David Donoho COMMENTARY 52 Cliff Ord J
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Daily U.S. Virus Cases Climb to Highest Level Since August
P2JW290000-6-A00100-17FFFF5178F ****** FRIDAY,OCTOBER 16,2020~VOL. CCLXXVI NO.91 WSJ.com HHHH $4.00 DJIA 28494.20 g 19.80 0.1% NASDAQ 11713.87 g 0.5% STOXX 600 362.91 g 2.1% 10-YR. TREAS. g 3/32 , yield 0.730% OIL $40.96 g $0.08 GOLD $1,903.20 À $1.90 EURO $1.1709 YEN 105.45 Trump and Biden Field Questions in Dueling TV Forums Jobless What’s News Claims Point to Business&Finance Slowing ew jobless-benefits ap- Nplications rose last week to the highest level sincelate Rebound August, as fresh layoffs add to other signs the economic GES recovery is losing steam IMA New applications amid the pandemic. A1 GETTY reach a recent high, Softwareexecutive Rob- SE/ adding to signs of a ert T. Brockman wascharged with hiding about $2 billion cooling recovery in income from U.S. taxau- ANCE-PRES FR thorities over 20 years. A1 BY SARAH CHANEY ENCE LVMH said strong growth AG AND GWYNN GUILFORD at itsbiggest fashion brands ON/ buoyedquarterly revenue, TS Thenumber of people in partly offsetting steep drops WA the U.S. filing newapplications in other luxurysegments. B1 JIM forunemployment benefits S; rose last week to the highest MorgaN Stanley said its PRES level sincelateAugust, as third-quarter profit rose 25%, TED fresh layoffs add to other signs another big U.S. bank to CIA SO the economic recovery is los- skateunscathed through the AS ing steam amid the pandemic. rockiest economyinyears. B1 CI/ Claims increased to Petrochemical makers VUC 898,000 last week,holding AN are pausing multibillion- EV well abovethe pre-pandemic dollar U.S. -
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. -
Geometric Measure Theory and the Calculus of Variations PROCEEDINGS of SYMPOSIA in PURE MATHEMATICS Volume 44
http://dx.doi.org/10.1090/pspum/044 Geometric Measure Theory and the Calculus of Variations PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS Volume 44 Geometric Measure Theory and the Calculus of Variations William K. Allard and Frederick J. Almgren, Jr., Editors AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND PROCEEDINGS OF THE SUMMER INSTITUTE ON GEOMETRIC MEASURE THEORY AND THE CALCULUS OF VARIATIONS HELD AT HUMBOLDT STATE UNIVERSITY ARCATA, CALIFORNIA JULY 16-AUGUST 3, 1984 with support from the National Science Foundation, Grant DMS-8317890 1980 Mathematics Subject Classification. Primary 49F22, 49F20, 53A10, 53C42; Secondary 49F10, 53C20, 35J65, 58-XX. Library of Congress Cataloging-in-Publication Data Main entry under title: Geometric measure theory and the calculus of variations. (Proceedings of symposia in pure mathematics; v. 44) Includes bibliographies. 1. Geometric measure theory-Addresses, essays, lectures. I. Allard, William K., 1941- II. Almgren, Frederick J. III. Series. QA312.G394 1985 516.3'6 85-18641 ISBN 0-8218-1470-2 (alk. paper) COPYING AND REPRINTING. Individual leaders of this publication, and nonprofit libraries acting for them are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this pubUcation in reviews provided the customary acknowledgement of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Executive Director, American Mathemat ical Society, P.O. Box 6248, Providence, Rhode Island 02940. -
Jeffrey Hoffstein Jill Pipher Joseph H. Silverman
Undergraduate Texts in Mathematics Je rey Ho stein Jill Pipher Joseph H. Silverman An Introduction to Mathematical Cryptography Second Edition Undergraduate Texts in Mathematics Undergraduate Texts in Mathematics Series Editors: Sheldon Axler San Francisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA Advisory Board: Colin Adams, Williams College, Williamstown, MA, USA Alejandro Adem, University of British Columbia, Vancouver, BC, Canada Ruth Charney, Brandeis University, Waltham, MA, USA Irene M. Gamba, The University of Texas at Austin, Austin, TX, USA Roger E. Howe, Yale University, New Haven, CT, USA David Jerison, Massachusetts Institute of Technology, Cambridge, MA, USA Jeffrey C. Lagarias, University