DOCSLIB.ORG

Pattern Theory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Pattern Theory i i i i Pattern Theory i i i i i i i i APPLYING MATHEMATICS A Collection of Texts and Monographs ADVISORY BOARD Robert Calderbank Jennifer Chayes David Donoho Weinan E George Papanicolaou i i i i i i i i Pattern Theory The Stochastic Analysis of Real-World Signals David Mumford Agnes` Desolneux A K Peters, Ltd. Natick, Massachusetts i i i i Cover illustrations courtesy of Alex May CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20150515 International Standard Book Number-13: 978-1-4398-6556-9 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, trans- mitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com i i i i To Ulf Grenander, who has dared to propose mathematical models for virtually all of life, pursuing the motto on the wall of his study Using Pattern Theory to create mathematical structures both in the natural and the man-made world i i i i i i i i i i i i i i i i Contents Preface ix Notation xi 0 What Is Pattern Theory? 1 0.1TheManifestoofPatternTheory................ 1 0.2TheBasicTypesofPatterns................... 5 0.3 Bayesian Probability Theory: Pattern Analysis andPatternSynthesis...................... 9 1 English Text and Markov Chains 17 1.1BasicsI:EntropyandInformation............... 21 1.2 Measuring the n-gramApproximationwithEntropy...... 26 1.3 Markov Chains and the n-gramModels............ 29 1.4Words.............................. 39 1.5 Word Boundaries via Dynamic Programming and Maximum Likelihood . ................... 45 1.6MachineTranslationviaBayes’Theorem........... 48 1.7Exercises............................ 51 2 Music and Piecewise Gaussian Models 61 2.1 Basics III: Gaussian Distributions ............... 62 2.2BasicsIV:FourierAnalysis................... 68 2.3GaussianModelsforSingleMusicalNotes........... 72 2.4 Discontinuities in One-Dimensional Signals . .... 79 2.5TheGeometricModelforNotesviaPoissonProcesses.... 86 2.6RelatedModels......................... 91 2.7Exercises............................ 100 3 Character Recognition and Syntactic Grouping 111 3.1FindingSalientContoursinImages.............. 113 3.2StochasticModelsofContours................. 122 3.3TheMedialAxisforPlanarShapes............... 134 3.4 Gestalt Laws and Grouping Principles . ........... 142 3.5GrammaticalFormalisms.................... 147 3.6Exercises............................ 163 vii i i i i i i i i viii Contents 4 Image Texture, Segmentation and Gibbs Models 173 4.1BasicsIX:GibbsFields..................... 176 4.2 (u + v)-ModelsforImageSegmentation............ 186 4.3SamplingGibbsFields..................... 195 4.4 Deterministic Algorithms to Approximate the Mode of a GibbsField........................... 202 4.5TextureModels......................... 214 4.6 Synthesizing Texture via Exponential Models . ........ 221 4.7TextureSegmentation...................... 228 4.8Exercises............................ 234 5 Faces and Flexible Templates 249 5.1ModelingLightingVariations.................. 253 5.2ModelingGeometricVariationsbyElasticity.......... 259 5.3 Basics XI: Manifolds, Lie Groups, and Lie Algebras . .... 262 5.4ModelingGeometricVariationsbyMetricsonDiff...... 276 5.5ComparingElasticandRiemannianEnergies......... 285 5.6 Empirical Data on Deformations of Faces . ........ 291 5.7TheFullFaceModel...................... 294 5.8Appendix:GeodesicsinDiffandLandmarkSpace...... 301 5.9Exercises............................ 307 6 Natural Scenes and their Multiscale Analysis 317 6.1HighKurtosisintheImageDomain.............. 318 6.2 Scale Invariance in the Discrete and Continuous Setting .... 322 6.3 The Continuous and Discrete Gaussian Pyramids . .... 328 6.4Waveletsandthe“Local”StructureofImages......... 335 6.5DistributionsAreNeeded.................... 348 6.6 Basics XIII: Gaussian Measures on Function Spaces . .... 353 6.7 The Scale-, Rotation- and Translation-Invariant GaussianDistribution...................... 360 6.8ModelII:ImagesMadeUpofIndependentObjects...... 366 6.9FurtherModels......................... 374 6.10 Appendix: A Stability Property of the Discrete GaussianPyramid........................ 377 6.11Exercises............................ 