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On the Circuit Diameter Conjecture
On the Circuit Diameter Conjecture Steffen Borgwardt1, Tamon Stephen2, and Timothy Yusun2 1 University of Colorado Denver [email protected] 2 Simon Fraser University {tamon,tyusun}@sfu.ca Abstract. From the point of view of optimization, a critical issue is relating the combina- torial diameter of a polyhedron to its number of facets f and dimension d. In the seminal paper of Klee and Walkup [KW67], the Hirsch conjecture of an upper bound of f − d was shown to be equivalent to several seemingly simpler statements, and was disproved for unbounded polyhedra through the construction of a particular 4-dimensional polyhedron U4 with 8 facets. The Hirsch bound for bounded polyhedra was only recently disproved by Santos [San12]. We consider analogous properties for a variant of the combinatorial diameter called the circuit diameter. In this variant, the walks are built from the circuit directions of the poly- hedron, which are the minimal non-trivial solutions to the system defining the polyhedron. We are able to prove that circuit variants of the so-called non-revisiting conjecture and d-step conjecture both imply the circuit analogue of the Hirsch conjecture. For the equiva- lences in [KW67], the wedge construction was a fundamental proof technique. We exhibit why it is not available in the circuit setting, and what are the implications of losing it as a tool. Further, we show the circuit analogue of the non-revisiting conjecture implies a linear bound on the circuit diameter of all unbounded polyhedra – in contrast to what is known for the combinatorial diameter. Finally, we give two proofs of a circuit version of the 4-step conjecture. -
Gromov Receives 2009 Abel Prize
Gromov Receives 2009 Abel Prize . The Norwegian Academy of Science Medal (1997), and the Wolf Prize (1993). He is a and Letters has decided to award the foreign member of the U.S. National Academy of Abel Prize for 2009 to the Russian- Sciences and of the American Academy of Arts French mathematician Mikhail L. and Sciences, and a member of the Académie des Gromov for “his revolutionary con- Sciences of France. tributions to geometry”. The Abel Prize recognizes contributions of Citation http://www.abelprisen.no/en/ extraordinary depth and influence Geometry is one of the oldest fields of mathemat- to the mathematical sciences and ics; it has engaged the attention of great mathema- has been awarded annually since ticians through the centuries but has undergone Photo from from Photo 2003. It carries a cash award of revolutionary change during the last fifty years. Mikhail L. Gromov 6,000,000 Norwegian kroner (ap- Mikhail Gromov has led some of the most impor- proximately US$950,000). Gromov tant developments, producing profoundly original will receive the Abel Prize from His Majesty King general ideas, which have resulted in new perspec- Harald at an award ceremony in Oslo, Norway, on tives on geometry and other areas of mathematics. May 19, 2009. Riemannian geometry developed from the study Biographical Sketch of curved surfaces and their higher-dimensional analogues and has found applications, for in- Mikhail Leonidovich Gromov was born on Decem- stance, in the theory of general relativity. Gromov ber 23, 1943, in Boksitogorsk, USSR. He obtained played a decisive role in the creation of modern his master’s degree (1965) and his doctorate (1969) global Riemannian geometry. -
Diameter of Simplicial Complexes, a Computational Approach
University of Cantabria Master’s thesis. Masters degree in Mathematics and Computing Diameter of simplicial complexes, a computational approach Author: Advisor: Francisco Criado Gallart Francisco Santos Leal 2015-2016 This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Desvarío laborioso y empobrecedor el de componer vastos libros; el de explayar en quinientas páginas una idea cuya perfecta exposición oral cabe en pocos minutos. Mejor procedimiento es simular que esos libros ya existen y ofrecer un resumen, un comentario. Borges, Ficciones Acknowledgements First, I would like to thank my advisor, professor Francisco Santos. He has been supportive years before I arrived in Santander, and even more when I arrived. Also, I want to thank professor Michael Joswig and his team in the discrete ge- ometry group of the Technical University of Berlin, for all the help and advice that they provided during my (short) visit to their department. Finally, I want to thank my friends at Cantabria, and my “disciples”: Álvaro, Ana, Beatriz, Cristina, David, Esther, Jesús, Jon, Manu, Néstor, Sara and Susana. i Diameter of simplicial complexes, a computational approach Abstract The computational complexity of the simplex method, widely used for linear program- ming, depends on the combinatorial diameter of the edge graph of a polyhedron with n facets and dimension d. Despite its popularity, little is known about the (combinatorial) diameter of polytopes, and even for simpler types of complexes. For the case of polytopes, it was conjectured by Hirsch (1957) that the diameter is smaller than (n − d), but this was disproved by Francisco Santos (2010). -
