Thu, 21 Aug 2008 07:41:28 BST CiteULike: zouzias' library [8 articles] http://www.citeulike.org/user/zouzias CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/zouzias/article/2691930 <i></i><br /><br />simplicial complexes : : : : : : : : : : : : : : : : : : : 4 1.4 Simplicial mappings : : : : : : : : : : : : : : : : : : : : : : : : 5 1.5 Correspondence between posets and simplicial complexes : : : 5 2 The theorem of Borsuk and Ulam 6 2.1 Several equivalent formulations : : : : : : : : : : : : : : : : : : 6 2.2 A combinatorial proof of the Borsuk-Ulam theorem : : : : : : : 7 2.3 Application: The necklace problem : : : : : : : : : : : : : : : : 9 2.4 Application: The ham-sandwich theorem : : ... Topological Methods in Combinatorics and Geometry Jiri Matousek 2008-04-20T05:54:00-00:00 combinatorics embeddings geometry theory topology http://www.citeulike.org/user/zouzias/article/244193 <i>(1 Jul 2005)</i><br /><br />Let A be an n by n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A^-1 does not exceed Cn^3/2 with probability close to 1. Invertibility of random matrices: norm of the inverse Mark Rudelson (1 Jul 2005) 2005-07-04T08:50:16-00:00 2005 inverse matrix random theory http://www.citeulike.org/user/zouzias/article/579841 <i>Commun. ACM, Vol. 22, No. 11. (November 1979), pp. 612-613.</i> How to share a secret Adi Shamir doi:10.1145/359168.359176 Commun. ACM, Vol. 22, No. 11. (November 1979), pp. 612-613. 2006-04-07T20:45:09-00:00 1979 Commun. ACM 0001-0782 22 11 612 613 ACM Press coding cryptography theory http://www.citeulike.org/user/zouzias/article/854319 <i>(18 Sep 2006)</i><br /><br />We discuss how to generate random unitary matrices from the classical compact groups U(N), O(N) and USp(N) with probability distributions given by the respective invariant measures. The algorithm is straightforward to implement using standard linear algebra packages. This approach extends to the Dyson circular ensembles too. This article is based on a lecture given by the author at the summer school on Number Theory and Random Matrix Theory held at the University of Rochester in June 2006. The exposition is addressed to a general mathematical audience. How to generate random matrices from the classical compact groups Francesco Mezzadri (18 Sep 2006) 2006-09-22T10:05:12-00:00 2006 decomposition matrix qr random http://www.citeulike.org/user/zouzias/article/1031420 <i>(2003)</i><br /><br />We study the common problem of approximating a target matrix with a matrix of lower rank. We provide a simple and e#cient (EM) algorithm for solving weighted low-rank approximation problems, which, unlike their unweighted version, do not admit a closedform solution in general. We analyze, in addition, the nature of locally optimal solutions that arise in this context, demonstrate the utility of accommodating the weights in reconstructing the underlying low-rank representation, and... Weighted low rank approximation N Srebro T Jaakkola (2003) 2007-01-09T11:54:59-00:00 2003 no-tag http://www.citeulike.org/user/zouzias/article/508058 <i>J. Comb. Theory Ser. A, Vol. 44, No. 3. (June 1987), pp. 355-362.</i> The Johnson-Lindenstrauss Lemma and the sphericity of some graphs P Frankl H Maehara J. Comb. Theory Ser. A, Vol. 44, No. 3. (June 1987), pp. 355-362. 2006-02-17T22:27:06-00:00 1987 J. Comb. Theory Ser. A 0097-3165 44 3 355 362 Academic Press, Inc. johnson lemma lindenstrauss http://www.citeulike.org/user/zouzias/article/1280964 <i>No. TR-99-006. (1999)</i><br /><br />The Johnson-Lindenstrauss lemma shows that a set of n points in high dimensional Euclidean space can be mapped down into an O(log n=ffl 2 ) dimensional Euclidean space such that the distance between any two points changes by only a factor of (1 Σ ffl). In this note, we prove this lemma using elementary probabilistic techniques. Computer Science Division, UC Berkeley. Email: dasgupta@cs.berkeley.edu. y Computer Science Division, UC Berkeley. Email: angup@cs.berkeley.edu. Supported by... An elementary proof of the Johnson-Lindenstrauss Lemma Sanjoy Dasgupta Anupam Gupta No. TR-99-006. (1999) 2007-05-06T19:01:50-00:00 1999 TR-99-006 johnson lemma lindenstrauss