Monte Carlo Methods for Particle Transport
Fully updated with the latest developments in the eigenvalue Monte Carlo calculations and automatic variance reduction techniques and containing an entirely new chapter on fission matrix and alternative hybrid techniques.
Introduction to Probability, An: With Mathematica(r)
The main objective of this text is to facilitate a student's smooth learning transition from a course on probability to its applications in various areas. To achieve this goal, students are encouraged to experiment numerically with problems requiring computer solutions.
Introduction to Probability, An: With Mathematica(r)
The main objective of this text is to facilitate a student's smooth learning transition from a course on probability to its applications in various areas. To achieve this goal, students are encouraged to experiment numerically with problems requiring computer solutions.
Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory
The approach presented includes detailed and rigorous studies on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. The conclusion section introduces readers to Riemannian geometry, which is used in the subsequent chapters.
A Course in Stochastic Game Theory
Stochastic games have an element of chance: the state of the next round is determined probabilistically depending upon players' actions and the current state. Successful players need to balance the need for short-term payoffs while ensuring future opportunities remain high. The various techniques needed to analyze these often highly non-trivial games are a showcase of attractive mathematics, including methods from probability, differential equations, algebra, and combinatorics. This book presents a course on the theory of stochastic games going from the basics through to topics of modern research, focusing on conceptual clarity over complete generality. Each of its chapters introduces a new mathematical tool - including contracting mappings, semi-algebraic sets, infinite orbits, and Ramsey's theorem, among others - before discussing the game-theoretic results they can be used to obtain. The author assumes no more than a basic undergraduate curriculum and illustrates the theory with numerous examples and exercises, with solutions available online.
Architecture of Mathematics
This book describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike.
The Python Guide for New Data Scientists
The Python Guide for New Data Scientists is written for someone who has graduated from college and has either had some discipline related course or has a desire to learn some of the basic data science building blocks. Data science is interdisciplinary, and I have work with people who have backgrounds in business or economics and are competent data scientists with some additional coursework. Ordinarily, we look for potential data scientists who have degrees in statistics, computer science, econometrics, information technology, operations research, mathematics, or engineering. That encompasses a wide range of disciplines. People who become data scientists generally have coursework in statistics, data analysis, basic programming, and college mathematics. During or after college, they have been exposed to machine learning models and prediction, R or Python programming, and some data wrangling. This book is designed to help with the latter. We'll cover basic data science tools and Python programming with Jupyter Lab. We'll cover getting and cleaning data, data preprocessing, exploratory data analysis (EDA), inferential statistics, regression models, generalized linear models, machine learning and prediction using random forests, and other algorithms. There is Python coding in every chapter, with many examples. Leaning the content is driven by very involved examples, including some using COVID-19 data. You'll find data scientists at banks, insurance companies, railroads, hospitals, utilities, and pharmaceutical companies. They work at Google, Amazon, Facebook, Netflix, Wal-Mart, Caterpillar. They are employed by the Department of Transportation (DoT), the Federal Bureau of Investigation (FBI), the Centers for Disease Control (CDC), the National Aeronautics and Space Administration (NASA). and the Department of Defense (DoD). All source code and markdown are in my GitHub repositories (there are 32 repositories) and are accessible to the public. We have a chapter covering GitHub"
Computation of Greeks Using the Discrete Malliavin Calculus and Binomial Tree
Focuses on the resemblance between Bernoulli random variable and Brownian motion, a similarity providing deep insights into stochastic analysis Introduces a spectral binomial tree method, a new methodology for pricing barrier options, which allows the price of barrier options to be computed much more quickly Introduces the discrete Malliavin calculus, a new method for evaluating the sensitivity of options
Statistical Design and Analysis of Biological Experiments
This richly illustrated book provides an overview of the design and analysis of experiments with a focus on non-clinical experiments in the life sciences, including animal research. It covers the most common aspects of experimental design such as handling multiple treatment factors and improving precision. In addition, it addresses experiments with large numbers of treatment factors and response surface methods for optimizing experimental conditions or biotechnological yields.The book emphasizes the estimation of effect sizes and the principled use of statistical arguments in the broader scientific context. It gradually transitions from classical analysis of variance to modern linear mixed models, and provides detailed information on power analysis and sample size determination, including 'portable power' formulas for making quick approximate calculations. In turn, detailed discussions of several real-life examples illustrate the complexities and aberrations that can arise in practice.Chiefly intended for students, teachers and researchers in the fields of experimental biology and biomedicine, the book is largely self-contained and starts with the necessary background on basic statistical concepts. The underlying ideas and necessary mathematics are gradually introduced in increasingly complex variants of a single example. Hasse diagrams serve as a powerful method for visualizing and comparing experimental designs and deriving appropriate models for their analysis. Manual calculations are provided for early examples, allowing the reader to follow the analyses in detail. More complex calculations rely on the statistical software R, but are easily transferable to other software. Though there are few prerequisites for effectively using the book, previous exposure to basic statistical ideas and the software R would be advisable.
