter.</p> <p>The construction itself was done using techniques like these:</p> <p><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.133.8746&amp;rep=rep1&amp;type=pdf" rel="nofollow">http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.133.8746&amp;rep=rep1&amp;type=pdf</a></p> http://mathoverflow.net/questions/50837/is-there-a-systematic-method-for-differentiating-under-the-integral-sign/50846#50846 Answer by optima for Is there a systematic method for differentiating under the integral sign? optima 2011-01-01T03:09:58Z 2011-01-01T03:09:58Z <p>"Devise a technique of this type that successfully evaluates some class of definite integrals that is not evaluable by other known techniques (such as those implemented in existing computer algebra packages)."</p> <p>Wait what about the Risch algorithm?</p> <p><a href="http://en.wikipedia.org/wiki/Risch_algorithm" rel="nofollow">http://en.wikipedia.org/wiki/Risch_algorithm</a></p> http://mathoverflow.net/questions/50806/expected-value-as-decision-criterion-in-the-context-of-rare-events/50807#50807 Answer by optima for Expected value as decision criterion in the context of rare events optima 2010-12-31T14:50:07Z 2010-12-31T14:50:07Z <p>No there is not any justification for using expected value alone as a criterion in these types of rare events. Also <a href="http://stats.stackexchange.com" rel="nofollow">http://stats.stackexchange.com</a>.</p> http://mathoverflow.net/questions/50743/moore-penrose-pseudo-inverse/50745#50745 Answer by optima for Moore-Penrose pseudo inverse optima 2010-12-30T17:58:33Z 2010-12-30T17:58:33Z <p>If by 'knwon relation' you mean whether you can convert between these matrices unambiguously then the answer is yes. The Moore-Penrose pseudoinverse always exists and is unique, and A is nonsingular. That is all you need.</p> http://mathoverflow.net/questions/50739/the-mystic-rose/50740#50740 Answer by optima for The Mystic Rose optima 2010-12-30T17:09:20Z 2010-12-30T17:09:20Z <p><a href="http://oeis.org/A006600" rel="nofollow">http://oeis.org/A006600</a></p> http://mathoverflow.net/questions/50572/optimally-directing-switches-for-a-random-walk/50588#50588 Answer by optima for Optimally directing switches for a random walk optima 2010-12-28T19:12:05Z 2010-12-28T19:59:30Z <p>Edit: apparently I'm linking to a paper that has a different definition of 'switch'</p> <p>The reachability problem is NP-complete for unweighted directed switch graphs.</p> <p><a href="http://www.springerlink.com/content/f2722481747l2170/" rel="nofollow">http://www.springerlink.com/content/f2722481747l2170/</a></p> <p>This means that in the weighted case it is NP hard to even find switch settings that can reach the target from the starting vertex, let alone reach the target with maximum probability.</p> http://mathoverflow.net/questions/50561/3d-width-and-cross-section/50562#50562 Answer by optima for 3d width and cross section optima 2010-12-28T14:18:50Z 2010-12-28T14:18:50Z <p>These are applied computational geometry questions, not really mathematics research questions.</p> <p><a href="http://en.wikipedia.org/wiki/Computational_geometry" rel="nofollow">http://en.wikipedia.org/wiki/Computational_geometry</a></p> <p>Maybe try asking on stackoverflow or on a blender or CAD forum or something.</p> <p><a href="http://www.blender.org/" rel="nofollow">http://www.blender.org/</a></p> http://mathoverflow.net/questions/50528/probability-that-a-number-and-its-digit-reversal-are-relatively-prime/50529#50529 Answer by optima for Probability that a number and its digit reversal are relatively prime optima 2010-12-28T02:12:34Z 2010-12-28T02:12:34Z <p>There is some relevant discussion here:</p> <p><a href="http://forums.xkcd.com/viewtopic.php?f=17&amp;t=23136" rel="nofollow">http://forums.xkcd.com/viewtopic.php?f=17&amp;t=23136</a></p> http://mathoverflow.net/questions/50522/obtaining-all-vectors-of-given-length-and-with-with-1-entries-from-a-given-o/50526#50526 Answer by optima for obtaining all vectors of given length and with with $+-1$ entries from a given one optima 2010-12-28T00:49:30Z 2010-12-28T00:49:30Z <p>There are like $2^n$ of these vectors. If you "need to try some computations on all such vectors" then, unless you can factor something out of your computation, you will need an amount of time roughly proportional to $(2^n) \times$ (time it takes to do each computation).