Bayesian Inference and Maximum Entropy Methods in Science and Engineering

Data assimilation is a hugely important mathematical technique, relevant in fields as diverse as geophysics, data science, and neuroscience. This modern book provides an authoritative treatment of the field as it relates to several scientific disciplines, with a particular emphasis on recent developments from machine learning and its role in the optimisation of data assimilation. Underlying theory from statistical physics, such as path integrals and Monte Carlo methods, are developed in the text as a basis for data assimilation, and the author then explores examples from current multidisciplinary research such as the modelling of shallow water systems, ocean dynamics, and neuronal dynamics in the avian brain. The theory of data assimilation and machine learning is introduced in an accessible and unified manner, and the book is suitable for undergraduate and graduate students from science and engineering without specialized experience of statistical physics.

This modern and self-contained book offers a clear and accessible introduction to the important topic of machine learning with neural networks. In addition to describing the mathematical principles of the topic, and its historical evolution, strong connections are drawn with underlying methods from statistical physics and current applications within science and engineering. Closely based around a well-established undergraduate course, this pedagogical text provides a solid understanding of the key aspects of modern machine learning with artificial neural networks, for students in physics, mathematics, and engineering. Numerous exercises expand and reinforce key concepts within the book and allow students to hone their programming skills. Frequent references to current research develop a detailed perspective on the state-of-the-art in machine learning research.

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

Macroevolutionary inference has historically been treated as a two-step process, involving the inference of a tree, and then inference of a macroevolutionary model using that tree. Newer models blend the two steps. These methods make more complete use of fossils than the previous generation of Bayesian phylogenetic models. They also involve many more parameters than prior models, including parameters about which empiricists may have little intuition. In this Element, we set forth a framework for fitting complex, hierarchical models. The authors ultimately fit and use a joint tree and diversification model to estimate a dated phylogeny of the Cincta (Echinodermata), a morphologically distinct group of Cambrian echinoderms that lack the fivefold radial symmetry characteristic of extant members of the phylum. Although the phylogeny of cinctans remains poorly supported in places, this Element shows how models of character change and diversification contribute to understanding patterns of p

In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, includi

The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus

The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus

This research textbook, designed for young Human-Computer Interaction (HCI) researchers beginning their careers, surveys the research models and methods in use today and offers a general framework to bring together the disparate concepts. HCI spans many disciplines and professions, including information science, applied psychology, computer science, informatics, software engineering and social science making it difficult for newcomers to get a good overview of the field and the available approaches. The book's rigorous 'approach-and-framework' response is to the challenge of retaining growth and diversification in HCI research by building up a general framework from approaches for Innovation, Art, Craft, Applied, Science and Engineering. This general framework is compared with other HCI frameworks and theories for completeness and coherence, all within a historical perspective of dissemination success. Readers can use this as a model to design and assess their own research frameworks a

'Phase-only Fresnel holograms,' which can be displayed on a single SLM without the need for lenses or complicated optical accessories, substantially simplifies 3-D holographic display systems. Exploring essential concepts, theories, and formulations of these phase-only Fresnel holograms, this book provides comprehensive coverage of modern methods for generating such holograms, which pave the way for commercial products such as compact holographic projectors, heads-up displays, and data security enhancement. Relevant MATLAB codes are provided for readers to implement and evaluate the theories and formulations of different methods, and can be used as a quick start framework for further research and development. This is a crucial and up-to-date treatment of phase-only Fresnel holograms for students and researchers in electrical and electronic engineering, computer science/engineering, applied physics, information technology, and multimedia technology, as well as engineers and scientists

Philosophy of Molecular Medicine: Foundational Issues in Theory and Practice aims at a systematic investigation of a number of foundational issues in the field of molecular medicine. The volume is organized around four broad modules focusing, respectively, on the following key aspects: What are the nature, scope, and limits of molecular medicine? How does it provide explanations? How does it represent and model phenomena of interest? How does it infer new knowledge from data and experiments? The essays collected here, authored by prominent scientists and philosophers of science, focus on a handful of mainstream topics in the philosophical literature, such as causation, explanation, modeling, and scientific inference. These previously unpublished contributions shed new light on these traditional topics by integrating them with problems, methods, and results from three prominent areas of contemporary biomedical science: basic research, translational and clinical research, and clinical pr

