most recent 30 from http://mathoverflow.net 2013-05-24T19:39:53Z http://mathoverflow.net/feeds/user/807 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17048/compute-the-centroid-of-a-3d-planar-polygon Graviton 2010-03-04T03:07:39Z 2011-11-07T17:53:48Z

<p>Given a list of 3D coordinates that define the surface( <code>Point3D1</code>, <code>Point3D2</code>, <code>Point3D3</code>, and so on), how to calculate the centroid of the surface?</p> <p>More specifically, I am looking for a natural extension of the following <a href="http://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon" rel="nofollow">2D centroid algorithm</a> in 3 or more dimension:</p> <p><img src="http://upload.wikimedia.org/math/e/e/1/ee14cbb2b170c4bb435f1d84e78f6d66.png" alt="alt text"> <img src="http://upload.wikimedia.org/math/a/4/c/a4cee81a1d18e4d067f66d4d40a8a1fe.png" alt="alt text"></p> <p><img src="http://upload.wikimedia.org/math/0/2/a/02aecb75f67f8c7b2fc11fdcbcb6ea80.png" alt="alt text"></p> <p>Any idea?</p> <p><strong>P/S: All the points are coplanar, this is the assumption.</strong> </p>

http://mathoverflow.net/questions/1887/given-a-spanning-tree-and-an-edge-not-on-the-spanning-tree-how-to-form-a-cycle-b Graviton 2009-10-22T15:44:06Z 2011-07-13T18:45:44Z

<p>I have a graph with Edge <code>E</code> and Vertex <code>V</code>, I can find the spanning tree using <a href="http://www-b2.is.tokushima-u.ac.jp/~ikeda/suuri/kruskal/Kruskal.shtml" rel="nofollow">Kruskal algorithm</a>, now I want to find all the cycle bases that are created by utilitizing that spanning tree and the edges that are not on the tree, any algorithm that allows me to do that, besides brute force search?</p> <p>I can, of course, starts from one vertex of the non-spanning tree edge, gets all the edges, explore all of them, retracts if I find dead end, until I come back to the other vertex of the edge. But this is a bit, err... brutal. Any other ideas?</p>

http://mathoverflow.net/questions/30759/in-a-graph-is-it-always-possible-to-construct-a-set-of-cycle-bases-with-each-an Graviton 2010-07-06T11:34:37Z 2010-07-06T13:03:33Z

<p>Given a graph with a list of edges, is it possible to always construct a set of cycle bases for those edges, such that each and every edge is shared by at most 2 cycle bases?</p> <p>The above question assumes that each and every edge must somehow belong to at least one cycle. IN other words, there is no vertex that is connected to one and only one edge. </p>

http://mathoverflow.net/questions/2054/data-mining-how-do-you-know-whether-the-pattern-you-extract-is-valid Graviton 2009-10-23T08:21:41Z 2010-06-17T07:05:25Z

<p>I've been asking myself this question all the time. Let's say you are given a large set of time series data. Your task is to find out patterns that are meaningful or that you can use for future trend prediction.</p> <p>The issue now is, how do you know for sure that the patterns you extract are valid, in the sense that they don't suffer from data snooping bias or a case of "torture-the-data-until-it-confesses"?</p> <p>I can always test my hypothesis as new data comes in, but even if it can predict all the trends in the past, that doesn't mean that it will continue to do so in the future. No?</p>

http://mathoverflow.net/questions/21532/prove-or-disprove-that-lower-eigenvalues-always-have-more-dominant-correspondi Graviton 2010-04-16T03:43:27Z 2010-04-16T04:17:16Z

<p>Assuming that I have a multiple DOF system of second order differential equations of this form with <code>n</code> degree of freedom:</p> <p><img src="http://upload.wikimedia.org/math/8/7/e/87ea19cbaf05b7af560a9b17c00dd7c5.png" alt="alt text"></p> <p>where C=&alpha;M+&beta;K.</p> <p>For this kind of system we can compute the eigenvalue( frequency) and eigenvector( normal modes).</p> <p>We know that for computation purpose, only a few lowest eigenvalue modes need to be taken into account because higher modes rarely impact the total response. </p> <p>My question is, is it possible to prove ( or disprove) that, under <em>any</em> sort of initial condition, that the lower the eigenvalue is, the more dominant the mode is in contributing to the total response of the system? Or, is it that although generally the higher the eigenvalue is the smaller the mode contribution, but nonetheless there are some exceptional modes that don't follow this pattern?</p>

http://mathoverflow.net/questions/21296/is-it-possible-to-find-out-the-relative-magnitude-of-different-modes-in-multidof Graviton 2010-04-14T03:53:31Z 2010-04-16T04:14:59Z

