The book includes articles from eminent international scientists discussing a wide spectrum of topics of current importance in mathematics and statistics and their applications. It presents state-of-the-art material along with a clear and detailed review of the relevant topics and issues concerned. The topics discussed include message transmission, colouring problem, control of stochastic structures and information dynamics, image denoising, life testing and reliability, survival and frailty models, analysis of drought periods, prediction of genomic profiles, competing risks, environmental applications and chronic disease control. It is a valuable resource for researchers and practitioners in the relevant areas of mathematics and statistics.

The second volume of this authoritative work traces the material outlined in the first, but in far greater detail and with a much higher degree of sophistication. The authors begin with the theory of the electromagnetic interaction, and then consider hadronic structure, exploring the accuracy of the quark model by examining the excited states of baryons and mesons. They introduce the color variable as a prelude to the development of quantum chromodynamics, the theory of the strong interaction, and go on to discuss the electroweak interaction--the broken symmetry of which they explain by the Higgs mechanism--and conclude with a consideration of grand unification theories.

Microcontinuum Field Theories constitutes an extension of classical field theories - of elastic solids, viscous fluids, electromagnetism, and the like - to microscopic length and time scales. Material bodies are viewed as collections of a large number of deformable particles (sub-continua), suitable for modeling blood, porous media, polymers, liquid crystals, slurries, and composite materials. This volume extends and applies the ideas developed in the first volume, Microcontinuum Field Theories: Foundations and Solids, to liquid crystals, biological fluids, and other microstretch and micomorphic fluids. The theory makes it possible to discuss properties of such materials that are beyond the scope of classical field theories and may provide a basis for the resolution of some outstanding problems, such as turbulence.

This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

The book presents research that contributes to the development of intelligent dialog systems to simplify diverse aspects of everyday life, such as medical diagnosis and entertainment. Covering major thematic areas: machine learning and artificial neural networks; algorithms and models; and social and biometric data for applications in human-computer interfaces, it discusses processing of audio-visual signals for the detection of user-perceived states, the latest scientific discoveries in processing verbal (lexicon, syntax, and pragmatics), auditory (voice, intonation, vocal expressions) and visual signals (gestures, body language, facial expressions), as well as algorithms for detecting communication disorders, remote health-status monitoring, sentiment and affect analysis, social behaviors and engagement. Further, it examines neural and machine learning algorithms for the implementation of advanced telecommunication systems, communication with people with special needs, emotion modulation by computer contents, advanced sensors for tracking changes in real-life and automatic systems, as well as the development of advanced human-computer interfaces. The book does not focus on solving a particular problem, but instead describes the results of research that has positive effects in different fields and applications.

The book presents a state-of-the-art overview of biomechanical and mechanobiological modeling and simulation of soft biological tissues. Seven well-known scientists working in that particular field discuss topics such as biomolecules, networks and cells as well as failure, multi-scale, agent-based, bio-chemo-mechanical and finite element models appropriate for computational analysis. Applications include arteries, the heart, vascular stents and valve implants as well as adipose, brain, collagenous and engineered tissues. The mechanics of the whole cell and sub-cellular components as well as the extracellular matrix structure and mechanotransduction are described. In particular, the formation and remodeling of stress fibers, cytoskeletal contractility, cell adhesion and the mechanical regulation of fibroblast migration in healing myocardial infarcts are discussed. The essential ingredients of continuum mechanics are provided. Constitutive models of fiber-reinforced materials with an emphasis on arterial walls and the myocardium are discussed and the important influence of residual stresses on material response emphasized. The mechanics and function of the heart, the brain and adipose tissues are discussed as well. Particular attention is focused on microstructural and multi-scale modeling, finite element implementation and simulation of cells and tissues.

