Matrix-analytic Methods in Stochastic Models

Flood inundation models enable us to make hazard predictions for floodplains, mitigating increasing flood fatalities and losses. This book provides an understanding of hydraulic modelling and floodplain dynamics, with a key focus on state-of-the-art remote sensing data, and methods to estimate and communicate uncertainty. Academic researchers in the fields of hydrology, climate change, environmental science and natural hazards, and professionals and policy-makers working in flood risk mitigation, hydraulic engineering and remote sensing will find this an invaluable resource. This volume is the third in a collection of four books on flood disaster management theory and practice within the context of anthropogenic climate change. The others are: Floods in a Changing Climate: Extreme Precipitation by Ramesh Teegavarapu, Floods in a Changing Climate: Hydrological Modeling by P. P. Mujumdar and D. Nagesh Kumar and Floods in a Changing Climate: Risk Management by Slodoban Simonović.

This is the first book to promote the use of stochastic, or random, processes to understand, model and predict our climate system. One of the most important applications of this technique is in the representation of comprehensive climate models of processes which, although crucial, are too small or fast to be explicitly modelled. The book shows how stochastic methods can lead to improvements in climate simulation and prediction, compared with more conventional bulk-formula parameterization procedures. Beginning with expositions of the relevant mathematical theory, the book moves on to describe numerous practical applications. It covers the complete range of time scales of climate variability, from seasonal to decadal, centennial, and millennial. With contributions from leading experts in climate physics, this book is invaluable to anyone working on climate models, including graduate students and researchers in the atmospheric and oceanic sciences, numerical weather forecasting, climate

Fully updated and expanded, this new edition presents a cutting-edge summary of planetary rings, including results from Cassini's Saturn System, Equinox and Solstice missions, and the New Horizons flyby of Jupiter. The book introduces basic physical processes and simple mathematical approaches in an accessible manner, including N-body and stochastic models of ring dynamics. Further revised chapters present highlighted topics including Saturn's F ring, Uranus' rings and moons, Neptune's partial rings, dusty rings, and Jupiter's ring-moon system after Galileo and New Horizons. Cassini results are fully integrated throughout, including new images in color, and a new Afterword links ring images in the Cassini 'Hall of Fame' gallery to the relevant explanation in the text. An online cache of images and videos from NASA's collection makes it easy to locate relevant and beautiful illustrative materials. This is a key resource for students, researchers and professionals in planetary science, a

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appe

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appe

The third edition of Radiogenic Isotope Geology examines revolutionary changes in geochemical thinking that have occurred over the past fifteen years. Extinct-nuclide studies on meteorites have called into question fundamental geochemical models of the Earth, while new dating methods have challenged conventional views of Earth history. At the same time, the problem of global warming has raised new questions about the causes of past and present climate change. In the new edition, these and other recent issues are evaluated in their scholarly and historical context, so readers can understand the development of current ideas. Controversial theories, new analytical techniques, classic papers, and illustrative case studies all come under scrutiny in this book, providing an accessible introduction for students and critical commentary for researchers.

The third edition of Radiogenic Isotope Geology examines revolutionary changes in geochemical thinking that have occurred over the past fifteen years. Extinct-nuclide studies on meteorites have called into question fundamental geochemical models of the Earth, while new dating methods have challenged conventional views of Earth history. At the same time, the problem of global warming has raised new questions about the causes of past and present climate change. In the new edition, these and other recent issues are evaluated in their scholarly and historical context, so readers can understand the development of current ideas. Controversial theories, new analytical techniques, classic papers, and illustrative case studies all come under scrutiny in this book, providing an accessible introduction for students and critical commentary for researchers.

This volume focuses on procedures for the development and application of several research animal models and in vitro methods that allow researchers to gain insight into the underlying cellular, bioche

Statistical methods in modern research increasingly entail developing, estimating and testing models for data. Rather than rigid methods of data analysis, the need today is for more flexible methods f

Statistical methods in modern research increasingly entail developing, estimating and testing models for data. Rather than rigid methods of data analysis, the need today is for more flexible methods f

This comprehensive treatise covers in detail practical methods of analysis as well as advanced mathematical models for structures highly sensitive to creep and shrinkage. Effective computational algor