<p>Given that I have a matrix of second order differential equations <a href="http://en.wikipedia.org/wiki/Vibration" rel="nofollow">of this form</a>: <img src="http://upload.wikimedia.org/math/8/7/e/87ea19cbaf05b7af560a9b17c00dd7c5.png" alt="alt text"></p> <p>Where <code>M</code>, <code>x</code>, <code>C</code>, <code>K</code> are matrix and vectors.</p> <p>I can decomposed the solutions into different eigenvalues and eigenvectors, as dictacted by the theory of eigenvalue problem, and then solve the equations for each mode of eigenvectors, provided that I have the initial condition for the <code>x</code> and the first derivative of <code>x</code>.</p> <p>My question is, if the initial conditions are unknown, is there anyway I can still tell the relative magnitude for different eigenvectors?</p>

http://mathoverflow.net/questions/8863/the-application-of-lanczos-algorithm-on-sparse-matrix Graviton 2009-12-14T09:56:44Z 2010-02-04T19:08:53Z

<p>I am looking for suitable algorithm to compute the eigenvalues and eigenvectors of a matrix. My matrix is sparse ( think of Finite Element Matrix), and it is very, very big ( think of hundreds of thousands or even million degrees of freedom).</p> <p>The leading candidate for this task seems to be Lanczos algorithm.</p> <p>The issue now is, how well Lanczos algorithm fare if the matrix is sparse? The reason I ask this is because I want to know if there are a lot of zero terms in a matrix, will Lanczos take advantage of this by storing only nonzero terms and operate on them? Since my matrix is big, I want to conserve as much memory space as possible. </p>

http://mathoverflow.net/questions/8433/given-a-3d-point-cloud-does-points-far-away-from-a-neighbourhood-influence-the-3 Graviton 2009-12-10T08:20:07Z 2009-12-11T15:01:08Z

<p>I have a 3D point cloud, which I can reconstruct back the 3D surface easily by using any existing 3D interpolation algorithm.</p> <p>The question now is, let's say I have only a small neighbourhood of the 3D point cloud, and I am required to reconstruct back the 3D surface for that particular neighbourhood, how influential is the 3D points not in the neighbourhood contribute to the 3D surface shape of that particular chosen neighbourhood? </p> <p>Obviously, the answer would depend on how densely populated the 3D points are, and how big the neighbourhood is. But is it possible to quantify those? </p> <p><del>My question is algorithm independent. I just want to know the general characteristics of the influence of points from afar on a neighbourhood .</del></p> <p>I am aiming to compare the following interpolation method:</p> <ol> <li>Triangle-based linear interpolation </li> <li>Triangle-based cubic interpolation</li> <li>Nearest neighbor interpolation</li> </ol> <p>Note: when I say 3D surface, I mean a 2-manifold embedded in 3D.</p>

http://mathoverflow.net/questions/7647/break-polyhedron-into-tetrahedron Graviton 2009-12-03T08:37:16Z 2009-12-03T15:57:27Z

<p>Given a polyhedron consists of a list of vertices (<code>v</code>), a list of edges (<code>e</code>), and a list of surfaces connecting those edges (<code>s</code>), how to break the polyhedron into a list of tetrahedron?</p> <p>I have a convex polyhedron.</p>

http://mathoverflow.net/questions/4063/iso-lines-to-3d-surface-generation Graviton 2009-11-04T08:26:57Z 2009-11-04T11:28:01Z

<p>I have a set of isolines points ( or contour points) such as this:</p> <p><img src="http://www.rcad.eu/triang&amp;isolines%20example1.jpg" alt="alt text" /></p> <p>Each point has their own respective X, Y and Z. Since they are isolines, that means that all of the points will have a unique X-Y pair, i.e., they will be no two points with the same X and Y but different Z. </p> <p>Now, is there any algorithm, or any software packages ( either in C# or matlab) that I can use to interpolate this isoline points into full 3D surface points?</p> <p>P/S: I am not just the final output, I am interested in getting the interpolated lines myself so that I can plot the surface myself.</p>

http://mathoverflow.net/questions/1443/algorithm-to-find-all-the-cycle-bases-in-a-graph Graviton 2009-10-20T15:54:31Z 2009-10-22T15:09:39Z

<p>I am given a graph defined by vertexes and edges. I have to obtain all the cycle bases in a network. <strong>No coordinates will be given for the nodes.</strong></p> <p>Here's a <a href="http://deluxecourse.com/network.png" rel="nofollow">sketch</a> that illustrates my point.</p> <p><strong>Note that inside a cycle it must not contain any edge</strong></p>

http://mathoverflow.net/questions/30759/in-a-graph-is-it-always-possible-to-construct-a-set-of-cycle-bases-with-each-an/30767#30767 Graviton 2010-11-30T06:53:16Z 2010-11-30T06:53:16Z

