The “New” Science of Networks
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January 1993 Council Minutes
AMERICAN MATHEMATICAL SOCIETY COUNCIL MINUTES San Antonio, Texas 12 January 1993 November 21, 1995 Abstract The Council met at 2:00 pm on Tuesday, 12 January 1993 in the Fiesta Room E of the San Antonio Convention Center. The following members were present for all or part of the meeting: Steve Armentrout, Michael Artin, Sheldon Axler, M. Salah Baouendi, James E. Baumgartner, Lenore Blum, Ruth M. Charney, Charles Herbert Clemens, W. W. Com- fort (Associate Secretary, voting), Carl C. Cowen, Jr., David A. Cox, Robert Daverman (Associate Secretary-designate, non-voting) , Chandler Davis, Robert M. Fossum, John M. Franks, Herbert Friedman (Canadian Mathematical Society observer, non-voting), Ronald L. Graham, Judy Green, Rebecca Herb, William H. Jaco (Executive Director, non-voting), Linda Keen, Irwin Kra, Elliott Lieb, Franklin Peterson, Carl Pomerance, Frank Quinn, Marc Rieffel, Hugo Rossi, Wilfried Schmid, Lance Small (Associate Secre- tary, non-voting), B. A. Taylor (Mathematical Reviews Editorial Committee and Associate Treasurer-designate), Lars B. Wahlbin (representing Mathematics of Computation Edito- rial Committee), Frank W. Warner, Steve H. Weintraub, Ruth Williams, and Shing-Tung Yau. President Artin presided. 1 2 CONTENTS Contents 0 CALL TO ORDER AND INTRODUCTIONS. 4 0.1 Call to Order. ............................................. 4 0.2 Retiring Members. .......................................... 4 0.3 Introduction of Newly Elected Council Members. ......................... 4 1 MINUTES 4 1.1 September 92 Council. ........................................ 4 1.2 11/92 Executive Committee and Board of Trustees (ECBT) Meeting. .............. 5 2 CONSENT AGENDA. 5 2.1 INNS .................................................. 5 2.2 Second International Conference on Ordinal Data Analysis. ................... 5 2.3 AMS Prizes. .............................................. 5 2.4 Special Committee on Nominating Procedures. -
Applied Combinatorics 2017 Edition
Keller Trotter Applied Combinatorics 2017 Edition 2017 Edition Mitchel T. Keller William T. Trotter Applied Combinatorics Applied Combinatorics Mitchel T. Keller Washington and Lee University Lexington, Virginia William T. Trotter Georgia Institute of Technology Atlanta, Georgia 2017 Edition Edition: 2017 Edition Website: http://rellek.net/appcomb/ © 2006–2017 Mitchel T. Keller, William T. Trotter This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Interna- tional License. To view a copy of this license, visit http://creativecommons.org/licenses/ by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. Summary of Contents About the Authors ix Acknowledgements xi Preface xiii Preface to 2017 Edition xv Preface to 2016 Edition xvii Prologue 1 1 An Introduction to Combinatorics 3 2 Strings, Sets, and Binomial Coefficients 17 3 Induction 39 4 Combinatorial Basics 59 5 Graph Theory 69 6 Partially Ordered Sets 113 7 Inclusion-Exclusion 141 8 Generating Functions 157 9 Recurrence Equations 183 10 Probability 213 11 Applying Probability to Combinatorics 229 12 Graph Algorithms 239 vii SUMMARY OF CONTENTS 13 Network Flows 259 14 Combinatorial Applications of Network Flows 279 15 Pólya’s Enumeration Theorem 291 16 The Many Faces of Combinatorics 315 A Epilogue 331 B Background Material for Combinatorics 333 C List of Notation 361 Index 363 viii About the Authors About William T. Trotter William T. Trotter is a Professor in the School of Mathematics at Georgia Tech. He was first exposed to combinatorial mathematics through the 1971 Bowdoin Combi- natorics Conference which featured an array of superstars of that era, including Gian Carlo Rota, Paul Erdős, Marshall Hall, Herb Ryzer, Herb Wilf, William Tutte, Ron Gra- ham, Daniel Kleitman and Ray Fulkerson. -
MSRI Celebrates Its Twentieth Birthday, Volume 50, Number 3