Decision-making in the face of uncertainty is a significant challenge in machine learning, and the multi-armed bandit model is a commonly used framework to address it. This comprehensive and rigorous introduction to the multi-armed bandit problem examines all the major settings, including stochastic, adversarial, and Bayesian frameworks. A focus on both mathematical intuition and carefully worked proofs makes this an excellent reference for established researchers and a helpful resource for graduate students in computer science, engineering, statistics, applied mathematics and economics. Linear bandits receive special attention as one of the most useful models in applications, while other chapters are dedicated to combinatorial bandits, ranking, non-stationary problems, Thompson sampling and pure exploration. The book ends with a peek into the world beyond bandits with an introduction to partial monitoring and learning in Markov decision processes.

The new edition of this popular textbook provides a fundamental approach to phase transformations and thermodynamics of materials. Explanations are emphasised at the level of atoms and electrons, and it comprehensively covers the classical topics from classical metallurgy to nanoscience and magnetic phase transitions. The book has three parts, covering the fundamentals of phase transformations, the origins of the Gibbs free energy, and the major phase transformations in materials science. A fourth part on advanced topics is available online. Much of the content from the first edition has been expanded, notably precipitation transformations in solids, heterogeneous nucleation, and energy, entropy and pressure. Three new chapters have been added to cover interactions within microstructures, surfaces, and solidification. Containing over 170 end-of-chapter problems, it is a valuable companion for graduate students and researchers in materials science, engineering, and applied physics.

Analysing language data systematically and looking closely at how people formulate their thoughts can reveal astonishing insights about the human mind. Without presupposing specific subject knowledge, this book gently introduces its readers to theoretical insights as well as practical principles for systematic linguistic analysis from a cognitive perspective. Drawing on Thora Tenbrink's twenty years' experience in both linguistics and cognitive science, this book offers theoretical guidance and practical advice for doing cognitive discourse analysis. It covers areas of analysis as diverse as attention, perspective, granularity, certainty, inference, transformation, communication, and cognitive strategies, using inspiring examples from many different projects. Simple techniques and tools are used to allow readers new to the subject easy ways to apply the methods, without the need for complex technologies, whilst the cross-disciplinary approach can be applied to a diverse range of resear

Analysing language data systematically and looking closely at how people formulate their thoughts can reveal astonishing insights about the human mind. Without presupposing specific subject knowledge, this book gently introduces its readers to theoretical insights as well as practical principles for systematic linguistic analysis from a cognitive perspective. Drawing on Thora Tenbrink's twenty years' experience in both linguistics and cognitive science, this book offers theoretical guidance and practical advice for doing cognitive discourse analysis. It covers areas of analysis as diverse as attention, perspective, granularity, certainty, inference, transformation, communication, and cognitive strategies, using inspiring examples from many different projects. Simple techniques and tools are used to allow readers new to the subject easy ways to apply the methods, without the need for complex technologies, whilst the cross-disciplinary approach can be applied to a diverse range of resear

Graphene is one of the most intensively studied materials, and has unusual electrical, mechanical and thermal properties, which provide almost unlimited potential applications. This book provides an introduction to the electrical and transport properties of graphene and other two-dimensional nanomaterials, covering ab-initio to multiscale methods. Updated from the first edition, the authors have added chapters on other two-dimensional materials, spin-related phenomena, and an improved overview of Berry phase effects. Other topics include powerful order N electronic structure, transport calculations, and ac transport and multiscale transport methodologies. Chapters are complemented with concrete examples and case studies, questions and exercises, detailed appendices and computational codes. It is a valuable resource for graduate students and researchers working in physics, materials science or engineering who are interested in the field of graphene-based nanomaterials.