Recent Advances in Industrial and Applied Mathematics
This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.
Recent Advances in Industrial and Applied Mathematics
This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.
Bayesian Reasoning and Gaussian Processes for Machine Learning Applications
This book introduces Bayesian reasoning and Gaussian processes into machine learning applications. Bayesian methods are applied in many areas, such as game development, decision making, and drug discovery. It is very effective for machine learning algorithms in handling missing data and extracting information from small datasets. Bayesian Reasoning and Gaussian Processes for Machine Learning Applications uses a statistical background to understand continuous distributions and how learning can be viewed from a probabilistic framework. The chapters progress into such machine learning topics as belief network and Bayesian reinforcement learning, which is followed by Gaussian process introduction, classification, regression, covariance, and performance analysis of Gaussian processes with other models. FEATURES Contains recent advancements in machine learning Highlights applications of machine learning algorithms Offers both quantitative and qualitative research Includes numerous case studies This book is aimed at graduates, researchers, and professionals in the field of data science and machine learning.
The Pricing Model Revolution
An incisive and accessible blueprint to pricing your company's products and services In The Pricing Model Revolution: How Pricing Will Change the Way We Sell and Buy On and Offline, world renowned pricing expert Danilo Zatta delivers an essential and engaging blueprint to building an enduring competitive advantage with insightful pricing models. In the book, you'll learn to identify the best monetization approaches for your products and how to execute the one that makes the most sense for your business. From freemium to subscription, pay-per-use, and even neuropricing, the author discusses every available option and shows you how to choose. Although it's rigorous and evidence backed, The Pricing Model Revolution avoids an overly academic perspective in favour of providing you with concrete, practical guidance you can apply immediately to start generating more revenue. You'll learn things like: How to make smart and innovative pricing a core component of your next product offering How to distinguish between every new, future-oriented monetization approach Which factors to consider when you're choosing on a new pricing model for your most popular products An essential read for C-level executives, managers, entrepreneurs, and sales team leaders, The Pricing Model Revolution belongs on the bookshelves of every business leader seeking to learn more about one of the foundational topics driving top-line revenue and bottom-line profitability today.
Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions
This book investigates statistical observables for anomalous and nonergodic dynamics, focusing on the dynamical behaviors of particles modelled by non-Brownian stochastic processes in the complex real-world environment.
Turnpike Phenomenon and Symmetric Optimization Problems
Written by a leading expert in turnpike phenomenon, this book is devoted to the study of symmetric optimization, variational and optimal control problems in infinite dimensional spaces and turnpike properties of their approximate solutions. The book presents a systematic and comprehensive study of general classes of problems in optimization, calculus of variations, and optimal control with symmetric structures from the viewpoint of the turnpike phenomenon. The author establishes generic existence and well-posedness results for optimization problems and individual (not generic) turnpike results for variational and optimal control problems. Rich in impressive theoretical results, the author presents applications to crystallography and discrete dispersive dynamical systems which have prototypes in economic growth theory.This book will be useful for researchers interested in optimal control, calculus of variations turnpike theory and their applications, suchas mathematicians, mathematical economists, and researchers in crystallography, to name just a few.
Theory of Games and Economic Behavior
John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.
Statistical Regression Modeling with R
This book provides a concise point of reference for the most commonly used regression methods. It begins with linear and nonlinear regression for normally distributed data, logistic regression for binomially distributed data, and Poisson regression and negative-binomial regression for count data. It then progresses to these regression models that work with longitudinal and multi-level data structures. The volume is designed to guide the transition from classical to more advanced regression modeling, as well as to contribute to the rapid development of statistics and data science. With data and computing programs available to facilitate readers' learning experience, Statistical Regression Modeling promotes the applications of R in linear, nonlinear, longitudinal and multi-level regression. All included datasets, as well as the associated R program in packages nlme and lme4 for multi-level regression, are detailed in Appendix A. This book will be valuable in graduate courses on applied regression, as well as for practitioners and researchers in the fields of data science, statistical analytics, public health, and related fields.
