The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.

This book focuses on modelling and simulation, control and optimization, signal processing, and forecasting in selected nonlinear dynamical systems, presenting both literature reviews and novel concepts. It develops analytical or numerical approaches, which are simple to use, robust, stable, flexible and universally applicable to the analysis of complex nonlinear dynamical systems. As such it addresses key challenges are addressed, e.g. efficient handling of time-varying dynamics, efficient design, faster numerical computations, robustness, stability and convergence of algorithms. The book provides a series of contributions discussing either the design or analysis of complex systems in sciences and engineering, and the concepts developed involve nonlinear dynamics, synchronization, optimization, machine learning, and forecasting. Both theoretical and practical aspects of diverse areas are investigated, specifically neurocomputing, transportation engineering, theoretical electrical engineering, signal processing, communications engineering, and computational intelligence. It is a valuable resource for students and researchers interested in nonlinear dynamics and synchronization with applications in selected areas.

This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics. Contents Rigid Body Equations of Motion and Their Integration The Euler - Poisson Equations and Their Generalizations The Kirchhoff Equations and Related Problems of Rigid Body Dynamics Linear Integrals and Reduction Generalizations of Integrability Cases. Explicit Integration Periodic Solutions, Nonintegrability, and Transition to Chaos Appendix A : Derivation of the Kirchhoff, Poincare - Zhukovskii, and Four-Dimensional Top Equations Appendix B: The Lie Algebra e(4) and Its Orbits Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev - Chaplygin Top Appendix D: The Hess Case and Quantization of the Rotation Number Appendix E: Ferromagnetic Dynamics in a Magnetic Field Appendix F: The Landau - Lifshitz Equation, Discrete Systems, and the Neumann Problem Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids

The present volume contains selected papers issued from the sixth edition of the International Conference "Numerical methods for hyperbolic problems" that took place in 2019 in Malaga (Spain). NumHyp conferences, which began in 2009, focus on recent developments and new directions in the field of numerical methods for hyperbolic partial differential equations (PDEs) and their applications. The 11 chapters of the book cover several state-of-the-art numerical techniques and applications, including the design of numerical methods with good properties (well-balanced, asymptotic-preserving, high-order accurate, domain invariant preserving, uncertainty quantification, etc.), applications to models issued from different fields (Euler equations of gas dynamics, Navier-Stokes equations, multilayer shallow-water systems, ideal magnetohydrodynamics or fluid models to simulate multiphase flow, sediment transport, turbulent deflagrations, etc.), and the development of new nonlinear dispersive shallow-water models. The volume is addressed to PhD students and researchers in Applied Mathematics, Fluid Mechanics, or Engineering whose investigation focuses on or uses numerical methods for hyperbolic systems. It may also be a useful tool for practitioners who look for state-of-the-art methods for flow simulation.

Discrete-Time and Discrete-Space Dynamical Systems provides a systematic characterization of the similarities and differences of several types of discrete-time and discrete-space dynamical systems, including: Boolean control networks; nondeterministic finite-transition systems; finite automata; labelled Petri nets; and cellular automata. The book's perspective is primarily based on topological properties though it also employs semitensor-product and graph-theoretic methods where appropriate. It presents a series of fundamental results: invertibility, observability, detectability, reversiblity, etc., with applications to systems biology. Academic researchers with backgrounds in applied mathematics, engineering or computer science and practising engineers working with discrete-time and discrete-space systems will find this book a helpful source of new understanding for this increasingly important class of systems. The basic results to be found within are of fundamental importance for further study of related problems such as automated synthesis and safety control in cyber-physical systems using formal methods.

This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.

At the heart of this book is the generalized theoretical approach that is applied to investigate the geoelectrical structure of the Earth's mantle. It also analyzes the results of regional and global induction sounding of the Earth's mantle and compares them with the results obtained by other geophysical methods. The generalized theoretical approach employs the Induction Law as a basis for identifying extended relations between magnetic field components, including their plane divergence, impedances and spatial derivatives. The estimations of impedance values and spatial derivatives are performed using the theory of stochastic processes. The book also considers the external sources of magnetic fields used for sounding the Earths mantle from the modern theory perspective, as well as the problem of coincidence of magneto-variation and magnetotelluric methods. Further, it discusses secular variations in the Earth's resistance caused by non-induction sources, factors that are correlated with the number of earthquakes in the region and shifted in time with global indexes. It is a valuable resource for scientists applying deep induction soundings or interested in the structures of and processes in the Earth's interior.

This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier-Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asy mptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is a valuable resource for researchers, PhD and master's level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.

