Matrix-analytic Methods in Stochastic Models

Carnap, Quine, and Putnam held that in our pursuit of truth we can do no better than to start in the middle, relying on already-established beliefs and inferences and applying our best methods for re-evaluating particular beliefs and inferences and arriving at new ones. In this collection of essays, Gary Ebbs interprets these thinkers' methodological views in the light of their own philosophical commitments, and in the process refutes some widespread misunderstandings of their views, reveals the real strengths of their arguments, and exposes a number of problems that they face. To solve these problems, in many of the essays Ebbs also develops new philosophical approaches, including new theories of logical truth, language use, reference and truth, truth by convention, realism, trans-theoretical terms, agreement and disagreement, radical belief revision, and contextually a priori statements. His essays will be valuable for a wide range of readers in analytic philosophy.

Faced with ever-increasing complexity on a daily basis, the decision-makers of today are struggling to find the appropriate models, methods and tools to face the issues arising in complex systems acro

This book introduces carbon nanotubes as a matrix for efficient nanohybrid catalysis. The preparation and use of such materials in ultra-grade water purification is described. Simple chemical methods

This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and self-similarity; central and non-central limit theorems for long-range dependent series, and the limiting Hermite processes; fractional Brownian motion and its stochastic calculus; several celebrated decompositions of fractional Brownian motion; multidimensional models for long-range dependence and self-similarity; and maximum likelihood estimation methods for long-range dependent time series. Designed for graduate students and researchers, each chapter of the book is supplemented by numerous exercises, some designed to test the reader's understanding, while others invite the reader to consider some of the open research problems in the field today.

Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.

This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and eng

This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincaré inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.

Quantum annealing is a new-generation tool of information technology, which helps in solving combinatorial optimization problems with high precision, based on the concepts of quantum statistical physics. Detailed discussion on quantum spin glasses and its application in solving combinatorial optimization problems is required for better understanding of quantum annealing concepts. Fulfilling this requirement, the book highlights recent development in quantum spin glasses including Nishimori line, replica method and quantum annealing methods along with the essential principles. Separate chapters on simulated annealing, quantum dynamics and classical spin models are provided for enhanced learning. Important topics including adiabatic quantum computers and quenching dynamics are discussed in detail. This text will be useful for students of quantum computation, quantum information, statistical physics and computer science.

Bone is the tissue most frequently recovered archaeologically and is the material most commonly studied by biological anthropologists, who are interested in how skeletons change shape during growth and across evolutionary time. This volume brings together a range of contemporary studies of bone growth and development to highlight how cross-disciplinary research and new methods can enhance our anthropological understanding of skeletal variation. The novel use of imaging techniques from developmental biology, advanced sequencing methods from genetics, and perspectives from evolutionary developmental biology improve our ability to understand the bases of modern human and primate variation. Animal models can also be used to provide a broad biological perspective to the systematic study of humans. This volume is a testament to the drive of anthropologists to understand biological and evolutionary processes that underlie changes in bone morphology and illustrates the continued value of incor

One of the major problems of macroeconomic theory is the way in which the people exchange goods in decentralized market economies. There are major disagreements among macroeconomists regarding tools to influence required outcomes. Since the mainstream efficient market theory fails to provide an internal coherent framework, there is a need for an alternative theory. The book provides an innovative approach for the analysis of agent based models, populated by the heterogeneous and interacting agents in the field of financial fragility. The text is divided in two parts; the first presents analytical developments of stochastic aggregation and macro-dynamics inference methods. The second part introduces macroeconomic models of financial fragility for complex systems populated by heterogeneous and interacting agents. The concepts of financial fragility and macroeconomic dynamics are explained in detail in separate chapters. The statistical physics approach is applied to explain theories of m

Offering a fresh take on laser engineering, Laser Modeling: A Numerical Approach with Algebra and Calculus presents algebraic models and traditional calculus-based methods in tandem to make concepts e

Professor Cramer, author of the pivotal Mathematical Methods of Statistics (1946), examines problems in the theory of stochastic processes that can be considered as generalizations of problems in the

Professor Cramer, author of the pivotal Mathematical Methods of Statistics (1946), examines problems in the theory of stochastic processes that can be considered as generalizations of problems in the

Mathematical modeling of atmospheric composition is a formidable scientific and computational challenge. This comprehensive presentation of the modeling methods used in atmospheric chemistry focuses on both theory and practice, from the fundamental principles behind models, through to their applications in interpreting observations. An encyclopaedic coverage of methods used in atmospheric modeling, including their advantages and disadvantages, makes this a one-stop resource with a large scope. Particular emphasis is given to the mathematical formulation of chemical, radiative, and aerosol processes; advection and turbulent transport; emission and deposition processes; as well as major chapters on model evaluation and inverse modeling. The modeling of atmospheric chemistry is an intrinsically interdisciplinary endeavour, bringing together meteorology, radiative transfer, physical chemistry and biogeochemistry, making the book of value to a broad readership. Introductory chapters and a r