The Lambert W Function
This book is the very first one in the English language dedicated to the Lambert W function, its generalizations, and its applications. One goal is to promote future research on the topic. The book contains all the information one needs when trying to find a result. The most important formulas and results are framed
Large Sample Techniques for Statistics
This book offers a comprehensive guide to large sample techniques in statistics. With a focus on developing analytical skills and understanding motivation, Large Sample Techniques for Statistics begins with fundamental techniques, and connects theory and applications in engaging ways.The first five chapters review some of the basic techniques, such as the fundamental epsilon-delta arguments, Taylor expansion, different types of convergence, and inequalities. The next five chapters discuss limit theorems in specific situations of observational data. Each of the first ten chapters contains at least one section of case study. The last six chapters are devoted to special areas of applications. This new edition introduces a final chapter dedicated to random matrix theory, as well as expanded treatment of inequalities and mixed effects models. The book's case studies and applications-oriented chapters demonstrate how to use methods developed from large sample theory in real world situations. The book is supplemented by a large number of exercises, giving readers opportunity to practice what they have learned. Appendices provide context for matrix algebra and mathematical statistics. The Second Edition seeks to address new challenges in data science.This text is intended for a wide audience, ranging from senior undergraduate students to researchers with doctorates. A first course in mathematical statistics and a course in calculus are prerequisites..
Advanced Statistics for Physical and Occupational Therapy
Advanced Statistics for Physical and Occupational Therapy explains the basis for statistical analyses that are commonly used to answer clinical research questions related to physical and occupational therapy. This textbook provides a resource to help students and faculty in physical and occupational therapy graduate programs understand the basis for common statistical analyses and be able to apply these techniques in their own research. This textbook provides readers with the basis for common statistical analyses, including t-tests, analysis of variance, regression, and nonparametric tests. Each chapter includes step-by-step tutorials with corresponding example data sets explaining how to conduct these statistical analyses using Statistical Package for the Social Sciences (SPSS) software and the Excel Analysis ToolPak, as well as how to identify and interpret relevant output and report results. Advanced Statistics for Physical and Occupational Therapy is key reading for students in physical therapy, occupational therapy, sport performance, and sport rehabilitation graduate programs as well as students in athletic training courses, applied statistics in sport, and research methods in sport modules. This new text will also be of interest to practicing clinicians who hope to better understand the research they are reading and/or are interested in starting to conduct their own clinical research.
The Enjoyment of Math
The classic book that shares the enjoyment of mathematics with readers of all skill levels What is so special about the number 30? Do the prime numbers go on forever? Are there more whole numbers than even numbers? The Enjoyment of Math explores these and other captivating problems and puzzles, introducing readers to some of the most fundamental ideas in mathematics. Written by two eminent mathematicians and requiring only a background in plane geometry and elementary algebra, this delightful book covers topics such as the theory of sets, the four-color problem, regular polyhedrons, Euler's proof of the infinitude of prime numbers, and curves of constant breadth. Along the way, it discusses the history behind the problems, carefully explaining how each has arisen and, in some cases, how to resolve it. With an incisive foreword by Alex Kontorovich, this Princeton Science Library edition shares the enjoyment of math with a new generation of readers.
Introduction to Computational Engineering with Matlab(r)
This book teaches readers how to use MATLAB programming to solve numerical engineering problems. The book focuses on computational engineering with the objective of helping engineering students improve their numerical problem-solving skills.
Statistics Behind the Headlines
Constructed from series of headlines and articles connected to scientific or government report. Exploration of statistical concepts in report: source of data, issues with quantifying and measuring variables/features, representation and analysis of statistical models, discussion of whether headline and article fairly captured original report.
Optimization of Pharmaceutical Processes
Optimization of Pharmaceutical Processes presents contributions from leading authorities in the fields of optimization and pharmaceutical manufacturing. Formulated within structured frameworks, practical examples and applications are given as guidance to apply optimization techniques to most aspects of pharmaceutical processes from design, to lab and pilot scale, and finally to manufacturing. The increasing demand for better quality, higher yield, more efficient-optimized and green pharmaceutical processes, indicates that optimal conditions for production must be applied to achieve simplicity, lower costs and superior yield. The application of such methods in the pharmaceutical industry is not trivial. Quality of the final product is of major importance to human health and the need for deep knowledge of the process parameters and the optimization of the processes are imperative. The volume, which includes new methods as well as review contributions will benefit awide readership including engineers in pharmaceuticals, chemical, biological, to name just a few.
