Betti number

Results: 71



#Item
31Algebraic topology / Topological data analysis / Vietoris–Rips complex / Homology / Triangulation / Chain complex / Manifold / Betti number / Cohomology / Topology / Mathematics / Abstract algebra

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

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Source URL: www.birs.ca

Language: English - Date: 2013-01-07 15:21:43
32General topology / Topological spaces / Homotopy theory / Data analysis / Abstract simplicial complex / Cluster analysis / Filter / Simplicial complex / Betti number / Topology / Mathematics / Algebraic topology

PDF Document

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Source URL: www.ayasdi.com

Language: English - Date: 2013-01-14 13:04:33
33General topology / Topological spaces / Homotopy theory / Data analysis / Abstract simplicial complex / Cluster analysis / Filter / Simplicial complex / Betti number / Topology / Mathematics / Algebraic topology

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

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Source URL: comptop.stanford.edu

Language: English - Date: 2007-07-18 19:51:04
34Algebraic topology / Field theory / Algebraic geometry / Differential topology / Betti number / Morse theory / CW complex / Field / Algebraic variety / Abstract algebra / Mathematics / Topology

Discrete Comput Geom 29:41–[removed]DOI: [removed]s00454[removed]z Discrete & Computational Geometry

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Source URL: www.math.purdue.edu

Language: English - Date: 2010-06-16 13:35:45
35Quadratic forms / Algebraic topology / Betti number / Topological graph theory / Algebraic geometry / Real algebraic geometry / Algebraic variety / Weil conjectures / Algebra / Mathematics / Abstract algebra

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

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Source URL: www.math.purdue.edu

Language: English - Date: 2010-06-16 13:31:16
36Algebraic topology / Algebraic geometry / Field theory / Polynomials / Betti number / Homogeneous polynomial / Algebraic variety / Symmetric polynomial / Real algebraic geometry / Abstract algebra / Algebra / Mathematics

BOUNDING THE EQUIVARIANT BETTI NUMBERS AND COMPUTING ´ CHARACTERISTIC OF THE GENERALIZED EULER-POINCARE SYMMETRIC SEMI-ALGEBRAIC SETS SAUGATA BASU AND CORDIAN RIENER

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Source URL: www.math.purdue.edu

Language: English - Date: 2014-01-17 21:15:39
37Algebraic topology / Homological algebra / Homology theory / Algebraic geometry / Group theory / Betti number / Sheaf / Spectral sequence / Cohomology / Abstract algebra / Algebra / Mathematics

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

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Source URL: www.math.purdue.edu

Language: English - Date: 2010-06-16 13:36:46
38Field theory / Algebraic topology / Betti number / Topological graph theory / Algebraic number theory / Algebraic geometry / Field extension / Field / Intersection number / Abstract algebra / Mathematics / Algebra

Discrete Comput Geom 30:65–[removed]DOI: [removed]s00454[removed]Discrete & Computational Geometry

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Source URL: www.math.purdue.edu

Language: English - Date: 2010-06-16 13:35:46
39Field theory / Real algebraic geometry / Algebraic geometry / Real closed field / Betti number / Polynomial / Algebraic variety / Field / Semialgebraic set / Abstract algebra / Mathematics / Algebra

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#

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Source URL: www.math.purdue.edu

Language: English - Date: 2010-06-16 13:44:12
40Algebraic topology / Field theory / Betti number / Topological graph theory / Algebraically closed field / Holomorphic functional calculus / Mathematics / Abstract algebra / Algebra

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

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Source URL: www.math.purdue.edu

Language: English - Date: 2010-06-16 13:35:24
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