Electroencephalography and magnetoencephalography are the two most efficient techniques to study the functional brain. This book completely aswers the fundamental mathematical question of uniqueness of the representations obtained using these techniques, and also covers many other concrete results for special geometric models of the brain, presenting the research of the authors and their groups in the last two decades.

Today, virtually any advance in the life sciences requires a sophisticated mathematical approach. The methods of mathematics and computer science have emerged as critical tools to modeling biological phenomena, understanding patterns, and making sense of large data sets, such as those generated by the human genome project. An Invitation to Biomathematics provides a comprehensive, yet easily digested entry into the diverse world of mathematical biology--the union of biology, mathematics, and computer science.
This textbook, expertly written by a team of experienced educators, is divided into two parts. The first section presents core principles as elucidated by classical problems such as population growth, predator-prey interactions, epidemic models, and population genetics, while the second applies these principles to modern biomedical research. In addition, the supplementary work Laboratory Manual of Biomathematics (available separately) is designed to enable hands-on exploration of model development, model validation, and model refinement.
* Provides a complete guide for development of quantification skills crucial for applying mathematical methods to biological problems.
* Includes well-known examples from across disciplines in the life sciences including modern biomedical research.
* Explains how to use data sets or dynamical processes to build mathematical models.
* Offers extensive illustrative materials.
* Written in clear and easy-to-follow language without assuming a background in math or biology.
* A laboratory manual is available for hands-on, computer-assisted projects based on material covered in the text.

This book emphasizes those topological methods (of dynamical systems) and theories that are useful in the study of different classes of nonautonomous evolutionary equations. The content is developed over six chapters, providing a thorough introduction to the techniques used in the Chapters III-VI described by Chapter I-II. The author gives a systematic treatment of the basic mathematical theory and constructive methods for Nonautonomous Dynamics. They show how these diverse topics are connected to other important parts of mathematics, including Topology, Functional Analysis and Qualitative Theory of Differential/Difference Equations. Throughout the book a nice balance is maintained between rigorous mathematics and applications (ordinary differential/difference equations, functional differential equations and partial difference equations). The primary readership includes graduate and PhD students and researchers in in the field of dynamical systems and their applications (control theory, economic dynamics, mathematical theory of climate, population dynamics, oscillation theory etc).

This book focuses on multi-model systems, describing how to apply intelligent technologies to model complex multi-model systems by combining stochastic jumping system, neural network and fuzzy models. It focuses on robust filtering, including finite-time robust filtering, finite-frequency robust filtering and higher order moment robust filtering schemes, as well as fault detection problems for multi-model jump systems, such as observer-based robust fault detection, filtering-based robust fault detection and neural network-based robust fault detection methods. The book also demonstrates the validity and practicability of the theoretical results using simulation and practical examples, like circuit systems, robot systems and power systems. Further, it introduces readers to methods such as finite-time filtering, finite-frequency robust filtering, as well as higher order moment and neural network-based fault detection methods for multi-model jumping systems, allowing them to grasp the modeling, analysis and design of the multi-model systems presented and implement filtering and fault detection analysis for various systems, including circuit, network and mechanical systems.

This study aid on numerical optimization techniques is intended for university undergraduate and postgraduate mechanical engineering students. Optimization procedures are becoming more and more important for lightweight design, where weight reduction can, for example in the case of automotive or aerospace industry, lead to lower fuel consumption and a corresponding reduction in operational costs as well as beneficial effects on the environment. Based on the free computer algebra system Maxima, the authors present procedures for numerically solving problems in engineering mathematics as well as applications taken from traditional courses on the strength of materials. The mechanical theories focus on the typical one-dimensional structural elements, i.e., springs, bars, and Euler-Bernoulli beams, in order to reduce the complexity of the numerical framework and limit the resulting design to a low number of variables. The use of a computer algebra system and the incorporated functions, e.g., for derivatives or equation solving, allows a greater focus on the methodology of the optimization methods and not on standard procedures. The book also provides numerous examples, including some that can be solved using a graphical approach to help readers gain a better understanding of the computer implementation.

