IEEE Information Theory Society Newsletter
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Solving 8 × 8 Domineering
Theoretical Computer Science 230 (2000) 195–206 www.elsevier.com/locate/tcs View metadata, citation and similar papers at core.ac.uk brought to you by CORE Mathematical Games provided by Elsevier - Publisher Connector Solving 8 × 8 Domineering D.M. Breuker, J.W.H.M. Uiterwijk ∗, H.J. van den Herik Department of Computer Science, MATRIKS Research Institute, Universiteit Maastricht, P.O. Box 616, 6200 MD Maastricht, Netherlands Received May 1998; revised October 1998 Communicated by A.S. Fraenkel Abstract So far the game of Domineering has mainly been investigated by combinatorial-games re- searchers. Yet, it is a genuine two-player zero-sum game with perfect information, of which the general formulation is a topic of AI research. In that domain, many techniques have been developed for two-person games, especially for chess. In this article we show that one such technique, i.e., transposition tables, is ÿt for solving standard Domineering (i.e., on an 8×8 board). The game turns out to be a win for the player ÿrst to move. This result coincides with a result obtained independently by Morita Kazuro. Moreover, the technique of transposition tables is also applied to di erently sized m × n boards, m ranging from 2 to 8, and n from m to 9. The results are given in tabular form. Finally, some conclusions on replacement schemes are drawn. In an appendix an analysis of four tournament games is provided. c 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: Domineering; Solving games; Transposition tables; Replacement schemes 1. Introduction Domineering is a two-player zero-sum game with perfect information. -
By Glenn A. Emelko
A NEW ALGORITHM FOR EFFICIENT SOFTWARE IMPLEMENTATION OF REED-SOLOMON ENCODERS FOR WIRELESS SENSOR NETWORKS by Glenn A. Emelko Submitted to the Office of Graduate Studies at Case Western Reserve University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in ELECTRICAL ENGINEERING Department of Electrical Engineering and Computer Science Case Western Reserve University Glennan 321, 10900 Euclid Ave. Cleveland, Ohio 44106 May 2009 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of _Glenn A. Emelko____________________________________ candidate for the _Doctor of Philosophy_ degree *. (signed)_Francis L. Merat______________________________ (chair of the committee) _Wyatt S. Newman______________________________ _H. Andy Podgurski_____________________________ _William L. Schultz______________________________ _David A. Singer________________________________ ________________________________________________ (date) _March 2, 2009__________ * We also certify that written approval has been obtained for any proprietary material contained therein. i Dedication For my loving wife Liz, and for my children Tom and Leigh Anne. I thank you for giving me love and support and for believing in me every step along my journey. ii Table of Contents Dedication........................................................................................................................... ii List of Figures......................................................................................................................4 -
Claude Elwood Shannon (1916–2001) Solomon W
Claude Elwood Shannon (1916–2001) Solomon W. Golomb, Elwyn Berlekamp, Thomas M. Cover, Robert G. Gallager, James L. Massey, and Andrew J. Viterbi Solomon W. Golomb Done in complete isolation from the community of population geneticists, this work went unpublished While his incredibly inventive mind enriched until it appeared in 1993 in Shannon’s Collected many fields, Claude Shannon’s enduring fame will Papers [5], by which time its results were known surely rest on his 1948 work “A mathematical independently and genetics had become a very theory of communication” [7] and the ongoing rev- different subject. After his Ph.D. thesis Shannon olution in information technology it engendered. wrote nothing further about genetics, and he Shannon, born April 30, 1916, in Petoskey, Michi- expressed skepticism about attempts to expand gan, obtained bachelor’s degrees in both mathe- the domain of information theory beyond the matics and electrical engineering at the University communications area for which he created it. of Michigan in 1936. He then went to M.I.T., and Starting in 1938 Shannon worked at M.I.T. with after spending the summer of 1937 at Bell Tele- Vannevar Bush’s “differential analyzer”, the an- phone Laboratories, he wrote one of the greatest cestral analog computer. After another summer master’s theses ever, published in 1938 as “A sym- (1940) at Bell Labs, he spent the academic year bolic analysis of relay and switching circuits” [8], 1940–41 working under the famous mathemati- in which he showed that the symbolic logic of cian Hermann Weyl at the Institute for Advanced George Boole’s nineteenth century Laws of Thought Study in Princeton, where he also began thinking provided the perfect mathematical model for about recasting communications on a proper switching theory (and indeed for the subsequent mathematical foundation. -