Over the past several decades, computational approaches to studying strongly-interacting systems have become increasingly varied and sophisticated. This book provides a comprehensive introduction to state-of-the-art quantum Monte Carlo techniques relevant for applications in correlated systems. Providing a clear overview of variational wave functions, and featuring a detailed presentation of stochastic samplings including Markov chains and Langevin dynamics, which are developed into a discussion of Monte Carlo methods. The variational technique is described, from foundations to a detailed description of its algorithms. Further topics discussed include optimisation techniques, real-time dynamics and projection methods, including Green's function, reptation and auxiliary-field Monte Carlo, from basic definitions to advanced algorithms for efficient codes, and the book concludes with recent developments on the continuum space. Quantum Monte Carlo Approaches for Correlated Systems provides

Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrate

Instantons, or pseudoparticles, are solutions to the equations of motion in classical field theories on a Euclidean spacetime. Instantons are found everywhere in quantum theories as they have many applications in quantum tunnelling. Diverse physical phenomena may be described through quantum tunnelling, for example: the Josephson effect, the decay of meta-stable nuclear states, band formation in tight binding models of crystalline solids, the structure of the gauge theory vacuum, confinement in 2+1 dimensions, and the decay of superheated or supercooled phases. Drawing inspiration from Sidney Coleman's Erice lectures, this volume provides an accessible, detailed introduction to instanton methods, with many applications, making it a valuable resource for graduate students in many areas of physics, from condensed matter, particle and nuclear physics, to string theory.

Digital Signal Processing with Kernel Methods will review the milestones in the mixing of classical digital signal processing models and advanced kernel machines statistical learning tools. In additio

Networks constitute the backbone of complex systems, from the human brain to computer communications, transport infrastructures to online social systems and metabolic reactions to financial markets. Characterising their structure improves our understanding of the physical, biological, economic and social phenomena that shape our world. Rigorous and thorough, this textbook presents a detailed overview of the new theory and methods of network science. Covering algorithms for graph exploration, node ranking and network generation, among others, the book allows students to experiment with network models and real-world data sets, providing them with a deep understanding of the basics of network theory and its practical applications. Systems of growing complexity are examined in detail, challenging students to increase their level of skill. An engaging presentation of the important principles of network science makes this the perfect reference for researchers and undergraduate and graduate s

Presenting a coherent synthesis of lithosphere studies, this book covers a range of geophysical methods (seismic reflection, refraction, and receiver function methods; elastic and anelastic seismic tomography; electromagnetic and magnetotelluric methods; thermal, gravity and rheological models), complemented by petrologic and laboratory data on rock properties. It also provides a critical discussion of the uncertainties, assumptions, and resolution issues that are inherent in the different methods and models of the lithosphere. Multidisciplinary in scope, global in geographical extent, and covering a wide variety of tectonics settings across 3.5 billion years of Earth history, this book presents a comprehensive overview of lithospheric structure and evolution. It is a core reference for researchers and advanced students in geophysics, geodynamics, tectonics, petrology, and geochemistry, and for petroleum and mining industry professionals.

Both state-space models and Markov switching models have been highly productive paths for empirical research in macroeconomics and finance. This book presents recent advances in econometric methods th

Critical Sociolinguistic Research Methods is a guide to conducting concrete ethnographic and discourse analytic research projects, written by top scholars for students and researchers in social scienc

How do infants learn a language? Why and how do languages evolve? How do we understand a sentence? This book explores these questions using recent computational models that shed new light on issues related to language and cognition. The chapters in this collection propose original analyses of specific problems and develop computational models that have been tested and evaluated on real data. Featuring contributions from a diverse group of experts, this interdisciplinary book bridges the gap between natural language processing and cognitive sciences. It is divided into three sections, focusing respectively on models of neural and cognitive processing, data driven methods, and social issues in language evolution. This book will be useful to any researcher and advanced student interested in the analysis of the links between the brain and the language faculty.

Structural vector autoregressive (VAR) models are important tools for empirical work in macroeconomics, finance, and related fields. This book not only reviews the many alternative structural VAR approaches discussed in the literature, but also highlights their pros and cons in practice. It provides guidance to empirical researchers as to the most appropriate modeling choices, methods of estimating, and evaluating structural VAR models. The book traces the evolution of the structural VAR methodology and contrasts it with other common methodologies, including dynamic stochastic general equilibrium (DSGE) models. It is intended as a bridge between the often quite technical econometric literature on structural VAR modeling and the needs of empirical researchers. The focus is not on providing the most rigorous theoretical arguments, but on enhancing the reader's understanding of the methods in question and their assumptions. Empirical examples are provided for illustration.

