Princeton Series in Applied Mathematics

Paul Embrechts is Professor of Mathematics at the Swiss Federal Institute of Technology (ETHZ), Zürich, Switzerland. He is the author of numerous scientific papers on stochastic processes and their applications and the coauthor of the influential book on Modelling of Extremal Events for Insurance and Finance. Makoto Maejima is Professor of Mathematics at Keio University, Yokohama, Japan. He has published extensively on selfsimilarity and stable processes. The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity. "Authoritative and written by leading experts, this book is a significant contribution to a growing field. Selfsimilar processes crop up in a wide range of subjects from finance to physics, so this book will have a correspondingly wide readership."-Chris Rogers, Bath University "This is a timely book. Everybody is talking about scaling, and selfsimilar stochastic processes are the basic and the clearest examples of models with scaling. In applications from finance to communication networks, selfsimilar processes are believed to be important. Yet much of what is known about them is folklore; this book fills the void and gives reader access to some hard facts. And because this book requires only modest mathematical sophistication, it is accessible to a wide audience."-Gennady Samorodnitsky, Cornell University

Jiming Peng is Professor of Mathematics at McMaster University and has published widely on nonlinear programming and interior-points methods. Cornelis Roos holds joint professorships at Delft University of Technology and Leiden University. He is an editor of several journals, coauthor of more than 100 papers, and coauthor (with Tamás Terlaky and Jean-Philippe Vial) of Theory and Algorithms for Linear Optimization. Tamás Terlaky is Professor in the Department of Computing and Software at McMaster University, founding Editor in Chief of Optimization and Engineering, coauthor of more than 100 papers, and an editor of several journals and two books. Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work. "The new idea of self-regular functions is very elegant and I am sure that this book will have a major impact on the field of optimization."-Robert Vanderbei, Princeton University "The progress outlined in Self-Regularity represents one of the really major events in our field during the last five years or so. This book requires just standard mathematical background on the part of the reader and is thus accessible to beginners as well as experts."-Arkadi Nemirovski, Technion-Israel Institute of Technology

"Wassim Haddad, Winner of the 2014 Pendray Aerospace Literature Award, American Institute of Aeronautics and Astronautics" Wassim M. Haddad is Professor of Aerospace Engineering at the Georgia Institute of Technology. VijaySekhar Chellaboina is Associate Professor in the Department of Mechanical, Aerospace, and Biomedical Engineering at the University of Tennessee, Knoxville. Sergey G. Nersesov is a Ph.D. student in aerospace engineering at Georgia Institute of Technology. This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science. "The mathematical approach taken by the authors, as originally initiated by C. Caratheodory on the advice of Max Born, results in a book that makes a fundamental contribution to the field. The main emphasis is on the notion of large-scale dynamical systems applied to the multitude of small objects contained in the macroscale description. Indeed, thermodynamics is the dynamics of an extremely large number of objects numbering on the order of Avogadro's number. That some definite results arise from that setting is the marvel of it all."---Gérard A. Maugin, IEEE Control Systems "This is an original theory with many attractive features and which captures the known statements from classical thermodynamics, avoiding at the same time imprecise formulations. The techniques are based on dynamical systems and control theory, which is unusual in the field, but the presentation is precise and well crafted."---Manuel Portilheiro, Mathematical Reviews "This is an original contribution to the important, but very diverse, field of thermodynamics. The book's self-contained system-theoretic approach makes it accessible to a wide audience of readers."-Jan Willems, University of Gronigen "This is a truly original and fundamental contribution to the field of thermodynamics. It will make a lasting contribution to the literature."-Naira Hovakimyan, Virginia Polytechnic Institute and State University

Rajendra Bhatia is Professor of Mathematics at the Indian Statistical Institute in New Delhi. He is the author of five books, including Matrix Analysis. This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices. Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses. "Written by an expert in the area, the book presents in an accessible manner a lot of important results from the realm of positive matrices and of their applications. . . . The book can be used for graduate courses in linear algebra, or as supplementary material for courses in operator theory, and as a reference book by engineers and researchers working in the applied field of quantum information."---S. Cobzas, Studia Universitatis Babes-Bolyai, Mathematica "There is no obvious competitor for Bhatia's book, due in part to its focus, but also because it contains some very recent material drawn from research articles. Beautifully written and intelligently organised, Positive Definite Matrices is a welcome addition to the literature. Readers who admired his Matrix Analysis will no doubt appreciate this latest book of Rajendra Bhatia."---Douglas Farenick, Image "This is an outstanding book. Its exposition is both concise and leisurely at the same time."---Jaspal Singh Aujla, Zentralblatt MATH "This is a monograph for mathematicians interested in an important realm of matrix-analytic ideas. Like the author's distinguished book, Matrix Analysis, it will be a convenient and much-quoted reference source. There are many wonderful insights in a first-rate exposition of important ideas not easily extracted from other sources. The scholarship is impeccable."-Roger A. Horn, University of Utah "I believe that every expert in matrix analysis can find something new in this book. Bhatia presents some important material in several topics related to positive definite matrices including positive linear maps, completely positive maps, matrix means, positive definite functions, and geometry of positive definite matrices. There are many beautiful results, useful techniques, and ingenious ideas here. Bhatia's writing style has always been concise, clear, and illuminating."-Xingzhi Zhan, East China Normal University