Digital Communication Systems 2.2 Optimal Source Coding
Digital Communication Systems EES 452 Asst. Prof. Dr. Prapun Suksompong [email protected] 2. Source Coding 2.2 Optimal Source Coding: Huffman Coding: Origin, Recipe, MATLAB Implementation 1 Examples of Prefix Codes Nonsingular Fixed-Length Code Shannon–Fano code Huffman Code 2 Prof. Robert Fano (1917-2016) Shannon Award (1976 ) Shannon–Fano Code Proposed in Shannon’s “A Mathematical Theory of Communication” in 1948 The method was attributed to Fano, who later published it as a technical report. Fano, R.M. (1949). “The transmission of information”. Technical Report No. 65. Cambridge (Mass.), USA: Research Laboratory of Electronics at MIT. Should not be confused with Shannon coding, the coding method used to prove Shannon's noiseless coding theorem, or with Shannon–Fano–Elias coding (also known as Elias coding), the precursor to arithmetic coding. 3 Claude E. Shannon Award Claude E. Shannon (1972) Elwyn R. Berlekamp (1993) Sergio Verdu (2007) David S. Slepian (1974) Aaron D. Wyner (1994) Robert M. Gray (2008) Robert M. Fano (1976) G. David Forney, Jr. (1995) Jorma Rissanen (2009) Peter Elias (1977) Imre Csiszár (1996) Te Sun Han (2010) Mark S. Pinsker (1978) Jacob Ziv (1997) Shlomo Shamai (Shitz) (2011) Jacob Wolfowitz (1979) Neil J. A. Sloane (1998) Abbas El Gamal (2012) W. Wesley Peterson (1981) Tadao Kasami (1999) Katalin Marton (2013) Irving S. Reed (1982) Thomas Kailath (2000) János Körner (2014) Robert G. Gallager (1983) Jack KeilWolf (2001) Arthur Robert Calderbank (2015) Solomon W. Golomb (1985) Toby Berger (2002) Alexander S. Holevo (2016) William L. Root (1986) Lloyd R. Welch (2003) David Tse (2017) James L. -
Principles of Communications ECS 332
Principles of Communications ECS 332 Asst. Prof. Dr. Prapun Suksompong (ผศ.ดร.ประพันธ ์ สขสมปองุ ) [email protected] 1. Intro to Communication Systems Office Hours: Check Google Calendar on the course website. Dr.Prapun’s Office: 6th floor of Sirindhralai building, 1 BKD 2 Remark 1 If the downloaded file crashed your device/browser, try another one posted on the course website: 3 Remark 2 There is also three more sections from the Appendices of the lecture notes: 4 Shannon's insight 5 “The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.” Shannon, Claude. A Mathematical Theory Of Communication. (1948) 6 Shannon: Father of the Info. Age Documentary Co-produced by the Jacobs School, UCSD- TV, and the California Institute for Telecommunic ations and Information Technology 7 [http://www.uctv.tv/shows/Claude-Shannon-Father-of-the-Information-Age-6090] [http://www.youtube.com/watch?v=z2Whj_nL-x8] C. E. Shannon (1916-2001) Hello. I'm Claude Shannon a mathematician here at the Bell Telephone laboratories He didn't create the compact disc, the fax machine, digital wireless telephones Or mp3 files, but in 1948 Claude Shannon paved the way for all of them with the Basic theory underlying digital communications and storage he called it 8 information theory. C. E. Shannon (1916-2001) 9 https://www.youtube.com/watch?v=47ag2sXRDeU C. E. Shannon (1916-2001) One of the most influential minds of the 20th century yet when he died on February 24, 2001, Shannon was virtually unknown to the public at large 10 C. -
Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi
HEXAFLEXAGONS, PROBABILITY PARADOXES, AND THE TOWER OF HANOI For 25 of his 90 years, Martin Gard- ner wrote “Mathematical Games and Recreations,” a monthly column for Scientific American magazine. These columns have inspired hundreds of thousands of readers to delve more deeply into the large world of math- ematics. He has also made signifi- cant contributions to magic, philos- ophy, debunking pseudoscience, and children’s literature. He has produced more than 60 books, including many best sellers, most of which are still in print. His Annotated Alice has sold more than a million copies. He continues to write a regular column for the Skeptical Inquirer magazine. (The photograph is of the author at the time of the first edition.) THE NEW MARTIN GARDNER MATHEMATICAL LIBRARY Editorial Board Donald J. Albers, Menlo College Gerald L. Alexanderson, Santa Clara University John H. Conway, F.R. S., Princeton University Richard K. Guy, University of Calgary Harold R. Jacobs Donald E. Knuth, Stanford University Peter L. Renz From 1957 through 1986 Martin Gardner wrote the “Mathematical Games” columns for Scientific American that are the basis for these books. Scientific American editor Dennis Flanagan noted that this column contributed substantially to the success of the magazine. The exchanges between Martin Gardner and his readers gave life to these columns and books. These exchanges have continued and the impact of the columns and books has grown. These new editions give Martin Gardner the chance to bring readers up to date on newer twists on old puzzles and games, on new explanations and proofs, and on links to recent developments and discoveries. -
