Search results for """ "Statistics and Dynamics""

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Book SynopsisThe general area of geophysical fluid mechanics is truly interdisciplinary. Now ideas from statistical physics are being applied in novel ways to inhomogeneous complex systems such as atmospheres and oceans. In this book, the basic ideas of geophysics, probability theory, information theory, nonlinear dynamics and equilibrium statistical mechanics are introduced and applied to large time-selective decay, the effect of large scale forcing, nonlinear stability, fluid flow on a sphere and Jupiter's Great Red Spot. The book is the first to adopt this approach and it contains many recent ideas and results. Its audience ranges from graduate students and researchers in both applied mathematics and the geophysical sciences. It illustrates the richness of the interplay of mathematical analysis, qualitative models and numerical simulations which combine in the emerging area of computational science.Trade Review'… this book is a valuable contribution to the fascinating intersection of applied mathematics and geophysical fluid dynamics. … The authors are adept at illuminating and motivating rigorous mathematical analysis, qualitative models and physical intuition through exceptionally lucid exposition and a rich collection of examples.' Mathematical ReviewsTable of Contents1. Barotropic geophysical flows and two-dimensional fluid flows: an elementary introduction; 2. The Response to large scale forcing; 3. The selective decay principle for basic geophysical flows; 4. Nonlinear stability of steady geophysical flows; 5. Topographic mean-flow interaction, nonlinear instability, and chaotic dynamics; 6. Introduction to empirical statistical theory; 7. Equilibrium statistical mechanics for systems of ordinary differential equations; 8. Statistical mechanics for the truncated quasi-geostrophic equations; 9. Empirical statistical theories for most probable states; 10. Assessing the potential applicability of equilibrium statistical theories for geophysical flows: an overview; 11. Predictions and comparison of equilibrium statistical theories; 12. Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation; 13. Predicting the jets and spots on Jupiter by equilibrium statistical mechanics; 14. Statistically relevant and irrelevant conserved quantities for truncated quasi-geostrophic flow and the Burger–Hopf model; 15. A mathematical framework for quantifying predictability utilizing relative entropy; 16. Barotropic quasi-geostrophic equations on the sphere; Bibliography; Index.

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Book SynopsisThis book is devoted to the system analysis of statistical experiments, determined by the averaged sums of sampling random variables. The dynamics of statistical experiments are given by difference stochastic equations with a speci?ed regression function of increments – linear or nonlinear. The statistical experiments are studied by the sample volume increasing (N ??), as well as in discrete-continuous time by the number of stages increasing (k ??) for different conditions imposed on the regression function of increments. The proofs of limit theorems employ modern methods for the operator and martingale characterization of Markov processes, including singular perturbation methods. Furthermore, they justify the representation of a stationary Gaussian statistical experiment with the Markov property, as a stochastic difference equation solution, applying the theorem of normal correlation. The statistical hypotheses verification problem is formulated in the classification of evolutionary processes, which determine the dynamics of the predictable component. The method of stochastic approximation is used for classifying statistical experiments.Table of ContentsPreface ix List of Abbreviations xi Introduction xiii Chapter 1 Statistical Experiments 1 1.1 Statistical experiments with linear regression 1 1.1.1 Basic definitions 1 1.1.2 Difference evolution equations 3 1.1.3 The equilibrium state 4 1.1.4 Stochastic difference equations 7 1.1.5 Convergence to the equilibrium state 9 1.1.6 Normal approximation of the stochastic component 11 1.2 Binary SEs with nonlinear regression 13 1.2.1 Basic assumptions 13 1.2.2 Equilibrium 15 1.2.3 Stochastic difference equations 17 1.2.4 Convergence to the equilibrium state 18 1.2.5 Normal approximation of the stochastic component 20 1.3 Multivariate statistical experiments 22 1.3.1 Regression function of increments 22 1.3.2 The equilibrium state of multivariate EPs 25 1.3.3 Stochastic difference equations 26 1.3.4 Convergence to the equilibrium state 28 1.3.5 Normal approximation of the stochastic component 29 1.4 SEs with Wright–Fisher normalization 31 1.4.1 Binary RFs 31 1.4.2 Multivariate RFIs 33 1.5 Exponential statistical experiments 35 1.5.1 Binary ESEs 36 1.5.2 Steady regime of ESEs 37 1.5.3 Approximation of ESEs by geometric Brownian motion 38 Chapter 2 Diffusion Approximation of Statistical Experiments in Discrete–Continuous Time 43 2.1 Binary DMPs 44 2.1.1 DMPs in discrete–continuous time 45 2.1.2 Justification of diffusion approximation 47 2.2 Multivariate DMPs in discrete–continuous time 51 2.2.1 Evolutionary DMPs in discrete–continuous time 52 2.2.2 SDEs for the DMP in discrete–continuous time 53 2.2.3 Diffusion approximation of DMPs in discrete–continuous time 55 2.3 A DMP in an MRE 58 2.3.1 Discrete and continuous MRE 58 2.3.2 Proof of limit theorems 2.3.1 and 2.3.2 62 2.4 The DMPs in a balanced MRE 65 2.4.1 Basic assumptions 66 2.4.2 Proof of limit theorem 2.4.1 70 2.5 Adapted SEs 74 2.5.1 Bernoulli approximation of the SE stochastic component 75 2.5.2 Adapted SEs 77 2.5.3 Adapted SEs in a series scheme 79 2.6 DMPs in an asymptotical diffusion environment 84 2.6.1 Asymptotic diffusion perturbation 85 2.7 A DMP with ASD 91 2.7.1 Asymptotically small diffusion 91 2.7.2 EGs of DMP 94 2.7.3 AF of DMPs 97 Chapter 3 Statistics of Statistical Experiments 103 3.1 Parameter estimation of one-dimensional stationary SEs 103 3.1.1 Stationarity 103 3.1.2 Covariance statistics 108 3.1.3 A priori statistics 110 3.1.4 Optimal estimating function 111 3.1.5 Stationary Gaussian SEs 114 3.2 Parameter estimators for multivariate stationary SEs 115 3.2.1 Vector difference SDEs and stationarity conditions 116 3.2.2 Optimal estimating function 118 3.2.3 Stationary Gaussian Markov SEs 119 3.3 Estimates of continuous process parameters 122 3.3.1 Diffusion-type processes 122 3.3.2 Estimation of a continuous parameter 123 3.4 Classification of EPs 124 3.4.1 Basic assumption 125 3.4.2 Classification of EPs 126 3.4.3 Justification of EP models classification 127 3.4.4 Proof of Theorem 3.4.1 129 3.4.5 Interpretation of EPs 133 3.4.6 Interpretation of EPs in models of collective behavior 138 3.5 Classification of SEs 139 3.5.1 The SA of SEs 139 3.5.2 Classifiers 140 3.5.3 Classification of SEs 142 3.6 Evolutionary model of ternary SEs 144 3.6.1 Basic assumptions 144 3.6.2 The model interpretation and analysis 146 3.7 Equilibrium states in the dynamics of ternary SEs 149 3.7.1 Building a model 149 3.7.2 The equilibrium state and fluctuations 150 3.7.3 Classification of TSEs 151 Chapter 4 Modeling and Numerical Analysis of Statistical Experiments 153 4.1 Numerical verification of generic model 153 4.1.1 Evolutionary processes with linear and nonlinear RFIs 153 4.1.2 Generic model of trajectory generation 156 4.2 Numerical verification of DMD 158 4.2.1 Simulation of DMD trajectories 158 4.2.2 Estimation of DMD parameters 163 4.3 DMD and modeling of the dynamics of macromolecules in biophysics 167 4.3.1 The model motivation 168 4.3.2 Statistical model of a stationary DMD 169 4.3.3 Stokes–Einstein kinetic diffusion model 171 4.3.4 Verification of the model of stationary DMD by direct numerical simulation 172 4.3.5 Numerical verification of DMD characteristics using the model of Stokes–Einstein 173 4.3.6 The ability of the DMD model to detect the proportion of fast and slow particles 176 4.3.7 Interpretation of the mixes of Brownian motions 182 References 189 Index 193