Mehran Mesbahi is associate professor of aeronautics and astronautics at the University of Washington. Magnus Egerstedt is associate professor of electrical and computer engineering at Georgia Institute of Technology. This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: ? • University of Stuttgart, Germany • Royal Institute of Technology, Sweden • Johannes Kepler University, Austria • Georgia Tech, USA • University of Washington, USA • Ohio University, USA "Presently, there are few books on multiagent systems. Thus, this book can be a useful reference book for graduate students and researchers focusing on systems, controls, and robotics, and help them to better know and study multiagent systems."---Long Wang, Mathematical Reviews "This well-organized book is an extensive and complete introduction to graph theoretic methods in the context of multiagent and multivehicle cooperative networks. The presentation of the material is elegant and in addition to basic results, the book includes new topics not commonly found in the literature. Ideal for graduate students and researchers, the book represents a significant contribution to the emerging field of cooperative control and consensus."-Randy Beard, Brigham Young University "This comprehensive overview of multiagent coordination brings together the existing literature on the subject and presents it in a clean, pedagogical fashion. The book will be useful to those in the areas of control theory, signal processing, and related disciplines."-Ali Jadbabaie, University of Pennsylvania "This book focuses on graph theoretic techniques in multiagent systems, with a strong emphasis on agreement problems. It covers a good selection of issues and will make a solid textbook for advanced courses in the field."-Richard Murray, California Institute of Technology

Shaun M. Fallat is professor of mathematics and statistics at the University of Regina. Charles R. Johnson is the Class of 1961 Professor of Mathematics at the College of William & Mary. Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics. The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references. "This book is a very useful new reference on the subject of TN matrices and it will be of interest to researchers on matrix theory as well as to researchers of any field where total positivity has applications."---Juan Manuel Pefia, Mathematical Reviews "This book is a valuable new reference on the subject of totally nonnegative matrices and its insights will be much appreciated by a broad community of readers interested in matrix theory and its applications."-Charles Micchelli, City University of Hong Kong and State University of New York, Albany

Luca Zaccarian is associate professor of control engineering at the University of Rome, Tor Vergata. Andrew R. Teel is a professor in the Electrical and Computer Engineering Department at the University of California, Santa Barbara. This book provides a wide variety of state-space--based numerical algorithms for the synthesis of feedback algorithms for linear systems with input saturation. Specifically, it addresses and solves the anti-windup problem, presenting the objectives and terminology of the problem, the mathematical tools behind anti-windup algorithms, and more than twenty algorithms for anti-windup synthesis, illustrated with examples. Luca Zaccarian and Andrew Teel's modern method--combining a state-space approach with algorithms generated by solving linear matrix inequalities--treats MIMO and SISO systems with equal ease. The book, aimed at control engineers as well as graduate students, ranges from very simple anti-windup construction to sophisticated anti-windup algorithms for nonlinear systems. • Describes the fundamental objectives and principles behind anti-windup synthesis for control systems with actuator saturation • Takes a modern, state-space approach to synthesis that applies to both SISO and MIMO systems • Presents algorithms as linear matrix inequalities that can be readily solved with widely available software • Explains mathematical concepts that motivate synthesis algorithms • Uses nonlinear performance curves to quantify performance relative to disturbances of varying magnitudes • Includes anti-windup algorithms for a class of Euler-Lagrange nonlinear systems • Traces the history of anti-windup research through an extensive annotated bibliography "This book goes a long way toward providing comprehensive coverage of systematic procedures for anti-windup synthesis, emphasizing algorithmic issues and modern design techniques. A valuable resource for researchers and practitioners, it should interest a broad audience in control engineering, as well as in other disciplines, such as mechanical and chemical engineering."-Prodromos Daoutidis, University of Minnesota

Mihály Bakonyi (1962-2010) was professor of mathematics at Georgia State University and coauthor of Schur's Algorithm and Several Applications. Hugo J. Woerdeman is professor and head of the Department of Mathematics at Drexel University. Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines. "This volume is warmly recommended to those students who want to get acquainted with the important field of matrix completion, interpolation and moment problems, having many applications in areas such as electrical engineering, computer science and physics. It will certainly serve also as an indispensable, basic reference for researchers."---László Kérchy, Acta-Scientiarum-Mathematicarum