Norbert Wiener: A Mathematician Among Engineers
Norbert Wiener (1894-1964) is well known by the general public as the founder of Cybernetics, by mathematicians as one of the first north-American mathematicians who win international prestige -- as the person who formalized Brownian motion, solved the Zaremba problem and was the author of two seminal papers devoted to Generalized Harmonic Analysis and Tauberian Theorems -- and by engineers as the person who proposed much of the Fourier analysis used by them and contributed to the foundation of the statistical theory of communication -- which includes the use of wave filter theory, information theory and prediction theory in control and communications as well as the automation of all types of electronic devices.Wiener's research, which was frequently motivated by physics, engineering, or biology, was a clever mixture of Fourier analysis and probability theory. His contributions to electronics through his work on filtering (that is, the separation of noise from a message), and the theory of prediction made him very valuable to electronics engineering. In addition, Wiener addressed many other topics, including the formalization of the Brownian motion, ergodic theory, wave filter theory, and information theory. Taking all these ingredients together, he ventured to create a new scientific paradigm: cybernetics.This book contains a detailed explanation of Wiener's life, his many colleagues, and the historical context in which he lived, as well as Wiener's work. It also contains a large appendix about 'Wiener, Shannon, and the rise of a Digital World'. The main focus of the book is on Wiener's work related to electrical and electronic engineering and the way he used his mathematics to create the main concepts and techniques of the statistical theory of communication. In particular, the author presents Wiener surrounded by the engineers that worked at MIT with whom he maintained strong contact. It was in this atmosphere that information theory arose, and Wiener was a main influence on the people who developed that theory.
Durable-Strategies Dynamic Games
Durable strategies that have prolonged effects are prevalent in real-world situations. Revenue-generating investments, toxic waste disposal, long-lived goods, regulatory measures, coalition agreements, diffusion of knowledge, advertisement and investments to accumulate physical capital are concrete and common examples of durable strategies. This book provides an augmentation of dynamic game theory and advances a new game paradigm with durable strategies in decision-making schemes. It covers theories, solution techniques, and the applications of a general class of dynamic games with multiple durable strategies. Non-cooperative equilibria and cooperative solutions are derived, along with advanced topics including random termination, asynchronous game horizons, and stochastic analysis. The techniques presented here will enable readers to solve numerous practical dynamic interactive problems with durable strategies. This book not only expands the scope of applied dynamic game theory, but also provides a solid foundation for further theoretical and technical advancements. As such, it will appeal to scholars and students of quantitative economics, game theory, operations research, and computational mathematics."Not too many new concepts have been introduced in dynamic games since their inception. The introduction of the concept of durable strategies changes this trend and yields important contributions to environmental and business applications." Dusan M Stipanovic, Professor, University of Illinois at Urbana-Champaign "Before this book, the field simply did not realize that most of our strategies are durable and entail profound effects in the future. Putting them into the mathematical framework of dynamic games is a great innovative effort." Vladimir Turetsky, Professor, Ort Braude College "Durable-strategies Dynamic Games is trulya world-leading addition to the field of dynamic games. It is a much needed publication to tackle increasingly crucial problems under the reality of durable strategies." Vladimir Mazalov, Director of Mathematical Research, Russian Academy of Sciences & President of the International Society of Dynamic Games
Fundamentals of Partial Differential Equations
Classical Vector Analysis.- Ordinary Differential Equations.- Partial Differential Equation Models.- Partial Differential Equations.- General Solution and Complete Integral.- Method of Characteristics.- Separation of Variables.- Method of Eigenfunctions Expansion.- Fourier Transforms.- Laplace Transform.
Perturbed Semi-Markov Type Processes I
This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes. The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications.
Numerical Simulation in Physics and Engineering: Trends and Applications
This book results from the XVIII Spanish-French School 'Jacques Louis Lions' on Numerical Simulation in Physics and Engineering, that took place in Las Palmas de Gran Canaria from 25th to 29th June 2018. These conferences are held biennially since 1984 and sponsored by the Spanish Society of Applied Mathematics (SEMA). They also have the sponsorship of the Soci矇t矇 de Math矇matiques Appliqu矇es et Industrielles (SMAI) of France since 2008. Each edition is organized around several main courses and talks delivered by renowned French/Spanish scientists. This volume is highly recommended to graduate students in Engineering or Science who want to focus on numerical simulation, either as a research topic or in the field of industrial applications. It can also benefit senior researchers and technicians working in industry who are interested in the use of state-of-the-art numerical techniques. Moreover, the book can be used as a textbook for master courses in Mathematics, Physics, or Engineering.