IEEE Information Theory Society Newsletter
IEEE Information Theory Society Newsletter Vol. 53, No.4, December 2003 Editor: Lance C. Pérez ISSN 1059-2362 The Shannon Lecture Hidden Markov Models and the Baum-Welch Algorithm Lloyd R. Welch Content of This Talk what the ‘running variable’ is. The lectures of previous Shannon Lecturers fall into several Of particular use will be the concept of conditional probabil- categories such as introducing new areas of research, resusci- ity and recursive factorization. The recursive factorization tating areas of research, surveying areas identified with the idea says that the joint probability of a collection of events can lecturer, or reminiscing on the career of the lecturer. In this be expressed as a product of conditional probabilities, where talk I decided to restrict the subject to the Baum-Welch “algo- each is the probability of an event conditioned on all previous rithm” and some of the ideas that led to its development. events. For example, let A, B, and C be three events. Then I am sure that most of you are familiar with Markov chains Pr(A ∩ B ∩ C) = Pr(A)Pr(B | A)Pr(C | A ∩ B) and Markov processes. They are natural models for various communication channels in which channel conditions change Using the bracket notation, we can display the recursive fac- with time. In many cases it is not the state sequence of the torization of the joint probability distribution of a sequence of model which is observed but the effects of the process on a discrete random variables: signal. That is, the states are not observable but some func- tions, possibly random, of the states are observed. -
Information Theory and Statistics: a Tutorial
Foundations and Trends™ in Communications and Information Theory Volume 1 Issue 4, 2004 Editorial Board Editor-in-Chief: Sergio Verdú Department of Electrical Engineering Princeton University Princeton, New Jersey 08544, USA [email protected] Editors Venkat Anantharam (Berkeley) Amos Lapidoth (ETH Zurich) Ezio Biglieri (Torino) Bob McEliece (Caltech) Giuseppe Caire (Eurecom) Neri Merhav (Technion) Roger Cheng (Hong Kong) David Neuhoff (Michigan) K.C. Chen (Taipei) Alon Orlitsky (San Diego) Daniel Costello (NotreDame) Vincent Poor (Princeton) Thomas Cover (Stanford) Kannan Ramchandran (Berkeley) Anthony Ephremides (Maryland) Bixio Rimoldi (EPFL) Andrea Goldsmith (Stanford) Shlomo Shamai (Technion) Dave Forney (MIT) Amin Shokrollahi (EPFL) Georgios Giannakis (Minnesota) Gadiel Seroussi (HP-Palo Alto) Joachim Hagenauer (Munich) Wojciech Szpankowski (Purdue) Te Sun Han (Tokyo) Vahid Tarokh (Harvard) Babak Hassibi (Caltech) David Tse (Berkeley) Michael Honig (Northwestern) Ruediger Urbanke (EPFL) Johannes Huber (Erlangen) Steve Wicker (GeorgiaTech) Hideki Imai (Tokyo) Raymond Yeung (Hong Kong) Rodney Kennedy (Canberra) Bin Yu (Berkeley) Sanjeev Kulkarni (Princeton) Editorial Scope Foundations and Trends™ in Communications and Information Theory will publish survey and tutorial articles in the following topics: • Coded modulation • Multiuser detection • Coding theory and practice • Multiuser information theory • Communication complexity • Optical communication channels • Communication system design • Pattern recognition and learning • Cryptology -
IEEE Information Theory Society Newsletter
IEEE Information Theory Society Newsletter Vol. 63, No. 3, September 2013 Editor: Tara Javidi ISSN 1059-2362 Editorial committee: Ioannis Kontoyiannis, Giuseppe Caire, Meir Feder, Tracey Ho, Joerg Kliewer, Anand Sarwate, Andy Singer, and Sergio Verdú Annual Awards Announced The main annual awards of the • 2013 IEEE Jack Keil Wolf ISIT IEEE Information Theory Society Student Paper Awards were were announced at the 2013 ISIT selected and announced at in Istanbul this summer. the banquet of the Istanbul • The 2014 Claude E. Shannon Symposium. The winners were Award goes to János Körner. the following: He will give the Shannon Lecture at the 2014 ISIT in 1) Mohammad H. Yassaee, for Hawaii. the paper “A Technique for Deriving One-Shot Achiev - • The 2013 