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Book SynopsisThe theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to Trade Review'A very valuable addition to the growing field of random graphs, providing a systematic coverage of these novel models.' Michael Krivelevich, Mathematical Reviews'The book is written in a friendly, chatty style, making it easy to read; I very much like that. In summary, Random Graph Dynamics is a nice contribution to the area of random graphs and a source of valuable insights.' Malwina J. Luczak, Journal of the American Statistical AssociationTable of Contents1. Overview; 2. Erdos–Renyi random graphs; 3. Fixed degree distributions; 4. Power laws; 5. Small worlds; 6. Random walks; 7. CHKNS model.

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Book SynopsisStatistical Methods for Dynamic Treatment Regimes shares state of the art of statistical methods developed to address questions of estimation and inference for dynamic treatment regimes, a branch of personalized medicine.Trade ReviewFrom the reviews:"Overall, the book provides an excellent reviewof DTRs up to date. After finishing reading the book, I planned to create a post-graduate seminar course on this topic using this book as a textbook. I enthusiastically recommend this book. This book will be a valuable reference for anyone interested and involved in research on personalized medicine." (Hyonggin An, Journal of Agricultural, Biological, and Environmental Statistics, April, 2015)“The intended audience includes physicians, clinical researchers, physicians in training, statisticians, and medical students, as well as master’s and doctoral students in the field of biostatistics and epidemiology and computer scientists. … This book provides a concise summary of the key findings in the statistical literature of dynamic treatment regimes. … The simple language and well-organized chapters are unsurpassed attributes of this book. It will be an exceptional resource for quick review.” (Parthiv Amin, Doody’s Book Reviews, November, 2013)Table of ContentsIntroduction.- The Data: Observational Studies and Sequentially Randomized Trials.- Statistical Reinforcement Learning.- Estimation of Optimal DTRs by Modeling Contrasts of Conditional Mean Outcomes.- Estimation of Optimal DTRs by Directly Modeling Regimes.- G-computation: Parametric Estimation of Optimal DTRs.- Estimation DTRs for Alternative Outcome Types.- Inference and Non-regularity.- Additional Considerations and Final Thoughts.- Glossary.- Index.- References.

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Book SynopsisThe study of dynamical systems is a well established field. This book provides a panorama of several aspects of interest to mathematicians and physicists. It collects the material of several courses at the graduate level given by the authors, avoiding detailed proofs in exchange for numerous illustrations and examples. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.Trade ReviewFrom the reviews: "The book is a good introduction to the field of dynamical systems with a particular emphasis on statistical properties and applications. In particular, the relations both with real experiments with numerical simulations are discussed. … The book contains many figures that really help the understanding of the text. The book can be used as a text for an introductory course in dynamical systems (at the master’s or Ph.D. level). It is particularly suited for students with interests in applications (either physics, economy or biology)." (Carlangelo Liverani, Mathematical Reviews, Issue 2007 m) "Two thoughts crossed my mind when I picked up this book. The first was: ‘what a physically attractive book.’ The second was: ‘what a short book to have on such a wide ranging topic.’ … It is a perfect size to carry in a knapsack, the print is clear and the layout of text, equations, and figures is marvelously done. … images are multi-colored stereo images, and allow the reader to ‘see’ a three dimensional effect that helps illustrate the phenomena." (David S. Mazel, MathDL, December, 2007)Table of ContentsA Basic Problem.- Dynamical Systems.- Topological Properties.- Hyperbolicity.- Invariant Measures.- Entropy.- Statistics and Statistical Mechanics.- Other Probabilistic Results.- Experimental Aspects.

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Book SynopsisThis text is concerned with Bayesian learning, inference and forecasting in dynamic environments.Table of Contentsto the DLM: The First-Order Polynomial Model.- to the DLM: The Dynamic Regression Model.- The Dynamic Linear Model.- Univariate Time Series DLM Theory.- Model Specification and Design.- Polynomial Trend Models.- Seasonal Models.- Regression, Autoregression, and Related Models.- Illustrations and Extensions of Standard DLMs.- Intervention and Monitoring.- Multi-Process Models.- Non-Linear Dynamic Models: Analytic and Numerical Approximations.- Exponential Family Dynamic Models.- Simulation-Based Methods in Dynamic Models.- Multivariate Modelling and Forecasting.- Distribution Theory and Linear Algebra.

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Book SynopsisStatistical Mechanics reflects the latest techniques and developments in statistical mechanics. Covering a variety of concepts and topics - molecular dynamic methods, renormalization theory, chaos, polymer chain folding, oscillating chemical reactions, and cellular automata. 15 computer programs written in FORTRAN are provided to illustrate the concepts as well as more than 100 chapter-end exercises.Trade Review"...a course based on the book will expose the richness and beauty of statistical mechanics to the students and...incite their curiosity for further study and research in this fascinating field." (Zentralblatt MATH, Vol. 973, 2001/23)Table of ContentsESSENTIALS. Classical Statistical Mechanics. Quantum Statistical Mechanics. EQUILIBRIUM STATISTICAL MECHANICS. Phase Transitions and Critical Phenomena. The Liquid State. Molecular Dynamics Methods. Monte Carlo Methods. Polymers, Proteins, and Spin Glass Models. NONEQUILIBRIUM STATISTICAL MECHANICS. The Boltzmann Equation. Approaches to Brownian Motion. Zwanzig-Mori Formalism. Activated Barrier-Crossing Problem. Oscillating Chemical Reactions and Chaos. Introduction to Cellular Automation Models. Appendices. Bibliography. Indexes.

