This revised edition offers an approach to information theory that is more general than the classical approach of Shannon. Classically, information is defined for an alphabet of symbols or for a set of mutually exclusive propositions (a partition of the probability space ) with corresponding probabilities adding up to 1. The new definition is given for an arbitrary cover of , i.e. for a set of possibly overlapping propositions. The generalized information concept is called novelty and it is accompanied by two concepts derived from it, designated as information and surprise, which describe "opposite" versions of novelty, information being related more to classical information theory and surprise being related more to the classical concept of statistical significance. In the discussion of these three concepts and their interrelations several properties or classes of covers are defined, which turn out to be lattices. The book also presents applications of these concepts, mostly in statistics and in neuroscience.

This book addresses the challenging tasks of verifying and debugging structurally complex multipliers. In the area of verification, the authors first investigate the challenges of Symbolic Computer Algebra (SCA)-based verification, when it comes to proving the correctness of multipliers. They then describe three techniques to improve and extend SCA: vanishing monomials removal, reverse engineering, and dynamic backward rewriting. This enables readers to verify a wide variety of multipliers, including highly complex and optimized industrial benchmarks. The authors also describe a complete debugging flow, including bug localization and fixing, to find the location of bugs in structurally complex multipliers and make corrections.

The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.

This text presents notions and ideas at the foundations of a statistical treatment of risks. The focus is on statistical applications within the field of engineering risk and safety analysis. Coverage includes Bayesian methods. Such knowledge facilitates the understanding of the influence of random phenomena and gives a deeper understanding of the role of probability in risk analysis. The text is written for students who have studied elementary undergraduate courses in engineering mathematics, perhaps including a minor course in statistics. This book differs from typical textbooks in its verbal approach to many explanations and examples.

Computational Optimization of Internal Combustion Engines presents the state of the art of computational models and optimization methods for internal combustion engine development using multi-dimensional computational fluid dynamics (CFD) tools and genetic algorithms. Strategies to reduce computational cost and mesh dependency are discussed, as well as regression analysis methods. Several case studies are presented in a section devoted to applications, including assessments of: spark-ignition engines, dual-fuel engines, heavy duty and light duty diesel engines. Through regression analysis, optimization results are used to explain complex interactions between engine design parameters, such as nozzle design, injection timing, swirl, exhaust gas recirculation, bore size, and piston bowl shape. Computational Optimization of Internal Combustion Engines demonstrates that the current multi-dimensional CFD tools are mature enough for practical development of internal combustion engines. It is written for researchers and designers in mechanical engineering and the automotive industry.

Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics," "CFD," "completely integrable systems," "chaos, synergetics and large-scale order," which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics."

This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. The conditions required to satisfy the no-slip boundary conditions in the various formulations are discussed in detail. Rather than focussing on a particular spatial discretization method, the text provides a unitary view of several methods currently in use for the numerical solution of incompressible Navier-Stokes equations, using either finite differences, finite elements or spectral approximations. For each formulation, a complete statement of the mathematical problem is provided, comprising the various boundary, possibly integral, and initial conditions, suitable for any theoretical and/or computational development of the governing equations. The text is suitable for courses in fluid mechanics and computational fluid dynamics. It covers that part of the subject matter dealing with the equations for incompressible viscous flows and their determination by means of numerical methods. A substantial portion of the book contains new results and unpublished material.

This book includes selected papers from the ECCOMAS Thematic Conference on Multibody Dynamics, that took place in Barcelona, Spain, from June 29 to July 2, 2015. By having its origin in analytical and continuum mechanics, as well as in computer science and applied mathematics, multibody dynamics provides a basis for analysis and virtual prototyping of innovative applications in many fields of contemporary engineering. With the utilization of computational models and algorithms that classically belonged to different fields of applied science, multibody dynamics delivers reliable simulation platforms for diverse highly-developed industrial products such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, smart structures, biomechanical systems, and nanotechnologies.

Essential Mathematics for Chemists is ideally suited for students who have a limited mathematical background and who wish to build their confidence in the use of mathematics that is relevant to their chemistry studies. John Gormally has many years' experience of teaching mathematics to chemistry students and has set out specifically to address common difficulties in understanding the subject. Assuming little knowledge of mathematics, this book first introduces basic skills in handling numbers before covering key topics relevant to chemistry including functions, elementary algebraic manipulation, differential and integral calculus and matrix algebra. The order of the chapters reflects the way in which chemistry courses are often structured and relates to both lecture and laboratory courses. Self-test questions are provided within the text and answers are given at the end of each chapter. Together with the numerous worked examples and sets of graded problems provided, these will help students to acquire relevant skills and gain confidence.