This book offers a comprehensive overview of fading and shadowing in wireless channels. A number of statistical models including simple, hybrid, compound and cascaded ones are presented along with a detailed discussion of diversity techniques employed to mitigate the effects of fading and shadowing. The effects of co-channel interference before and after the implementation of diversity are also analyzed. To facilitate easy understanding of the models and the analysis, the background on probability and random variables is presented with relevant derivations of densities of the sums, products, ratios as well as order statistics of random variables. The book also provides material on digital modems of interest in wireless systems. The updated edition expands the background materials on probability by offering sections on Laplace and Mellin transforms, parameter estimation, statistical testing and receiver operating characteristics. Newer models for fading, shadowing and shadowed fading are included along with the analysis of diversity combining algorithms. In addition, this edition contains a new chapter on Cognitive Radio. Based on the response from readers of the First Edition, detailed Matlab scripts used in the preparation of this edition are provided. Wherever necessary, Maple scripts used are also provided.

This book concentrates on the topic of evaluation of Jacobians in some specific linear as well as nonlinear matrix transformations, in the real and complex cases, which are widely applied in the statistical, physical, engineering, biological and social sciences. It aims to develop some techniques systematically so that anyone with a little exposure to multivariable calculus can easily follow the steps and understand the various methods by which the Jacobians in complicated matrix transformations are evaluated. The material is developed slowly, with lots of worked examples, aimed at self-study. Some exercises are also given, at the end of each section.The book is a valuable reference for statisticians, engineers, physicists, econometricians, applied mathematicians and people working in many other areas. It can be used for a one-semester graduate level course on Jacobians and functions of matrix argument.

This book provides a comprehensive treatment of the physics of hysteresis in magnetism and of the mathematical tools used to describe it. Hysteresis in Magnetism discusses from a unified viewpoint the relationsof hysteresis to Maxwells equations, equilibrium and non-equilibrium thermodynamics, non-linear system dynamics, micromagnetics, and domain theory. These aspects are then applied to the interpretation of magnetization reversal mechanisms: coherent rotation and switching in magnetic particles, stochastic domain wall motion and the Barkhausen effect, coercivity mechanisms and magnetic viscosity, rate-dependent hysteresis and eddy-current losses. The book emphasizes the connection between basic physical ideas and phenomenological models of interest to applications, and, in particular, to the conceptual path going from Maxwells equations and thermodynamics to micromagnetics and to Preisach hysteresis modeling.
Key Features
* The reader will get insight into the importance and role of hysteresis in magnetism; In particular, he will learn:
* which are the fingerprints of hysteresis in magnetism
* which are the situations in which hysteresis may appear
* how to describe mathematically these situations
* how to apply these descriptions to magnetic materials
* how to interpret and predict magnetic hysteresis phenomena observed experimentally

Gathering 20 chapters contributed by respected experts, this book reports on the latest advances in and applications of sliding mode control in science and engineering. The respective chapters address applications of sliding mode control in the broad areas of chaos theory, robotics, electrical engineering, physics, chemical engineering, memristors, mechanical engineering, environmental engineering, finance, and biology. Special emphasis has been given to papers that offer practical solutions, and which examine design and modeling involving new types of sliding mode control such as higher order sliding mode control, terminal sliding mode control, super-twisting sliding mode control, and integral sliding mode control. This book serves as a unique reference guide to sliding mode control and its recent applications for graduate students and researchers with a basic knowledge of electrical and control systems engineering.

This book presents the latest findings on train operation theories and methods in the context of emergencies. It examines and assesses a range of aspects-including the definition of a railway emergency, transport organization modes in emergencies, calculating railway transport capacity in emergencies, line planning in emergencies, train re-pathing in emergencies and train re-scheduling in emergencies-that are urgently needed in the railway transportation field, which faces the serious challenge of dealing with emergencies worldwide. The book highlights the latest research results in an integrated and systematic way, and the methodology presented is oriented on real-world problems, allowing it to be used not only directly in railway operational management, but also as the point of departure for further applications or theoretical research. As such, the book will be of considerable interest to graduate students and researchers in the field of traffic and transportation engineering.>

This book develops two exciting areas of particle physics research. It applies the recent new insights about the usefulness of helicity amplitudes in understanding gauge theory to the long-standing effort to understand theories with both electric and magnetic charges. It is known that for some supersymmetric theories there is an exact duality that relates two descriptions of the physics, one where the electric charges are weakly coupled and another where the electric charges are strongly coupled. The calculations in this thesis suggest that this duality can also hold in the low-energy limit of nonsupersymmetric gauge theories. The idea of addressing the hierarchy problem of the standard model Higgs mechanism using conformal symmetry is also explored. Analogously to "Little Higgs" models, where divergences are cancelled only at one-loop order, models are studied that have infrared conformal fixed points which related gauge and Yukawa couplings, allowing for a cancellation between seemingly unrelated quantum loop diagrams.