The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale

It is now widely recognized that the climate system is governed by nonlinear, multi-scale processes, whereby memory effects and stochastic forcing by fast processes, such as weather and convective systems, can induce regime behavior. Motivated by present difficulties in understanding the climate system and to aid the improvement of numerical weather and climate models, this book gathers contributions from mathematics, physics and climate science to highlight the latest developments and current research questions in nonlinear and stochastic climate dynamics. Leading researchers discuss some of the most challenging and exciting areas of research in the mathematical geosciences, such as the theory of tipping points and of extreme events including spatial extremes, climate networks, data assimilation and dynamical systems. This book provides graduate students and researchers with a broad overview of the physical climate system and introduces powerful data analysis and modeling methods for

This comprehensive guide helps readers understand the theory and techniques needed to analyze and model radio wave propagation in complex environments. All of the essential topics are covered, from the fundamental concepts of radio systems, to complex propagation phenomena. These topics include diffraction, ray tracing, scattering, atmospheric ducting, ionospheric ducting, scintillation, and propagation through both urban and non-urban environments. Emphasis is placed on practical procedures, with detailed discussion of numerical and mathematical methods providing readers with the necessary skills to build their own propagation models and develop their own techniques. MATLAB functions illustrating key modeling ideas are provided online. This is an invaluable resource for anyone wanting to use propagation models to understand the performance of radio systems for navigation, radar, communications, or broadcasting.

The Zebrafish: Disease Models and Chemical Screens, Fourth Edition, the latest volume in the Methods in Cell Biology series, looks at methods for analyzing genetics, genomics, and transcriptomics of z

This detailed volume gathers basic and advanced methods and protocols from in vitro assays and in vivo models to address the molecular and functional aspects of tau physiopathology. Divided into five

This volume aims to provide a new perspective on the broader usage of Hidden Markov Models (HMMs) in biology. Hidden Markov Models: Methods and Protocols guides readers through chapters on biological

Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototy

The Complexity of Self Government represents a revolutionary approach to political science. Bottom-up theory turns political and social analysis upside down by focusing analytic attention not on vacuous abstractions but on the individual men and women who either consciously or inadvertently create the institutions within which they live. Understanding this practical level of human activity is made possible through complexity theory, recently developed in computer models, but of wider use in understanding everyday human behaviour. To this complexity framework, the book adds social science to give life and colour to the analytical picture: micro-sociology from Garfinkel and Goffman, anthropology from Bourdieu, and non-technical game theory based on Thomas Schelling's microanalytics, to give rigour and bite. Theoretical examples include India's Mumbai, Iran, the marshes of southern Iraq, Berlusconi's Italy, backcountry China, Zimbabwe, and Nelson Mandela's revolution in South Africa.

With over half of the world's population now living in urban areas, the ability to model and understand the structure and dynamics of cities is becoming increasingly valuable. Combining new data with tools and concepts from statistical physics and urban economics, this book presents a modern and interdisciplinary perspective on cities and urban systems. Both empirical observations and theoretical approaches are critically reviewed, with particular emphasis placed on derivations of classical models and results, along with analysis of their limits and validity. Key aspects of cities are thoroughly analyzed, including mobility patterns, the impact of multimodality, the coupling between different transportation modes, the evolution of infrastructure networks, spatial and social organisation, and interactions between cities. Drawing upon knowledge and methods from areas of mathematics, physics, economics and geography, the resulting quantitative description of cities will be of interest to

The constantly increasing demand for more computing power can seem impossible to keep up with. However, multicore processors capable of performing computations in parallel allow computers to tackle ever larger problems in a wide variety of applications. This book provides a comprehensive introduction to parallel computing, discussing theoretical issues such as the fundamentals of concurrent processes, models of parallel and distributed computing, and metrics for evaluating and comparing parallel algorithms, as well as practical issues, including methods of designing and implementing shared- and distributed-memory programs, and standards for parallel program implementation, in particular MPI and OpenMP interfaces. Each chapter presents the basics in one place followed by advanced topics, allowing novices and experienced practitioners to quickly find what they need. A glossary and more than 80 exercises with selected solutions aid comprehension. The book is recommended as a text for adva

The Complexity of Self Government represents a revolutionary approach to political science. Bottom-up theory turns political and social analysis upside down by focusing analytic attention not on vacuous abstractions but on the individual men and women who either consciously or inadvertently create the institutions within which they live. Understanding this practical level of human activity is made possible through complexity theory, recently developed in computer models, but of wider use in understanding everyday human behaviour. To this complexity framework, the book adds social science to give life and colour to the analytical picture: micro-sociology from Garfinkel and Goffman, anthropology from Bourdieu, and non-technical game theory based on Thomas Schelling's microanalytics, to give rigour and bite. Theoretical examples include India's Mumbai, Iran, the marshes of southern Iraq, Berlusconi's Italy, backcountry China, Zimbabwe, and Nelson Mandela's revolution in South Africa.