Although numerical approximation and statistical inference are traditionally covered as entirely separate subjects, they are intimately connected through the common purpose of making estimations with partial information. This book explores these connections from a game and decision theoretic perspective, showing how they constitute a pathway to developing simple and general methods for solving fundamental problems in both areas. It illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, fast solvers, and Gaussian processes. This perspective reveals much of their essential anatomy and greatly facilitates advances in these areas, thereby appearing to establish a general principle for guiding the process of scientific discovery. This book is designed for graduate students, researchers, and engineers in mathematics, applied mathematics, and computer science, and particularly researchers interested in drawing on and developing this

Instabilities are present in all natural fluids from rivers to atmospheres. This book considers the physical processes that generate instability. Part I describes the normal mode instabilities most important in geophysical applications, including convection, shear instability and baroclinic instability. Classical analytical approaches are covered, while also emphasising numerical methods, mechanisms such as internal wave resonance, and simple `rules of thumb' that permit assessment of instability quickly and intuitively. Part II introduces the cutting edge: nonmodal instabilities, the relationship between instability and turbulence, self-organised criticality, and advanced numerical techniques. Featuring numerous exercises and projects, the book is ideal for advanced students and researchers wishing to understand flow instability and apply it to their own research. It can be used to teach courses in oceanography, atmospheric science, coastal engineering, applied mathematics and environ

This textbook presents key theoretical approaches to understanding issues of sustainability and environmental management, perfectly bridging the gap between engineering and environmental science. It begins with the fundamentals of environmental modelling and toxicology, which are then used to discuss qualitative and quantitative risk assessment methods, and environmental assessments of product design. It discusses how business and government can work towards sustainability, focusing on managerial and legal tools, before considering ethics and how decisions on environmental management can be made. Students will learn quantitative methods while also gaining an understanding of qualitative, legal, and ethical aspects of sustainability. Practical applications are included throughout, and there are study questions at the end of each chapter. PowerPoint slides and jpegs of all the figures in the book are provided online. This is the perfect textbook on environmental studies for engineering a

This textbook presents key theoretical approaches to understanding issues of sustainability and environmental management, perfectly bridging the gap between engineering and environmental science. It begins with the fundamentals of environmental modelling and toxicology, which are then used to discuss qualitative and quantitative risk assessment methods, and environmental assessments of product design. It discusses how business and government can work towards sustainability, focusing on managerial and legal tools, before considering ethics and how decisions on environmental management can be made. Students will learn quantitative methods while also gaining an understanding of qualitative, legal, and ethical aspects of sustainability. Practical applications are included throughout, and there are study questions at the end of each chapter. PowerPoint slides and jpegs of all the figures in the book are provided online. This is the perfect textbook on environmental studies for engineering a

The Handbook of Psychophysiology has been the authoritative resource for more than a quarter of a century. Since the third edition was published a decade ago, the field of psychophysiological science has seen significant advances, both in traditional measures such as electroencephalography, event-related brain potentials, and cardiovascular assessments, and in novel approaches and methods in behavioural epigenetics, neuroimaging, psychoneuroimmunology, psychoneuroendocrinology, neuropsychology, behavioural genetics, connectivity analyses, and non-contact sensors. At the same time, a thoroughgoing interdisciplinary focus has emerged as essential to scientific progress. Emphasizing the need for multiple measures, careful experimental design, and logical inference, the fourth edition of the Handbook provides updated and expanded coverage of approaches, methods, and analyses in the field. With state-of-the-art reviews of research in topical areas such as stress, emotion, development, langu

This book sheds new light on Transform methods, which dominate the study of linear time-invariant systems in all areas of science and engineering, such as circuit theory, signal/image processing, comm

Machine learning is an interdisciplinary field of science and engineering that studies mathematical theories and practical applications of systems that learn. This book introduces theories, methods and applications of density ratio estimation, which is a newly emerging paradigm in the machine learning community. Various machine learning problems such as non-stationarity adaptation, outlier detection, dimensionality reduction, independent component analysis, clustering, classification and conditional density estimation can be systematically solved via the estimation of probability density ratios. The authors offer a comprehensive introduction of various density ratio estimators including methods via density estimation, moment matching, probabilistic classification, density fitting and density ratio fitting, as well as describing how these can be applied to machine learning. The book provides mathematical theories for density ratio estimation including parametric and non-parametric conve

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.

Mathematics is the science of numbers, space, change and structures. Modern theories and methods of mathematics are applied in fields such as engineering, computer science, etc. Applied mathematics fi

Computational modeling is now ubiquitous in psychology, and researchers who are not modelers may find it increasingly difficult to follow the theoretical developments in their field. This book presents an integrated framework for the development and application of models in psychology and related disciplines. Researchers and students are given the knowledge and tools to interpret models published in their area, as well as to develop, fit, and test their own models. Both the development of models and key features of any model are covered, as are the applications of models in a variety of domains across the behavioural sciences. A number of chapters are devoted to fitting models using maximum likelihood and Bayesian estimation, including fitting hierarchical and mixture models. Model comparison is described as a core philosophy of scientific inference, and the use of models to understand theories and advance scientific discourse is explained.

