User - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T09:06:39Z http://mathoverflow.net/feeds/user/984 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/11676/uniformly-distribute-a-population-in-a-given-search-space Uniformly distribute a population in a given search space hyperboreean 2010-01-13T18:11:26Z 2010-12-24T11:20:28Z <p>I am trying to uniformly distribute a finite number of particles into a 2D search space to get me started with an optimization problem, but I am having a hard time doing it. I am thinking that it might have something to do with convex sets, but I might as well be totally off, so I am asking you guys of a proper way to do it .</p> <p><b>Edit: </b> Ok, so I have to implement the Particle Swarm Optimization algorithm in order to get the polynomial input for Baker's algorithm and to get started with PSO, I have to uniformly distribute the particles in the search space (the initial example I got was of the distribution of particles inside of a cube, but that's kind of vague for me). What does it mean to uniformly distribute in the search space?</p> http://mathoverflow.net/questions/28476/spectral-factorization spectral factorization hyperboreean 2010-06-17T09:02:45Z 2010-06-17T10:07:14Z <p>I am trying to find some examples on how to compute a spectral factorization for a given transfer function for MIMO systems. I currently found only the exercises, but not how you could actually solve them; i.e compute a spectral factorization for:</p> <p><code>$$G(s) = \begin{pmatrix}\frac{1}{s}\\ \frac{s-1}{s+1}\end{pmatrix}$$</code></p> http://mathoverflow.net/questions/26564/understanding-some-concept-about-linear-discrimination understanding some concept about linear discrimination hyperboreean 2010-05-31T11:35:24Z 2010-05-31T11:35:24Z <p>I am walking through Stephen Boyd's Convex Optimization <a href="http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf" rel="nofollow">book</a> and I don't understand probably some &lt; very > basic concepts. Take for example section 8.6.1 - I don't know how he got to formula 8.21. If someone would be kind enough to give me a hint it'll be greately appreciated.</p> http://mathoverflow.net/questions/1722/free-high-quality-mathematical-writing-online/11678#11678 Answer by hyperboreean for Free, high quality mathematical writing online? hyperboreean 2010-01-13T18:21:23Z 2010-01-13T18:21:23Z <p>Stephen Boyd has some good books on his Stanford home page: <a href="http://www.stanford.edu/~boyd/books.html" rel="nofollow">http://www.stanford.edu/~boyd/books.html</a> ... especially the one on convex optimization is very good.</p> http://mathoverflow.net/questions/1722/free-high-quality-mathematical-writing-online/1873#1873 Answer by hyperboreean for Free, high quality mathematical writing online? hyperboreean 2009-10-22T13:46:05Z 2009-10-22T13:46:05Z <p><a href="http://www.cs.utk.edu/~dongarra/etemplates/book.html" rel="nofollow">http://www.cs.utk.edu/~dongarra/etemplates/book.html</a></p> http://mathoverflow.net/questions/11676/uniformly-distribute-a-population-in-a-given-search-space Comment by 2010-01-16T11:25:57Z 2010-01-16T11:25:57Z @Scott Morrison: I've updated it, thanks for pointing things out, I hope now it's a little bit more clear. Sorry for my turgid way of describing stuff, but I am not a native English speaker. http://mathoverflow.net/questions/11676/uniformly-distribute-a-population-in-a-given-search-space Comment by 2010-01-14T17:57:20Z 2010-01-14T17:57:20Z @Leonid: yes you are right ... I am not talking about the probability density function, but rather how to uniformly distribute those points in the space. http://mathoverflow.net/questions/11676/uniformly-distribute-a-population-in-a-given-search-space Comment by 2010-01-13T20:30:28Z 2010-01-13T20:30:28Z Well, what if the search space is a rectangle, say with a 2^16 size ? I guess your solution will still work. http://mathoverflow.net/questions/1872/transposed-jagged-storage Comment by 2009-10-22T16:43:08Z 2009-10-22T16:43:08Z I don't agree with your decision, Scott. Could you please explain a little bit or maybe send me to some kind of faq ? That's what I am interested now and that's what I'd like to ask - don't know where's the problem here. http://mathoverflow.net/questions/1872/transposed-jagged-storage/1875#1875 Comment by 2009-10-22T14:06:09Z 2009-10-22T14:06:09Z No,checking now, thanks for the link!