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Book SynopsisDisease screening and disease surveillance (DSDS) constitute two critical areas in public health, each presenting distinctive challenges primarily due to their sequential decision-making nature and complex data structures. Statistical Methods for Dynamic Disease Screening and Spatio-Temporal Disease Surveillance explores numerous recent analytic methodologies that enhance traditional techniques. The author, a prominent researcher specializing in innovative sequential decision-making techniques, demonstrates how these novel methods effectively address the challenges of DSDS.After a concise introduction that lays the groundwork for comprehending the challenges inherent in DSDS, the book delves into fundamental statistical concepts and methods relevant to DSDS. This includes exploration of statistical process control (SPC) charts specifically crafted for sequential decision-making purposes. The subsequent chapters systematically outline recent advancements in dynamic scre

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Book SynopsisScientists are increasingly finding themselves engaged in research problems that cross the traditional disciplinary lines of physics, chemistry, biology, materials science, and engineering. Because of its broad scope, statistical mechanics is an essential tool for students and more experienced researchers planning to become active in such an interdisciplinary research environment. Powerful computational methods that are based in statistical mechanics allow complex systems to be studied at an unprecedented level of detail. This book synthesizes the underlying theory of statistical mechanics with the computational techniques and algorithms used to solve real-world problems and provides readers with a solid foundation in topics that reflect the modern landscape of statistical mechanics. Topics covered include detailed reviews of classical and quantum mechanics, in-depth discussions of the equilibrium ensembles and the use of molecular dynamics and Monte Carlo to sample classical and quantum ensemble distributions, Feynman path integrals, classical and quantum linear-response theory, nonequilibrium molecular dynamics, the Langevin and generalized Langevin equations, critical phenomena, techniques for free energy calculations, machine learning models, and the use of these models in statistical mechanics applications. The book is structured such that the theoretical underpinnings of each topic are covered side by side with computational methods used for practical implementation of the theoretical concepts.Trade ReviewReview from previous edition A good contribution to scholarship in this area. * Paul Madden, University of Oxford *Addresses an important area in a nicely coherent and systematic way. * Marshall Stoneham, University College London *A welcome addition to the literature. * Daan Frenkel, University of Cambridge *Table of Contents1: Classical mechanics 2: Theoretical foundations of classical statistical mechanics 3: The microcanonical ensemble and introduction to molecular dynamics 4: The canonical ensemble 5: The isobaric ensembles 6: The grand canonical ensemble 7: Monte Carlo 8: Free-energy calculations 9: Quantum mechanics 10: Quantum ensembles and the density matrix 11: The quantum ideal gases: Fermi-Dirac and Bose-Einstein statistics 12: The Feynman path integral 13: Classical time-dependent statistical mechanics 14: Quantum time-dependent statistical mechanics 15: The Langevin and generalized Langevin equations 16: Discrete models and critical phenomena 17: Introduction to machine learning in statistical mechanics Free

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Book SynopsisMechanics and Dynamics of Quantum Systems.- Statistical Mechanics: Basic Principles.- Statistical Mechanics: Application to Chemical Thermodynamics.- Statistical Mechanics: Application to Chemical Kinetics.- Appendix.

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Book SynopsisThis book provides a fresh approach to the subjects, integrating classical thermodynamics and statistical mechanics to give students a solid understanding of the fundamentals and how macroscopic and microscopic ideas interweave. Includes numerous worked examples, and well over 400 guided, often multi-step, end-of-chapter problems that address conceptual, fundamental, and applied skill sets.Trade Review'This textbook presents an accessible (but still rigorous) treatment of the material at a beginning-graduate level, including many worked examples. By making the concept of entropy central to the book, Professor Shell provides an organizing principle that makes it easier for the students to achieve mastery of this important area.' Athanassios Z. Panagiotopoulos, Princeton University'Other integrated treatments of thermodynamics and statistical mechanics exist, but this one stands out as remarkably thoughtful and clear in its selection and illumination of key concepts needed for understanding and modeling materials and processes.' Thomas Truskett, University of Texas, Austin'This text provides a long-awaited and modern approach that integrates statistical mechanics with classical thermodynamics, rather than the traditional sequential approach, in which teaching of the molecular origins of thermodynamic laws and models only follows later, after classical thermodynamics. The author clearly shows how classical thermodynamic concepts result from the underlying behavior of the molecules themselves.' Keith E. Gubbins, North Carolina State UniversityTable of Contents1. Introduction and guide to this text; 2. Equilibrium and entropy; 3. Energy and how the microscopic world works; 4. Entropy and how the macroscopic world works; 5. The fundamental equation; 6. The first law and reversibility; 7. Legendre transforms and other potentials; 8. Maxwell relations and measurable quantities; 9. Gases; 10. Phase equilibrium; 11. Stability; 12. Solutions - fundamentals; 13. Solutions - advanced and special cases; 14. Solids; 15. The third law; 16. The canonical partition function; 17. Fluctuations; 18. Statistical mechanics of classical systems; 19. Other ensembles; 20. Reaction equilibrium; 21. Reaction coordinates and rates; 22. Molecular simulation methods.

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Book SynopsisA collection of research and expository papers reflecting the interfacing of two fields: nonlinear dynamics and statistics. It presents the proceedings of a workshop entitled 'Nonlinear Dynamics and Time Series: Building a Bridge Between the Natural and Statistical Sciences' held at the Centre de Recherches Mathematiques in Montreal in July 1995.Table of ContentsOpening lectures: Tools for the analysis of chaotic data by H. I. Abarbanel Some comments on nonlinear time series analysis by H. Tong Embeddings, dimension, and system reconstruction: A general approach to predictive and fractal scaling dimensions in discrete-index time series by C. D. Cutler Statistics for continuity and differentiability: An application to attractor reconstruction from time series by L. M. Pecora, T. L. Carroll, and J. F. Heagy Reconstruction of integrate-and-fire dynamics by T. Sauer Surrogate data methodology: On the validity of the method of surrogate data by K.-S. Chan Using "surrogate surrogate data" to calibrate the actual rate of false positives in tests for nonlinearity in time series by J. Theiler and D. Prichard Local Lyapunov exponents: Chaos with confidence: Asymptotics and applications of local Lyapunov exponents by B. A. Bailey, S. Ellner, and D. W. Nychka Estimating local Lyapunov exponents by Z.-Q. Lu and R. L. Smith Long-range dependence: Defining and measuring long-range dependence by P. Hall Modelling nonlinearity and long memory in time series by P. M. Robinson and P. Zaffaroni Data analysis and applications: Ergodic distributions of random dynamical systems by L. M. Berliner, S. N. MacEachern, and C. S. Forbes Detecting structure in noise by L. Borland Characterizing nonlinearity in weather and epilepsy data: A personal view by M. C. Casdagli Assessment of linear and nonlinear correlations between neural firing events by A. Longtin and D. M. Racicot Markov chain methods in the analysis of heart rate variability by S. J. Merrill and J. R. Cochran.

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Book SynopsisThis third edition of Statistical Physics of Complex Systems has been expanded to provide more examples of applications of concepts and methods from statistical physics to the modeling of complex systems. These include avalanche dynamics in materials, models of social agents like road traffic or wealth repartition, the real space aspects of biological evolution dynamics, propagation phenomena on complex networks, formal neural networks and their connection to constraint satisfaction problems.This course-tested textbook provides graduate students and non-specialists with a basic understanding of the concepts and methods of statistical physics and demonstrates their wide range of applications to interdisciplinary topics in the field of complex system sciences, including selected aspects of theoretical modeling in biology and the social sciences. It covers topics such as non-conserved particles, evolutionary population dynamics, networks, properties of both individual and coupled simple dynamical systems, and convergence theorems, as well as short appendices that offer helpful hints on how to perform simple stochastic simulations in practice. The original spirit of the book is to remain accessible to a broad, non-specialized readership. The format is a set of concise, modular, and self-contained topical chapters, avoiding technicalities and jargon as much as possible, and complemented by a wealth of worked-out examples, so as to make this work useful as a self-study text or as textbook for short courses.Table of ContentsChapter 1. Equilibrium Statistical Physics.- Chapter 2. Non-equilibrium Dynamics and Stochastic Formalism.- Chapter 3. Models of particles driven out of equilibrium.- Chapter 4. Simple models of socials agents.- Chapter 5. Evolutionary dynamics.- Chapter 6. Complex networks.- Chapter 7. Statistical description of chaotic deterministic systems.- Chapter 8. A probabilistic viewpoint on fluctuations and rare events.