Tools for Tutoring Theoretical Computer Science Topics
University of Massachusetts Amherst ScholarWorks@UMass Amherst Doctoral Dissertations Dissertations and Theses November 2019 Tools for Tutoring Theoretical Computer Science Topics Mark McCartin-Lim University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/dissertations_2 Part of the Artificial Intelligence and Robotics Commons, Graphics and Human Computer Interfaces Commons, Other Computer Sciences Commons, and the Theory and Algorithms Commons Recommended Citation McCartin-Lim, Mark, "Tools for Tutoring Theoretical Computer Science Topics" (2019). Doctoral Dissertations. 1797. https://doi.org/10.7275/15233091 https://scholarworks.umass.edu/dissertations_2/1797 This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. TOOLS FOR TUTORING THEORETICAL COMPUTER SCIENCE TOPICS A Dissertation Presented by MARK MCCARTIN-LIM Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY September 2019 College of Information and Computer Sciences c Copyright by Mark McCartin-Lim 2019 All Rights Reserved TOOLS FOR TUTORING THEORETICAL COMPUTER SCIENCE TOPICS A Dissertation Presented by MARK MCCARTIN-LIM Approved as to style and content by: Andrew McGregor, Co-chair Beverly Woolf, Co-chair David Mix Barrington, Member Siman Wong, Member James Allan, Department Chair College of Information and Computer Sciences DEDICATION To the students who faithfully came to my office hours, whose struggles and perseverance inspired this dissertation. To my good friend Lucas, who provided much needed moral support during the hardest times, and who gave me the courage to choose this dissertation topic. -
Ira Sprague Bowen Papers, 1940-1973
http://oac.cdlib.org/findaid/ark:/13030/tf2p300278 No online items Inventory of the Ira Sprague Bowen Papers, 1940-1973 Processed by Ronald S. Brashear; machine-readable finding aid created by Gabriela A. Montoya Manuscripts Department The Huntington Library 1151 Oxford Road San Marino, California 91108 Phone: (626) 405-2203 Fax: (626) 449-5720 Email: [email protected] URL: http://www.huntington.org/huntingtonlibrary.aspx?id=554 © 1998 The Huntington Library. All rights reserved. Observatories of the Carnegie Institution of Washington Collection Inventory of the Ira Sprague 1 Bowen Papers, 1940-1973 Observatories of the Carnegie Institution of Washington Collection Inventory of the Ira Sprague Bowen Paper, 1940-1973 The Huntington Library San Marino, California Contact Information Manuscripts Department The Huntington Library 1151 Oxford Road San Marino, California 91108 Phone: (626) 405-2203 Fax: (626) 449-5720 Email: [email protected] URL: http://www.huntington.org/huntingtonlibrary.aspx?id=554 Processed by: Ronald S. Brashear Encoded by: Gabriela A. Montoya © 1998 The Huntington Library. All rights reserved. Descriptive Summary Title: Ira Sprague Bowen Papers, Date (inclusive): 1940-1973 Creator: Bowen, Ira Sprague Extent: Approximately 29,000 pieces in 88 boxes Repository: The Huntington Library San Marino, California 91108 Language: English. Provenance Placed on permanent deposit in the Huntington Library by the Observatories of the Carnegie Institution of Washington Collection. This was done in 1989 as part of a letter of agreement (dated November 5, 1987) between the Huntington and the Carnegie Observatories. The papers have yet to be officially accessioned. Cataloging of the papers was completed in 1989 prior to their transfer to the Huntington. -
Prvních Deset Abelových Cen Za Matematiku
Prvních deset Abelových cen za matematiku The first ten Abel Prizes for mathematics [English summary] In: Michal Křížek (author); Lawrence Somer (author); Martin Markl (author); Oldřich Kowalski (author); Pavel Pudlák (author); Ivo Vrkoč (author); Hana Bílková (other): Prvních deset Abelových cen za matematiku. (English). Praha: Jednota českých matematiků a fyziků, 2013. pp. 87–88. Persistent URL: http://dml.cz/dmlcz/402234 Terms of use: © M. Křížek © L. Somer © M. Markl © O. Kowalski © P. Pudlák © I. Vrkoč Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz Summary The First Ten Abel Prizes for Mathematics Michal Křížek, Lawrence Somer, Martin Markl, Oldřich Kowalski, Pavel Pudlák, Ivo Vrkoč The Abel Prize for mathematics is an international prize presented by the King of Norway for outstanding results in mathematics. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) who found that there is no explicit formula for the roots of a general polynomial of degree five. The financial support of the Abel Prize is comparable with the Nobel Prize, i.e., about one million American dollars. Niels Henrik Abel (1802–1829) M. Křížek a kol.: Prvních deset Abelových cen za matematiku, JČMF, Praha, 2013 87 Already in 1899, another famous Norwegian mathematician Sophus Lie proposed to establish an Abel Prize, when he learned that Alfred Nobel would not include a prize in mathematics among his five proposed Nobel Prizes. -