I think I manage to understand this argument, thanks.

http://mathoverflow.net/questions/30759/in-a-graph-is-it-always-possible-to-construct-a-set-of-cycle-bases-with-each-an/30767#30767 Graviton 2010-07-13T14:37:06Z 2010-07-13T14:37:06Z

@Thorny, I <i>still</i> don't quite follow your logic. If you may, you might want to construct a diagram that answers my question negatively in graphical terms, that would be tremendously helpful. Sorry and thanks a lot!

http://mathoverflow.net/questions/30759/in-a-graph-is-it-always-possible-to-construct-a-set-of-cycle-bases-with-each-an/30767#30767 Graviton 2010-07-07T12:49:21Z 2010-07-07T12:49:21Z

Thorny, first are you saying that you assume a graph with 7 vertices and 21 edges? If yes, then your reasoning at most hold for that case, what about other case? Second, how do you actually define <i>dimension of the cycle base</i>?

http://mathoverflow.net/questions/30759/in-a-graph-is-it-always-possible-to-construct-a-set-of-cycle-bases-with-each-an Graviton 2010-07-07T07:01:43Z 2010-07-07T07:01:43Z

@BS, do you have a refernece on that?

http://mathoverflow.net/questions/30759/in-a-graph-is-it-always-possible-to-construct-a-set-of-cycle-bases-with-each-an/30767#30767 Graviton 2010-07-07T07:01:26Z 2010-07-07T07:01:26Z

I don't follow your logic, is there any nonintuitive properties of graphs and edges that you make use of when you make this deduction?

http://mathoverflow.net/questions/21296/is-it-possible-to-find-out-the-relative-magnitude-of-different-modes-in-multidof Graviton 2010-04-16T03:24:00Z 2010-04-16T03:24:00Z

@jc, why don't you answer this question so that I can accept it?

http://mathoverflow.net/questions/17048/compute-the-centroid-of-a-3d-planar-polygon Graviton 2010-03-04T03:33:31Z 2010-03-04T03:33:31Z

@Michael, all the points are coplanar

http://mathoverflow.net/questions/17048/compute-the-centroid-of-a-3d-planar-polygon Graviton 2010-03-04T03:33:17Z 2010-03-04T03:33:17Z

@David, yes, all vertices are required to lie on the same plane

http://mathoverflow.net/questions/8433/given-a-3d-point-cloud-does-points-far-away-from-a-neighbourhood-influence-the-3/8463#8463 Graviton 2009-12-11T02:44:58Z 2009-12-11T02:44:58Z

Thanks, you have any papers on that?

http://mathoverflow.net/questions/2054/data-mining-how-do-you-know-whether-the-pattern-you-extract-is-valid/2062#2062 Graviton 2009-10-28T08:28:56Z 2009-10-28T08:28:56Z

But let's say if you have to commit a large amount of $$$ to it? And even if those prediction can predict the upcoming trend <i>now</i>, it doesn't mean that it will continue to do so, forever.

http://mathoverflow.net/questions/2054/data-mining-how-do-you-know-whether-the-pattern-you-extract-is-valid/2062#2062 Graviton 2009-10-24T01:51:46Z 2009-10-24T01:51:46Z

The thing is that even if it can predict new data in the past, that doesn't mean that it will continue to do so in the future.

http://mathoverflow.net/questions/1887/given-a-spanning-tree-and-an-edge-not-on-the-spanning-tree-how-to-form-a-cycle-b/1901#1901 Graviton 2009-10-23T01:34:50Z 2009-10-23T01:34:50Z

&gt;if your graph doesn't have weights on edges I agree, but But my question is how to form the cycle base without resorting to something what I call 'brute force'.

http://mathoverflow.net/questions/1887/given-a-spanning-tree-and-an-edge-not-on-the-spanning-tree-how-to-form-a-cycle-b Graviton 2009-10-23T01:34:12Z 2009-10-23T01:34:12Z

Sure, I can find spanning tree-- with or without Kruskal. But my question is how to form the cycle base without resorting to something what I call 'brute force'.

http://mathoverflow.net/questions/1443/algorithm-to-find-all-the-cycle-bases-in-a-graph/1879#1879 Graviton 2009-10-22T15:07:33Z 2009-10-22T15:07:33Z

I mean, the cycles that travel the least number of vertex

http://mathoverflow.net/questions/1443/algorithm-to-find-all-the-cycle-bases-in-a-graph/1466#1466 Graviton 2009-10-22T15:06:27Z 2009-10-22T15:06:27Z

David, let's say if I don't know the coordinates of the vertexes, how can I &quot;report the cycle formed by that edge together with the tree path connecting its endpoints&quot; for the non-spanning-tree edge?