This book offers a detailed investigation of breakdowns in traffic and transportation networks. It shows empirically that transitions from free flow to so-called synchronized flow, initiated by local disturbances at network bottlenecks, display a nucleation-type behavior: while small disturbances in free flow decay, larger ones grow further and lead to breakdowns at the bottlenecks. Further, it discusses in detail the significance of this nucleation effect for traffic and transportation theories, and the consequences this has for future automatic driving, traffic control, dynamic traffic assignment, and optimization in traffic and transportation networks. Starting from a large volume of field traffic data collected from various sources obtained solely through measurements in real world traffic, the author develops his insights, with an emphasis less on reviewing existing methodologies, models and theories, and more on providing a detailed analysis of empirical traffic data and drawing consequences regarding the minimum requirements for any traffic and transportation theories to be valid. The book - proves the empirical nucleation nature of traffic breakdown in networks - discusses the origin of the failure of classical traffic and transportation theories - shows that the three-phase theory is incommensurable with the classical traffic theories, and - explains why current state-of-the art dynamic traffic assignments tend to provoke heavy traffic congestion, making it a valuable reference resource for a wide audience of scientists and postgraduate students interested in the fundamental understanding of empirical traffic phenomena and related data-driven phenomenology, as well as for practitioners working in the fields of traffic and transportation engineering.

This book presents a new, multidisciplinary perspective on and paradigm for integrative experimental design research. It addresses various perspectives on methods, analysis and overall research approach, and how they can be synthesized to advance understanding of design. It explores the foundations of experimental approaches and their utility in this domain, and brings together analytical approaches to promote an integrated understanding. The book also investigates where these approaches lead to and how they link design research more fully with other disciplines (e.g. psychology, cognition, sociology, computer science, management). Above all, the book emphasizes the integrative nature of design research in terms of the methods, theories, and units of study-from the individual to the organizational level. Although this approach offers many advantages, it has inherently led to a situation in current research practice where methods are diverging and integration between individual, team and organizational understanding is becoming increasingly tenuous, calling for a multidisciplinary and transdiscipinary perspective. Experimental design research thus offers a powerful tool and platform for resolving these challenges. Providing an invaluable resource for the design research community, this book paves the way for the next generation of researchers in the field by bridging methods and methodology. As such, it will especially benefit postgraduate students and researchers in design research, as well as engineering designers.

This book presents up-to-date research developments and novel methodologies to solve various stability and control problems of dynamic systems with time delays. First, it provides the new introduction of integral and summation inequalities for stability analysis of nominal time-delay systems in continuous and discrete time domain, and presents corresponding stability conditions for the nominal system and an applicable nonlinear system. Next, it investigates several control problems for dynamic systems with delays including H(infinity) control problem Event-triggered control problems; Dynamic output feedback control problems; Reliable sampled-data control problems. Finally, some application topics covering filtering, state estimation, and synchronization are considered. The book will be a valuable resource and guide for graduate students, scientists, and engineers in the system sciences and control communities.

Highly topical and original monograph, introducing the author's work on the Riemann zeta function and its adelic interpretation of interest to a wide range of mathematicians and physicists.

This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Loewner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive bibliography covering over twelve decades of results and an introduction rich in historical and biographical details complement the eight main chapters of this monograph. Given its systematic and consistent notation and background results, this book provides a self-contained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics.

This book offers a theoretical description of topological matter in terms of effective field theories, and in particular topological field theories, focusing on two main topics: topological superconductors and topological insulators.Even though there is vast literature on these subjects, the book fills an important gap by providing a concise introduction to both topological order and symmetry-protected phases using a modern mathematical language, and developing the theoretical concepts by highlighting the physics and the physical properties of the systems. Further, it discusses in detail the topological interactions for topologically ordered matter, and the response to smooth external fields for symmetry protected matter. The book also covers more specialized topics that cannot be found elsewhere. Specifically, the response of superconductors to geometry, including the newly discovered geo-Meissner effect; and a correction to the usual Meissner effect, only present in the topologically interesting chiral superconductors.

Comprehensive and thorough, this monograph emphasizes the main role differential geometry and convex analysis play in the understanding of physical, chemical, and mechanical notions. Central focus is placed on specifying the agreement between the functional framework and its physical necessity and on making clear the intrinsic character of physical elements, independent from specific charts or frames. The book is divided into four sections, covering thermostructure, classical mechanics, fluid mechanics modelling, and behavior laws. An extensive appendix provides notations and definitions as well as brief explanation of integral manifolds, symplectic structure, and contact structure. Plenty of examples are provided throughout the book, and reviews of basic principles in differential geometry and convex analysis are presented as needed. This book is a useful resource for graduate students and researchers in the field.