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Book SynopsisProviding a detailed and pedagogical account of the rapidly-growing field of computational statistical physics, this book covers both the theoretical foundations of equilibrium and non-equilibrium statistical physics, and also modern, computational applications such as percolation, random walks, magnetic systems, machine learning dynamics, and spreading processes on complex networks. A detailed discussion of molecular dynamics simulations is also included, a topic of great importance in biophysics and physical chemistry. The accessible and self-contained approach adopted by the authors makes this book suitable for teaching courses at graduate level, and numerous worked examples and end of chapter problems allow students to test their progress and understanding.Table of ContentsPreface; Part I. Stochastic Methods: 1. Random Numbers; 2. Random-Geometrical Models; 3. Equilibrium Systems; 4. Monte-Carlo Methods; 5. Phase Transitions; 6. Cluster Algorithms; 7. Histogram Methods; 8. Renormalization Group; 9. Learning and Optimizing; 10. Parallelization; 11. Non-Equilibrium Systems; Part II. Molecular Dynamics: 12. Basic Molecular Dynamics; 13. Optimizing Molecular Dynamics; 14. Dynamics of Composed Particles; 15. Long-Range Potentials; 16. Canonical Ensemble; 17. Inelastic Collisions in Molecular Dynamics; 18. Event-Driven Molecular Dynamics; 19. Non-Spherical Particles; 20. Contact Dynamics; 21. Discrete Fluid Models; 22. Ab-Initio Simulations; References; Index.

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Book SynopsisAll students, practitioners and researchers in forestry and related disciplines need a good grounding in statistics and probability. This need is increasing as techniques for gathering and analysing large amounts of data are becoming commonplace. This revised edition of this unique textbook is specifically designed for statistics and probability courses taught to students of forestry and related disciplines. It introduces probability, statistical techniques, data analysis, hypothesis testing, experimental design, sampling methods, nonparametric tests and statistical quality control, using examples drawn from a forestry, wood science and conservation context. The book now includes several new practical exercises for students to practice data analysis and experimental design themselves. It has been updated throughout, and its scope has been broadened to reflect the evolving and dynamic nature of forestry, bringing in examples from conservation science, recreation and urban forestry. - Specifically written and designed to teach statistics and probability to students of forestry and related disciplines in the natural sciences - This revised edition has been broadened to reflect the dynamism of modern forestry -Chapters in this revised edition include new practical exercises allowing students to practice data analysis and experimental designTable of Contents1: STATISTICS AND DATA: What do Numbers have to do with Trees? 2: DESCRIPTIVE STATISTICS: Making Sense of Data 3: PROBABILITY: The Foundation of Statistics 4: RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS: Outcomes of Random Experiments 5: SOME DISCRETE PROBABILITY DISTRIBUTIONS: Describing Data that is Counted 6: CONTINUOUS DISTRIBUTIONS AND THE NORMAL DISTRIBUTION: Describing Data that is Measured 7: SAMPLING DISTRIBUTIONS: The Foundation of Inference 8: ESTIMATION: Determining the Value of Population Parameters 9: TESTS OF HYPOTHESES: Making Claims about Population Parameters 10: GOODNESS-OF-FIT AND TEST FOR INDEPENDENCE: Testing Distributions 11: REGRESSION AND CORRELATION: Relationships between Variables 12: ANALYSIS OF VARIANCE: Testing Differences between Several Means 13: SAMPLING METHODS AND DESIGN OF EXPERIMENTS: Collecting Data 14: NONPARAMETRIC TESTS: Testing when Distributions are Unknown 15: QUALITY CONTROL: Statistics for Production and Processing

