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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. -
M-Adic Perturbations in Noetherian Local Rings
Perturbations in Noetherian Local Rings m-adic Perturbations in Noetherian Local Rings Nick Cox-Steib [email protected] University of Missouri Abstract We develop new methods to study m-adic stability in an arbitrary Noetherian local ring. These tech- niques are used to prove results about the behavior of Hilbert-Samuel and Hilbert-Kunz multiplicities under fine m-adic perturbations. 1 Introduction The topic of this paper involves comparing a fixed ideal, I =( f1,..., fc) = f , inside a Noetherian local ring, (R,m ), with ideals of the form ( f + ε , f + ε ,..., f + ε ) = f + ε , where ε ,...,ε are in R 1 1 2 2 c c 1 c some large power of the maximal ideal of R. When it is in the interest of clarity and space and the ideal I is understood, we often use the notation M M M M := = , and M := IM f M ( f +ε) f + ε M where M is an R-module. We will refer to the ideals f + ε , as mR-adic perturbations of I, and, more generally, we may also speak of the quotients M as perturbations of M. At the most basic level, we ( f +ε) want to understand the relationship between I and its perturbations. Recent interest in these problems stems from their relationship to the deformation of properties. This arXiv:2011.08044v2 [math.AC] 14 Dec 2020 relationship has been formalized in a recent paper by De Stefani and Smirnov with the concept of m-adic stability [SS20]. A property, P, of Noetherian local rings is m-adically stable if it is stable under sufficiently small perturbations of ideals generated by a regular element — that is, for every regular element f in a Noetherian local ring (R,m) such that R/( f ) has property P, there is an N ∈ N such that R/( f + ε) also has property P for all ε ∈ mN. -
Topology and Data
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 46, Number 2, April 2009, Pages 255–308 S 0273-0979(09)01249-X Article electronically published on January 29, 2009 TOPOLOGY AND DATA GUNNAR CARLSSON 1. Introduction An important feature of modern science and engineering is that data of various kinds is being produced at an unprecedented rate. This is so in part because of new experimental methods, and in part because of the increase in the availability of high powered computing technology. It is also clear that the nature of the data we are obtaining is significantly different. For example, it is now often the case that we are given data in the form of very long vectors, where all but a few of the coordinates turn out to be irrelevant to the questions of interest, and further that we don’t necessarily know which coordinates are the interesting ones. A related fact is that the data is often very high-dimensional, which severely restricts our ability to visualize it. The data obtained is also often much noisier than in the past and has more missing information (missing data). This is particularly so in the case of biological data, particularly high throughput data from microarray or other sources. Our ability to analyze this data, both in terms of quantity and the nature of the data, is clearly not keeping pace with the data being produced. In this paper, we will discuss how geometry and topology can be applied to make useful contributions to the analysis of various kinds of data. -
Algebra & Number Theory Vol. 7 (2013)
Algebra & Number Theory Volume 7 2013 No. 3 msp Algebra & Number Theory msp.org/ant EDITORS MANAGING EDITOR EDITORIAL BOARD CHAIR Bjorn Poonen David Eisenbud Massachusetts Institute of Technology University of California Cambridge, USA Berkeley, USA BOARD OF EDITORS Georgia Benkart University of Wisconsin, Madison, USA Susan Montgomery University of Southern California, USA Dave Benson University of Aberdeen, Scotland Shigefumi Mori RIMS, Kyoto University, Japan Richard E. Borcherds University of California, Berkeley, USA Raman Parimala Emory University, USA John H. Coates University of Cambridge, UK Jonathan Pila University of Oxford, UK J-L. Colliot-Thélène CNRS, Université Paris-Sud, France Victor Reiner University of Minnesota, USA Brian D. Conrad University of Michigan, USA Karl Rubin University of California, Irvine, USA Hélène Esnault Freie Universität Berlin, Germany Peter Sarnak Princeton University, USA Hubert Flenner Ruhr-Universität, Germany Joseph H. Silverman Brown University, USA Edward Frenkel University of California, Berkeley, USA Michael Singer North Carolina State University, USA Andrew Granville Université de Montréal, Canada Vasudevan Srinivas Tata Inst. of Fund. Research, India Joseph Gubeladze San Francisco State University, USA J. Toby Stafford University of Michigan, USA Ehud Hrushovski Hebrew University, Israel Bernd Sturmfels University of California, Berkeley, USA Craig Huneke University of Virginia, USA Richard Taylor Harvard University, USA Mikhail Kapranov Yale University, USA Ravi Vakil Stanford University, -
