This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories.

Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.

Critical regimes of two-phase flows with a polydisperse solid phase form the basis of such widespread industrial processes as separation of various powdery materials and minerals dressing. It is impossible to describe such complicated flows analytically. Therefore, this study concentrates on invariants experimentally revealed and theoretically grounded for such flows.

This approach can be compared with the situation in gases, where in order to determine principal parameters of their state, one does not need to measure the kinetic energy and velocity of each molecule and find its contribution to the temperature and pressure. These parameters are determined in a simple way for the system on the whole.

A novel conception of two-phase flows allowing the formulation of their statistical parameters is physically substantiated. On the basis of the invariants and these parameters, a comprehensive method of estimating and predicting mass transfer in such flows is developed.

It is noteworthy that the presented results are mostly phenomenological. Such an approach can be successfully extended to the separation of liquids, gases and isotopes.

The book is intended for students and specialists engaged in chemical technology, mineral dressing, ceramics, microelectronics, pharmacology, power generation, thermal engineering and other fields in which flows carrying solid particles are used in the technological process.

This book, to reflect the system's diverse, relevant characteristics, uses three different mathematical tools, namely probability theory, fuzzy theory and random fuzzy theory, to model and analyze the reliability of each system. Reliability system engineering is an interdisciplinary area that chiefly focuses on the lifecycle characteristics of products and involves many fields of basic mathematics, technical science and management science. In recent years, there have been many books on reliability theory, but comparatively few on the reliability of mathematical models, or the reliability of mathematical models based on single probability theory or fuzzy theory. The findings presented here will not only enrich and expand traditional reliability theory, but also promote the development of related disciplines, lending the book considerable theoretical significance.

This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields. Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Ito Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations. An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularly the applications explored in the second half of the book.

The topic of dynamic models tends to be splintered across various disciplines, making it difficult to uniformly study the subject. Moreover, the models have a variety of representations, from traditional mathematical notations to diagrammatic and immersive depictions. Collecting all of these expressions of dynamic models, the Handbook of Dynamic System Modeling explores a panoply of different types of modeling methods available for dynamical systems. Featuring an interdisciplinary, balanced approach, the handbook focuses on both generalized dynamic knowledge and specific models. It first introduces the general concepts, representations, and philosophy of dynamic models, followed by a section on modeling methodologies that explains how to portray designed models on a computer. After addressing scale, heterogeneity, and composition issues, the book covers specific model types that are often characterized by specific visual- or text-based grammars. It concludes with case studies that employ two well-known commercial packages to construct, simulate, and analyze dynamic models. A complete guide to the fundamentals, types, and applications of dynamic models, this handbook shows how systems function and are represented over time and space and illustrates how to select a particular model based on a specific area of interest.

This book gathers the peer-reviewed proceedings of the 13th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM'18, held in Sofia, Bulgaria. The general theme of BGSIAM'18 was industrial and applied mathematics with particular focus on: mathematical physics, numerical analysis, high performance computing, optimization and control, mathematical biology, stochastic modeling, machine learning, digitization and imaging, advanced computing in environmental, biomedical and engineering applications.

This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.

KEY BENEFIT This reference introduces a variety of mathematical models for biological systems, and presents the mathematical theory and techniques useful in analyzing those models. Material is organized according to the mathematical theory rather than the biological application. Contains applications of mathematical theory to biological examples in each chapter. Focuses on deterministic mathematical models with an emphasis on predicting the qualitative solution behavior over time. Discusses classical mathematical models from population, including the Leslie matrix model, the Nicholson-Bailey model, and the Lotka-Volterra predator-prey model. Also discusses more recent models, such as a model for the Human Immunodeficiency Virus - HIV and a model for flour beetles. KEY MARKET Readers seeking a solid background in the mathematics behind modeling in biology and exposure to a wide variety of mathematical models in biology.

This book shows how neural networks are applied to computational mechanics. Part I presents the fundamentals of neural networks and other machine learning method in computational mechanics. Part II highlights the applications of neural networks to a variety of problems of computational mechanics. The final chapter gives perspectives to the applications of the deep learning to computational mechanics.