This monograph is focused on control law design methods for asymptotic tracking and disturbance rejection in the presence of uncertainties. The methods are based on adaptive implementation of the Internal Model Principle (IMP). The monograph shows how this principle can be applied to the problems of asymptotic rejection/tracking of a priori uncertain exogenous signals for linear and nonlinear plants with known and unknown parameters. The book begins by introducing the problems of adaptive control, the challenges that are faced, modern methods and an overview of the IMP. It then introduces special observers for uncertain exogeneous signals affecting linear and nonlinear systems with known and unknown parameters. The basic algorithms of adaptation applied to the canonical closed-loop error models are presented. The authors then address the systematic design of adaptive systems for asymptotic rejection/tracking of a priori uncertain exosignals. The monograph also discusses the adaptive rejection/tracking of a priori uncertain exogenous signals in systems with input delay, the problems of performance improvement in disturbance rejection and reference tracking and the issue of robustness of closed-loop systems. Adaptive Regulation provides a systematic discussion of the IMP applied to a variety of control problems, making it of interest to researchers and industrial practitioners.

A collection of articles emphasizing modern interpolation theory, a topic which has seen much progress in recent years. These ideas and problems in operator theory, often arising from systems and control theories, bring the reader to the forefront of current research in this area.

The book presents recently developed efficient metaheuristic optimization algorithms and their applications for solving various optimization problems in civil engineering. The concepts can also be used for optimizing problems in mechanical and electrical engineering.

This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 16th Symposium of the International Society of Dynamic Games, held July 9-12, 2014, in Amsterdam. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including differential games, evolutionary games, and stochastic games. They discuss theoretical developments, algorithmic methods, issues relating to lack of information, and applications in areas such as biological or economical competition, stability in communication networks, and maintenance decisions in an electricity market, just to name a few. Advances in Dynamic and Evolutionary Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinary audience of researchers, practitioners, and advanced graduate students.

The language-communication-society triangle defies traditional scientific approaches. Rather, it is a phenomenon that calls for an integration of complex, transdisciplinary perspectives, if we are to make any progress in understanding how it works. The highly diverse agents in play are not merely cognitive and/or cultural, but also emotional and behavioural in their specificity. Indeed, the effort may require building a theoretical and methodological body of knowledge that can effectively convey the characteristic properties of phenomena in human terms.

New complexity approaches allow us to rethink our limited and mechanistic images of human societies and create more appropriate emo-cognitive dynamic and holistic models. We have to enter into dialogue with the complexity views coming out of other more material sciences, but we also need to take steps in the linguistic and psycho-sociological fields towards creating perspectives and concepts better fitted to human characteristics.

Our understanding of complexity is different but not opposed to the one that is more commonly found in texts written by people working in physics or computer science, for example. The goal of this book is to extend the knowledge of these other more human or socially oriented perspectives on complexity, taking account of the language and communication singularities of human agents in society.

Our understanding of complexity is different but not opposed to the one that is more commonly found in texts written by people working in physics or computer science, for example. The goal of this book is to extend the knowledge of these other more human or socially oriented perspectives on complexity, taking account of the language and communication singularities of human agents in society.

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This book offers the first comprehensive account of the new method of density matrix renormalization. Recent years have seen enormous progress in the numerical treatment of low-dimensional quantum sytems. With this new technique, which selects a reduced set of basis states via density matrices, it has become possible to treat large systems with amazing accuracy. The method has been applied successfully to a variety of important one-dimensional problems such as spin chains, Kondo models, and correlated electron systems. Extensions to other systems and higher dimensions are currently being developed. The contributions to this book are written by leading experts in the field. The two parts contain an introduction to the subject and a review of physical applications. As a combination of advanced textbook and guide to current research the book should become a standard source for everyone interested in the topic.

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors' interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors' fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

This book discusses state estimation of stochastic dynamic systems from noisy measurements, specifically sequential Bayesian estimation and nonlinear or stochastic filtering. The class of solutions presented in this book is based on the Monte Carlo statistical method. Although the resulting algorithms, known as particle filters, have been around for more than a decade, the recent theoretical developments of sequential Bayesian estimation in the framework of random set theory have provided new opportunities which are not widely known and are covered in this book. This book is ideal for graduate students, researchers, scientists and engineers interested in Bayesian estimation.