"Winner of the 2007 Lanchester Prize, Informs" David L. Applegate is a researcher at AT&T Labs. Robert E. Bixby is Research Professor of Management and Noah Harding Professor of Computational and Applied Mathematics at Rice University. Vasek Chvátal is Canada Research Chair in Combinatorial Optimization at Concordia University. William J. Cook is Chandler Family Chair in Industrial and Systems Engineering at the Georgia Institute of Technology. This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple enough: given a set of cities and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience. The authors of this book are the same pioneers who for nearly two decades have led the investigation into the traveling salesman problem. They have derived solutions to almost eighty-six thousand cities, yet a general solution to the problem has yet to be discovered. Here they describe the method and computer code they used to solve a broad range of large-scale problems, and along the way they demonstrate the interplay of applied mathematics with increasingly powerful computing platforms. They also give the fascinating history of the problem--how it developed, and why it continues to intrigue us. "The authors have done a wonderful job of explaining how they developed new techniques in response to the challenges posed by ever larger instances of the Traveling Salesman Problem." "By bringing together the best work from a wide array of researchers, advancing the field where needed, describing their findings in a book, and implementing everything in an extremely well-written computer program, the authors show how research in computational combinatorial optimization should be done."---Michael Trick, Operations Research Letters "The book is certainly a must for every researcher in practical TSP-computation."---Ulrich Faigle, Mathematical Reviews "It is very well written and clearly structured. Many examples are provided, which help the reader to better understand the presented results. The authors succeed in describing the TSP problem, beginning with its history, and the first approaches, and ending with the state of the art."---Stefan Nickel, Zentralblatt MATH "[T]the text read[s] more like a best-seller than a tome of mathematics. . . . The resulting book provides not only a map for understanding TSP computation, but should be the starting point for anyone interested in launching a computational assault on any combinatorial optimization problem."---Jan Karel Lenstra, SIAM Review "[T]he book provides a comprehensive treatment of the traveling salesman problem and I highly recommend it not only to specialists in the area but to anyone interested in combinatorial optimization." "This book addresses one of the most famous and important combinatorial-optimization problems-the traveling salesman problem. It is very well written, with a vivid style that captures the reader's attention. Many examples are provided that are very useful to motivate and help the reader to better understand the results presented in the book."-Matteo Fischetti, University of Padova "This is a fantastic book. Ever since the early days of discrete optimization, the traveling salesman problem has served as the model for computationally hard problems. The authors are main players in this area who forged a team in 1988 to push the frontiers on how good we are in solving hard and large traveling salesman problems. Now they lay out their views, experience, and findings in this book."-Bert Gerards, Centrum voor Wiskunde en Informati

"Wassim Haddad, Winner of the 2014 Pendray Aerospace Literature Award, American Institute of Aeronautics and Astronautics" Wassim M. Haddad is a professor in the School of Aerospace Engineering and chair of the Flight Mechanics and Control Discipline at Georgia Institute of Technology. Sergey G. Nersesov is an associate professor in the Department of Mechanical Engineering at Villanova University. Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control. "The monograph is an excellent up-to-date authoritative reference covering original results which are presented in a rigorous, unified framework with examples. . . . The book will be useful primarily to applied mathematicians, control theorists and engineers, and anyone dealing with Lyapunov stability and control of nonlinear interconnected dynamic systems."---Lubomir Bakule, Zentralblatt MATH "This solid book provides a unique perspective and detailed account of the theory and applications of vector Lyapunov functions. I am confident it will be well received by researchers and graduate students working in control theory and large-scale systems."-Mehran Mesbahi, University of Washington "With admirable and sound scholarship, and great scientific maturity, this book gives a methodical development of vector Lyapunov functions and vector control Lyapunov functions for the design of distributed control systems. It is a welcome addition to the literature and develops a rigorous foundation for applications in an important emerging new area."-Frank L. Lewis, University of Texas, Arlington

G. F. Roach is professor emeritus in the Department of Mathematics and Statistics at the University of Strathclyde. I. G. Stratis is professor in the Department of Mathematics at the National and Kapodistrian University, Athens. A. N. Yannacopoulos is professor in the Department of Statistics at the Athens University of Economics and Business. Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians. "This monograph is of a very high standard, allowing the reader to learn many facets of the rapidly growing field of complex media and to get up-to-date information on a number of open research problems."---Vilmos Komornik, Mathematical Reviews "This is an outstanding book that has the potential to become a real classic. It is the first to systematically address the mathematics of electromagnetic wave propagation in complex media. It will be useful not only to mathematicians but also graduate students, physicists, and engineers who want to get a state-of-the-art picture of scattering by complex media."-Gerhard Kristensson, Lund University, Sweden