</p> http://mathoverflow.net/questions/50837/is-there-a-systematic-method-for-differentiating-under-the-integral-sign Comment by optima optima 2011-01-01T15:06:36Z 2011-01-01T15:06:36Z I doubt Richard &quot;let's get organized&quot; Feynman would disapprove of his systematisation. http://mathoverflow.net/questions/50837/is-there-a-systematic-method-for-differentiating-under-the-integral-sign/50846#50846 Comment by optima optima 2011-01-01T10:48:07Z 2011-01-01T10:48:07Z i see. definite vs. indefinite. never mind then. http://mathoverflow.net/questions/50800/finding-points-inside-innermost-convex-hull Comment by optima optima 2010-12-31T15:52:00Z 2010-12-31T15:52:00Z I think OP is talking about an 'analytical formula' to find any point inside the innermost hull, where the onion peels can be constructed like N log N as in page 8 of <a href="http://www.montefiore.ulg.ac.be/~briquet/algo3-chull-20070206.pdf" rel="nofollow">montefiore.ulg.ac.be/~briquet/&hellip;</a> . By 'analytical formula' I think OP means something like centroid. I'm not saying that centroid would work, this is just an example of something which might qualify as an analytical formula. http://mathoverflow.net/questions/50738/mathscinet-reviews-everyone-should-read Comment by optima optima 2010-12-30T18:25:40Z 2010-12-30T18:25:40Z @Roy: this is because you now have a subscription. http://mathoverflow.net/questions/50738/mathscinet-reviews-everyone-should-read Comment by optima optima 2010-12-30T18:20:06Z 2010-12-30T18:20:06Z @Roy: I don't see in what sense mathscinet is freely available. For example when I click on the 'Joel on El Naschie' link <a href="http://www.ams.org/mathscinet-getitem?mr=MR1428296" rel="nofollow">ams.org/mathscinet-getitem?mr=MR1428296</a> I get &quot;For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.&quot; http://mathoverflow.net/questions/50744/hapy-pi-day-in-2015 Comment by optima optima 2010-12-30T17:51:03Z 2010-12-30T17:51:03Z 3/14/15 at 9:26:53.589! Pi day captures the essence of everything I love about math. http://mathoverflow.net/questions/50743/moore-penrose-pseudo-inverse Comment by optima optima 2010-12-30T17:48:34Z 2010-12-30T17:48:34Z could you clarify your question http://mathoverflow.net/questions/50738/mathscinet-reviews-everyone-should-read Comment by optima optima 2010-12-30T17:38:59Z 2010-12-30T17:38:59Z My favorite review on mathscinet is &quot;MathSciNet is available by subscription only. The computer you are using has not been registered for use with MathSciNet. Please contact your site's library or other appropriate department to verify that your site has a MathSciNet subscription.&quot; http://mathoverflow.net/questions/50718/how-do-i-tweak-a-linear-regression-equation-to-minimize-variance-rather-than-sd/50728#50728 Comment by optima optima 2010-12-30T14:45:41Z 2010-12-30T14:45:41Z @unknown(google): This does answer your question. It doesn't plot the line under all the points in the scatter graph. You are using the function wrong. To use the function correctly, the $y$ value on the regression line at a given $x$ value is equal to $mx + b$ where $m$ and $b$ are the values (slope and intercept) returned by your php function. http://mathoverflow.net/questions/50718/how-do-i-tweak-a-linear-regression-equation-to-minimize-variance-rather-than-sd/50728#50728 Comment by optima optima 2010-12-30T14:22:45Z 2010-12-30T14:22:45Z @unknown(google): This answer was voted down to discourage giving answers to stupid questions, not because the answer is wrong. http://mathoverflow.net/questions/50718/how-do-i-tweak-a-linear-regression-equation-to-minimize-variance-rather-than-sd Comment by optima optima 2010-12-30T13:46:07Z 2010-12-30T13:46:07Z The usual formulation of linear regression minimizes the sum of squares of errors. For your first list of residuals this sum of squares is 3, while for your second list it is 2. So indeed the line should rather go &quot;between the points.&quot; Therefore I assume that you are &quot;using the wrong terms&quot;, meaning either that the php regression code is wrong or you are misinterpreting the input or the output of the function. http://mathoverflow.net/questions/50572/optimally-directing-switches-for-a-random-walk Comment by optima optima 2010-12-28T20:07:33Z 2010-12-28T20:07:33Z @Rex: I guess I meant looking for two switch configurations which both connect $s$ to $t$, and where you can't get from one configuration to the other configuration by flipping single switches at a time unless $t$ becomes unreachable from $s$ at some point. These two configurations would be in different 'islands' of the solution space, and this is the kind of locality I was talking about. http://mathoverflow.net/questions/50572/optimally-directing-switches-for-a-random-walk Comment by optima optima 2010-12-28T19:04:32Z 2010-12-28T19:04:32Z @Rex: &quot;I don't know what it means for a 0/1-valued function to have a local but not global optimum.&quot; Then what did you mean by &quot;That is, is there a local optimum that is not a global optimum?&quot; in the original question? http://mathoverflow.net/questions/50572/optimally-directing-switches-for-a-random-walk Comment by optima optima 2010-12-28T18:56:18Z 2010-12-28T18:56:18Z To solve a simpler problem, what if you forget the weights and consider only the question of setting switch states so that there is a directed path from $s$ to $t$. Does the solution need to coordinate switches in this simpler case? This might help with the question about local vs global optimality in the weighted case. http://mathoverflow.net/questions/50577/how-to-solve-science-formula-equation/50579#50579 Comment by optima optima 2010-12-28T17:41:02Z 2010-12-28T17:41:02Z link|edit|flag|cite