MSRI Celebrates Its Twentieth Birthday The past twenty years have seen a great prolifera- renewed support. Since then, the NSF has launched tion in mathematics institutes worldwide. An in- four more institutes: the Institute for Pure and spiration for many of them has been the Applied Mathematics at the University of California, Mathematical Sciences Research Institute (MSRI), Los Angeles; the AIM Research Conference Center founded in Berkeley, California, in 1982. An es- at the American Institute of Mathematics (AIM) in tablished center for mathematical activity that Palo Alto, California; the Mathematical Biosciences draws researchers from all over the world, MSRI has Institute at the Ohio State University; and the distinguished itself for its programs in both pure Statistical and Applied Mathematical Sciences and applied areas and for its wide range of outreach Institute, which is a partnership of Duke University, activities. MSRI’s success has allowed it to attract North Carolina State University, the University of many donations toward financing the construc- North Carolina at Chapel Hill, and the National tion of a new extension to its building. In October Institute of Statistical Sciences. 2002 MSRI celebrated its twentieth year with a Shiing-Shen Chern, Calvin C. Moore, and I. M. series of special events that exemplified what MSRI Singer, all on the mathematics faculty at the Uni- has become—a focal point for mathematical culture versity of California, Berkeley, initiated the original in all its forms, with the discovery and delight of proposal for MSRI; Chern served as the founding new mathematical knowledge the top priority. director, and Moore was the deputy director. -
Short Cross-Disciplinary Cycles in Co-Authorship Graphs
How small is the center of science? Short cross-disciplinary cycles in co-authorship graphs Chris Fields 528 Zinnia Court Sonoma, CA 95476 USA fi[email protected] October 17, 2014 Abstract Cycles that cross two or more boundaries between disciplines in the co-authorship graph for all of science are used to set upper limits on the number of co-authored pa- pers required to cross 15 disciplines or subdisciplines ranging from macroeconomics to neurology. The upper limits obtained range from one (discrete mathematics, macroe- conomics and nuclear physics) to six (neuroscience). The 15 disciplines or subdis- ciplines examined form a “small world” with an average separation of only 2.0 co- authorship links. It is conjectured that the high-productivity, high average degree centers of all scientific disciplines form a small world, and therefore that the diameter of the co-authorship graph of all of science is only slightly larger than the average diameter of the co-authorship graphs of its subdisciplines. Keywords: Cross-displinary brokers; Field mobility; Graph centrality; Graph diameter; Nobel laureates; Preferential attachment; Small-world networks 1 Introduction Numerous studies have now confirmed the finding of Newman (2001, 2004) that the co- authorship graphs of many scientific disciplines can be characterized as “small worlds” comprising many dense clusters of researchers separated by relatively short (mean length 1 l ≤ 10) minimum paths (reviewed by Mali, Kronegger, Doreian and Ferligoj, 2012). Despite over two decades of efforts to make the world of science as a whole more interconnected by encouraging inter-, multi- or trans-disciplinary collaborations, however, the research enterprise remains organized into disciplines (Jacobs and Frickel, 2009). -
Field Guide 3 to 4
How to use the Building a Strong Foundation for School Success Series; Field Guide This field guide was created to offer an easy‐to‐read, practical supplement to the KY Early Childhood Standards (KYECS) for anyone who works with young children birth to four years old. This guide is intended to support early childhood professionals who work in the following settings: home settings, early intervention settings, and center‐based care. The field guide has chapters for each of the Kentucky Early Childhood Standards. Below is a description of the information you will find in each chapter. Each chapter will begin with a brief overview of the standard. In this paragraph, you will find information about what this standard is and the theory and research to support its use. Each chapter contains a section called Crossing Bridges. It is important to understand that the developmental domains of young children often cross and impact others. While a provider is concentrating on a young child learning communication skills, there are other domains or standards being experienced as well. This section tells the reader how this standard supports other standards and domains. For example, you will see that social emotional development of an infant supports or overlaps the infant’s communication development. Each chapter contains a section called Post Cards. This section offers supportive quotes about the standard. In this section, readers will also find narratives, written by early care providers for early care providers. These narratives provide a window into how the standard is supported in a variety of settings. Each chapter contains a section called Sights to See. -