M. Vidyasagar is the Cecil and Ida Green Chair in Systems Biology Science at the University of Texas, Dallas. His many books include Computational Cancer Biology: An Interaction Network Approach and Control System Synthesis: A Factorization Approach. This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. The book starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are taken from post-genomic biology, especially genomics and proteomics. The topics examined include standard material such as the Perron-Frobenius theorem, transient and recurrent states, hitting probabilities and hitting times, maximum likelihood estimation, the Viterbi algorithm, and the Baum-Welch algorithm. The book contains discussions of extremely useful topics not usually seen at the basic level, such as ergodicity of Markov processes, Markov Chain Monte Carlo (MCMC), information theory, and large deviation theory for both i.i.d and Markov processes. The book also presents state-of-the-art realization theory for hidden Markov models. Among biological applications, it offers an in-depth look at the BLAST (Basic Local Alignment Search Technique) algorithm, including a comprehensive explanation of the underlying theory. Other applications such as profile hidden Markov models are also explored. "This book will serve as a solid and invaluable reference."---Byung-Jun Yoon, Quarterly Review of Biology "This book provides a terrific introduction to an important and widely studied field-Markov processes (including hidden Markov processes)-with a particular view toward applications to problems in biology. With a wonderful balance of rigor, intuition, and choice of topics, the book gives a unique treatment of the subject for those interested in both fundamental theory and important applications."-Sanjeev Kulkarni, Princeton University "Vidyasagar uses sound scholarship to address hidden Markov processes and their application to problems in computational biology, in particular to genomics and proteomics. The well-organized book examines topics not often covered, such as realization theory and order determination for hidden Markov processes, and also looks at significant properties such as ergodicity and mixing. This work will be useful to systems researchers as well as computational biologists."-Steve Marcus, University of Maryland

"One of Choice's Outstanding Academic Titles for 2015" Leiba Rodman is professor of mathematics at the College of William & Mary. His books include Matrix Polynomials, Algebraic Riccati Equations, and Indefinite Linear Algebra and Applications. Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used. "Rodman fills a void in the monographic literature with this work." "The book is self-contained and well organized. . . . Full and detailed proofs are supplied. Another exciting point is the presence of many open problems throughout the book."---Gisele C. Ducati, MatchSciNet "[This book] will be an important reference for years to come for both researchers in the field of linear algebra and scientists who apply quaternions."---Ch. Baxa, Zentralblatt Math "This is a very serious treatise by an author who is a powerful researcher and a clear expositor. I know of no other book that treats both the basic theory and advanced material as carefully and as comprehensively as this one. Topics in Quaternion Linear Algebra is a singular contribution of considerable value."-Douglas R. Farenick, author of Algebras of Linear Transformations "This unique book brings under one cover various recent results obtained by Rodman, several of his collaborators, and other researchers. In addition to general topics in quaternionic linear algebra, it treats extensively the canonical forms of several types of quaternionic matrix pencils and the quaternionic numerical ranges of matrices. "-Dragomir Djokovic, distinguished professor emeritus, University of Waterloo

Habib Ammari is director of research at the French National Center for Scientific Research and professor of mathematics at the École Normale Superiéure. Elie Bretin is a postdoctoral researcher in mathematics at the École Polytechnique. Josselin Garnier is professor of mathematics at Université Paris VII. Hyeonbae Kang is the Jungseok Chair Professor of Mathematics at Inha University in South Korea. Hyundae Lee is assistant professor of mathematics at Inha University. Abdul Wahab is a postdoctoral researcher in mathematics at Université Paris VII. This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative–based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures. "This timely book that is devoted to a topic of paramount importance is very well written and it contains useful and interesting material. I strongly believe that it will be a valuable resource for researchers in elasticity imaging and related areas of nondestructive testing and inverse problems."---Akhtar A. Khan, MathSciNet "This book covers recent mathematical, numerical, and statistical approaches for elasticity imaging of inclusions and cracks. A precise and timely book, it is easy to follow and will interest readers."-Yanyan Li, Rutgers University "This book is the first to provide readers with a comprehensive overview of mathematical and computational studies of elasticity imaging. It is a useful resource for scientists and engineers in the relevant fields and a solid reference for any newcomers to elasticity imaging."-Gang Bao, Zhejiang University "This well-organized book explains recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. It makes an important contribution to the understanding of trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution in multistatic imaging."-Jin Keun Seo, Yonsei University