Algebraic Topology: Methods, Computation and Science 6 (ATMCS6)

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Algebraic Topology: Methods, Computation and Science 6 (ATMCS6). 2014 Confirmed participants: 1. Ali Abdallah University of Rome 2 2. Alejandro Adem UBC 3. Ulrich Bauer IST Austria 4. Omer Bobrowski Duke University 5. Magnus Botnan NTNU, Norway 6. Boris Botvinnik University of Oregon 7. Peter Bubenik Cleveland State University 8. Yiqing Cai IMA 9. Gunnar Carlsson Stanford University 10. Joao Costa Institute Jozef Stefan 11. Justin Curry University of Pennsylvania 12. Isabel Darcy University of Iowa 13. Sarah Day College of William and Mary 14. Vin de Silva Pomona College 15. Tamal Dey The Ohio State University 16. Barbara Di Fabio University of Bologna 17. Pawel Dlotko University of Pennsylvania 18. Carlos Dominguez PIMS-UBC 19. Raouf Dridi UBC 20. Kevin Emmett Columbia University 21. Jeff Erickson University of Illinois, Urbana-Champaign 22. Lisbeth Fajstrup Aalborg University 23. Eugene Ha Springer 24. Greg Henselman University of Pennsylvania 25. Yasuaki Hiraoka Kyushu University 26. Christopher Hoffman University of Washington 27. Ting Chen Leo Hsu University of British Columbia 28. Grzegorz Jablonski Jagiellonian University 29. Etienne Jacques Google 30. John Jardine University of Western Ontario 31. Inga Johnson Willamette University 32. Matthew Kahle Ohio State University 33. Sara Kalisnik Stanford University 1 34. Kevin Knudson University of Florida 35. Siupor Lam Capital Normal University 36. Ryan Lewis Stanford University 37. Anthea Monod Technion-Israel Institute of Technology 38. Marian Mrozek Jagiellonian University 39. Sayan Mukherjee Duke University 40. Elizabeth Munch University of Minnesota 41. Dimitri Papadimitriou Bell Labs 42. Amit Patel University of Minnesota 43. Florian Pausinger IST Austria 44. Jose Perea Duke University 45. Raul Rabadan Columbia University 46. Saeed Rahmati Thompson Rivers University 47. Martin Raussen Aalborg University 48. Vanessa Robins The Australian National University 49. Michael Robinson American University 50. Galo Rojo UBC 51. Ruben Sanchez-Garcia University of Southampton 52. Daniela Egas-Santander University of Bonn 53. Soumen Sarkar University of Regina 54. Radmila Sazdanovic NCSU & IMA 55. Robert Scharein Hypnagogic Software 56. Jonathan Scott Cleveland State University 57. Donald Sheehy University of Connecticut 58. Robert Short Lehigh University 59. Primoz Skraba Jozef Stefan Institute 60. Gard Spreemann Norwegian University of Science and Technology 61. Don Stanley University of Regina 62. Hiro Lee Tanaka Harvard University 63. Katharine Turner University of Chicago 64. Mikael Vejdemo Johansson Jozef Stefan Institute 65. Bernardo Villarreal University of British Columbia 66. Paul Villoutreix Stanford 67. Liqiu Wang The University of Hong Kong 68. Matthew Wright University of Minnesota Updated May 22, 2014 2 .

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Topological Pattern Recognition for Point Cloud Data∗
Acta Numerica (2014), pp. 289–368 c Cambridge University Press, 2014 doi:10.1017/S0962492914000051 Printed in the United Kingdom Topological pattern recognition for point cloud data∗ Gunnar Carlsson† Department of Mathematics, Stanford University, CA 94305, USA E-mail: [email protected] In this paper we discuss the adaptation of the methods of homology from algebraic topology to the problem of pattern recognition in point cloud data sets. The method is referred to as persistent homology, and has numerous applications to scientific problems. We discuss the definition and computation of homology in the standard setting of simplicial complexes and topological spaces, then show how one can obtain useful signatures, called barcodes, from finite metric spaces, thought of as sampled from a continuous object. We present several different cases where persistent homology is used, to illustrate the different ways in which the method can be applied. CONTENTS 1 Introduction 289 2 Topology 293 3 Shape of data 311 4 Structures on spaces of barcodes 331 5 Organizing data sets 343 References 365 1. Introduction Deriving knowledge from large and complex data sets is a fundamental prob- lem in modern science. All aspects of this problem need to be addressed by the mathematical and computational sciences. There are various dif- ferent aspects to the problem, including devising methods for (a) storing massive amounts of data, (b) efficiently managing it, and (c) developing un- derstanding of the data set. The past decade has seen a great deal of devel- opment of powerful computing infrastructure, as well as methodologies for ∗ Colour online for monochrome figures available at journals.cambridge.org/anu.
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Gunnar Carlsson Professor, Department of Mathematics Stanford University
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John Gunnar Carlsson Epstein Department of Industrial And
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