January 1994 Council Minutes
AMERICAN MATHEMATICAL SOCIETY COUNCIL MINUTES Cincinnati, Ohio 11 January 1994 Abstract The Council met at 1:00 pm on Tuesday, 11 January 1994 in the Regency Ball- room B, Hyatt Regency Cincinnati, Cincinnati, Ohio. Members in attendance were Michael Artin, M. Salah Baouendi, James E. Baum- gartner, Joan S. Birman, Ruth M. Charney, Carl C. Cowen, Jr., David A. Cox, Robert J. Daverman (Associate Secretary of record), Chandler Davis, Robert M. Fossum, John M. Franks, Walter Gautschi, Ronald L. Graham, Judy Green, Philip J. Hanlon, Rebecca A. Herb, Arthur M. Jaffe, Svetlana R. Katok, Linda Keen, Irwin Kra, Steven George Krantz, James I. Lepowsky, Peter W. K. Li, Elliott H. Lieb, Anil Nerode, Richard S. Palais (for Murray Protter, Bulletin), Franklin P. Peterson, Marc A. Rieffel, Lance W. Small (Associate Secretary, non-voting), Elias M. Stein (for Wilfried Schmid, Journal of the American Mathematical Soci- ety), B. A. Taylor, Frank Warner III, Steven H. Weintraub, Ruth J. Williams, and Susan Gayle Williams. Members of the Council who will take office on 01 February 1994 and who were in attendance were: Cathleen Morawetz, Jean Taylor, Frank Morgan, and Sylvia Wiegand. President Graham called the meeting to order at 1:10 PM. 1 2 CONTENTS Contents I MINUTES 5 0 CALL TO ORDER AND INTRODUCTIONS. 5 0.1 Call to Order. ........................................ 5 0.2 Retiring Members. ..................................... 5 0.3 Introduction of Newly Elected Council Members. .................... 5 1MINUTES 5 1.1 August 93 Council. ..................................... 5 1.2 11/93 Executive Committee and Board of Trustees (ECBT) Meeting. ......... 6 2 CONSENT AGENDA. 6 2.1 National Association of Mathematicians. -
May 2005.Pmd
American Mathematical Association of Two-Year Colleges Serving the professional needs of two-year college mathematics educators Volume 20, Number 3 May 2005 NNeewwss ISSN 0889-3845 Annual AMATYC Conference in San Diego oin your colleagues November 10–13, 2005, in San Diego, CA, for the 31st Annual AMATYC Conference. This year’s theme, Catch the Wave, will capture your imagina- tionJ as you participate in professional development opportunities designed with your students’ success in mind. Ride the wave of learning from your colleagues, build profes- sional relationships, and refresh yourself professionally. You can examine the latest textbooks and explore exciting new technology brought to you by our exhibitors. Featured presentations will include: The Mathematics of Juggling Ronald Graham, the Irwin and Joan Jacobs Professor in the Department of Computer Science and Engineering of UCSD and Chief Scientist at California Institute for Telecommunications and Information Technology, Cal-IT2, of UC San Diego, will be the Opening Session keynote speaker on Thursday at 3:00 p.m. Ron is a well-known, accom- plished mathematician. He is Past President of the Mathematical Association of America and was a long-time friend of Paul Erdös. He was Chief Scientist at AT&T Labs for many years and speaks fluent Chinese. Graham’s number was in the Guiness Book of Records as the “largest number,” and is inexpressible in ordinary notation and needs special notation devised by Don Knuth in 1976. An ex-president of the International Jugglers Associa- tion, Graham will highlight some of the new ways to describe juggling patterns that have led to previously un- known patterns and many new mathematical theorems on Friday evening. -
Large Complex Networks: Deterministic Models