Handbook of Statistics: Disease Modelling and Public Health, Part B, Volume 37 addresses new challenges in existing and emerging diseases. As a two part volume, this title covers an extensive range of techniques in the field, with this book including chapters on Reaction diffusion equations and their application on bacterial communication, Spike and slab methods in disease modeling, Mathematical modeling of mass screening and parameter estimation, Individual-based and agent-based models for infectious disease transmission and evolution: an overview, and a section on Visual Clustering of Static and Dynamic High Dimensional Data. This volume covers the lack of availability of complete data relating to disease symptoms and disease epidemiology, one of the biggest challenges facing vaccine developers, public health planners, epidemiologists and health sector researchers.

When trying to solve a complex, seemingly unsolvable problem, electrical engineers sometimes just need to start at the very beginning of the problem. To arrive at a solution, they have to go back to the basics and examine the mathematical rules, laws, and formulas that are at the root of every electrical engineering problem. This is why engineers need the Mathematical Handbook for Electrical Engineers. Written by electrical engineers, specifically for electrical engineers, this valuable resource presents the most common mathematical techniques used for problem solving and computer-aided analysis. It concisely, clearly, and easily explains the essential mathematics engineers use everyday on the job, and also serves as a time-saving reference for students. Examples are taken from a wide variety of electrical engineering disciplines, including circuits, devices and systems, antennas and propagation, waveforms and signal processing, and stochastic radio engineering.

This book introduces new models based on R-calculus and theories of belief revision for dealing with large and changing data. It extends R-calculus from first-order logic to propositional logic, description logics, modal logic and logic programming, and from minimal change semantics to subset minimal change, pseudo-subformula minimal change and deduction-based minimal change (the last two minimal changes are newly defined). And it proves soundness and completeness theorems with respect to the minimal changes in these logics. To make R-calculus computable, an approximate R-calculus is given which uses finite injury priority method in recursion theory. Moreover, two applications of R-calculus are given to default theory and semantic inheritance networks. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.

This book highlights recent advances of optical spatial solitons in photorefractive materials ranging broadly from the coupling, modulation instability, effect of pyroelectricity, and the stability of photorefractive solitons, among other topics. Photorefractive solitons have been at the forefront of research because of their formation at low laser powers and unique saturable nonlinearity present in photorefractive materials which supports solitons in (2+1) D. There has been a spurt in research on photorefractive solitons recently, which has contributed to a greater understanding of the theoretical foundation of photorefractive solitons as also of their various interesting and practical applications. The book elucidates the diversity of photorefractive solitons and provides a good resource for students, researchers, and professionals in the area of nonlinear optics.

The research and review papers presented in this volume provide an overview of the main issues, findings, and open questions in cutting-edge research on the fields of modeling, optimization and dynamics and their applications to biology, economics, energy, finance, industry, physics and psychology. Given the scientific relevance of the innovative applications and emerging issues they address, the contributions to this volume, written by some of the world's leading experts in mathematics, economics and other applied sciences, will be seminal to future research developments and will spark future works and collaborations. The majority of the papers presented in this volume were written by participants of the 4th International Conference on Dynamics, Games and Science: Decision Models in a Complex Economy (DGS IV), held at the National Distance Education University (UNED) in Madrid, Spain in June 2016 and of the 8th Berkeley Bioeconomy Conference: The Future of Biofuels, held at the UC Berkeley Alumni House in April 2015.

This book uses Ludwig Wittgenstein's philosophical methodology to solve a problem that has perplexed thinkers for thousands of years: 'how come (abstract) mathematics applies so wonderfully well to the (concrete, physical) world?' The book is distinctive in several ways. First, it gives the reader a route into understanding important features of Wittgenstein's writings and lectures by using his methodology to tackle this long-standing and seemingly intractable philosophical problem. More than this, though, it offers an outline of important (sometimes little-known) aspects of the development of mathematical thought through the ages, and an engagement of Wittgenstein's philosophy with this and with contemporary philosophy of mathematics on its own terms. A clear overview of all this in the context of Wittgenstein's philosophy of mathematics is interesting in its own right; it is also just what is needed to solve the problem of mathematics and world.