This new edition presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering. The filtering algorithms are derived via different approaches, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection. Other topics include Kalman filtering for systems with correlated noise or colored noise, limiting Kalman filtering for time-invariant systems, extended Kalman filtering for nonlinear systems, interval Kalman filtering for uncertain systems, and wavelet Kalman filtering for multiresolution analysis of random signals. Most filtering algorithms are illustrated by using simplified radar tracking examples. The style of the book is informal, and the mathematics is elementary but rigorous. The text is self-contained, suitable for self-study, and accessible to all readers with a minimum knowledge of linear algebra, probability theory, and system engineering. Over 100 exercises and problems with solutions help deepen the knowledge. This new edition has a new chapter on filtering communication networks and data processing, together with new exercises and new real-time applications.

In recent years meshless/meshfree methods have gained considerable attention in engineering and applied mathematics. The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available. The book presents a significant sample of the state of the art in the field with methods that have reached a certain level of maturity while also addressing many open issues.

The book collects extended original contributions presented at the Second ECCOMAS Conference on Meshless Methods held in 2007 in Porto. The list of contributors reveals a fortunate mix of highly distinguished authors as well as quite young but very active and promising researchers, thus giving the reader an interesting and updated view of different meshless approximation methods and their range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

A strong and fluent competency in mathematics is a necessary condition for scientific, technological and economic progress. However, it is widely recognized that problem solving, reasoning, and thinking processes are critical areas in which students' performance lags far behind what should be expected and desired. Mathematics is indeed an important subject, but is also important to be able to use it in extra-mathematical contexts. Thinking strictly in terms of mathematics or thinking in terms of its relations with the real world involve quite different processes and issues. This book includes the revised papers presented at the NATO ARW "Information Technology and Mathematical Problem Solving Research," held in April 1991, in Viana do Castelo, Portugal, which focused on the implications of computerized learning environments and cognitive psychology research for these mathematical activities. In recent years, several committees, professional associations, and distinguished individuals throughout the world have put forward proposals to renew mathematics curricula, all emphasizing the importance of problem solving. In order to be successful, these reforming intentions require a theory-driven research base. But mathematics problem solving may be considered a "chaotic field" in which progress has been quite slow.

Mathematical Analysis for Modeling is intended for those who want to understand the substance of mathematics, rather than just having familiarity with its techniques. It provides a thorough understanding of how mathematics is developed for and applies to solving scientific and engineering problems. The authors stress the construction of mathematical descriptions of scientific and engineering situations, rather than rote memorizations of proofs and formulas. Emphasis is placed on algorithms as solutions to problems and on insight rather than formal derivations.

Because elementary mathematics is vital to be able to properly design biological experiments and interpret their results. As a student of the life sciences you will only make your life harder by ignoring mathematics entirely. Equally, you do not want to spend your time struggling with complex mathematics that you will never use. This book is the perfect answer to your problems. Inside, it explains the necessary mathematics in easy-to-follow steps, introducing the basics and showing you how to apply these to biological situations.
Easy Mathematics for Biologists covers the basic mathematical ideas of fractions, decimals and percentages, through ratio and proportion, exponents and logarithms, to straight line graphs, graphs that are not straight lines, and their transformation. Direct application of each of these leads to a clear understanding of biological calculations such as those involving concentrations and dilutions, changing units, pH, and linear and non-linear rates of reaction. Each chapter contains worked examples, and is followed by numerous problems, both pure and applied, that can be worked through in your own time. Answers to these can be found at the back.

This textbook has been conceptualized to provide a detailed description of the various aspects of Systems and Synthetic Biology, keeping the requirements of M.Sc. and Ph.D. students in mind. Also, it is hoped that this book will mentor young scientists who are willing to contribute to this area but do not know from where to begin. The book has been divided into two sections. The first section will deal with systems biology - in terms of the foundational understanding, highlighting issues in biological complexity, methods of analysis and various aspects of modelling. The second section deals with the engineering concepts, design strategies of the biological systems ranging from simple DNA/RNA fragments, switches and oscillators, molecular pathways to a complete synthetic cell will be described. Finally, the book will offer expert opinions in legal, safety, security and social issues to present a well-balanced information both for students and scientists.

Along the years, rough set theory has earned a well-deserved reputation as a sound methodology for dealing with imperfect knowledge in a simple though mathematically sound way. This edited volume aims at continue stressing the benefits of applying rough sets in many real-life situations while still keeping an eye on topological aspects of the theory as well as strengthening its linkage with other soft computing paradigms. The volume comprises 11 chapters and is organized into three parts. Part 1 deals with theoretical contributions while Parts 2 and 3 focus on several real world data mining applications. Chapters authored by pioneers were selected on the basis of fundamental ideas/concepts rather than the thoroughness of techniques deployed. Academics, scientists as well as engineers working in the rough set, computational intelligence, soft computing and data mining research area will find the comprehensive coverage of this book invaluable.