Mathematics of Open Fluid Systems
Part I: Modelling.- Mathematical Models of Fluids in Continuum Mechanics.- Open vs. Closed Systems.- Part II: Analysis.- Generalized Solutions.- Constitutive Theory and Weak-Strong Uniqueness Revisited.-Existence Theory, Basic Approximation Scheme.- Vanishing Galerkin Limit and Domain Approximation.-Vanishing Artificial Diffusion Limit.- Vanishing Artificial Pressure Limit.- Existence Theory - Main Results.-Part III: Qualitative Properties.- Long Time Behavior.- Statistical Solutions, Ergodic Hypothesis, and Turbulence.- Systems with Prescribed Boundary Temperature.
Asymptotic Statistics
Here is a practical and mathematically rigorous introduction to the field of asymptotic statistics. In addition to most of the standard topics of an asymptotics course--likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures--the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, one of the book's unifying themes that mainly entails the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation.
New Perspectives on the Theory of Inequalities for Integral and Sum
This book provides new contributions to the theory of inequalities for integral and sum, and includes four chapters. In the first chapter, linear inequalities via interpolation polynomials and green functions are discussed. New results related to Popoviciu type linear inequalities via extension of the Montgomery identity, the Taylor formula, Abel-Gontscharoff's interpolation polynomials, Hermite interpolation polynomials and the Fink identity with Green's functions, are presented. The second chapter is dedicated to Ostrowski's inequality and results with applications to numerical integration and probability theory. The third chapter deals with results involving functions with nondecreasing increments. Real life applications are discussed, as well as and connection of functions with nondecreasing increments together with many important concepts including arithmetic integral mean, wright convex functions, convex functions, nabla-convex functions, Jensen m-convex functions, m-convex functions, m-nabla-convex functions, k-monotonic functions, absolutely monotonic functions, completely monotonic functions, Laplace transform and exponentially convex functions, by using the finite difference operator of order m. The fourth chapter is mainly based on Popoviciu and Cebysev-Popoviciu type identities and inequalities. In this last chapter, the authors present results by using delta and nabla operators of higher order.
Faces of Geometry
The volume reports on interdisciplinary discussions and interactions between theoretical research and practical studies on geometric structures and their applications in architecture, the arts, design, education, engineering, and mathematics. These related fields of research can enrich each other and renew their mutual interest in these topics through networks of shared inspiration, and can ultimately enhance the quality of geometry and graphics education. Particular attention is dedicated to the contributions that women have made to the scientific community and especially mathematics. The book introduces engineers, architects and designers interested in computer applications, graphics and geometry to the latest advances in the field, with a particular focus on science, the arts and mathematics education.
Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains
This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.
Math Games with Bad Drawings
Bestselling author and worst-drawing artist Ben Orlin expands his oeuvre with this interactive collection of mathematical games. With 70-plus games, each taking a minute to learn and a lifetime to master, this treasure trove will delight, educate, and entertain. From beloved math popularizer Ben Orlin comes a masterfully compiled collection of dozens of playable mathematical games.This ultimate game chest draws on mathematical curios, childhood classics, and soon-to-be classics, each hand-chosen to be (1) fun, (2) thought-provoking, and (3) easy to play. With just paper, pens, and the occasional handful of coins, you and a partner can enjoy hours of fun--and hours of challenge. Orlin's sly humor, expansive knowledge, and so-bad-they're-good drawings show us how simple rules summon our best thinking. Games include: Ultimate Tic-Tac-ToeSproutsBattleshipQuantum Go FishDots and BoxesBlack HoleOrder and ChaosSequenciumPaper BoxingPropheciesArpeggiosBankerFrancoprussian LabyrinthCats and DogsAnd many more.