379 Bibliography 387 i i i i i i i i Preface TheNatureofThisBook This book is an introduction to the ideas of Ulf Grenander and the group he has led at Brown University for analyzing all types of signals that the world presents to us. But it is not a basic introductory graduate text that systematically expounds some area of mathematics, as one would do in a graduate course in mathematics. Nor is our goal to explain how to develop all the basic tools for analyzing speech signals or images, as one would do in a graduate course in signal processing or computer vision. In our view, what makes applied mathematics distinctive is that one starts with a collection of problems from some area of science and then seeks the appropriate mathematics for clarifying the experimental data and the under- lying processes producing this data. One needs mathematical tools and, almost always, computational tools as well. The practitioner finds himself or herself en- gaged in a lifelong dialog: seeking models, testing them against data, identifying what is missing in the model, and refining the model. In some situations, the challenge is to find the right mathematical tools; in others, it is to find ways of efficiently calculating the consequences of the model, as well as finding the right parameters in the model. This book, then, seeks to actively bring the reader into such a dialog. To do this, each chapter begins with some example, a class of signals whose variability and patterns we seek to model. Typically, this endeavor calls for some mathematical tools. We put these in sections labeled Basics I, II, etc., and in these sections we put on our mathematical hats and simply develop the math. In most cases, we give the basic definitions, state some results, and prove a few of them. If the reader has not seen this set of mathematical ideas at all, it is probably essential to do some background reading elsewhere for a full exposition of the topic. But if the reader has some background, this section should serve as a refresher, highlighting the definitions and results that we need. Then we compare the model with the data. Usually, new twists emerge. At some point, questions of computability emerge. Here we also have special sections labeled Algorithm I, II, etc. Each chapter ends with a set of exercises. Both of the authors have taught some or part of this material multiple times and have drawn on these classes. In fact, the book is based on lectures delivered in 1998 at the Institut Henri Poincar´e (IHP) by the senior author and the notes made at the time by the junior author. ix i i i i i i i i x Preface The chapters are ordered by the complexity of the signal being studied. In Chapter 1, we study text strings: discrete-valued functions in discrete time. In Chapter 2, we look at music, a real-valued function of continuous time. In Chap- ter 3, we examine character recognition, this being mostly about curvilinear struc- tures in the domain of a function of two variables (namely, an image I(x, y)). In Chapter 4, we study the decomposition of an image into regions with distinct colors and textures, a fully two-dimensional aspect of images. In Chapter 5, we deal with faces, where diffeomorphisms of planar domains is the new player. In Chapter 6, we examine scaling effects present in natural images caused by their statistical self-similarity. For lack of time and space, we have not gone on to the logical next topic: signals with three-dimensional domains, such as various med- ical scans, or the reconstruction of three-dimensional scenes from one or more two-dimensional images
Load more

Recommended publications
  • Symmetric Products of Surfaces; a Unifying Theme for Topology
    Symmetric products of surfaces; a unifying theme for topology and physics Pavle Blagojevi´c Mathematics Institute SANU, Belgrade Vladimir Gruji´c Faculty of Mathematics, Belgrade Rade Zivaljevi´cˇ Mathematics Institute SANU, Belgrade Abstract This is a review paper about symmetric products of spaces SP n(X) := n X /Sn. We focus our attention on the case of 2-manifolds X and make a journey through selected topics of algebraic topology, algebraic geometry, mathematical physics, theoretical mechanics etc. where these objects play an important role, demonstrating along the way the fundamental unity of diverse fields of physics and mathematics. 1 Introduction In recent years we have all witnessed a remarkable and extremely stimulating exchange of deep and sophisticated ideas between Geometry and Physics and in particular between quantum physics and topology. The student or a young scientist in one of these fields is often urged to master elements of the other field as quickly as possible, and to develop basic skills and intuition necessary for understanding the contemporary research in both disciplines. The topology and geometry of manifolds plays a central role in mathematics and likewise in physics. The understanding of duality phenomena for manifolds, mastering the calculus of characteristic classes, as well as understanding the role of fundamental invariants like the signature or Euler characteristic are just examples of what is on the beginning of the growing list of prerequisites for a student in these areas. arXiv:math/0408417v1 [math.AT] 30 Aug 2004 A graduate student of mathematics alone is often in position to take many spe- cialized courses covering different aspects of manifold theory and related areas before an unified picture emerges and she or he reaches the necessary level of maturity.