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 -
Mori Dream Spaces and Birational Rigidity of Fano 3-Folds
Ahmadinezhad, H., & Zucconi, F. (2016). Mori dream spaces and birational rigidity of Fano 3-folds. Advances in Mathematics, 292, 410- 445. https://doi.org/10.1016/j.aim.2016.01.008 Peer reviewed version Link to published version (if available): 10.1016/j.aim.2016.01.008 Link to publication record in Explore Bristol Research PDF-document University of Bristol - Explore Bristol Research General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/red/research-policy/pure/user-guides/ebr-terms/ MORI DREAM SPACES AND BIRATIONAL RIGIDITY OF FANO 3-FOLDS HAMID AHMADINEZHAD AND FRANCESCO ZUCCONI Abstract. We highlight a relation between the existence of Sarkisov links and the finite generation of (certain) Cox rings. We introduce explicit methods to use this relation in order to prove birational rigidity statements. To illustrate, we complete the birational rigidity results of Okada for Fano complete intersection 3-folds in singular weighted projective spaces. 1. Introduction Rationality question for varieties covered by rational curves (e.g. unirational varieties) has been a fundamental problem in algebraic geometry, the answer to which has opened various subjects across the field. The first examples of unirational varieties that are irrational were found about the same time by Clemens and Griffiths [10], Iskovskikh and Manin [18], Artin and Mumford [3]. While the results of [10] and [3] indicate that the varieties under study (respectively, a smooth cubic 3-fold and some special singular quartic 3-folds in the weighted projective space P(1; 1; 1; 1; 2)) are irrational, the result in [18] shows that a smooth quartic 3-fold is not birational to any conic bundle or fibration into del 3 Pezzo surfaces, or any other Fano variety, including P , that is to say it is irrational in a strong sense. -
Resource-Competitive Algorithms1 1 Introduction
Resource-Competitive Algorithms1 Michael A. Bender Varsha Dani Department of Computer Science Department of Computer Science Stony Brook University University of New Mexico Stony Brook, NY, USA Albuquerque, NM, USA [email protected] [email protected] Jeremy T. Fineman Seth Gilbert Department of Computer Science Department of Computer Science Georgetown University National University of Singapore Washington, DC, USA Singapore [email protected] [email protected] Mahnush Movahedi Seth Pettie Department of Computer Science Electrical Eng. and Computer Science Dept. University of New Mexico University of Michigan Albuquerque, NM, USA Ann Arbor, MI, USA [email protected] [email protected] Jared Saia Maxwell Young Department of Computer Science Computer Science and Engineering Dept. University of New Mexico Mississippi State University Albuquerque, NM, USA Starkville, MS, USA [email protected] [email protected] Abstract The point of adversarial analysis is to model the worst-case performance of an algorithm. Un- fortunately, this analysis may not always reflect performance in practice because the adversarial assumption can be overly pessimistic. In such cases, several techniques have been developed to provide a more refined understanding of how an algorithm performs e.g., competitive analysis, parameterized analysis, and the theory of approximation algorithms. Here, we describe an analogous technique called resource competitiveness, tailored for dis- tributed systems. Often there is an operational cost for adversarial behavior arising from band- width usage, computational power, energy limitations, etc. Modeling this cost provides some notion of how much disruption the adversary can inflict on the system. In parameterizing by this cost, we can design an algorithm with the following guarantee: if the adversary pays T , then the additional cost of the algorithm is some function of T . -
Hyberbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves CBMS-NSF REGIONAL CONFERENCE SERIES in APPLIED MATHEMATICS
Hyberbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS A series of lectures on topics of current research interest in applied mathematics under the direction of the Conference Board of the Mathematical Sciences, supported by the National Science Foundation and published by SIAM. GARRETT BIRKHOFF, The Numerical Solution of Elliptic Equations D. V. LINDLEY, Bayesian Statistics, A Review R. S. VARGA, Functional Analysis and Approximation Theory in Numerical Analysis R. R. BAHADUR, Some Limit Theorems in Statistics PATRICK BILLINGSLEY, Weak Convergence of Measures: Applications in Probability J. L. LIONS, Some Aspects of the Optimal Control of Distributed Parameter Systems ROGER PENROSE, Techniques of Differential Topology in Relativity HERMAN CHERNOFF, Sequential Analysis and Optimal Design J. DURBIN, Distribution Theory for Tests Based on the Sample Distribution Function SOL I. RUBINOW, Mathematical Problems in the Biological Sciences P. D. LAX, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves I. J. SCHOENBERG, Cardinal Spline Interpolation IVAN SINGER, The Theory of Best Approximation and Functional Analysis WERNER C. RHEINBOLDT, Methods of Solving Systems of Nonlinear Equations HANS F. WEINBERGER, Variational Methods for Eigenvalue Approximation R. TYRRELL ROCKAFELLAR, Conjugate Duality and Optimization SIR JAMES LIGHTHILL, Mathematical Biofluiddynamics GERARD SALTON, Theory of Indexing CATHLEEN S. MORAWETZ, Notes on Time Decay and Scattering for Some Hyperbolic Problems F. HOPPENSTEADT, Mathematical Theories of Populations: Demographics, Genetics and Epidemics RICHARD ASKEY, Orthogonal Polynomials and Special Functions L. E. PAYNE, Improperly Posed Problems in Partial Differential Equations S. ROSEN, Lectures on the Measurement and Evaluation of the Performance of Computing Systems HERBERT B. -
Benjamin Rossman
Benjamin Rossman 40 St George Street, Room 6214 Phone: 416-946-7825 Toronto, ON M5S 3G4 Canada E-mail: [email protected] POSITIONS University of Toronto 2016 – present Assistant Professor of Mathematics and Computer Science National Institute of Informatics (Tokyo, Japan) 2013 – 2016 Assistant Professor in the Kawarabayashi Large Graph Project Simons Institute for the Theory of Computing (Berkeley, CA) 2014 – 2015 Simons-Berkeley Research Fellow Tokyo Institute of Technology 2010 – 2013 NSF Mathematical Sciences Postdoctoral Research Fellow EDUCATION Massachusetts Institute of Technology Ph.D. in Computer Science 2010 · Advisor: Madhu Sudan · Thesis: Average-Case Complexity of Detecting Cliques University of Pennsylvania M.A. in Mathematics 2002 B.A. in Mathematics, Summa Cum Laude 2001 HONORS AND AWARDS André Aisenstadt Prize in Mathematics 2018 Invited Speaker at the International Congress of Mathematicians 2018 Alfred P. Sloan Research Fellowship 2017 Best Paper Award at FOCS (IEEE Symposium on Foundations of Computer Science) 2015 Best Paper Award at CCC (Computational Complexity Conference) 2015 Best Paper Award at CSR (International Computer Science Symposium in Russia) 2014 Ackermann Award (Outstanding Dissertation Award of the European Association for 2011 Computer Science Logic) George M. Sprowls Award (Best Doctoral Theses in Computer Science at MIT) 2010 NSF Mathematical Sciences Postdoctoral Research Fellowship 2010 National Defense Science and Engineering Graduate Fellowship 2006 1 NSF Graduate Research Fellowship 2006 -
A Century of Mathematics in America, Peter Duren Et Ai., (Eds.), Vol
Garrett Birkhoff has had a lifelong connection with Harvard mathematics. He was an infant when his father, the famous mathematician G. D. Birkhoff, joined the Harvard faculty. He has had a long academic career at Harvard: A.B. in 1932, Society of Fellows in 1933-1936, and a faculty appointmentfrom 1936 until his retirement in 1981. His research has ranged widely through alge bra, lattice theory, hydrodynamics, differential equations, scientific computing, and history of mathematics. Among his many publications are books on lattice theory and hydrodynamics, and the pioneering textbook A Survey of Modern Algebra, written jointly with S. Mac Lane. He has served as president ofSIAM and is a member of the National Academy of Sciences. Mathematics at Harvard, 1836-1944 GARRETT BIRKHOFF O. OUTLINE As my contribution to the history of mathematics in America, I decided to write a connected account of mathematical activity at Harvard from 1836 (Harvard's bicentennial) to the present day. During that time, many mathe maticians at Harvard have tried to respond constructively to the challenges and opportunities confronting them in a rapidly changing world. This essay reviews what might be called the indigenous period, lasting through World War II, during which most members of the Harvard mathe matical faculty had also studied there. Indeed, as will be explained in §§ 1-3 below, mathematical activity at Harvard was dominated by Benjamin Peirce and his students in the first half of this period. Then, from 1890 until around 1920, while our country was becoming a great power economically, basic mathematical research of high quality, mostly in traditional areas of analysis and theoretical celestial mechanics, was carried on by several faculty members.