of Michigan, Ann Arbor, MI, USA Jill Pipher, Brown University, Providence, RI, USA Fadil Santosa, University of Minnesota, Minneapolis, MN, USA Amie Wilkinson, University of Chicago, Chicago, IL, USA Undergraduate Texts in Mathematics are generally aimed at third- and fourth- year undergraduate mathematics students at North American universities. These texts strive to provide students and teachers with new perspectives and novel approaches. The books include motivation that guides the reader to an appreciation of interre- lations among different aspects of the subject. They feature examples that illustrate key concepts as well as exercises that strengthen understanding. More information about this series at http://www.springer.com/series/666 Jeffrey Hoffstein • Jill Pipher Joseph -
Investigating Statistical Privacy Frameworks from the Perspective of Hypothesis Testing 234 Able Quantity
Investigating Statistical Privacy Frameworks from the Perspective of Hypothesis Testing 234 able quantity. Only a limited number of previous works which can provide a natural and interpretable guide- [29, 34, 35] have investigated the question of how to line for selecting proper privacy parameters by system select a proper value of ǫ, but these approaches ei- designers and researchers. Furthermore, we extend our ther require complicated economic models or lack the analysis on unbounded DP to bounded DP and the ap- analysis of adversaries with arbitrary auxiliary informa- proximate (ǫ, δ)-DP. tion (see Section 2.3 for more details). Our work is in- Impact of Auxiliary Information. The conjecture spired by the interpretation of differential privacy via that auxiliary information can influence the design of hypothesis testing, initially introduced by Wasserman DP mechanisms has been made in prior work [8, 28, 32, and Zhou [27, 30, 60]. However, this interpretation has 33, 39, 65]. We therefore investigate the adversary’s ca- not been systematically investigated before in the con- pability based on hypothesis testing under three types text of our research objective, i.e., reasoning about the of auxiliary information: the prior distribution of the in- choice of the privacy parameter ǫ (see Section 2.4 for put record, the correlation across records, and the corre- more details). lation across time. Our analysis demonstrates that the We consider hypothesis testing [2, 45, 61] as the tool auxiliary information indeed influences the appropriate used by the adversary to infer sensitive information of selection of ǫ. The results suggest that, when possible an individual record (e.g., the presence or absence of and available, the practitioners of DP should explicitly a record in the database for unbounded DP) from the incorporate adversary’s auxiliary information into the outputs of privacy mechanisms. -
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. -
I. Overview of Activities, April, 2005-March, 2006 …
MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 …......……………………. 2 Innovations ………………………………………………………..... 2 Scientific Highlights …..…………………………………………… 4 MSRI Experiences ….……………………………………………… 6 II. Programs …………………………………………………………………….. 13 III. Workshops ……………………………………………………………………. 17 IV. Postdoctoral Fellows …………………………………………………………. 19 Papers by Postdoctoral Fellows …………………………………… 21 V. Mathematics Education and Awareness …...………………………………. 23 VI. Industrial Participation ...…………………………………………………… 26 VII. Future Programs …………………………………………………………….. 28 VIII. Collaborations ………………………………………………………………… 30 IX. Papers Reported by Members ………………………………………………. 35 X. Appendix - Final Reports ……………………………………………………. 45 Programs Workshops Summer Graduate Workshops MSRI Network Conferences MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 This annual report covers MSRI projects and activities that have been concluded since the submission of the last report in May, 2005. This includes the Spring, 2005 semester programs, the 2005 summer graduate workshops, the Fall, 2005 programs and the January and February workshops of Spring, 2006. This report does not contain fiscal or demographic data. Those data will be submitted in the Fall, 2006 final report covering the completed fiscal 2006 year, based on audited financial reports. This report begins with a discussion of MSRI innovations undertaken this year, followed by highlights -