Computational modeling is now ubiquitous in psychology, and researchers who are not modelers may find it increasingly difficult to follow the theoretical developments in their field. This book presents an integrated framework for the development and application of models in psychology and related disciplines. Researchers and students are given the knowledge and tools to interpret models published in their area, as well as to develop, fit, and test their own models. Both the development of models and key features of any model are covered, as are the applications of models in a variety of domains across the behavioural sciences. A number of chapters are devoted to fitting models using maximum likelihood and Bayesian estimation, including fitting hierarchical and mixture models. Model comparison is described as a core philosophy of scientific inference, and the use of models to understand theories and advance scientific discourse is explained.

Probability has applications in many areas of modern science, not to mention in our daily life. Its importance as a mathematical discipline cannot be overrated, and it is a fascinating and surprising topic in its own right. This engaging textbook with its easy-to-follow writing style provides a comprehensive yet concise introduction to the subject. It covers all of the standard material for undergraduate and first-year-graduate-level courses as well as many topics that are usually not found in standard texts, such as Bayesian inference, Markov chain Monte Carlo simulation, and Chernoff bounds.

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.

Education, engineering, educational technology, and other researchers from the US provide 15 chapters on user experience design methods and the development of educational technology. In the first s

Targeted at graduate students, researchers and practitioners in the field of science and engineering, this book gives a self-contained introduction to a measure-theoretic framework in laying out the definitions and basic concepts of random variables and stochastic diffusion processes. It then continues to weave into a framework of several practical tools and applications involving stochastic dynamical systems. These include tools for the numerical integration of such dynamical systems, nonlinear stochastic filtering and generalized Bayesian update theories for solving inverse problems and a new stochastic search technique for treating a broad class of non-convex optimization problems. MATLAB® codes for all the applications are uploaded on the companion website.

Originally published in 1926, this informative and detailed textbook is primarily aimed at university students studying applied mathematics for a science or engineering degree and contains a large number of useful examples to work though. Basic knowledge of elementary dynamics is assumed throughout, as is a working knowledge of differential and integral calculus. Answers can be found at the back of the book, as well as a summary of the methods of solution of the equations contained. Examples are mostly collected from a variety of past university and college examination papers, and notably rigid dynamics has been confined to two-dimensional motion and omissions have been made to all reference of moving axes. Covering the topic in its entirety, this book gives a panoramic overview of the subject and will be of considerable value to anyone with a keen interest in mathematics and engineering, as well as the history of education.

The Handbook of Psychophysiology has been the authoritative resource for more than a quarter of a century. Since the third edition was published a decade ago, the field of psychophysiological science has seen significant advances, both in traditional measures such as electroencephalography, event-related brain potentials, and cardiovascular assessments, and in novel approaches and methods in behavioural epigenetics, neuroimaging, psychoneuroimmunology, psychoneuroendocrinology, neuropsychology, behavioural genetics, connectivity analyses, and non-contact sensors. At the same time, a thoroughgoing interdisciplinary focus has emerged as essential to scientific progress. Emphasizing the need for multiple measures, careful experimental design, and logical inference, the fourth edition of the Handbook provides updated and expanded coverage of approaches, methods, and analyses in the field. With state-of-the-art reviews of research in topical areas such as stress, emotion, development, langu

This book is an introductory text to a range of numerical methods used today to simulate time-dependent processes in Earth science, physics, engineering, and many other fields. The physical problem of

This book is an introductory text to a range of numerical methods used today to simulate time-dependent processes in Earth science, physics, engineering, and many other fields. The physical problem of

Scholars of engineering, business, art, medicine, and other fields explore methods and technologies for teaching creative problem solving in higher education. They discuss the context of higher educat

This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.

Various optimization methods for structural size, shape, topology designs have been developed and widely employed in engineering applications. Among which, topology optimization has been recognized as

The editors present readers with a collection of academic and professional contributions on emerging and contemporary methods and research in the systemic and strategic planning of energy usage. The n

This book discusses a development in institutional economics and management science, which provides engineering methods for institution design. Based on the “Sun Diagram” created by the author, it use