Business Process Modeling, Simulation and Design, Third Edition provides students with a comprehensive coverage of a range of analytical tools used to model, analyze, understand, and ultimately design business processes. The new edition of this very successful textbook includes a wide range of approaches such as graphical flowcharting tools, cycle time and capacity analyses, queuing models, discrete-event simulation, simulation-optimization, and data mining for process analytics. While most textbooks on business process management either focus on the intricacies of computer simulation or managerial aspects of business processes, this textbook does both. It presents the tools to design business processes and management techniques on operating them efficiently. The book focuses on the use of discrete event simulation as the main tool for analyzing, modeling, and designing effective business processes. The integration of graphic user-friendly simulation software enables a systematic approach to create optimal designs.

A concise and practical guide to financial modeling in Excel In The Essentials of Financial Modeling in Excel: A Concise Guide to Concepts and Methods, veteran quantitative modeling and business analysis expert Dr. Michael Rees delivers a practical and hands-on introduction to financial modeling in Excel. The author offers readers a well-structured and strategic toolkit to learn modeling from scratch, focusing on the core economic concepts and the structures commonly required within Excel models. Divided into six parts, the book discusses the use of models and the factors to consider when designing and building models so that they can be as powerful as possible, yet simple. . Readers will also find: The foundational structures and calculations most frequently used in modeling, including growth- and ratio-based methods, corkscrews, and waterfall analysis Walkthroughs of economic modeling, measurement, and evaluation, and the linking of these to the decision criteria. These include breakeven and payback analysis, compounding, discounting, calculation of returns, loan calculations, and others Structured approaches for modeling in corporate finance, including financial statement modeling, cash flow valuation, cost of capital, and ratio analysis Techniques to implement sensitivity and scenario analysis Core aspects of statistical analysis, including data preparation, manipulation, and integration The use of approximately 100 Excel functions within example modeling contexts Further Topics Sections, which introduce advanced aspects of many areas, in order to provide further benefit to more advance readers, whilst presenting the truly essential topics separately. Examples of these include introductions to PowerQuery and PowerPivot, as well as advanced waterfall structures An invaluable, all-in-one blueprint for learning financial modeling in Excel, this book is ideal for beginning and intermediate financial professionals and students seeking to build and reinforce essential topics in financial modeling.

This book provides novel concepts and techniques for air traffic management (ATM) and communications, navigation, and surveillance (CNS) systems. The book consists of selected papers from the 6th ENRI International Workshop on ATM/CNS (EIWAC2019) held in Tokyo in October 2019, the theme of which was "Exploring Ideas for World Aviation Challenges". Included are key topics to realize safer and more efficient skies in the future, linked to the integrated conference theme consisting of long-term visions based on presentations from various fields. The book is dedicated not only to researchers, academicians, and university students, but also to engineers in the industry, air navigation service providers (ANSPs), and regulators of aviation.

This book presents innovative ideas and technical contributions in the area of metasurfaces and antenna technologies. On the one hand, it presents an effective method to analyze metasurfaces constituted by metallic texture with certain geometries. It shows how this method can be applied to the design of metasurface (MTS) antennas for deep space communications and other planar microwave devices. On the other hand, the book reports on a general methodology developed for analyzing flat devices realized by using modulated MTSs, which opens new design possibilities for a large number of microwave devices based on the manipulation of SWs. Finally, a novel approach of reconfigurability, which is based on a class of checkerboard MTS, is explored. All in all, this book covers important insights and significant results on the emerging topic of metasurfaces, from theoretical and computational aspects to experiments.

Expert Trading Systems "This book is an excellent introduction to advanced statistical modeling of financial markets. Wolberg’s explanation of kernel regression is lucid and direct. The author carefully leads readers through each stage of a trade system design and points out to them any potential difficulties they might encounter along the way. In addition, the examples give a concrete grasp of the subject without getting tangled up in any lengthy mathematical derivation." —Peter F. Borish, President, Computer Trading Corporation "The successful application of advanced modeling methods to the development of expert trading systems and financial market forecasting models requires both theoretical and practical knowledge. Wolberg was a pioneer in the development and application of kernel regression modeling to this area, and his book displays both deep theoretical understanding and practical knowledge in a highly readable how-to manner. Moreover, Wolberg’s advanced kernel regression algorithm is orders of magnitude faster than existing methods, thus broadening its application tremendously. I highly recommend this book to any practitioner in this area." —David Aronson, President, Raden Research Group Inc. "Kernel regression is a powerful statistical modeling technique that gives excellent performance in a wide variety of applications, including financial market prediction. Its use has traditionally been limited by its potentially overwhelming computational requirements, but Wolberg provides an effective algorithm that speeds computation by orders of magnitude, making it universally available." —Timothy Masters, author of Neural, Novel & Hybrid Algorithms for Time Series Prediction "This book presents an excellent overview of nonlinear modeling techniques used to build predictive models for financial time series. It is suitable both as a text for a financial modeling course or for a financial analyst who wants to use kernel methods for modeling. Wolberg describes his innovative approach to speeding up kernel regression, which allows these methods to be applied to a more complex set of problems. His software can be used to develop, test, and generate technical trading systems with more flexibility than other software that is commonly available." —Sandor Straus, PhD, Merfin, LLC, former partner of Renaissance Technology Corp.