President's Report
Newsletter Volume 42, No. 5 • SePTemBeR–oCT oBeR 2012 PRESIDENT’S REPORT AWM Prize Winners. I am pleased to announce the winners of two of the three major prizes given by AWM at the Joint Mathematics Meetings (JMM). The Louise Hay Award is given to Amy Cohen, Rutgers University, in recognition of The purpose of the Association her “contributions to mathematics education through her writings, her talks, and for Women in Mathematics is her outstanding service to professional organizations.” The Gweneth Humphreys • to encourage women and girls to Award is given to James Morrow, University of Washington, in recognition of study and to have active careers in his “outstanding achievements in inspiring undergraduate women to discover and the mathematical sciences, and • to promote equal opportunity and pursue their passion for mathematics.” I quote from the citations written by the the equal treatment of women and selection committees and extend warm congratulations to the honorees. These girls in the mathematical sciences. awards will be presented at the Prize Session at JMM 2013 in San Diego. Congratulations to Raman Parimala, Emory University, who will present the AWM Noether Lecture at JMM 2013, entitled “A Hasse Principle for Quadratic Forms over Function Fields.” She is honored for her groundbreaking research in theory of quadratic forms, hermitian forms, linear algebraic groups, and Galois cohomology. The Noether Lecture is the oldest of the three named AWM Lectures. (The Falconer Lecture is presented at MathFest, and the Sonia Kovalevsky at the SIAM Annual Meeting.) The first Noether Lecture was given by F. Jessie MacWilliams in 1980 in recognition of her fundamental contributions to the theory of error correcting codes. -
2008 Annual Report
2008 Annual Report NATIONAL ACADEMY OF ENGINEERING ENGINEERING THE FUTURE 1 Letter from the President 3 In Service to the Nation 3 Mission Statement 4 Program Reports 4 Engineering Education 4 Center for the Advancement of Scholarship on Engineering Education 6 Technological Literacy 6 Public Understanding of Engineering Developing Effective Messages Media Relations Public Relations Grand Challenges for Engineering 8 Center for Engineering, Ethics, and Society 9 Diversity in the Engineering Workforce Engineer Girl! Website Engineer Your Life Project Engineering Equity Extension Service 10 Frontiers of Engineering Armstrong Endowment for Young Engineers-Gilbreth Lectures 12 Engineering and Health Care 14 Technology and Peace Building 14 Technology for a Quieter America 15 America’s Energy Future 16 Terrorism and the Electric Power-Delivery System 16 U.S.-China Cooperation on Electricity from Renewables 17 U.S.-China Symposium on Science and Technology Strategic Policy 17 Offshoring of Engineering 18 Gathering Storm Still Frames the Policy Debate 20 2008 NAE Awards Recipients 22 2008 New Members and Foreign Associates 24 2008 NAE Anniversary Members 28 2008 Private Contributions 28 Einstein Society 28 Heritage Society 29 Golden Bridge Society 29 Catalyst Society 30 Rosette Society 30 Challenge Society 30 Charter Society 31 Other Individual Donors 34 The Presidents’ Circle 34 Corporations, Foundations, and Other Organizations 35 National Academy of Engineering Fund Financial Report 37 Report of Independent Certified Public Accountants 41 Notes to Financial Statements 53 Officers 53 Councillors 54 Staff 54 NAE Publications Letter from the President Engineering is critical to meeting the fundamental challenges facing the U.S. economy in the 21st century. -
Re-: an Errant Glossary