Annual Meeting of Court Governance Team Governance & Executive Support
4 December 2020 Annual Meeting of Court Governance Team Governance & Executive Support Page 1 of 140 UNIVERSITY OF BRISTOL MEETING OF COURT: 4 DECEMBER 2020 AGENDA 1000 1. Welcome Verbal Chancellor 1005 2. Report of the Vice-Chancellor Verbal & Presentation Vice-Chancellor 1030 3. Update on the 2019 meeting: Global CRT/20-21/001 DVC & Provost Civic University Paper & Presentation 1040 4. Report of the Board of Trustees CRT/20-21/002 Chair of Board Verbal 1045 5. Annual Report and Financial CRT/20-21/003 Chief Operating Statements 2019/20 Officer To Note 1045 6. Minutes of the Annual Meeting 2019 CRT/20-21/004 Chancellor Members are asked to raise any issues or To Approve questions with the minutes in advance of the meeting. Please provide comment to [email protected]. 1050 7. Open Forum Question Time Verbal Vice-Chancellor & Senior Team 1130 Close Page 2 of 140 UNIVERSITY COURT MEETING DATE 04/12/2020 REPORT TITLE Bristol as a Global Civic University: Update CLASSIFICATION OPEN ☐ CONFIDENTIAL ☒ STRICTLY CONFIDENTIAL ☐ Report Authors: Job Titles: Guy Orpen Deputy Vice-Chancellor, New Campus Development Jon Hunt Executive Director, Research & Enterprise Development (RED ) John McWilliams Director of Business and Civic Engagement, RED Ellie Cripps Public Engagement Manager, RED. Sponsored by: Judith Squires Job Title: Deputy Vice-Chancellor and Provost To Note ☒ For discussion: ☐ Court is asked to: 1. NOTE the progress in this area. This paper will be supported by a presentation from the DVC & Provost 2. FEEDBACK as desired on the progress made to [email protected]. Court members may also wish to raise questions during the Open Forum Question Time. -
UNIVERSITY of WARWICK Minutes of the Meeting of the Steering Committee Held on 13 September 2004 Present: Vice-Chancellor (Chair
UNIVERSITY OF WARWICK Minutes of the meeting of the Steering Committee held on 13 September 2004 Present: Vice-Chancellor (Chair) Professor Y Carter Professor R Dyson Professor J Jones Professor M Whitby Professor M Luntley Professor A McFarlane Professor M McCrae Mr S Lucas Apologies: Deputy Vice-Chancellor, Professor H Thomas, Professor I Lauder, Professor A Easton. In Attendance: Professor A Caesar, Professor L Bridges, Academic Registrar, Director of Finance, Registrar, University Secretary, Ms N Snodgrass, for item 560/03-04 Dr C Sparrow. The Vice-Chancellor welcomed Professor A Caesar, the incoming Chair of the Board of the Faculty of Arts, to her first meeting of the Committee. 558/03-04 Minutes RESOLVED: (a) That the minutes of the meeting held on 23 August 2004 be approved. (b) That the minutes of the meeting held on 6 September be approved, subject to amendment to minute 549(g)/03-04 as follows (amendment underlined): That fees charged for market-based courses could be set temporarily below the University standard fee on the launch of new courses in order to attract recruits but that, after a given period of time, fees be brought in line with standard courses, as a minimum. 559/03-04 Vice-Chancellor’s Business RECEIVED: Oral reports from the Vice-Chancellor on the following: (a) His attendance at the AC21 International Forum in Sydney and his view that the University should seek to host the third International Forum of AC21 in 2006 pending formal agreement from Advantage West Midlands to the provision of funding to support the Forum and the submission of a further report from the International Office. -
Program of the Sessions San Diego, California, January 9–12, 2013
Program of the Sessions San Diego, California, January 9–12, 2013 AMS Short Course on Random Matrices, Part Monday, January 7 I MAA Short Course on Conceptual Climate Models, Part I 9:00 AM –3:45PM Room 4, Upper Level, San Diego Convention Center 8:30 AM –5:30PM Room 5B, Upper Level, San Diego Convention Center Organizer: Van Vu,YaleUniversity Organizers: Esther Widiasih,University of Arizona 8:00AM Registration outside Room 5A, SDCC Mary Lou Zeeman,Bowdoin upper level. College 9:00AM Random Matrices: The Universality James Walsh, Oberlin (5) phenomenon for Wigner ensemble. College Preliminary report. 7:30AM Registration outside Room 5A, SDCC Terence Tao, University of California Los upper level. Angles 8:30AM Zero-dimensional energy balance models. 10:45AM Universality of random matrices and (1) Hans Kaper, Georgetown University (6) Dyson Brownian Motion. Preliminary 10:30AM Hands-on Session: Dynamics of energy report. (2) balance models, I. Laszlo Erdos, LMU, Munich Anna Barry*, Institute for Math and Its Applications, and Samantha 2:30PM Free probability and Random matrices. Oestreicher*, University of Minnesota (7) Preliminary report. Alice Guionnet, Massachusetts Institute 2:00PM One-dimensional energy balance models. of Technology (3) Hans Kaper, Georgetown University 4:00PM Hands-on Session: Dynamics of energy NSF-EHR Grant Proposal Writing Workshop (4) balance models, II. Anna Barry*, Institute for Math and Its Applications, and Samantha 3:00 PM –6:00PM Marina Ballroom Oestreicher*, University of Minnesota F, 3rd Floor, Marriott The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 34, Issue 1 of Abstracts is ten minutes. -