Linear and Generalized Linear Mixed Models and Their Applications
Now in its second edition, this book covers two major classes of mixed effects models--linear mixed models and generalized linear mixed models--and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. It offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it discusses the latest developments and methods in the field, incorporating relevant updates since publication of the first edition. These include advances in high-dimensional linear mixed models in genome-wide association studies (GWAS), advances in inference about generalized linear mixed models with crossed random effects, new methods in mixed model prediction, mixed model selection, and mixed model diagnostics. This book is suitable for students, researchers, and practitioners who are interested in using mixed models for statistical data analysis with public health applications. It is best for graduate courses in statistics, or for those who have taken a first course in mathematical statistics, are familiar with using computers for data analysis, and have a foundational background in calculus and linear algebra.
Bifurcation Theory of Impulsive Dynamical Systems
Impulsive functional differential equations.- Preliminaries.- General linear systems.- Linear periodic systems.- Nonlinear systems and stability.- Invariant manifold theory.- Smooth bifurcations.- Finite-dimensional ordinary impulsive differential equations.- Preliminaries.- Linear systems.- Stability for nonlinear systems.- Invariant manifold theory.- Bifurcations.- Special topics and applications.- Continuous approximation.- Non-smooth bifurcations.- Bifurcations in models from mathematical epidemiology and ecology.
Let's Play Math
Transform your child's experience of math! Filled with stories and illustrations, Let's Play Math offers a practical, activity-filled exploration of what it means to learn math. A mixture of educational philosophy, inspiration, and coffee-chat wisdom. Bestselling author Denise Gaskins provides helpful tips for all families with children from preschool or high school, whether they are homeschooling, unschooling, or attending a traditional classroom. Even if you struggled with math in school, you can help your kids practice mental math skills, master the basic facts, and ask the kind of questions that encourage deeper thought. Sections include: How to Understand Math: Introduce your children to the thrill of conquering a challenge. Build deep understanding by thinking, playing, and asking questions like a mathematician. Playful Problem Solving: Awaken your children's minds to the beauty and wonder of mathematics. Discover the social side of math, and learn games for players of all ages. Math with Living Books: See how mathematical ideas ebb and flow through the centuries with this brief tour through history. Can your kids solve puzzles from China, India, or Ancient Egypt? Let's Get Practical: Fit math into your family's daily life, help your children develop mental calculation skills, and find out what to try when your child struggles. Resources and References: With so many library books and Internet sites, you'll never run out of playful mathematical adventures. All parents and teachers share one goal: we want our children to understand and be able to use math. Your children will gain a strong foundation when you approach math as a family game, playing with ideas. Don't let your children suffer from the epidemic of math anxiety. Grab a copy of Let's Play Math, and start enjoying math today.
Novel Mathematics Inspired by Industrial Challenges
This contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics.The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.
Pyomo -- Optimization Modeling in Python
This book provides a complete and comprehensive guide to Pyomo (Python Optimization Modeling Objects) for beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. Using many examples to illustrate the different techniques useful for formulating models, this text beautifully elucidates the breadth of modeling capabilities that are supported by Pyomo and its handling of complex real-world applications. In the third edition, much of the material has been reorganized, new examples have been added, and a new chapter has been added describing how modelers can improve the performance of their models. The authors have also modified their recommended method for importing Pyomo. A big change in this edition is the emphasis of concrete models, which provide fewer restrictions on the specification and use of Pyomo models. Pyomo is an open source software package for formulating and solving large-scale optimization problems. The software extends the modeling approach supported by modern AML (Algebraic Modeling Language) tools. Pyomo is a flexible, extensible, and portable AML that is embedded in Python, a full-featured scripting language. Python is a powerful and dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions.
Theory of Agglomerative Hierarchical Clustering
This book discusses recent theoretical developments in agglomerative hierarchical clustering. The general understanding of agglomerative hierarchical clustering is that its theory was completed long ago and there is no room for further methodological studies, at least in its fundamental structure. This book has been planned counter to that view: it will show that there are possibilities for further theoretical studies and they will be not only for methodological interests but also for usefulness in real applications. When compared with traditional textbooks, the present book has several notable features. First, standard linkage methods and agglomerative procedure are described by a general algorithm in which dendrogram output is expressed by a recursive subprogram. That subprogram describes an abstract tree structure, which is used for a two-stage linkage method for a greater number of objects. A fundamental theorem for single linkage using a fuzzy graph is proved, which uncovers several theoretical features of single linkage. Other theoretical properties such as dendrogram reversals are discussed. New methods using positive-definite kernels are considered, and some properties of the Ward method using kernels are studied. Overall, theoretical features are discussed, but the results are useful as well for application-oriented users of agglomerative clustering.