    [Show full text]
  • 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
    [Show full text]
  • Discurso De Investidura Como Doctor “Honoris Causa” Del Excmo. Sr
    Discurso de investidura como Doctor “Honoris Causa” del Excmo. Sr. Simon Kirwan Donaldson 20 de enero de 2017 Your Excellency Rector Andradas, Ladies and Gentlemen: It is great honour for me to receive the degree of Doctor Honoris Causa from Complutense University and I thank the University most sincerely for this and for the splendid ceremony that we are enjoying today. This University is an ancient institution and it is wonderful privilege to feel linked, through this honorary degree, to a long line of scholars reaching back seven and a half centuries. I would like to mention four names, all from comparatively recent times. First, Eduardo Caballe, a mathematician born in 1847 who was awarded a doctorate of Science by Complutense in 1873. Later, he was a professor in the University and, through his work and his students, had a profound influence in the development of mathematics in Spain, and worldwide. Second, a name that is familiar to all of us: Albert Einstein, who was awarded a doctorate Honoris Causa in 1923. Last, two great mathematicians from our era: Vladimir Arnold (Doctor Honoris Causa 1994) and Jean- Pierre Serre (2006). These are giants of the generation before my own from whom, at whose feet---metaphorically—I have learnt. Besides the huge honour of joining such a group, it is interesting to trace one grand theme running the work of all these four people named. The theme I have in mind is the interplay between notions of Geometry, Algebra and Space. Of course Geometry begins with the exploration of the space we live in—the space of everyday experience.
    [Show full text]
  • Memories of Vladimir Arnold Boris Khesin and Serge Tabachnikov, Coordinating Editors
    Memories of Vladimir Arnold Boris Khesin and Serge Tabachnikov, Coordinating Editors Vladimir Arnold, an eminent mathematician of functions of two variables. Dima presented a two- our time, passed away on June 3, 2010, nine days hour talk at a weekly meeting of the Moscow before his seventy-third birthday. This article, Mathematical Society; it was very uncommon along with one in the previous issue of the Notices, for the society to have such a young speaker. touches on his outstanding personality and his Everybody ad- great contribution to mathematics. mired him, and he certainly de- Dmitry Fuchs served that. Still there was some- thing that kept Dima Arnold in My Life me at a distance Unfortunately, I have never been Arnold’s student, from him. although as a mathematician, I owe him a lot. He I belonged to was just two years older than I, and according to a tiny group of the University records, the time distance between students, led by us was still less: when I was admitted to the Sergei Novikov, Moscow State university as a freshman, he was a which studied al- sophomore. We knew each other but did not com- gebraic topology. municate much. Once, I invited him to participate Just a decade in a ski hiking trip (we used to travel during the before, Pontrya- winter breaks in the almost unpopulated northern gin’s seminar in Russia), but he said that Kolmogorov wanted him Moscow was a to stay in Moscow during the break: they were true center of the going to work together.