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Book SynopsisAn introduction to thermodynamics and statistical mechanics. This book guides the reader through each of the two disciplines. It provides an understanding of the area and presents and discusses the connection between the two.Trade Review"…a thorough treatment of thermodynamics at a level somewhat higher level than that in a typical undergraduate physical chemistry work." (CHOICE, February 2005)Table of ContentsPREFACE. 1 INTRODUCTORY REMARKS. 1.1 Scope and Objectives. 1.2 Level of Course. 1.3 Course Outline. 1.4 Books. PART I: THERMODYNAMICS. 2 BASIC CONCEPTS AND DEFINITIONS. 2.1 Systems and Surroundings. 2.2 State Variables and Thermodynamic Properties. 2.3 Intensive and Extensive Variables. 2.4 Homogeneous and Heterogeneous Systems, Phases. 2.5 Work. 2.6 Reversible and Quasi-Static Processes. 2.6.1 Quasi-Static Process. 2.6.2 Reversible Process. 2.7 Adiabatic and Diathermal Walls. 2.8 Thermal Contact and Thermal Equilibrium. 3 THE LAWS OF THERMODYNAMICS I. 3.1 The Zeroth Law—Temperature. 3.2 The First Law—Traditional Approach. 3.3 Mathematical Interlude I: Exact and Inexact Differentials. 3.4 The First Law—Axiomatic Approach. 3.5 Some Applications of the First Law. 3.5.1 Heat Capacity. 3.5.2 Heat and Internal Energy. 3.5.3 Heat and Enthalpy. 3.6 Mathematical Interlude II: Partial Derivatives. 3.6.1 Relations Between Partials of Dependent Variables. 3.6.2 Relations Between Partials with Different Subscripts. 3.7 Other Applications of the First Law. 3.7.1 CP — CV. 3.7.2 Isothermal Change, Ideal Gas. 3.7.3 Adiabatic Change, Ideal Gas. 3.7.4 The Joule and the Joule-Thomson Coefficients. 4 THE LAWS OF THERMODYNAMICS II. 4.1 The Second Law—Traditional Approach. 4.2 Engine Efficiency: Absolute Temperature. 4.2.1 Ideal Gas. 4.2.2 Coupled Cycles. 4.3 Generalization: Arbitrary Cycle. 4.4 The Clausius Inequality. 4.5 The Second Law—Axiomatic Approach (Carathe´odory). 4.6 Mathematical Interlude III: Pfaffian Differential Forms. 4.7 Pfaffian Expressions in Two Variables. 4.8 Pfaffian Expressions in More Than Two Dimensions. 4.9 Carathe´odory’s Theorem. 4.10 Entropy—Axiomatic Approach. 4.11 Entropy Changes for Nonisolated Systems. 4.12 Summary. 4.13 Some Applications of the Second Law. 4.13.1 Reversible Processes (PV Work Only). 4.13.2 Irreversible Processes. 5 USEFUL FUNCTIONS: THE FREE ENERGY FUNCTIONS. 5.1 Mathematical Interlude IV: Legendre Transformations. 5.1.1 Application of the Legendre Transformation. 5.2 Maxwell Relations. 5.3 The Gibbs-Helmholtz Equations. 5.4 Relation of ΔA and ΔG to Work: Criteria for Spontaneity. 5.4.1 Expansion and Other Types of Work. 5.4.2 Comments. 5.5 Generalization to Open Systems and Systems of Variable Composition. 5.5.1 Single Component System. 5.5.2 Multicomponent Systems. 5.6 The Chemical Potential. 5.7 Mathematical Interlude V: Euler’s Theorem. 5.8 Thermodynamic Potentials. 6 THE THIRD LAW OF THERMODYNAMICS. 6.1 Statements of the Third Law. 6.2 Additional Comments and Conclusions. 7 GENERAL CONDITIONS FOR EQUILIBRIUM AND STABILITY. 7.1 Virtual Variations. 7.2 Thermodynamic Potentials—Inequalities. 7.3 Equilibrium Condition From Energy. 7.3.1 Boundary Fully Heat Conducting, Deformable, Permeable (Normal System). 7.3.2 Special Cases: Boundary Semi-Heat Conducting, Semi-Deformable, or Semi-Permeable. 7.4 Equilibrium Conditions From Other Potentials. 7.5 General Conditions for Stability. 7.6 Stability Conditions From E. 7.7 Stability Conditions From Cross Terms. 7.8 Stability Conditions From Other Potentials. 7.9 Derivatives of Thermodynamic Potentials With Respect to Intensive Variables. 8 APPLICATION OF THERMODYNAMICS TO GASES, LIQUIDS, AND SOLIDS. 8.1 Gases. 8.2 Enthalpy, Entropy, Chemical Potential, Fugacity. 8.2.1 Enthalpy. 8.2.2 Entropy. 8.2.3 Chemical Potential. 8.2.4 Fugacity. 8.3 Standard States of Gases. 8.4 Mixtures of Gases. 8.4.1 Partial Fugacity. 8.4.2 Free Energy, Entropy, Enthalpy, and Volume of Mixing of Gases. 8.5 Thermodynamics of Condensed Systems. 8.5.1 The Chemical Potential. 8.5.2 Entropy. 8.5.3 Enthalpy. 9 PHASE AND CHEMICAL EQUILIBRIA. 9.1 The Phase Rule. 9.2 The Clapeyron Equation. 9.3 The Clausius-Clapeyron Equation. 9.4 The Generalized Clapeyron Equation. 9.5 Chemical Equilibrium. 9.6 The Equilibrium Constant. 10 SOLUTIONS—NONELECTROLYTES. 10.1 Activities and Standard State Conventions. 10.1.1 Gases. 10.1.2 Pure Liquids and Solids. 10.1.3 Mixtures. 10.1.3.1 Liquid–Liquid Solutions—Convention I (Con I). 10.1.3.2 Solid–Liquid Solutions—Convention II (Con II). 10.2 Ideal and Ideally Dilute Solutions; Raoult’s and Henry’s Laws. 10.2.1 Ideal Solutions. 10.2.2 Ideally Dilute Solutions. 10.3 Thermodynamic Functions of Mixing. 10.3.1 For Ideal Solutions. 10.3.2 For Nonideal Solutions. 10.4 Colligative Properties. 10.4.1 Lowering of Solvent Vapor Pressure. 10.4.2 Freezing Point Depression. 10.4.3 Boiling Point Elevation. 10.4.4 Osmotic Pressure. 11 PROCESSES INVOLVING WORK OTHER THAN PRESSURE-VOLUME WORK. 11.1 P-V Work and One Other Type of Work. 11.2 P-V, σA, and fL Work. 12 PHASE TRANSITIONS AND CRITICAL PHENOMENA. 12.1 Stable, Metastable, and Unstable Isotherms. 12.2 The Critical Region. PART II: INTRODUCTORY STATISTICAL MECHANICS. 13 PRINCIPLES OF STATISTICAL MECHANICS. 13.1 Introduction. 13.2 Preliminary Discussion—Simple Problem. 13.3 Time and Ensemble Averages. 13.4 Number of Microstates, ΩD, Distributions DI. 13.5 Mathematical Interlude VI: Combinatory Analysis. 13.6 Fundamental Problem in Statistical Mechanics. 13.7 Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein Statistics ‘‘Corrected’’ Maxwell-Boltzmann Statistics. 13.7.1 Maxwell-Boltzmann Statistics. 13.7.2 Fermi-Dirac Statistics. 13.7.3 Bose-Einstein Statistics 13.7.4 ‘‘Corrected’’ Maxwell-Boltzmann Statistics. 13.8 Systems of Distinguishable (Localized) and Indistinguishable (Nonlocalized) Particles. 13.9 Maximizing ΩD 13.10 Probability of a Quantum State: The Partition Function. 13.10.1 Maxwell-Boltzmann Statistics. 13.10.2 Corrected Maxwell-Boltzmann Statistics. 14 THERMODYNAMIC CONNECTION. 14.1 Energy, Heat, and Work. 14.2 Entropy. 14.2.1 Entropy of Nonlocalized Systems (Gases). 14.2.2 Entropy of Localized Systems (Crystalline Solids). 14.3 Identification of β with 1/kT. 14.4 Pressure. 14.5 The Functions E, H, S, A, G, and μ. 15 MOLECULAR PARTITION FUNCTION. 15.1 Translational Partition Function. 15.2 Vibrational Partition Function: Diatomics. 15.3 Rotational Partition Function: Diatomics. 15.4 Electronic Partition Function. 15.5 Nuclear Spin States. 15.6 The ‘‘Zero’’ of Energy. 16 STATISTICAL MECHANICAL APPLICATIONS. 16.1 Population Ratios. 16.2 Thermodynamic Functions of Gases. 16.3 Equilibrium Constants. 16.4 Systems of Localized Particles: The Einstein Solid. 16.4.1 Energy. 16.4.2 Heat Capacity. 16.4.3 Entropy. 16.5 Summary. ANNOTATED BIBLIOGRAPHY. APPENDIX I: HOMEWORK PROBLEM SETS. Problem Set I. Problem Set II. Problem Set III. Problem Set IV. Problem Set V. Problem Set VI. Problem Set VII. Problem Set VIII. Problem Set IX. Problem Set X. APPENDIX II: SOLUTIONS TO PROBLEMS. Solution to Set I. Solution to Set II. Solution to Set III. Solution to Set IV. Solution to Set V. Solution to Set VI. Solution to Set VII. Solution to Set VIII. Solution to Set IX. Solution to Set X. INDEX.