This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, "Fractals and Related Fields II," held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.

The central subject of this thesis is the theoretical description of ultrafast dynamical processes in molecular systems of chemical interest and their control by laser pulses. This work encompasses different cutting-edge methods in quantum chemistry, quantum dynamics and for the rigorous description of the interaction of light and matter at the molecular level. It provides a general quantum mechanical framework for the description of chemical processes guided by laser pulses, in particular near conical intersections, i.e. geometries where the nuclear and electronic motions couple and the molecule undergoes non-adiabatic (or non-Born-Oppenheimer) dynamics. In close collaboration with experimentalists, the author succeeds in making a decisive step to link and to apply quantum physics to chemistry by transferring state of the art techniques and concepts developed in physics to chemistry, such as "light dressed atoms and molecules" and "adiabatic Floquet theory". He applies these techniques in three prototypic model systems (aniline, pyrazine and NHD2) using high-level electronic structure calculations. Readers will enjoy the comprehensive and accessible introduction to the topic and methodology, as well as the clear structure of the thesis.

Using phase-plane analysis, findings from the theory of topological horseshoes and linked-twist maps, this book presents a novel method to prove the existence of chaotic dynamics. In dynamical systems, complex behavior in a map can be indicated by showing the existence of a Smale-horseshoe-like structure, either for the map itself or its iterates. This usually requires some assumptions about the map, such as a diffeomorphism and some hyperbolicity conditions. In this text, less stringent definitions of a horseshoe have been suggested so as to reproduce some geometrical features typical of the Smale horseshoe, while leaving out the hyperbolicity conditions associated with it. This leads to the study of the so-called topological horseshoes. The presence of chaos-like dynamics in a vertically driven planar pendulum, a pendulum of variable length, and in other more general related equations is also proved.

"Understanding Complex Urban Systems" takes as its point of departure the insight that the challenges of global urbanization and the complexity of urban systems cannot be understood let alone managed by sectoral and disciplinary approaches alone. But while there has recently been significant progress in broadening and refining the methodologies for the quantitative modeling of complex urban systems, in deepening the theoretical understanding of cities as complex systems, or in illuminating the implications for urban planning, there is still a lack of well-founded conceptual thinking on the methodological foundations and the strategies of modeling urban complexity across the disciplines.

Bringing together experts from the fields of urban and spatial planning, ecology, urban geography, real estate analysis, organizational cybernetics, stochastic optimization, and literary studies, as well as specialists in various systems approaches and in transdisciplinary methodologies of urban analysis, the volume seeks to advance the discussion on multidisciplinary approaches to urban modeling. While engaging with the state of the art in their respective fields, the contributions are specifically written for both experts from a broad range of disciplines as well as for urban practitioners who feel the need for new approaches given the uncertainty of current developments.

The book presents the challenges inherent in the paradigm shift of network systems from static to highly dynamic distributed systems - it proposes solutions that the symbiotic nature of biological systems can provide into altering networking systems to adapt to these changes. The author discuss how biological systems - which have the inherent capabilities of evolving, self-organizing, self-repairing and flourishing with time - are inspiring researchers to take opportunities from the biology domain and map them with the problems faced in network domain. The book revolves around the central idea of bio-inspired systems -- it begins by exploring why biology and computer network research are such a natural match. This is followed by presenting a broad overview of biologically inspired research in network systems -- it is classified by the biological field that inspired each topic and by the area of networking in which that topic lies. Each case elucidates how biological concepts have been most successfully applied in various domains. Nevertheless, it also presents a case study discussing the security aspects of wireless sensor networks and how biological solution stand out in comparison to optimized solutions. Furthermore, it also discusses novel biological solutions for solving problems in diverse engineering domains such as mechanical, electrical, civil, aerospace, energy and agriculture. The readers will not only get proper understanding of the bio inspired systems but also better insight for developing novel bio inspired solutions.