Structural vector autoregressive (VAR) models are important tools for empirical work in macroeconomics, finance, and related fields. This book not only reviews the many alternative structural VAR approaches discussed in the literature, but also highlights their pros and cons in practice. It provides guidance to empirical researchers as to the most appropriate modeling choices, methods of estimating, and evaluating structural VAR models. The book traces the evolution of the structural VAR methodology and contrasts it with other common methodologies, including dynamic stochastic general equilibrium (DSGE) models. It is intended as a bridge between the often quite technical econometric literature on structural VAR modeling and the needs of empirical researchers. The focus is not on providing the most rigorous theoretical arguments, but on enhancing the reader's understanding of the methods in question and their assumptions. Empirical examples are provided for illustration.

Critical Sociolinguistic Research Methods is a guide to conducting concrete ethnographic and discourse analytic research projects, written by top scholars for students and researchers in social scienc

This is a comprehensive and accessible reference source that documents the theoretical and practical aspects of all the key deterministic and stochastic reserving methods that have been developed for use in general insurance. Worked examples and mathematical details are included, along with many of the broader topics associated with reserving in practice. The key features of reserving in a range of different contexts in the UK and elsewhere are also covered. The book contains material that will appeal to anyone with an interest in claims reserving. It can be used as a learning resource for actuarial students who are studying the relevant parts of their professional bodies' examinations, as well as by others who are new to the subject. More experienced insurance and other professionals can use the book to refresh or expand their knowledge in any of the wide range of reserving topics covered in the book.

This text is devoted to the development of certain probabilistic methods in the specific field of stochastic differential equations and limit theorems for Markov processes. Specialists, researchers, a

Continuous-Time Models in Corporate Finance synthesizes four decades of research to show how stochastic calculus can be used in corporate finance. Combining mathematical rigor with economic intuition,

Do you need to know what technique to use to evaluate the reliability of an engineered system? This self-contained guide provides comprehensive coverage of all the analytical and modeling techniques currently in use, from classical non-state and state space approaches, to newer and more advanced methods such as binary decision diagrams, dynamic fault trees, Bayesian belief networks, stochastic Petri nets, non-homogeneous Markov chains, semi-Markov processes, and phase type expansions. Readers will quickly understand the relative pros and cons of each technique, as well as how to combine different models together to address complex, real-world modeling scenarios. Numerous examples, case studies and problems provided throughout help readers put knowledge into practice, and a solutions manual and Powerpoint slides for instructors accompany the book online. This is the ideal self-study guide for students, researchers and practitioners in engineering and computer science.

This balanced and comprehensive study presents the theory, methods and applications of matrix analysis in a new theoretical framework, allowing readers to understand second-order and higher-order matrix analysis in a completely new light. Alongside the core subjects in matrix analysis, such as singular value analysis, the solution of matrix equations and eigenanalysis, the author introduces new applications and perspectives that are unique to this book. The very topical subjects of gradient analysis and optimization play a central role here. Also included are subspace analysis, projection analysis and tensor analysis, subjects which are often neglected in other books. Having provided a solid foundation to the subject, the author goes on to place particular emphasis on the many applications matrix analysis has in science and engineering, making this book suitable for scientists, engineers and graduate students alike.

This textbook presents basic numerical methods and applies them to a large variety of physical models in multiple computer experiments. Classical algorithms and more recent methods are explained. Part

A key aspect of robotics today is estimating the state, such as position and orientation, of a robot as it moves through the world. Most robots and autonomous vehicles depend on noisy data from sensors such as cameras or laser rangefinders to navigate in a three-dimensional world. This book presents common sensor models and practical advice on how to carry out state estimation for rotations and other state variables. It covers both classical state estimation methods such as the Kalman filter, as well as important modern topics such as batch estimation, the Bayes filter, sigmapoint and particle filters, robust estimation for outlier rejection, and continuous-time trajectory estimation and its connection to Gaussian-process regression. The methods are demonstrated in the context of important applications such as point-cloud alignment, pose-graph relaxation, bundle adjustment, and simultaneous localization and mapping. Students and practitioners of robotics alike will find this a valuable