Statistical Methods for Spatial and Spatio-Temporal Data Analysis provides a complete range of spatio-temporal covariance functions and discusses ways of constructing them. This book is a unified approach to modeling spatial and spatio-temporal data together with significant developments in statistical methodology with applications in R. This book includes: * Methods for selecting valid covariance functions from the empirical counterparts that overcome the existing limitations of the traditional methods. * The most innovative developments in the different steps of the kriging process. * An up-to-date account of strategies for dealing with data evolving in space and time. * An accompanying website featuring R code and examples

This book is based on a two-day symposium at the Paris Institute of Advanced Study titled "space-time geometries and movement in the brain and the arts". It includes over 20 chapters written by the leading scientists and artists who presented their related research studies at the symposium and includes six sections; the first three focus on space-time geometries in perception, action and memory while the last three focus on specific artistic domains: drawing and painting, dance, music, digital arts and robotics. The book is accompanied by a dedicated webpage including related images and videos. There is an ever-growing interest in the topics covered by this book. Space and time are of fundamental importance for our understanding of human perception, action, memory and cognition, and are entities which are equally important in physics, biology, neuroscience and psychology. Highly prominent scientists and mathematicians have expressed their belief that our bodies and minds shape the ways we perceive space and time and the physical laws we formulate. Understanding how the brain perceives motion and generates -bodily movements is of great significance. There is also growing interest in studying how space, time and movement subserve artistic creations in different artistic modalities (e.g., fine arts, digital and performing arts and music). This interest is inspired by the idea that artists make intuitive use of the principles and simplifying strategies used by the brain in movement generation and perception. Building upon new understanding of the spatio-temporal geometries subserving movement generation and perception by the brain we can start exploring how artists make use of such neuro --geometrical and neuro-dynamic representations in order to express artistic concepts and emotionally affect the human observers and listeners. Scientists have also started formulating new ideas of how aesthetic judgements emerge from the principles and brain mechanisms subserving motor control and motion perception. Covering novel and multidisciplinary topics, this advanced book will be of interest to neuroscientists, behavioral scientists, artificial intelligence and robotics experts, students and artists.

Written by one of the world's foremost authorities in time series modelling, this book explores goodness of fit tests in time series analysis. Starting with linear models, the author proceeds to nonlinear modelling with extensions to long-memory and generalized linear models--all areas of interest and activity. The focus is firmly on practical matters, and the author presents a range of applications, particularly from the financial arena. Until now, published work in this area has been scattered throughout the literature. Researchers and practitioners alike will welcome this book as a reference that will guide them through the final stages of their modelling tasks.

This book introduces game theory as a means to conceptualize, model, and analyze cyber deception. Drawing upon a collection of deception research from the past 10 years, the authors develop a taxonomy of six species of defensive cyber deception. Three of these six species are highlighted in the context of emerging problems such as privacy against ubiquitous tracking in the Internet of things (IoT), dynamic honeynets for the observation of advanced persistent threats (APTs), and active defense against physical denial-of-service (PDoS) attacks. Because of its uniquely thorough treatment of cyber deception, this book will serve as a timely contribution and valuable resource in this active field. The opening chapters introduce both cybersecurity in a manner suitable for game theorists and game theory as appropriate for cybersecurity professionals. Chapter Four then guides readers through the specific field of defensive cyber deception. A key feature of the remaining chapters is the development of a signaling game model for the species of leaky deception featured in honeypots and honeyfiles. This model is expanded to study interactions between multiple agents with varying abilities to detect deception. Game Theory for Cyber Deception will appeal to advanced undergraduates, graduate students, and researchers interested in applying game theory to cybersecurity. It will also be of value to researchers and professionals working on cybersecurity who seek an introduction to game theory.