The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles - the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems - are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.

What is the origin of game preferences and payoffs, how are they aggregated and what are the implications of interdependent preferences? What is the importance of information for building game models? How can game models be used to analyse empirical cases? At the cutting edge of current modelling in international relations using non-cooperative game theory, this collection of original contributions from political scientists and economists explores some of the fundamental assumptions of game theory modelling. It includes a theory of game payoff formation, a theory of preference aggregation, thorough discussions of the effects of interdependence between preferences upon various game structures, in-depth analyses of the impact of incomplete information upon dynamic games of negotiation, and a study using differential games. Numerous illustrations, case studies and comparative case studies show the relevance of the theoretical debate. The chapters are organised to allow readers with a limited knowledge of game theory to develop their understanding of the fundamental issues. Containing theoretical discussion of the basic game theory assumptions - as well as means of going beyond them - Game Theory and International Relations will be welcomed by all those interested in the empirical application of game theory models in international relations.

Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006.
Requires no preliminary knowledge of graduate and advanced mathematics
Discusses the fundamental results of last 15 years in this theory
Suitable for courses for undergraduate students as well as graduate students and specialists in physics mathematics and other sciences

The revised edition gives a comprehensive mathematical and physical presentation of fluid flows in non-classical models of convection - relevant in nature as well as in industry. After the concise coverage of fluid dynamics and heat transfer theory it discusses recent research. This monograph provides the theoretical foundation on a topic relevant to metallurgy, ecology, meteorology, geo-and astrophysics, aerospace industry, chemistry, crystal physics, and many other fields.

This thesis is concerned with flows through cascades, i.e. periodic arrays of obstacles. Such geometries are relevant to a range of physical scenarios, chiefly the aerodynamics and aeroacoustics of turbomachinery flows. Despite the fact that turbomachinery is of paramount importance to a number of industries, many of the underlying mechanisms in cascade flows remain opaque. In order to clarify the function of different physical parameters, the author considers six separate problems. For example, he explores the significance of realistic blade geometries in predicting turbomachinery performance, and the possibility that porous blades can achieve noise reductions. In order to solve these challenging problems, the author deploys and indeed develops techniques from across the spectrum of complex analysis: the Wiener-Hopf method, Riemann-Hilbert problems, and the Schottky-Klein prime function all feature prominently. These sophisticated tools are then used to elucidate the underlying mathematical and physical structures present in cascade flows. The ensuing solutions greatly extend previous works and offer new avenues for future research. The results are not of simply academic value but are also useful for aircraft designers seeking to balance aeroacoustic and aerodynamic effects.

This book reports on current challenges in bridge engineering faced by professionals around the globe, giving a special emphasis to recently developed techniques and methods for bridge design, construction and monitoring. Based on extended and revised papers selected from outstanding presentation at the Istanbul Bridge Conference 2018, held from November 5 - 6, 2018, in Istanbul, Turkey, and by highlighting major bridge studies, spanning from numerical and modeling studies to the applications of new construction techniques and monitoring systems, this book is intended to promote high standards in modern bridge engineering. It offers a timely reference to both academics and professionals in this field.

This book delivers the state of the art in deep learning (DL) methods hybridized with evolutionary computation (EC). Over the last decade, DL has dramatically reformed many domains: computer vision, speech recognition, healthcare, and automatic game playing, to mention only a few. All DL models, using different architectures and algorithms, utilize multiple processing layers for extracting a hierarchy of abstractions of data. Their remarkable successes notwithstanding, these powerful models are facing many challenges, and this book presents the collaborative efforts by researchers in EC to solve some of the problems in DL. EC comprises optimization techniques that are useful when problems are complex or poorly understood, or insufficient information about the problem domain is available. This family of algorithms has proven effective in solving problems with challenging characteristics such as non-convexity, non-linearity, noise, and irregularity, which dampen the performance of most classic optimization schemes. Furthermore, EC has been extensively and successfully applied in artificial neural network (ANN) research -from parameter estimation to structure optimization. Consequently, EC researchers are enthusiastic about applying their arsenal for the design and optimization of deep neural networks (DNN). This book brings together the recent progress in DL research where the focus is particularly on three sub-domains that integrate EC with DL: (1) EC for hyper-parameter optimization in DNN; (2) EC for DNN architecture design; and (3) Deep neuroevolution. The book also presents interesting applications of DL with EC in real-world problems, e.g., malware classification and object detection. Additionally, it covers recent applications of EC in DL, e.g. generative adversarial networks (GAN) training and adversarial attacks. The book aims to prompt and facilitate the research in DL with EC both in theory and in practice.