Internet C. Elegans Large Complex Networks: Deteministic Models (Recursive Clique-Trees) WWW Erdös number Air routes http://www.caida.org/tools/visualization/plankton/ Francesc Comellas Departament de Matemàtica Aplicada IV, Proteins Universitat Politècnica de Catalunya, Barcelona [email protected] Power grid Real networks very often are Most “real” networks are Large Complex systems small-world scale-free self-similar Small-world Different elements (nodes) Interaction among elements (links) small diameter log(|V|), large clustering Scale-free power law degree distribution ( “hubs” ) Complex networks Self-similar / fractal Mathematical model: Graphs Deterministic models Small diameter (logarithmic) Power law Fractal (degrees) Based on cliques Milgram 1967 Song, Havlin & (hierarchical graphs, recursive High clustering Barabási & Makse Watts & Albert 1999 2005,2006 clique-trees, Apollonian graphs) Strogatz 1998 6 degrees of separation ! Stanley Milgram (1967) Main parameters (invariants) 160 letters Omaha -Nebraska- -> Boston Diameter – average distance Degree Δ degree. Small-world networks P(k): Degree distribution. small diameter (or average dist.) Clustering Are neighbours of a vertex also neighbours among high clustering them? Small world phenomenon in social networks What a small-world ! Structured graph Small-world graph Random graph Network characteristics •highclustering •highclustering • small clustering • large diameter • small diameter • small diameter # of links among neighbors •regular Clustering C(v) = Erdös number •almostregular n(n-1)/2 http://www.oakland.edu/enp/ Diameter or Average distance Maximum communication delay 1- 509 Degree distribution 2- 7494 Resilience N= 268.000 Jul 2004 |V| = 1000 Δ =10 |V|=1000 Δ =8-13 |V|=1000 Δ = 5-18 Real life networks are clustered, large C(p), but have small (connected component) D = 100 d =49.51 D = 14 d = 11.1 D = 5 d = 4.46 average distance L(p ). -
S the Summation S Department of Mathematics & Computer Science Newsletter · Santa Clara University · 2018
S The SummaTion S Department of Mathematics & Computer Science Newsletter · Santa Clara University · 2018 Remarks from the Department Chair Hi. This is Ed Schaefer, I succeeded Fr. Dennis Smo- larksi, S.J. and Glenn Appleby as Chair. We hope you are all doing well and that we have been one of the pieces that helped prepare you for your life. Both nationwide and at SCU, the percentage of students majoring in STEM fields (Science, Technology, Engineering, and Mathematics) is increasing. At SCU, we are seeing huge growth in both Computer Science and Computer Engineering. In our De- partment, we currently have about 250 Computer Science majors and 100 Mathematics majors. The Department’s enrollment in Winter 2018 classes is about 2100 students. Each of the last three years we have hired a new tenure-track faculty member and we have plans to hire six more continuing faculty over the next two years. The Department has received two gifts to improve our first year mathematics curriculum and retention of students traditionally under-represented in STEM. One gift is from the Koret Foundation and the other is from anonymous donors – they total $700,000. This has enabled us to support several exciting new programs. We are piloting lab sections for precalculus, STEM Calculus 1 and Business Calculus 1 (Math 9, 11, and 30). Each lab meets once a week for an hour. Active learning pedagogies are used in the labs, including a lot of group work focused on longer, conceptual problems. Students in SCU’s successful LEAD program, for first generation undergraduates, all take the labs, which are optional for other students. -
View This Volume's Front and Back Matter
http://dx.doi.org/10.1090/psapm/026 PROCEEDINGS OF SYMPOSIA IN APPLIED MATHEMATICS VOLUME 1 NON-LINEAR PROBLEMS IN MECHANICS OF CONTINUA Edited by E. Reissner (Brown University, August 1947) VOLUME 2 ELECTROMAGNETIC THEORY Edited by A. H. Taub (Massachusetts Institute of Technology, July 1948) VOLUME 3 ELASTICITY Edited by R. V. Churchill (University of Michigan, June 1949) VOLUME 4 FLUID DYNAMICS Edited by M. H. Martin (University of Maryland, June 1951) VOLUME 5 WAVE MOTION AND VIBRATION THEORY Edited by A. E. Heins (Carnegie Institute of Technology, June 1952) VOLUME 6 NUMERICAL ANALYSIS Edited by /. H. Curtiss (Santa Monica City College, August 1953) VOLUME 7 APPLIED PROBABILITY Edited by L. A. MacColl (Polytechnic Institute of Brooklyn, April 1955) VOLUME 8 CALCULUS OF VARIATIONS AND