Features Minimal pre-requisites beyond a solid background in calculus, such as a calculus I course. Suitable for upper division mathematics and sciences students and graduate-level biology students. Provides sample MATLAB codes and instruction in Appendices.

This book intends to introduce some recent results on passivity of complex dynamical networks with single weight and multiple weights. The book collects novel research ideas and some definitions in complex dynamical networks, such as passivity, output strict passivity, input strict passivity, finite-time passivity, and multiple weights. Furthermore, the research results previously published in many flagship journals are methodically edited and presented in a unified form. The book is likely to be of interest to university researchers and graduate students in Engineering and Mathematics who wish to study the passivity of complex dynamical networks.

The investigation of the role of mechanical and mechano-chemical interactions in cellular processes and tissue development is a rapidly growing research field in the life sciences and in biomedical engineering. Quantitative understanding of this important area in the study of biological systems requires the development of adequate mathematical models for the simulation of the evolution of these systems in space and time. Since expertise in various fields is necessary, this calls for a multidisciplinary approach. This edited volume connects basic physical, biological, and physiological concepts to methods for the mathematical modeling of various materials by pursuing a multiscale approach, from subcellular to organ and system level. Written by active researchers, each chapter provides a detailed introduction to a given field, illustrates various approaches to creating models, and explores recent advances and future research perspectives. Topics covered include molecular dynamics simulations of lipid membranes, phenomenological continuum mechanics of tissue growth, and translational cardiovascular modeling. Modeling Biomaterials will be a valuable resource for both non-specialists and experienced researchers from various domains of science, such as applied mathematics, biophysics, computational physiology, and medicine.

Integrating concepts from deep learning, machine learning, and artificial neural networks, this highly unique textbook presents content progressively from easy to more complex, orienting its content about knowledge transfer from the viewpoint of machine intelligence. It adopts the methodology from graphical theory, mathematical models, and algorithmic implementation, as well as covers datasets preparation, programming, results analysis and evaluations. Beginning with a grounding about artificial neural networks with neurons and the activation functions, the work then explains the mechanism of deep learning using advanced mathematics. In particular, it emphasizes how to use TensorFlow and the latest MATLAB deep-learning toolboxes for implementing deep learning algorithms. As a prerequisite, readers should have a solid understanding especially of mathematical analysis, linear algebra, numerical analysis, optimizations, differential geometry, manifold, and information theory, as well as basic algebra, functional analysis, and graphical models. This computational knowledge will assist in comprehending the subject matter not only of this text/reference, but also in relevant deep learning journal articles and conference papers. This textbook/guide is aimed at Computer Science research students and engineers, as well as scientists interested in deep learning for theoretic research and analysis. More generally, this book is also helpful for those researchers who are interested in machine intelligence, pattern analysis, natural language processing, and machine vision. Dr. Wei Qi Yan is an Associate Professor in the Department of Computer Science at Auckland University of Technology, New Zealand. His other publications include the Springer title, Visual Cryptography for Image Processing and Security.

The book describes currently applied and newly developed advanced numerical methods for wave-induced ship motions and loads. Besides well-established computational methods based on strip theory, panel methods and finite volume methods for unsteady Reynolds-averaged Navier-Stokes equations (URANS), recent advances like a fully nonlinear Rankine panel method, URANS calculations including elastic hull deformations, and an improved method to predict added resistance in waves are explained in detail. Furthermore, statistical methods to assess extreme motions and loads are described both for linear and nonlinear responses in a stationary seaway as well as during long-term ship operations. Results of motions and loads, computed using the various methods, are compared with each other and with results of model experiments. Introductory chapters on fluid dynamics, motions of rigid and elastic ship hulls, numerical methods to compute fluid flows associated with wind waves, and the development and simulation of seaways complement the volume. The book will be of interest to post-graduate students, PhD candidates, as well as engineers in the field of naval architecture, ocean, and marine engineering.

This book features recent research in mathematical modeling of indirectly and directly transmitted infectious diseases in humans, animals, and plants. It compiles nine not previously published studies that illustrate the dynamic spread of infectious diseases, offering a broad range of models to enrich understanding. It demonstrates the capability of mathematical modeling to capture disease spread and interaction dynamics as well as the complicating factors of various evolutionary processes. In addition, it presents applications to real-world disease control by commenting on key parameters and dominant pathways related to transmission. While aimed at early-graduate level students, the book can also provide insights to established researchers in that it presents a survey of current topics and methodologies in a constantly evolving field.