This edited volume presents examples of social science research projects that employ new methods of quantitative analysis and mathematical modeling of social processes. This book presents the fascinating areas of empirical and theoretical investigations that use formal mathematics in a way that is accessible for individuals lacking extensive expertise but still desiring to expand their scope of research methodology and add to their data analysis toolbox. Mathematical Modeling of Social Relationships professes how mathematical modeling can help us understand the fundamental, compelling, and yet sometimes complicated concepts that arise in the social sciences. This volume will appeal to upper-level students and researchers in a broad area of fields within the social sciences, as well as the disciplines of social psychology, complex systems, and applied mathematics.

Simulation of ODE/PDE Models with MATLAB(r), OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration.

Besides conventional finite-difference and element techniques, more advanced spatial-approximation methods are examined in some detail, including nonoscillatory schemes and adaptive-grid approaches. A MOL toolbox has been developed within MATLAB(r)/OCTAVE/SCILAB. In addition to a set of spatial approximations and time integrators, this toolbox includes a collection of application examples, in specific areas, which can serve as templates for developing new programs.

Simulation of ODE/PDE Models with MATLAB(r), OCTAVE and SCILAB provides a practical introduction to some advanced computational techniques for dynamic system simulation, supported by many worked examples in the text, and a collection of codes available for download from the book s page at www.springer.com. This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.

The book provides a state-of-art overview of computational methods for nonlinear aeroelasticity and load analysis, focusing on key techniques and fundamental principles for CFD/CSD coupling in temporal domain. CFD/CSD coupling software design and applications of CFD/CSD coupling techniques are discussed in detail as well. It is an essential reference for researchers and students in mechanics and applied mathematics.

This thesis provides a systematic and integral answer to an open problem concerning the universality of dynamic fuzzy controllers. It presents a number of novel ideas and approaches to various issues including universal function approximation, universal fuzzy models, universal fuzzy stabilization controllers, and universal fuzzy integral sliding mode controllers. The proposed control design criteria can be conveniently verified using the MATLAB toolbox. Moreover, the thesis provides a new, easy-to-use form of fuzzy variable structure control. Emphasis is given to the point that, in the context of deterministic/stochastic systems in general, the authors are in fact discussing non-affine nonlinear systems using a class of generalized T-S fuzzy models, which offer considerable potential in a wide range of applications.

This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincare maps, chaos, fractals and strange attractors. The Baker s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painleve property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special emphasis on some aspects of fluid dynamics and plasma physics reflecting the author s involvement in these areas of physics. A few exercises have been provided that range from simple applications to occasional considerable extension of the theory. Finally, the list of references given at the end of the book contains primarily books and papers used in developing the lecture material this volume is based on.

This book has grown out of the author s lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism has been kept to a minimum.

This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theoretically inclined researcher in the physical sciences and engineering.

This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity and precision, updating and amplification of several sections, addition of new material like theory of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and critical phenomena perspectives on the fluid turbulence problem and many new exercises."

Hermann Haken (born 1927) is one of the "fathers" of the quantum-mechanical laser theory, formulated between 1962 and 1966, in strong competition with American researchers. Later on, he created Synergetics, the science of cooperation in multicomponent systems. The book concentrates on the development of his scientific work during the first thirty-five years of his career. In 1970 he and his doctoral student Robert Graham were able to show that the laser is an example of a nonlinear system far from thermal equilibrium that shows a phase-transition like behavior. Subsequently, this insight opened the way for the formulation of Synergetics. Synergetics is able to explain, how very large systems show the phenomenon of self-organization that can be mathematically described by only very few order parameters. The results of Haken's research were published in two seminal books Synergetics (1977) and Advanced Synergetics (1983). After the year 1985 Haken concentrated his research on the macroscopic foundation of Synergetics. This led him towards the application of synergetic principles in medicine, cognitive research and, finally, in psychology. A comprehensive bibliography of Hermann Haken's publications (nearly 600 numbers) is included in the book.