ITS APPLICATIONS Edited by L. M. Graves (University of Chicago, April 1956) VOLUME 9 ORBIT THEORY Edited by G. Birkhoff and R. E. Longer (New York University, April 1957) VOLUME 10 COMBINATORIAL ANALYSIS Edited by R. Bellman and M. Hall, Jr. (Columbia University, April 1958) VOLUME 11 NUCLEAR REACTOR THEORY Edited by G. Birkhoff and E. P. Wigner (New York City, April 1959) VOLUME 12 STRUCTURE OF LANGUAGE AND ITS MATHEMATICAL ASPECTS Edited by R. Jakobson (New York City, April 1960) VOLUME 13 HYDRODYNAMIC INSTABILITY Edited by R. Bellman, G. Birkhoff, C. C. Lin (New York City, April 1960) VOLUME 14 MATHEMATICAL PROBLEMS IN THE BIOLOGICAL SCIENCES Edited by R. Bellman (New York City, April 1961) VOLUME 15 EXPERIMENTAL ARITHMETIC, HIGH SPEED COMPUTING, AND MATHEMATICS Edited by N. C. Metropolis, A. H. Taub, /. Todd, C. -
Department of Mathematics
Department of Mathematics The Department of Mathematics seeks to sustain its top ranking in research and teaching by hiring the very best faculty, with special attention to the recruitment of women and candidates from underrepresented minorities, and by continuing to serve the varied educational needs of the department’s graduate students, mathematics majors, and all MIT undergraduates. New Faculty The Mathematics Department had a very successful year in faculty hires for FY2011. Alexei Borodin is a leading specialist from the California Institute of Technology in the interface between representation theory and probability that is linked to combinatorics, random matrix theory, and integrable systems. He will join the department’s faculty as professor in fall 2010. Peter Ozsváth, a major figure in low-dimensional geometric topology from Columbia University, will also join the department in fall 2010. Henry Cohn will be appointed adjunct professor of mathematics. He has been a principal researcher at Microsoft Research New England, working across several fields in discrete mathematics, including computational and analytic number theory, algebraic combinatorics, and theoretical computer science. Two MIT engineering faculty members are jointly appointed with the Mathematics Department. Martin Bazant, associate professor of chemical engineering, has been jointly appointed on the mathematics faculty since 2008. A specialist in microfluidics and electrochemical systems, he joined the mathematics faculty in 2000 before moving to chemical engineering. In addition to graduate student supervision in applied mathematics, Professor Bazant is the faculty mentor of the MIT teams competing in the International Mathematical Contest in Modeling. Anette (Peko) Hosoi, associate professor of mechanical engineering, will be jointly appointed in mathematics in fall 2010. -
No Slide Title
The “new” science of networks Hugues Bersini IRIDIA – ULB Outline • INTRO: Bio and emergent computation: A broad and shallow overview: 30’ • NETWORKS: 30’ – Introduction to Networks – Networks key properties • CONCLUSIONS: Networks main applications Bio and Emergent Computation IRIDIA = Bio and Emergent computation Emergent Computation The Whole is more than the sum of its Parts 1 + 1 = 3 Three emergent phenomena • The traffic jam How an ant colony find the shortest path Associative memories Philosophy: The three natural ingredients of emergence In biology: Natural selection In engineering: the out-of-control engineer Fig. 2: The three needed ingredients for a collective phenomenon to be qualified as emergent. Practical achievements at IRIDIA 1) Ant colony optimisation Pheromone trail Memory depositing ? Probabilistic rule to choose the path 2) Chaotic encoding of memories in brain 3) What really are immune systems for Artificial Immune Systems for engineers Linear causality vs circular causality Idiotypic network 4) Swarm robotics 5) Computational Chemical Reactor The origin of homochirality With Raphael Plasson 6) Data mining on Microarrays • Microarrays measure the mRNA activity of all the genes in a single experiment • One can cluster/classify gene or samples • These may have diagnostic or therapeutic value 7) Financial Network Intraday network structure Liasons Dangereuses: of payment activity in Incresing connectivity, the Canadian risk sharing and systemic risk Large Value Transfer System (LVTS) (by Stefano Battiston, Domenico