This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics.

Key Features:

.A unique book concentrated on theory of discrete dynamical systems and its traditional as well as advanced applications to economics.
.Mathematical definitions and theorems are introduced in a systematic and easily accessible way.
.Examples are from almost all fields of economics; technically proceeding from basic to advanced topics.
.Lively illustrations with numerous figures.
.Numerous simulation to see paths of economic dynamics.
.Comprehensive treatment of the subject with a comprehensive and easily accessible approach.
Key Features:

.A unique book concentrated on theory of discrete dynamical systems and its traditional as well as advanced applications to economics.
.Mathematical definitions and theorems are introduced in a systematic and easily accessible way.
.Examples are from almost all fields of economics; technically proceeding from basic to advanced topics.
.Lively illustrations with numerous figures.
.Numerous simulation to see paths of economic dynamics.
.Comprehensive treatment of the subject with a comprehensive and easily accessible approach."

The objective of this book is to construct a rigorous mathematical approach to linear hereditary problems of wave propagation theory and demonstrate the efficiency of mathematical theorems in hereditary mechanics. By using both real end complex Tauberian techniques for the Laplace transform, a classification of near-front asymptotics of solutions to considered equations is given-depending on the singularity character of the memory function. The book goes on to derive the description of the behavior of these solutions and demonstrates the importance of nonlinear Laplace transform in linear hereditary elasticity. This book is of undeniable value to researchers working in areas of mathematical physics and related fields.

Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.

Applied Dimensional Analysis and Modeling provides the full mathematical background and step-by-step procedures for employing dimensional analyses, along with a wide range of applications to problems in engineering and applied science, such as fluid dynamics, heat flow, electromagnetics, astronomy and economics. This new edition offers additional worked-out examples in mechanics, physics, geometry, hydrodynamics, and biometry.
* Covers 4 essential aspects and applications:
- principal characteristics of dimensional systems
- applications of dimensional techniques in engineering, mathematics and geometry
- applications in biosciences, biometry and economics
- applications in astronomy and physics
* Offers more than 250 worked-out examples and problems with solutions
* Provides detailed descriptions of techniques of both dimensional analysis and dimensional modeling

Reliability is a fundamental criterium in engineering systems. This book shows innovative concepts and applications of mathematics in solving reliability problems. The contents address in particular the interaction between engineers and mathematicians, as well as the cross-fertilization in the advancement of science and technology. It bridges the gap between theory and practice to aid in practical problem-solving in various contexts.

Quantum mechanics - central not only to physics, but also to chemistry, materials science, and other fields - is notoriously abstract and difficult. Essential Quantum Mechanics is a uniquely concise and explanatory book that fills the gap between introductory and advanced courses, between popularizations and technical treatises. By focusing on the fundamental structure, concepts, and methods of quantum mechanics, this introductory yet sophisticated work emphasizes both physical and mathematical understanding. A modern perspective is adopted throughout - the goal, in part, being to gain entry into the world of 'real' quantum mechanics, as used by practicing scientists. With over 60 original problems, Essential Quantum Mechanics is suitable as either a text or a reference. It will be invaluable to physics students as well as chemists, electrical engineers, philosophers, and others whose work is impacted by quantum mechanics, or who simply wish to better understand this fascinating subject.

Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

This book presents the stream-tube method (STM), a method offering computational means of dealing with the two- and three-dimensional properties of numerous incompressible materials in static and dynamic conditions. The authors show that the kinematics and stresses associated with the flow and deformation in such materials can be treated by breaking the system down into simple computational sub-domains in which streamlines are straight and parallel and using one or two mapping functions in steady-state and non-steady-state conditions. The STM is considered for various problems in non-Newtonian fluid mechanics with different geometries. The book makes use of examples and applications to illustrate the use of the STM. It explores the possibilities of computation on simple mapped rectangular domains and three-dimensional parallel-piped domains under different conditions. Complex materials with memory are considered simply without particle tracking problems. Readers, including researchers, engineers and graduate students, with a foundational knowledge of calculus, linear algebra, differential equations and fluid mechanics will benefit most greatly from this book.

This book provides a unique and comprehensive overview of the latest advances, challenges and accomplishments in the rapidly growing field of theoretical and computational materials science. Today, an increasing number of industrial communities rely more and more on advanced atomic-scale methods to obtain reliable predictions of materials properties, complement qualitative experimental analyses and circumvent experimental difficulties. The book examines some of the latest and most advanced simulation techniques currently available, as well as up-to-date theoretical approaches adopted by a selected panel of twelve international research teams. It covers a wide range of novel and advanced materials, exploring their structural, elastic, optical, mass and electronic transport properties. The cutting-edge techniques presented appeal to physicists, applied mathematicians and engineers interested in advanced simulation methods in materials science. The book can also be used as additional literature for undergraduate and postgraduate students with majors in physics, chemistry, applied mathematics and engineering.

This book examines the problems in the field of energy and related areas (including chemistry, transport, aerospace, construction, metallurgy and engineering) that Ukrainian scientists are currently investigating. The research presented focuses on ensuring the operational reliability, durability and safety of energy equipment, as well as the development of control, diagnostics and monitoring systems in the energy sector. Further, the book explores the ecological consequences of energy facilities , particularly environmental pollution in large cities and industrial areas. Written mainly by representatives of the Council of Young Scientists of the Department of Physical and Technical Problems of Energy at the NAS of Ukraine, it is intended for researchers and engineers, as well as lecturers and postgraduates at higher education institutions interested in the control, diagnosis and monitoring of energy facilities.

This book presents a survey of the aspects of economic complexity, with a focus on foundational, interdisciplinary ideas. The long-awaited follow up to his 2011 volume Complex Evolutionary Dynamics in Urban-Regional and Ecologic-Economic Systems: From Catastrophe to Chaos and Beyond, this volume draws together the threads of Rosser's earlier work on complexity theory and its wide applications in economics and an expanded list of related disciplines. The book begins with a full account of the broader categories of complexity in economics--dynamic, computational, hierarchical, and structural--before shifting to more detailed analysis. The next two chapters address problems associated with computational complexity, especially those of computability, and discuss the Godel Incompleteness Theorem with a focus on reflexivity. The middle chapters discuss the relationship between entropy, econophysics, evolution, and economic complexity, respectively, with applications in urban and regional dynamics, ecological economics, general equilibrium theory, as well as financial market dynamics. The final chapter works to bring together these themes into a broader framework and expose some of the limits concerning analysis of deeper foundational issues. With applications in all disciplines characterized by interconnected nonlinear adaptive systems, this book is appropriate for graduate students, professors and practitioners in economics and related disciplines such as regional science, mathematics, physics, biology, environmental sciences, philosophy, and psychology.

The aim of this book is to present recent results in both theoretical and applied knot theory-which are at the same time stimulating for leading researchers in the field as well as accessible to non-experts. The book comprises recent research results while covering a wide range of different sub-disciplines, such as the young field of geometric knot theory, combinatorial knot theory, as well as applications in microbiology and theoretical physics.

This volume collects the edited and reviewed contributions presented in the 8th iTi Conference on Turbulence, held in Bertinoro, Italy, in September 2018. In keeping with the spirit of the conference, the book was produced afterwards, so that the authors had the opportunity to incorporate comments and discussions raised during the event. The respective contributions, which address both fundamental and applied aspects of turbulence, have been structured according to the following main topics: I TheoryII Wall-bounded flowsIII Simulations and modellingIV ExperimentsV Miscellaneous topicsVI Wind energy