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Book SynopsisUnderstanding the behaviour of particles suspended in a fluid has many important applications across a range of fields, including engineering and geophysics. Comprising two main parts, this book begins with the well-developed theory of particles in viscous fluids, i.e. microhydrodynamics, particularly for single- and pair-body dynamics. Part II considers many-body dynamics, covering shear flows and sedimentation, bulk flow properties and collective phenomena. An interlude between the two parts provides the basic statistical techniques needed to employ the results of the first (microscopic) in the second (macroscopic). The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians. They also include some of the many open questions in the field to encourage further study. Consequently, this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the fTrade Review'The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians … this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the first time.' Sylvie Pic, zbMATHTable of ContentsPreface; Prologue; Part I. Microhydrodynamics: 1. Basic concepts in viscous flow; 2. One sphere in Stokes flow; 3. Sophisticated techniques; 4. Particle pair interactions; Interlude: from the microscopic to the macroscopic; 5. Statistical and stochastic concepts; Part II. Toward a Description of Macroscopic Phenomena in Suspensions: 6. Sedimentation; 7. Shear flow; 8. Beyond Stokes flow: finite inertia; Epilogue; References; Index.

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Book SynopsisOne of the first books to provide in-depth and systematic application of finite element methods to the field, Stochastic Structural Dynamics presents and illustrates direct integration methods for analyzing the statistics of the response of structures to stochastic loads.Table of ContentsDedication xi Preface xiii Acknowledgements xv 1. Introduction 1 1.1 Displacement Formulation Based Finite Element Method 2 1.2 Element Equations of Motion for Temporally and Spatially Stochastic Systems 13 1.3 Hybrid Stress Based Element Equations of Motion 14 1.4 Incremental Variational Principle and Mixed Formulation Based Nonlinear Element Matrices 18 1.5 Constitutive Relations and Updating of Configurations and Stresses 36 1.6 Concluding Remarks 48 References 49 2. Spectral Analysis and Response Statistics of Linear Structural Systems 53 2.1 Spectral Analysis 53 2.2 Evolutionary Spectral Analysis 56 2.3 Evolutionary Spectra of Engineering Structures 60 2.4 Modal Analysis and Time-Dependent Response Statistics 76 2.5 Response Statistics of Engineering Structures 79 References 94 3. Direct Integration Methods for Linear Structural Systems 97 3.1 Stochastic Central Difference Method 97 3.2 Stochastic Central Difference Method with Time Co-ordinate Transformation 100 3.3 Applications 102 3.4 Extended Stochastic Central Difference Method and Narrow-band Force Vector 114 3.5 Stochastic Newmark Family of Algorithms 122 References 128 4. Modal Analysis and Response Statistics of Quasi-linear Structural Systems 131 4.1 Modal Analysis of Temporally Stochastic Quasi-linear Systems 131 4.2 Response Analysis Based on Melosh-Zienkiewicz-Cheung Bending Plate Finite Element 141 4.3 Response Analysis Based on High Precision Triangular Plate Finite Element 156 4.4 Concluding Remarks 166 References 166 5. Direct Integration Methods for Response Statistics of Quasi-linear Structural Systems 169 5.1 Stochastic Central Difference Method for Quasi-linear Structural Systems 169 5.2 Recursive Covariance Matrix of Displacements of Cantilever Pipe Containing Turbulent Fluid 174 5.3 Quasi-linear Systems under Narrow-band Random Excitations 184 5.4 Concluding Remarks 188 References 190 6. Direct Integration Methods for Temporally Stochastic Nonlinear Structural Systems 191 6.1 Statistical Linearization Techniques 191 6.2 Symplectic Algorithms of Newmark Family of Integration Schemes 194 6.3 Stochastic Central Difference Method with Time Co-ordinate Transformation and Adaptive Time Schemes 199 6.4 Outline of steps in computer program 211 6.5 Large Deformations of Plate and Shell Structures 213 6.6 Concluding Remarks 224 References 226 7. Direct Integration Methods for Temporally and Spatially Stochastic Nonlinear Structural Systems 231 7.1 Perturbation Approximation Techniques and Stochastic Finite Element Methods 232 7.2 Stochastic Central Difference Methods for Temporally and Spatially Stochastic Nonlinear Systems 241 7.3 Finite Deformations of Spherical Shells with Large Spatially Stochastic Parameters 251 7.4 Closing Remarks 255 References 257 Appendices 1A Mass and Stiffness Matrices of Higher Order Tapered Beam Element 261 1B Consistent Stiffness Matrix of Lower Order Triangular Shell Element 267 1B.1 Inverse of Element Generalized Stiffness Matrix 267 1B.2 Element Leverage Matrices 268 1B.3 Element Component Stiffness Matrix Associated with Torsion 271 References 276 1C Consistent Mass Matrix of Lower Order Triangular Shell Element 277 Reference 280 2A Eigenvalue Solution 281 References 282 2B Derivation of Evolutionary Spectral Densities and Variances of Displacements 283 2B.1 Evolutionary Spectral Densities Due to Exponentially Decaying Random Excitations 283 2B.2 Evolutionary Spectral Densities Due to Uniformly Modulated Random Excitations 286 2B.3 Variances of Displacements 288 References 297 2C Time-dependent Covariances of Displacements 299 2D Covariances of Displacements and Velocities 311 2E Time-dependent Covariances of Velocities 317 2F Cylindrical Shell Element Matrices 323 3A Deterministic Newmark Family of Algorithms 327 Reference 331 Index 333

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Book SynopsisThis book presents the main principles and methods of nonequilibrium statistical mechanics, a topic studied by both chemists and physicists. This book is written for graduate students and scientists who already have knowledge of basic equilibrium statistical mechanics and who are interested in the more complex field of time-dependent nonequilibrium statistical mechanics.Table of Contents1. Brownian Motion and Langevin equations ; 2. Fokker-Planck equations ; 3. Master equations ; 4. Reaction rates ; 5. Kinetic models ; 6. Quantum dynamics ; 7. Linear response theory ; 8. Projection operators ; 9. Nonlinear problems ; 10. The paradoxes of irreversibility ; Appendices

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Book SynopsisThis volume of the Encyclopedia of Complexity and Systems Science, Second Edition, focuses on current challenges in the field from materials and mechanics to applications of statistical and nonlinear physics in the life sciences.Table of ContentsStatistical and Non-linear Physics: IntroductionComplex Systems and Emergent PhenomenaPolymer PhysicsChaotic Dynamics in Nonequilibrium Statistical MechanicsMonte Carlo Simulations in Statistical PhysicsNonlinear Fluid Flow, Pattern Formation, Mixing, and TurbulenceFluid Dynamics in CloudsCollective Transport and DepinningDisordered Elastic MediaPhysics of Jerky Motion in Slowly Driven Magnetic and Earthquake Fault SystemsFlexible mechanical structures and their topologically protected deformationsA Statistical Mechanics Perspective on Glasses and AgingStress Localization in Soft Particulate GelsNonlinear Mechanics of Colloidal Gels: Creep, Fatigue, and Shear-Induced YieldingStatistical physics of the yielding transitionGranular FlowsStatistical Mechanics of CloggingJamming of Granular MatterRigidity Percolation and Frictional JammingCell Biology: Networks , Regulation and PathwaysFluctuation Theorems, Brownian Motors and Thermodynamics of Small SystemsNeuronal DynamicsDense Active MatterUltracold Atomic Gases: Novel States of MatterQuantum ChaosNetworks: Structure and DynamicsCentralities in complex networksOptimization Problems and Algorithms from Computer ScienceStatistical Mechanics Approach to Econophysics