    [Show full text]
  • 1914 Martin Gardner
    ΠME Journal, Vol. 13, No. 10, pp 577–609, 2014. 577 THE PI MU EPSILON 100TH ANNIVERSARY PROBLEMS: PART II STEVEN J. MILLER∗, JAMES M. ANDREWS†, AND AVERY T. CARR‡ As 2014 marks the 100th anniversary of Pi Mu Epsilon, we thought it would be fun to celebrate with 100 problems related to important mathematics milestones of the past century. The problems and notes below are meant to provide a brief tour through some of the most exciting and influential moments in recent mathematics. No list can be complete, and of course there are far too many items to celebrate. This list must painfully miss many people’s favorites. As the goal is to introduce students to some of the history of mathematics, ac- cessibility counted far more than importance in breaking ties, and thus the list below is populated with many problems that are more recreational. Many others are well known and extensively studied in the literature; however, as our goal is to introduce people to what can be done in and with mathematics, we’ve decided to include many of these as exercises since attacking them is a great way to learn. We have tried to include some background text before each problem framing it, and references for further reading. This has led to a very long document, so for space issues we split it into four parts (based on the congruence of the year modulo 4). That said: Enjoy! 1914 Martin Gardner Few twentieth-century mathematical authors have written on such diverse sub- jects as Martin Gardner (1914–2010), whose books, numbering over seventy, cover not only numerous fields of mathematics but also literature, philosophy, pseudoscience, religion, and magic.
    [Show full text]
  • Clay Mathematics Institute 2005 James A
    Contents Clay Mathematics Institute 2005 James A. Carlson Letter from the President 2 The Prize Problems The Millennium Prize Problems 3 Recognizing Achievement 2005 Clay Research Awards 4 CMI Researchers Summary of 2005 6 Workshops & Conferences CMI Programs & Research Activities Student Programs Collected Works James Arthur Archive 9 Raoul Bott Library CMI Profile Interview with Research Fellow 10 Maria Chudnovsky Feature Article Can Biology Lead to New Theorems? 13 by Bernd Sturmfels CMI Summer Schools Summary 14 Ricci Flow, 3–Manifolds, and Geometry 15 at MSRI Program Overview CMI Senior Scholars Program 17 Institute News Euclid and His Heritage Meeting 18 Appointments & Honors 20 CMI Publications Selected Articles by Research Fellows 27 Books & Videos 28 About CMI Profile of Bow Street Staff 30 CMI Activities 2006 Institute Calendar 32 2005 Euclid: www.claymath.org/euclid James Arthur Collected Works: www.claymath.org/cw/arthur Hanoi Institute of Mathematics: www.math.ac.vn Ramanujan Society: www.ramanujanmathsociety.org $.* $MBZ.BUIFNBUJDT*OTUJUVUF ".4 "NFSJDBO.BUIFNBUJDBM4PDJFUZ In addition to major,0O"VHVTU BUUIFTFDPOE*OUFSOBUJPOBM$POHSFTTPG.BUIFNBUJDJBOT ongoing activities such as JO1BSJT %BWJE)JMCFSUEFMJWFSFEIJTGBNPVTMFDUVSFJOXIJDIIFEFTDSJCFE the summer schools,UXFOUZUISFFQSPCMFNTUIBUXFSFUPQMBZBOJOnVFOUJBMSPMFJONBUIFNBUJDBM the Institute undertakes a 5IF.JMMFOOJVN1SJ[F1SPCMFNT SFTFBSDI"DFOUVSZMBUFS PO.BZ BUBNFFUJOHBUUIF$PMMÒHFEF number of smaller'SBODF UIF$MBZ.BUIFNBUJDT*OTUJUVUF $.* BOOPVODFEUIFDSFBUJPOPGB special projects
    [Show full text]
  • Statistical Pattern Recognition: a Review
    4 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 22, NO. 1, JANUARY 2000 Statistical Pattern Recognition: A Review Anil K. Jain, Fellow, IEEE, Robert P.W. Duin, and Jianchang Mao, Senior Member, IEEE AbstractÐThe primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques and methods imported from statistical learning theory have been receiving increasing attention. The design of a recognition system requires careful attention to the following issues: definition of pattern classes, sensing environment, pattern representation, feature extraction and selection, cluster analysis, classifier design and learning, selection of training and test samples, and performance evaluation. In spite of almost 50 years of research and development in this field, the general problem of recognizing complex patterns with arbitrary orientation, location, and scale remains unsolved. New and emerging applications, such as data mining, web searching, retrieval of multimedia data, face recognition, and cursive handwriting recognition, require robust and efficient pattern recognition techniques. The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field. Index TermsÐStatistical pattern recognition, classification, clustering, feature extraction, feature selection, error estimation, classifier combination, neural networks. æ 1INTRODUCTION Y the time they are five years old, most children can depend in some way on pattern recognition..