This book reviews the state of the art in deep learning approaches to high-performance robust disease detection, robust and accurate organ segmentation in medical image computing (radiological and pathological imaging modalities), and the construction and mining of large-scale radiology databases. It particularly focuses on the application of convolutional neural networks, and on recurrent neural networks like LSTM, using numerous practical examples to complement the theory. The book's chief features are as follows: It highlights how deep neural networks can be used to address new questions and protocols, and to tackle current challenges in medical image computing; presents a comprehensive review of the latest research and literature; and describes a range of different methods that employ deep learning for object or landmark detection tasks in 2D and 3D medical imaging. In addition, the book examines a broad selection of techniques for semantic segmentation using deep learning principles in medical imaging; introduces a novel approach to text and image deep embedding for a large-scale chest x-ray image database; and discusses how deep learning relational graphs can be used to organize a sizable collection of radiology findings from real clinical practice, allowing semantic similarity-based retrieval.The intended reader of this edited book is a professional engineer, scientist or a graduate student who is able to comprehend general concepts of image processing, computer vision and medical image analysis. They can apply computer science and mathematical principles into problem solving practices. It may be necessary to have a certain level of familiarity with a number of more advanced subjects: image formation and enhancement, image understanding, visual recognition in medical applications, statistical learning, deep neural networks, structured prediction and image segmentation.

This book explores the question of whether and how meme theory or "memetics" can be fruitfully utilized in evolutionary economics and proposes an approach known as "economemetics" which is a combination of meme theory and complexity theory that has the potential to combat the fragmentation of evolutionary economics while re-connecting the field with cultural evolutionary theory. By studying the intersection of cultural and economic evolution, complexity economics, computational economics, and network science, the authors establish a connection between memetics and evolutionary economics at different levels of investigation. The book first demonstrates how a memetic approach to economic evolution can help to reveal links and build bridges between different but complementary concepts in evolutionary economics. Secondly, it shows how organizational memetics can help to capture the complexity of organizational culture using meme mapping. Thirdly, it presents an agent-based simulation model of knowledge diffusion and assimilation in innovation networks from a memetic perspective. The authors then use agent-based modeling and social network analysis to evaluate the diffusion pattern of the Ice Bucket Challenge as an example of a "viral meme." Lastly, the book discusses the central issues of agency, creativity, and normativity in the context of economemetics and suggests promising avenues for further research.

"Stability of NonLinear Shells" is a compilation of the author's work on analyzing the behaviour of spherical caps and related shell structures under various (axisymmetric) load systems. Differing from other texts on shells of revolution, it is one of the first attempts to deal with effects of multi-parameter load systems. This extension leads to the discovery of some new, hitherto unknown phenomena exhibited by these structures. In addition, the book presents a novel way to characterize properties of solutions of the governing equations for spherical caps - a classification anchored in a theory called reciprocal systems. The author has introduced a deformation map, a projection of multi-dimensional solutions to two-dimensional graphs, to enable analysts to gain insight into the physical meaning of the results obtained.
Numerous examples illustrate the concepts introduced. This book also comes to grips with many misconceptions existing in engineering literature about the question of the stability of solutions.

Data-driven discovery is revolutionizing how we model, predict, and control complex systems. Now with Python and MATLAB (R), this textbook trains mathematical scientists and engineers for the next generation of scientific discovery by offering a broad overview of the growing intersection of data-driven methods, machine learning, applied optimization, and classical fields of engineering mathematics and mathematical physics. With a focus on integrating dynamical systems modeling and control with modern methods in applied machine learning, this text includes methods that were chosen for their relevance, simplicity, and generality. Topics range from introductory to research-level material, making it accessible to advanced undergraduate and beginning graduate students from the engineering and physical sciences. The second edition features new chapters on reinforcement learning and physics-informed machine learning, significant new sections throughout, and chapter exercises. Online supplementary material - including lecture videos per section, homeworks, data, and code in MATLAB (R), Python, Julia, and R - available on databookuw.com.

This book continues the process of systematization of knowledge about convection. It is important to put the current knowledge on weakly and strongly stratified convection in order, and provide a comprehensive description of the marginal, weakly nonlinear and fully developed stages of convective flow in both cases. The book provides a short compendium of knowledge on the linear and weakly nonlinear limits of the Boussinesq convection, and a review of the theory on fully developed Boussinesq convection. The third chapter is devoted to a detailed derivation and a study of the three aforementioned stages of stratified (anelastic) convection, with a full solution in the marginal stage provided for the first time. Detailed and systematic explanations are given. The book is intended mainly as a textbook for courses on hydrodynamics and convective flows, for the use of lecturers and students; however, it also serves for the entire scientific community as a practical reference.