RE- Cultural Inquiry EDITED BY CHRISTOPH F. E. HOLZHEY AND MANUELE GRAGNOLATI The series ‘Cultural Inquiry’ is dedicated to exploring how di- verse cultures can be brought into fruitful rather than pernicious confrontation. Taking culture in a deliberately broad sense that also includes different discourses and disciplines, it aims to open up spaces of inquiry, experimentation, and intervention. Its em- phasis lies in critical reflection and in identifying and highlight- ing contemporary issues and concerns, even in publications with a historical orientation. Following a decidedly cross-disciplinary approach, it seeks to enact and provoke transfers among the hu- manities, the natural and social sciences, and the arts. The series includes a plurality of methodologies and approaches, binding them through the tension of mutual confrontation and negoti- ation rather than through homogenization or exclusion. Christoph F. E. Holzhey is the Founding Director of the ICI Berlin Institute for Cultural Inquiry. Manuele Gragnolati is Pro- fessor of Italian Literature at the Sorbonne Université in Paris and Associate Director of the ICI Berlin. RE- An Errant Glossary EDITED BY CHRISTOPH F. E. HOLZHEY ANDARNDWEDEMEYER ISBN (Print): 978-3-96558-000-8 ISBN (PDF): 978-3-96558-001-5 ISBN (EPUB): 978-3-96558-002-2 DOI: 10.25620/ci-15 Bibliographical Information of the German National Library The German National Library lists this publication in the Deutsche Nationalbibliografie (German National Bibliography); detailed bibliographic information is available online at http://dnb.d-nb.de. © 2019 ICI Berlin. Copyright of individual chapters is maintained by the chapter’s author. Cover design: Studio Bens with a photograph by Claudia Peppel This publication is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. -
The Geometry of Asymptotically Hyperbolic Manifolds a Dissertation Submitted to the Department of Mathematics and the Committee
THE GEOMETRY OF ASYMPTOTICALLY HYPERBOLIC MANIFOLDS A DISSERTATION SUBMITTED TO THE DEPARTMENT OF MATHEMATICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Otis Chodosh June 2015 © 2015 by Otis Avram Chodosh. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/mp634xn8004 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Simon Brendle, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Michael Eichmair, Co-Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Leon Simon I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Brian White Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost for Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. -
Meetings & Conferences of the AMS, Volume 49, Number 5
Meetings & Conferences of the AMS IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website.See http://www.ams.org/meetings/. Programs and abstracts will continue to be displayed on the AMS website in the Meetings and Conferences section until about three weeks after the meeting is over. Final programs for Sectional Meetings will be archived on the AMS website in an electronic issue of the Notices as noted below for each meeting. Niky Kamran, McGill University, Wave equations in Kerr Montréal, Quebec geometry. Rafael de la Llave, University of Texas at Austin, Title to Canada be announced. Centre de Recherches Mathématiques, Special Sessions Université de Montréal Asymptotics for Random Matrix Models and Their Appli- cations, Nicholas M. Ercolani, University of Arizona, and May 3–5, 2002 Kenneth T.-R. McLaughlin, University of North Carolina at Chapel Hill and University of Arizona. Meeting #976 Combinatorial Hopf Algebras, Marcelo Aguiar, Texas A&M Eastern Section University, and François Bergeron and Christophe Associate secretary: Lesley M. Sibner Reutenauer, Université du Québec á Montréal. Announcement issue of Notices: March 2002 Combinatorial and Geometric Group Theory, Olga G. Khar- Program first available on AMS website: March 21, 2002 lampovich, McGill University, Alexei Myasnikov and Program issue of electronic Notices: May 2002 Vladimir Shpilrain, City College, New York, and Daniel Issue of Abstracts: Volume 23, Issue 3 Wise, McGill University. Commutative Algebra and Algebraic Geometry, Irena Deadlines Peeva, Cornell University, and Hema Srinivasan, Univer- For organizers: Expired sity of Missouri-Columbia.