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Book SynopsisOne of the first books to provide in-depth and systematic application of finite element methods to the field of stochastic structural dynamicsThe parallel developments of the Finite Element Methods in the 1950's and the engineering applications of stochastic processes in the 1940's provided a combined numerical analysis tool for the studies of dynamics of structures and structural systems under random loadings. In the open literature, there are books on statistical dynamics of structures and books on structural dynamics with chapters dealing with random response analysis. However, a systematic treatment of stochastic structural dynamics applying the finite element methods seems to be lacking. Aimed at advanced and specialist levels, the author presents and illustrates analytical and direct integration methods for analyzing the statistics of the response of structures to stochastic loads. The analysis methods are based on structural models represented via the Finite ElemTable of ContentsSeries Preface xiii Preface xv Acknowledgments xvii 1 Introduction 1 1.1 Important Difference between Static and Dynamic Responses 1 1.2 Classification of Dynamic Systems 2 1.3 Applications of Control Theory 3 1.4 Organization of Presentation 4 References 5 2 Review of Laplace Transforms 7 2.1 Definition 8 2.2 First and Second Shifting Theorems 10 2.3 Dirac Delta Function (Unit Impulse Function) 10 2.4 Laplace Transforms of Derivatives and Integrals 11 2.5 Convolution Theorem 11 2.6 Initial and Final Value Theorems 13 2.7 Laplace Transforms of Periodic Functions 13 2.8 Partial Fraction Method 15 2.9 Questions and Solutions 16 2.10 Applications of MATLAB 22 Exercise Questions 26 References 27 3 Dynamic Behaviors of Hydraulic and Pneumatic Systems 29 3.1 Basic Elements of Liquid and Gas Systems 29 3.1.1 Liquids 30 3.1.3 Remarks 31 3.2 Hydraulic Tank Systems 32 3.2.1 Non-interacting Hydraulic Tank Systems 32 3.2.2 Interacting Hydraulic Tank Systems 34 3.3 Nonlinear Hydraulic Tank and Linear Transfer Function 35 3.4 Pneumatically Actuated Valves 37 3.5 Questions and Solutions 39 Appendix 3A: Transfer Function of Two Interacting Hydraulic Tanks 49 Exercise Questions 52 4 Dynamic Behaviors of Oscillatory Systems 57 4.1 Elements of Oscillatory Systems 57 4.2 Free Vibration of Single Degree-of-Freedom Systems 59 4.3 Single Degree-of-Freedom Systems under Harmonic Forces 63 4.4 Single Degree-of-Freedom Systems under Non-Harmonic Forces 65 4.5 Vibration Analysis of Multi-Degrees-of-Freedom Systems 67 4.5.1 Formulation and Solution for Two-Degrees-of-Freedom Systems 67 4.5.2 Vibration Analysis of a System with a Dynamic Absorber 72 4.5.3 Normal Mode Analysis 73 4.6 Vibration of Continuous Systems 77 4.6.1 Vibrating Strings or Cables 78 4.6.2 Remarks 80 4.7 Questions and Solutions 81 Appendix 4A: Proof of Equation (4.19b) 97 Exercise Questions 99 References 104 5 Formulation and Dynamic Behavior of Thermal Systems 105 5.1 Elements of Thermal Systems 105 5.1.1 Thermal Resistance 105 5.1.2 Thermal Capacitance 106 5.1.3 Thermal Radiation 107 5.2 Thermal Systems 107 5.2.1 Process Control 107 5.2.2 Space Heating 108 5.2.3 Three-Capacitance Oven 109 5.3 Questions and Solutions 112 Exercise Questions 117 6 Formulation and Dynamic Behavior of Electrical Systems 121 6.1 Basic Electrical Elements 121 6.2 Fundamentals of Electrical Circuits 122 6.2.1 Resistors Connected in Series 122 6.2.2 Resistors Connected in Parallel 123 6.2.3 Kirchhoff’s Laws 124 6.4 Electromechanical Systems 126 6.4.1 Armature-Controlled DC Motor 127 6.4.2 Field-Controlled DC Motor 129 6.4.3 DC Generator 130 6.5 Questions and Solutions 131 Exercise Questions 134 References 135 7 Dynamic Characteristics of Transducers 137 7.1 Basic Theory of the Tachometer 137 7.2 Principles and Applications of Oscillatory Motion Transducers 138 7.2.1 Equation of Motion 139 7.2.2 Design Considerations of Two Types of Transducer 140 7.3 Principles and Applications of Microphones 141 7.3.1 Moving-Coil Microphone 141 7.3.2 Condenser Microphone 144 7.4 Principles and Applications of the Piezoelectric Hydrophone 146 7.5 Questions and Solutions 148 Appendix 7A: Proof of Approximated Current Solution 150 Exercise Questions 153 References 154 8 Fundamentals of Control Systems 155 8.1 Classification of Control Systems 156 8.2 Representation of Control Systems 156 8.3 Transfer Functions 156 8.3.1 Transfer Function of Elements in Cascade Connection 157 8.3.2 Transfer Function of Elements in Parallel Connection 157 8.3.3 Remarks 158 8.4 Closed-Loop Control Systems 158 8.4.1 Closed-Loop Transfer Functions and System Response 159 8.4.2 Summary of Steps for Determination of Closed-Loop Transfer Functions 161 8.5 Block Diagram Reduction 161 8.5.1 Moving Starting Points of Signals 161 8.5.2 Moving Summing Points 162 8.5.3 System Transfer Function by Block Diagram Reduction 162 8.6 Questions and Solutions 164 Exercise Questions 170 References 172 9 Analysis and Performance of Control Systems 173 9.1 Response in the Time Domain 173 9.2 Transient Responses as Functions of Closed-Loop Poles 175 9.3 Control System Design Based on Transient Responses 177 9.4 Control Types 180 9.4.2 Integral Control 181 9.4.3 Derivative Control 181 9.5 Steady-State Errors 182 9.5.1 Unit Step Input 182 9.5.2 Unit Ramp Input 183 9.5.3 Unit Parabolic Input 183 9.6 Performance Indices and Sensitivity Functions 184 9.6.1 Performance Indices 184 9.6.2 Sensitivity Functions 185 9.7 Questions and Solutions 185 Exercise Questions 190 10 Stability Analysis of Control Systems 195 10.1 Concept of Stability in Linear Control Systems 195 10.2 Routh–Hurwitz Stability Criterion 195 10.3 Applications of Routh–Hurwitz Stability Criterion 197 10.4 Questions and Solutions 202 Exercise Questions 208 References 210 11 Graphical Methods for Control Systems 211 11.1 Root Locus Method and Root Locus Plots 211 11.1.1 Rules for Root Locus Plots of Negative Feedback Control Systems 212 11.1.2 Construction of Root Loci 213 11.2 Polar and Bode Plots 215 11.3 Nyquist Plots and Stability Criterion 221 11.3.1 Conformal Mapping and Cauchy’s Theorem 221 11.3.2 Nyquist Method and Stability Criterion 223 11.4 Gain Margin and Phase Margin 226 11.5 Lines of Constant Magnitude: M Circles 229 11.6 Lines of Constant Phase: N Circles 233 11.7 Nichols Charts 234 11.8 Applications of MATLAB for Graphical Constructions 236 11.8.1 Root Locus Plots 236 11.8.2 Bode Plots 243 11.8.3 Nyquist Plots 249 Exercise Questions 257 References 260 12 Modern Control System Analysis 261 12.1 State Space Method 261 12.2 State Transition Matrix 262 12.3 Relationship between Laplace Transformed State Equation and Transfer Function 264 12.4 Stability Based on Eigenvalues of the Coefficient Matrix 267 12.6 Stabilizability and Detectability 277 12.7 Applications of MATLAB 277 Appendix 12A: Solution of System of First-Order Differential Equations 286 Appendix 12B: Maclaurin’s Series 291 Appendix 12C: Rank of A Matrix 294 Exercise Questions 294 References 296 Index 297