    [Show full text]
  • November 2014
    LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 441 November 2014 Society Meetings ELECTIONS TO COUNCIL AND and Events NOMINATING COMMITTEE 2014 Members should now have for the election can be found on 2014 received a communication from the LMS website at www.lms. Friday the Electoral Reform Society (ERS) ac.uk/about/council/lms-elections. 14 November for both e-voting and paper ballot. For both electronic and postal LMS AGM For online voting, members may voting the deadline for receipt Naylor Lecture cast a vote by going to www. of votes is Thursday 6 November. London votebyinternet.com/LMS2014 and Members may still cast a vote in page 7 using the two part security code person at the AGM, although an Wednesday on the email sent by the ERS and in-person vote must be cast via a 17 December also on their ballot paper. paper ballot. 1 SW & South Wales All members are asked to look Members may like to note that Regional Meeting out for communication from an LMS Election blog, moderated Plymouth page 27 the ERS. We hope that as many by the Scrutineers, can be members as possible will cast their found at http://discussions.lms. 2015 vote. If you have not received ac.uk/elections2014. ballot material, please contact Friday 16 January [email protected], con- Future Elections 150th Anniversary firming the address (post or email) Members are invited to make sug- Launch, London page 9 to which you would like material gestions for nominees for future sent. election to Council. These should Friday 27 February With respect to the election itself, be addressed to the Nominat- Mary Cartwright there are ten candidates proposed ing Committee (nominations@ Lecture, London for six vacancies for Member-at- lms.ac.uk).
    [Show full text]
  • David Donoho COMMENTARY 52 Cliff Ord J
    ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society January 2018 Volume 65, Number 1 JMM 2018 Lecture Sampler page 6 Taking Mathematics to Heart y e n r a page 19 h C th T Ru a Columbus Meeting l i t h i page 90 a W il lia m s r e lk a W ca G Eri u n n a r C a rl ss on l l a d n a R na Da J i ll C . P ip her s e v e N ré F And e d e r i c o A rd ila s n e k c i M . E d al Ron Notices of the American Mathematical Society January 2018 FEATURED 6684 19 26 29 JMM 2018 Lecture Taking Mathematics to Graduate Student Section Sampler Heart Interview with Sharon Arroyo Conducted by Melinda Lanius Talithia Williams, Gunnar Carlsson, Alfi o Quarteroni Jill C. Pipher, Federico Ardila, Ruth WHAT IS...an Acylindrical Group Action? Charney, Erica Walker, Dana Randall, by omas Koberda André Neves, and Ronald E. Mickens AMS Graduate Student Blog All of us, wherever we are, can celebrate together here in this issue of Notices the San Diego Joint Mathematics Meetings. Our lecture sampler includes for the first time the AMS-MAA-SIAM Hrabowski-Gates-Tapia-McBay Lecture, this year by Talithia Williams on the new PBS series NOVA Wonders. After the sampler, other articles describe modeling the heart, Dürer's unfolding problem (which remains open), gerrymandering after the fall Supreme Court decision, a story for Congress about how geometry has advanced MRI, “My Father André Weil” (2018 is the 20th anniversary of his death), and a profile on Donald Knuth and native script by former Notices Senior Writer and Deputy Editor Allyn Jackson.
    [Show full text]
  • October 2008
    THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 374 October 2008 Society THE PROPOSAL FOR A NEW SOCIETY Meetings In all likelihood you will now have present form fulfil many of the and Events received a copy of the proposal hopes and expectations of their for a new society, combining the members, times are changing and 2008 present London Mathematical the need for mathematics as a uni- Friday 21 November Society and Institute of Mathe- fied activity to hold and defend AGM, London matics and its Applications. For its position in the public sphere [page 3] a new society to be formed, the grows constantly greater. IMA and the LMS must both vote As the Presidents’ letter which 12–13 December separately in favour of the accompanies the report makes Joint Meeting with proposal. clear, there is a pressing need to the Edinburgh There has been debate about engage effectively with govern- Mathematical Society this for several years but mem- ment, with external bodies, with Edinburgh [page 7] bers could be forgiven for think- the media and with the public. ing that, despite progress reports A society that represents the 2009 appearing in Mathematics Today broad spectrum of the mathemat- Friday 27 February and the Newsletter, things had ical community and has a larger Mary Cartwright ‘gone quiet’. The process leading membership must inevitably carry Lecture, London up to the present proposal has greater weight. been protracted not because the Your view is important and you 31 March – 4 April two societies disagree with one will soon have an opportunity to LMS Invited Lectures another, which they do not, but take part in this important deci- Edinburgh because those developing the new sion.