Proceedings of the Conference on Promoting Undergraduate Research in Mathematics Proceedings of the Conference on Promoting Undergraduate Research in Mathematics
In the span of twenty years, research in Proceedings mathematics by undergraduates has gone from rare to commonplace. To examine Promoting Undergraduate Research in Mathematics Gallian, Editor of the and promote this trend, the AMS and Proceedings NSA sponsored a three-day conference Conference in September 2006 to bring together of the mathematicians who were involving on Promoting undergraduates across the country in Conference on mathematics research to exchange ideas, Undergraduate discuss issues of common concern, establish contacts, and gather information Research in that would be of value to others interested Promoting in engaging undergraduates in mathematics Mathematics research. The conference featured plenary talks, panel discussions, and small group sessions. The topics included summer Undergraduate research programs, academic year research Joseph A. Gallian opportunities, diversity issues, assessment Editor methods, and perspectives from alumni Research in of research programs. This volume is the proceedings of that conference. Mathematics Joseph A. Gallian Editor AMS on the Web PURM/GALLIAN2 www.ams.org AMS 472 pages • Spine Width: 7/8 inch • Two Color Cover: This plate PMS 4515 (Beige) This plate PMS 323 (Teal) Proceedings of the Conference on Promoting Undergraduate Research in Mathematics Proceedings of the Conference on Promoting Undergraduate Research in Mathematics Joseph A. Gallian Editor American Mathematical Society Providence, Rhode Island Cover photography courtesy of Cindy Wyels, CSU Channel Islands, Camarillo, CA, and Darren Narayan, Rochester Institute of Technology, Rochester, NY. This material is based upon work supported by National Security Agency under grant H98230-06-1-0095. ISBN-13: 978-0-8218-4321-5 ISBN-10: 0-8218-4321-4 Copyright c 2007 American Mathematical Society Printed in the United States of America. -
Supporting Staff International Mobility Professor Bob Gilmour
Supporting Staff International Mobility Professor Bob Gilmour REALISE workshop May 1st 2019 Overview • Context ? – Why should I? – What is in it for me? • Mobility data • Challenges and overcoming them • REALISE at GCU • Examples showing benefits/impacts • Summary Why? On your smart phones Google search Socrative Student Student Login (can select language) Insert “Gilmour2787” into room name Follow the instructions (Enter your name) Do not log off The why question • Socrative 1 • What’s in it for me? What are your staff mobility data at your univ • Socrative s2 What do we know about staff mobility in the UK? • Returns for Erasmus staff funding • Available at (2014-2017) https://www.erasmusplus.org.uk/statistics • Returns for non Erasmus staff funding? Table 1. Outgoing staff numbers by sending institution 2014/15 2015/16 2016/17 Total Cumulative Institution Name Country Teach Train Total Teach Train Total Teach Train Total Teach Train Total 1Coventry University England 74 11 85 34 53 87 42 27 69 150 91 241 2University Of Portsmouth Higher Education Corporation England 44 10 54 34 39 73 44 27 71 122 76 198 3The University Of Hertfordshire Higher Education Corporation England 37 12 49 44 18 62 26 31 57 107 61 168 4The University Of Edinburgh Scotland 20 4 24 31 9 40 54 46 100 105 59 164 5Birmingham City University England 30 8 38 35 33 68 44 12 56 109 53 162 6Middlesex University Higher Education Corporation England 24 17 41 35 30 65 33 19 52 92 66 158 7The University Of The Arts London England 13 32 45 22 39 61 11 40 51 46 111 157 8The -
Commutative Algebra Provides a Big Surprise for Craig Huneke's Birthday