Why are some African countries trapped in vicious cycles of ethnic exclusion and civil war, while others experience relative peace? In this groundbreaking book, Philip Roessler addresses this question. Roessler models Africa's weak, ethnically-divided states as confronting rulers with a coup-civil war trap - sharing power with ethnic rivals is necessary to underwrite societal peace and prevent civil war, but increases rivals' capabilities to seize sovereign power in a coup d'état. How rulers respond to this strategic trade-off is shown to be a function of their country's ethnic geography and the distribution of threat capabilities it produces. Moving between in-depth case studies of Sudan and the Democratic Republic of the Congo based on years of field work and statistical analyses of powersharing, coups and civil war across sub-Saharan Africa, the book serves as an exemplar of the benefits of mixed methods research for theory-building and testing in comparative politics.

Why are some African countries trapped in vicious cycles of ethnic exclusion and civil war, while others experience relative peace? In this groundbreaking book, Philip Roessler addresses this question. Roessler models Africa's weak, ethnically-divided states as confronting rulers with a coup-civil war trap - sharing power with ethnic rivals is necessary to underwrite societal peace and prevent civil war, but increases rivals' capabilities to seize sovereign power in a coup d'état. How rulers respond to this strategic trade-off is shown to be a function of their country's ethnic geography and the distribution of threat capabilities it produces. Moving between in-depth case studies of Sudan and the Democratic Republic of the Congo based on years of field work and statistical analyses of powersharing, coups and civil war across sub-Saharan Africa, the book serves as an exemplar of the benefits of mixed methods research for theory-building and testing in comparative politics.

New Methods of Teaching and Learning: A Handbook for Librarians is a one-stop introduction to the role of technology in teaching and learning in libraries. Emerging models of library instruction and l

New Methods of Teaching and Learning: A Handbook for Librarians is a one-stop introduction to the role of technology in teaching and learning in libraries. Emerging models of library instruction and l

The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application in

Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theor

Quantitative Methods in Reservoir Engineering, Second Edition, brings together the critical aspects of the industry to create more accurate models and better financial forecasts for oil and gas assets

This report examines the debate about the Islamic State in Iraq and Syria (ISIS) on Arabic Twitter and uses a mixed-methods analytic approach to identify and characterize in detail the Twitter network

This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this the perfect reference companion on the topic.

Combustion is a fascinating phenomenon coupling complex chemistry to transport mechanisms and nonlinear fluid dynamics. This book provides an up-to-date and comprehensive presentation of the nonlinear dynamics of combustion waves and other non-equilibrium energetic systems. The major advances in this field have resulted from analytical studies of simplified models performed in close relation with carefully controlled laboratory experiments. The key to understanding the complex phenomena is a systematic reduction of the complexity of the basic equations. Focusing on this fundamental approach, the book is split into three parts. Part I provides physical insights for physics-oriented readers, Part II presents detailed technical analysis using perturbation methods for theoreticians, and Part III recalls the necessary background knowledge in physics, chemistry and fluid dynamics. This structure makes the content accessible to newcomers to the physics of unstable fronts in flows, whilst also

This book reviews cutting-edge developments in neural signalling processing (NSP), systematically introducing readers to various models and methods in the context of NSP.Neuronal Signal Processing is

The Data and Analytics Playbook: Proven Methods for Governed Data and Analytic Quality explores the way in which data continues to dominate budgets, along with the varying efforts made across a variet

Changes in the shape of the yield curve have traditionally been one of the key macroeconomic indicators of a likely change in economic outlook. However, the recent financial crises have created a challenge to the management of monetary policy, demanding a revision in the way that policymakers model expected changes in the economy. This volume brings together central bank economists and leading academic monetary economists to propose new methods for modelling the behaviour of interest rates. Topics covered include: the analysis and extraction of expectations of future monetary policy and inflation; the analysis of the short-term dynamics of money market interest rates; the reliability of existing models in periods of extreme market volatility and how to adjust them accordingly; and the role of government debt and deficits in affecting sovereign bond yields and spreads. This book will interest financial researchers and practitioners as well as academic and central bank economists.

In this book three main aspects are considered together: mathematical models for engineering systems reliability, the main concepts for technogeneous risk study, and insurance as methods for risks man

This handbook covers established and advanced techniques for biomarker analysis, such as guidelines and strategies for assay validation methods; different mathematical models that are necessary in con