    [Show full text]
  • Crash Prediction and Collision Avoidance Using Hidden
    CRASH PREDICTION AND COLLISION AVOIDANCE USING HIDDEN MARKOV MODEL A Thesis Submitted to the Faculty of Purdue University by Avinash Prabu In Partial Fulfillment of the Requirements for the Degree of Master of Science in Electrical and Computer Engineering August 2019 Purdue University Indianapolis, Indiana ii THE PURDUE UNIVERSITY GRADUATE SCHOOL STATEMENT OF THESIS APPROVAL Dr. Lingxi Li, Chair Department of Electrical and Computer Engineering Dr. Yaobin Chen Department of Electrical and Computer Engineering Dr. Brian King Department of Electrical and Computer Engineering Approved by: Dr. Brian King Head of Graduate Program iii Dedicated to my family, friends and my Professors, for their support and encouragement. iv ACKNOWLEDGMENTS Firstly, I would like to thank Dr. Lingxi Li for his continuous support and en- couragement. He has been a wonderful advisor and an exceptional mentor, without whom, my academic journey will not be where it is now. I would also like to to thank Dr. Yaobin Chen, whose course on Control theory has had a great impact in shaping this thesis. I would like to extend my appreciation to Dr. Brian King, who has been a great resource of guidance throughout the course of my Master's degree. A special thanks to Dr. Renran Tian, who is my principle investigator at TASI, IUPUI, for his guidance and encouragement. I also wish to thank Sherrie Tucker, who has always been available to answer my questions, despite her busy schedule. I would like to acknowledge my parents, Mr. & Mrs. Prabhu and my sister Chathurma for their continuous belief and endless love towards me.
    [Show full text]
  • IMS Council Election Results
    Volume 42 • Issue 5 IMS Bulletin August 2013 IMS Council election results The annual IMS Council election results are in! CONTENTS We are pleased to announce that the next IMS 1 Council election results President-Elect is Erwin Bolthausen. This year 12 candidates stood for six places 2 Members’ News: David on Council (including one two-year term to fill Donoho; Kathryn Roeder; Erwin Bolthausen Richard Davis the place vacated by Erwin Bolthausen). The new Maurice Priestley; C R Rao; IMS Council members are: Richard Davis, Rick Durrett, Steffen Donald Richards; Wenbo Li Lauritzen, Susan Murphy, Jane-Ling Wang and Ofer Zeitouni. 4 X-L Files: From t to T Ofer will serve the shorter term, until August 2015, and the others 5 Anirban’s Angle: will serve three-year terms, until August 2016. Thanks to Council Randomization, Bootstrap members Arnoldo Frigessi, Nancy Lopes Garcia, Steve Lalley, Ingrid and Sherlock Holmes Van Keilegom and Wing Wong, whose terms will finish at the IMS Rick Durrett Annual Meeting at JSM Montreal. 6 Obituaries: George Box; William Studden IMS members also voted to accept two amendments to the IMS Constitution and Bylaws. The first of these arose because this year 8 Donors to IMS Funds the IMS Nominating Committee has proposed for President-Elect a 10 Medallion Lecture Preview: current member of Council (Erwin Bolthausen). This brought up an Peter Guttorp; Wald Lecture interesting consideration regarding the IMS Bylaws, which are now Preview: Piet Groeneboom reworded to take this into account. Steffen Lauritzen 14 Viewpoint: Are professional The second amendment concerned Organizational Membership.
    [Show full text]