This new and completely updated edition gives a detailed description of radiative transfer processes at a level accessible to advanced students. The volume gives the reader a basic understanding of global warming and enhanced levels of harmful ultraviolet radiation caused by ozone depletion. It teaches the basic physics of absorption, scattering and emission processes in turbid media, such as the atmosphere and ocean, using simple semi-classical models. The radiative transfer equation, including multiple scattering, is formulated and solved for several prototype problems, using both simple approximate and accurate numerical methods. In addition, the reader has access to a powerful, state-of-the-art computational code for simulating radiative transfer processes in coupled atmosphere-water systems including snow and ice. This computational code can be regarded as a powerful educational aid, but also as a research tool that can be applied to solve a variety of research problems in environ

"This book focuses on the application of the methods organized in statistical physics, fuzzy logic, neuro nets and combinatorial stochastic processes which have been proven useful in analyzing complex

This valuable source for graduate students and researchers provides a comprehensive introduction to current theories and applications in optimization methods and network models. Contributions to this

This book introduces state-of-the-art models and methods based on the matrix in the field of product design and change management. It develops several types of matrix models for a broad range of appli

This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.

Science is fundamentally about learning from data, and doing so in the presence of uncertainty. This volume is an introduction to the major concepts of probability and statistics, and the computational tools for analysing and interpreting data. It describes the Bayesian approach, and explains how this can be used to fit and compare models in a range of problems. Topics covered include regression, parameter estimation, model assessment, and Monte Carlo methods, as well as widely used classical methods such as regularization and hypothesis testing. The emphasis throughout is on the principles, the unifying probabilistic approach, and showing how the methods can be implemented in practice. R code (with explanations) is included and is available online, so readers can reproduce the plots and results for themselves. Aimed primarily at undergraduate and graduate students, these techniques can be applied to a wide range of data analysis problems beyond the scope of this work.

The field of artificial intelligence (AI) and the law is on the cusp of a revolution that began with text analytic programs like IBM's Watson and Debater and the open-source information management architectures on which they are based. Today, new legal applications are beginning to appear and this book - designed to explain computational processes to non-programmers - describes how they will change the practice of law, specifically by connecting computational models of legal reasoning directly with legal text, generating arguments for and against particular outcomes, predicting outcomes and explaining these predictions with reasons that legal professionals will be able to evaluate for themselves. These legal applications will support conceptual legal information retrieval and allow cognitive computing, enabling a collaboration between humans and computers in which each does what it can do best. Anyone interested in how AI is changing the practice of law should read this illuminating wo

Science is fundamentally about learning from data, and doing so in the presence of uncertainty. This volume is an introduction to the major concepts of probability and statistics, and the computational tools for analysing and interpreting data. It describes the Bayesian approach, and explains how this can be used to fit and compare models in a range of problems. Topics covered include regression, parameter estimation, model assessment, and Monte Carlo methods, as well as widely used classical methods such as regularization and hypothesis testing. The emphasis throughout is on the principles, the unifying probabilistic approach, and showing how the methods can be implemented in practice. R code (with explanations) is included and is available online, so readers can reproduce the plots and results for themselves. Aimed primarily at undergraduate and graduate students, these techniques can be applied to a wide range of data analysis problems beyond the scope of this work.

The field of artificial intelligence (AI) and the law is on the cusp of a revolution that began with text analytic programs like IBM's Watson and Debater and the open-source information management architectures on which they are based. Today, new legal applications are beginning to appear and this book - designed to explain computational processes to non-programmers - describes how they will change the practice of law, specifically by connecting computational models of legal reasoning directly with legal text, generating arguments for and against particular outcomes, predicting outcomes and explaining these predictions with reasons that legal professionals will be able to evaluate for themselves. These legal applications will support conceptual legal information retrieval and allow cognitive computing, enabling a collaboration between humans and computers in which each does what it can do best. Anyone interested in how AI is changing the practice of law should read this illuminating wo

With this self-contained, introductory text, readers will easily understand the fundamentals of microwave and radar image generation. Written with the complete novice in mind, and including an easy-to-follow introduction to electromagnetic scattering theory, it covers key topics such as forward models of scattering for interpreting S-parameter and time-dependent voltage data, S-parameters and their analytical sensitivity formulae, basic methods for real-time image reconstruction using frequency-sweep and pulsed-radar signals, and metrics for evaluating system performance. Numerous application examples and practical tutorial exercises provided throughout allow quick understanding of key concepts, and sample MATLAB codes implementing key reconstruction algorithms accompany the book online. This one-stop resource is ideal for graduate students taking introductory courses in microwave imaging, as well as researchers and industry professionals wanting to learn the fundamentals of the field.