Claude E. Shannon ability Results in Network Award was given to Katalin János Körner Daniel Costello Information Theory”, co- Marton in Istanbul. Katalin authored with Mohammad presented her Shannon R. Aref and Amin A. Gohari Lecture on the Wednesday of the Symposium. If you wish to see her slides again or were unable to attend, a copy of 2) Mansoor I. Yousefi, for the paper “Integrable the slides have been posted on our Society website. Communication Channels and the Nonlinear Fourier Transform”, co-authored with Frank. R. Kschischang • The 2013 Aaron D. Wyner Distinguished Service Award goes to Daniel J. Costello. • Several members of our community became IEEE Fellows or received IEEE Medals, please see our web- • The 2013 IT Society Paper Award was given to Shrinivas site for more information: www.itsoc.org/honors Kudekar, Tom Richardson, and Rüdiger Urbanke for their paper “Threshold Saturation via Spatial Coupling: The Claude E. -
Network Information Theory
Network Information Theory This comprehensive treatment of network information theory and its applications pro- vides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon’s point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless com- munication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia. Abbas El Gamal is the Hitachi America Chaired Professor in the School of Engineering and the Director of the Information Systems Laboratory in the Department of Electri- cal Engineering at Stanford University. In the field of network information theory, he is best known for his seminal contributions to the relay, broadcast, and interference chan- nels; multiple description coding; coding for noisy networks; and energy-efficient packet scheduling and throughput–delay tradeoffs in wireless networks. He is a Fellow of IEEE and the winner of the 2012 Claude E. Shannon Award, the highest honor in the field of information theory. Young-Han Kim is an Assistant Professor in the Department of Electrical and Com- puter Engineering at the University of California, San Diego. -
Combinatorial Game Theory
Combinatorial Game Theory Aaron N. Siegel Graduate Studies MR1EXLIQEXMGW Volume 146 %QIVMGER1EXLIQEXMGEP7SGMIX] Combinatorial Game Theory https://doi.org/10.1090//gsm/146 Combinatorial Game Theory Aaron N. Siegel Graduate Studies in Mathematics Volume 146 American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE David Cox (Chair) Daniel S. Freed Rafe Mazzeo Gigliola Staffilani 2010 Mathematics Subject Classification. Primary 91A46. For additional information and updates on this book, visit www.ams.org/bookpages/gsm-146 Library of Congress Cataloging-in-Publication Data Siegel, Aaron N., 1977– Combinatorial game theory / Aaron N. Siegel. pages cm. — (Graduate studies in mathematics ; volume 146) Includes bibliographical references and index. ISBN 978-0-8218-5190-6 (alk. paper) 1. Game theory. 2. Combinatorial analysis. I. Title. QA269.S5735 2013 519.3—dc23 2012043675 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA. Requests can also be made by e-mail to [email protected]. c 2013 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. -
Sharp Threshold Rates for Random Codes∗
Sharp threshold rates for random codes∗ Venkatesan Guruswami1, Jonathan Mosheiff1, Nicolas Resch2, Shashwat Silas3, and Mary Wootters3 1Carnegie Mellon University 2Centrum Wiskunde en Informatica 3Stanford University September 11, 2020 Abstract Suppose that P is a property that may be satisfied by a random code C ⊂ Σn. For example, for some p 2 (0; 1), P might be the property that there exist three elements of C that lie in some Hamming ball of radius pn. We say that R∗ is the threshold rate for P if a random code of rate R∗ + " is very likely to satisfy P, while a random code of rate R∗ − " is very unlikely to satisfy P. While random codes are well-studied in coding theory, even the threshold rates for relatively simple properties like the one above are not well understood. We characterize threshold rates for a rich class of properties. These properties, like the example above, are defined by the inclusion of specific sets of codewords which are also suitably \symmetric." For properties in this class, we show that the threshold rate is in fact equal to the lower bound that a simple first-moment calculation obtains. Our techniques not only pin down the threshold rate for the property P above, they give sharp bounds on the threshold rate for list-recovery in several parameter regimes, as well as an efficient algorithm for estimating the threshold rates for list-recovery in general. arXiv:2009.04553v1 [cs.IT] 9 Sep 2020 ∗SS and MW are partially funded by NSF-CAREER grant CCF-1844628, NSF-BSF grant CCF-1814629, and a Sloan Research Fellowship.