CÓÑÑÙØaØiÚe aÐgebÖa ÔÖÓÚide× a big ×ÙÖÔÖi×e fÓÖ CÖaig ÀÙÒeke³× biÖØhdaÝ Irena Swanson Communicated by Tom Garrity A commutative algebra conference in July, 2016, on the occasion of Craig Huneke’s 65th birthday, included a major mathematical surprise. Craig Huneke has been at the forefront of research in commutative algebra, introducing and advancing several influential notions, such as d-sequences, licci ideals, symbolic powers, homological methods, computational methods, tight closure, uniform bounds, and prime characteristic methods. He has mentored 24 PhD students and many postdocs; he has co-organized conferences, such as the Kansas-Missouri-Nebraska KUMUNU commutative algebra conference; he has served on the Executive Committee of the AMS and on the Board of Trustees of the MSRI. Almost all the talks were directly related to Huneke’s work, and most speakers started their talks describing how Huneke affected their work as a mathematician and as a person; they talked about his mathematical productivity, extensive collaborations, productive and precious lunches with napkin notes, excellent and influential talks, his advising, mentoring, his friendly competitiveness, and so on. Claudia Polini addressed how commutative algebra in general is friendly to women (possibly due to Emmy Noether being one of us), and in particular how Huneke has been a tremendous role model as a teacher, collaborator, mentor, and organizer. His own family life, with wife Edith Clowes, Professor of Slavic Languages and Literatures, and their children Sam and Ned, has been a shining example for possibilities in home and professional life for women in academia. During the banquet, Hochster read his poem honoring Huneke. -
Georgian Court University Fall/Winter 2018 Magazine
Volume 16 | Number 1 Fall/Winter 2018 Georgian Court University Magazine President’s Annual Report & Honor Roll of Donors 2017–2018 Georgian Court–Hackensack Meridian Health School of Nursing Celebrates 10 Years From the President Dear Alumni, Donors, Students, and Friends: Happy New Year! The holiday season is behind us, but the activities and accolades of 2018 still give us to plenty to celebrate. That is why this edition of GCU Magazine is packed with examples of good news worth sharing—with you and with those you know. First, the Georgian Court–Hackensack Meridian Health School of Nursing is celebrating its 10-year anniversary. Our first decade has produced successful health care professionals serving patients from coast to coast, and the program is among the fastest growing at GCU. In this issue of the magazine, I’d like you to meet two unforgettable alumni. Florence “Riccie” Riccobono Johnson ’45 (pp. 28–29) has worked at CBS for more than six decades and reflects on her time at 60 Minutes, where she’s been employed since 1968. Gemma Brennan ’84, ’93 (pp. 6–9), a longtime teacher, principal, and part-time GCU professor, is sharing her passion in unique ways. Likewise, our newest honorary degree recipient, His Royal Highness The Prince Edward, Earl of Wessex, shared his passion for court tennis during a September visit to GCU (p. 13). Georgian Court was at its absolute finest as the prince met students, faculty, staff, and coaches, and played several matches in the Casino. A few weeks later, I was proud to see alumni join in the fun of Reunion and Homecoming Weekend 2018 (p. -
UNIVERSITY of ABERDEEN UNIVERSITY COURT Minutes Of
UNIVERSITY OF ABERDEEN UNIVERSITY COURT Minutes of Meeting held on 5 November 2002 Present: Mr A Mair (in the Chair), Principal, Mr D Cockburn, Dr A Dawson, Mr H Duncan, Professor G Graham, Miss A Harper, Cllr P Johnston, Dr P Kinnear, Mr J Leiper, Professor S Logan, Professor B MacGregor, Dr M Mackie, Dr N Milne, Dr G Roberts, Professor T Salmon, Professor J Sewel, Mr C Sheldon, Professor W Smith, Mr G Stevenson, Professor I Torrance with Professor D Houlihan, Professor A Rodger, Ms C Macaslan, Mr S Cannon, Ms I Bews, Mr A Donaldson, Mrs C Inglis, Dr P Murray, Mr B Purdon Mr R Taylor, and Mrs H Stephen (Clerk). Mr Mair welcomed Mr Chris Sheldon who was attending his first meeting as one of the two Assessors appointed by the Rector. He also welcomed Mr J Daube, Head of Manchester Community Technical College, Connecticut, who was attending as an observer. Mr Mair congratulated Professor Torrance on his nomination as the next Moderator of the General Assembly of the Church of Scotland. Mr Mair congratulated the Faculty of Medicine & Medical Sciences on the success of the Institute of Medical Sciences and the IMS building in which the Court was meeting that day. Apologies for absence were received from The Rector, Mr A Amoore, Lady Catto, Cllr D Clyne, Dr N Dower, Mr M Lockhead and Mr D Marr. MINUTES 28 The Minutes of meeting held on 17 September 2002 were approved. STATEMENT BY PRINCIPAL 29 The Principal referred to a number of current issues in the higher education sector, including top-up fees and merger talks between London institutions, the recent report from the Scottish Executive Committee on Lifelong Learning, the forthcoming report of the ministerial review of the Scottish system and the White Paper on higher education in England.