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Betti number
Results: 71

#	Item
31	Topological Data Analysis and Machine Learning Theory Gunnar Carlsson (Stanford University), Rick Jardine (University of Western Ontario), Dmitry Feichtner-Kozlov (University of Bremen), Dmitriy Morozov (Lawrence Berkele Add to Reading List Source URL: www.birs.ca Language: English - Date: 2013-01-07 15:21:43 Algebraic topology Topological data analysis Vietoris–Rips complex Homology Triangulation Chain complex Manifold Betti number Cohomology Topology Mathematics Abstract algebra
32	PDF Document Add to Reading List Source URL: www.ayasdi.com Language: English - Date: 2013-01-14 13:04:33 General topology Topological spaces Homotopy theory Data analysis Abstract simplicial complex Cluster analysis Filter Simplicial complex Betti number Topology Mathematics Algebraic topology
33	Eurographics Symposium on Point-Based Graphics[removed]M. Botsch, R. Pajarola (Editors) Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition Gurjeet Singh1 , Facundo Mémoli2 and Gu Add to Reading List Source URL: comptop.stanford.edu Language: English - Date: 2007-07-18 19:51:04 General topology Topological spaces Homotopy theory Data analysis Abstract simplicial complex Cluster analysis Filter Simplicial complex Betti number Topology Mathematics Algebraic topology
34	Discrete Comput Geom 29:41–[removed]DOI: [removed]s00454[removed]z Discrete & Computational Geometry Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:35:45 Algebraic topology Field theory Algebraic geometry Differential topology Betti number Morse theory CW complex Field Algebraic variety Abstract algebra Mathematics Topology
35	A SHARPER ESTIMATE ON THE BETTI NUMBERS OF SETS DEFINED BY QUADRATIC INEQUALITIES SAUGATA BASU AND MICHAEL KETTNER Abstract. In this paper we consider the problem of bounding the Betti numbers, bi (S), of a semi-algebrai Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:31:16 Quadratic forms Algebraic topology Betti number Topological graph theory Algebraic geometry Real algebraic geometry Algebraic variety Weil conjectures Algebra Mathematics Abstract algebra
36	BOUNDING THE EQUIVARIANT BETTI NUMBERS AND COMPUTING ´ CHARACTERISTIC OF THE GENERALIZED EULER-POINCARE SYMMETRIC SEMI-ALGEBRAIC SETS SAUGATA BASU AND CORDIAN RIENER Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2014-01-17 21:15:39 Algebraic topology Algebraic geometry Field theory Polynomials Betti number Homogeneous polynomial Algebraic variety Symmetric polynomial Real algebraic geometry Abstract algebra Algebra Mathematics
37	ON PROJECTIONS OF SEMI-ALGEBRAIC SETS DEFINED BY FEW QUADRATIC INEQUALITIES SAUGATA BASU AND THIERRY ZELL Abstract. Let S ⊂ Rk+m be a compact semi-algebraic set defined by P1 ≥ 0, . . . , P` ≥ 0, where Pi ∈ R[X1 Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:46 Algebraic topology Homological algebra Homology theory Algebraic geometry Group theory Betti number Sheaf Spectral sequence Cohomology Abstract algebra Algebra Mathematics
38	Discrete Comput Geom 30:65–[removed]DOI: [removed]s00454[removed]Discrete & Computational Geometry Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:35:46 Field theory Algebraic topology Betti number Topological graph theory Algebraic number theory Algebraic geometry Field extension Field Intersection number Abstract algebra Mathematics Algebra
39	POLYNOMIAL HIERARCHY, BETTI NUMBERS AND A REAL ANALOGUE OF TODA’S THEOREM SAUGATA BASU AND THIERRY ZELL Abstract. Toda [36] proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the class P# Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:44:12 Field theory Real algebraic geometry Algebraic geometry Real closed field Betti number Polynomial Algebraic variety Field Semialgebraic set Abstract algebra Mathematics Algebra
40	AN ASYMPTOTICALLY TIGHT BOUND ON THE NUMBER OF SEMI-ALGEBRAICALLY CONNECTED COMPONENTS OF REALIZABLE SIGN CONDITIONS SAUGATA BASU, RICHARD POLLACK, AND MARIE-FRANC ¸ OISE ROY Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:35:24 Algebraic topology Field theory Betti number Topological graph theory Algebraically closed field Holomorphic functional calculus Mathematics Abstract algebra Algebra