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Book SynopsisThis book is an introduction to the concepts behind the popular understanding of climate and global warming. The author provides readers with a survey and reference to the subject to be used before, during and after they delve into the details of statistics, dynamics and thermodynamics. Dynamic Climatology reviews the basic concepts in the study of dynamic climatology, their expression in the form of equations and the physics of models used to reproduce the weather phenomena of a specific location. It takes a historical approach concentrating on the development of ideas during the last four hundred years. Unlike most books in this field, which are devoted to a single aspect of dynamic climatology, the intent of this volume is to present a coherent narrative of the different components of climate thus providing a solid basis of understanding.Trade Review"One of the best textbooks I have read... In not trying to do too much it achieves everything." Times Higher Education Supplement "Graduate students and advanced undergraduates will find this book very useful for both refreshing forgotten material and learning the essentials of atmosphere science for the first time. Carefully and clearly written, interesting historical accounts enliven most topics, making for a work that is simultaneously rigorous, concise, and interesting." – Professor James Burt, University of Wisconsin, MadisonTable of ContentsList of Figures. List of Tables. Preface. Part I: The Field of Dynamic Climatology: . Part II: Mathematics:. 1. Geometry. 2. Differential Calculus. 3. Partial Derivatives. 4. Integral Calculus. 5. Development of Calculus. 6. Vectors. 7. The Exponential and Complex Numbers. 8. Finite Differences. 9. Comment. Part III: Statistics:. 10. Data. 11. One Variable Descriptive Statistics. 12. Two Variables. 13. Dependence. 14. Dependence for More Than One Variable. 15. Comment. Part IV: Mechanics:. 16. Newton's Definitions and Laws. 17. Base Units. 18. Derived Units. 19. Discussion. Part V: Thermodynamics:. 20. Definitions. 21. The Equation of State - The Macroscopic Approach. 22. Atmospheric Composition. 23. Heat. 24. The First Law of Thermodynamics. 25. The Carnot Cycle. 26. Dry Adiabats and Potential Temperature. 27. The Second Law of Thermodynamics. 28. Water. 29. Discussion. Part VI: Radiation: . 30. Early Work. 31. Quanta. 32. Definitions of Laws of Radiation. 33. Applications to the Earth. 34. Comment. Part VII: Atmospheric Equations:. 35. The Nature of Fluids. 36. Continuity - Conservation of Mass. 37. Molecular Viscosity. 38. The Stress Tenor. 39. Navier-Stokes Equations. 40. Turbulent Eddy Viscosity. 41. The Vector Equation of Motion. 42. General Coordinates. 43. Some Simple Solutions. 44. Fluid Rotation. 45. The Equation Set. 46. Comment. Part VIII: Observed Angular Momentum and Energy: . 47. Perspective. 48. Angular Momentum. 49. The Partition of Energy. 50. The Lorenz Model of Energy Flow. 51. Heat Budget. 52. Water Budget. 53. Conversion between Scales of Motion. 54. The General Circulation. Part IX: Towards an Explanation of Climate: . 55. The Problem. 56. Numerical Modeling. 57. Climate Modeling. Part X: Concluding Remarks:. 58. Power Notation. 59. Constants. 60. Conversions. 61. World Data. Index.

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Book SynopsisThis textbook brings together the fundamentals of the macroscopic and microscopic aspects of thermal physics by presenting thermodynamics and statistical mechanics as complementary theories based on small numbers of postulates.Table of ContentsPreface xiii Part I Elements of Thermal Physics 1 1. Fundamentals 3 1.1 PVT Systems 3 1.2 Equilibrium States 6 1.3 Processes and Heat 10 1.4 Temperature 12 1.5 Size Dependence 13 1.6 Heat Capacity and Specific Heat 14 Problems 17 2. First Law of Thermodynamics 19 2.1 Work 19 2.2 Heat 21 2.3 The First Law 21 2.4 Applications 22 Problems 26 3. Properties and Partial Derivatives 27 3.1 Conventions 27 3.2 Equilibrium Properties 28 3.3 Relationships between Properties 34 3.4 Series Expansions 40 3.5 Summary 41 Problems 42 4. Processes in Gases 45 4.1 Ideal Gases 45 4.2 Temperature Change with Elevation 48 4.3 Cyclic Processes 50 4.4 Heat Engines 52 Problems 58 5. Phase Transitions 61 5.1 Solids, Liquids, and Gases 61 5.2 Latent Heats 65 5.3 Van der Waals Model 67 5.4 Classification of Phase Transitions 70 Problems 72 6. Reversible and Irreversible Processes 75 6.1 Idealization and Reversibility 75 6.2 Nonequilibrium Processes and Irreversibility 76 6.3 Electrical Systems 79 6.4 Heat Conduction 82 Problems 86 Part II Foundations of Thermodynamics 89 7. Second Law of Thermodynamics 91 7.1 Energy, Heat, and Reversibility 91 7.2 Cyclic Processes 93 7.3 Second Law of Thermodynamics 95 7.4 Carnot Cycles 98 7.5 Absolute Temperature 100 7.6 Applications 103 Problems 107 8. Temperature Scales and Absolute Zero 109 8.1 Temperature Scales 109 8.2 Uniform Scales and Absolute Zero 111 8.3 Other Temperature Scales 114 Problems 115 9. State Space and Differentials 117 9.1 Spaces 117 9.2 Differentials 121 9.3 Exact Versus Inexact Differentials 123 9.4 Integrating Differentials 127 9.5 Differentials in Thermodynamics 129 9.6 Discussion and Summary 134 Problems 136 10. Entropy 139 10.1 Definition of Entropy 139 10.2 Clausius’ Theorem 142 10.3 Entropy Principle 145 10.4 Entropy and Irreversibility 148 10.5 Useful Energy 151 10.6 The Third Law 155 10.7 Unattainability of Absolute Zero 156 Problems 158 Appendix 10.A. Entropy Statement of the Second Law 158 11. Consequences of Existence of Entropy 165 11.1 Differentials of Entropy and Energy 165 11.2 Ideal Gases 167 11.3 Relationships Between CV, CP, BT , BS, and αV 170 11.4 Clapeyron’s Equation 172 11.5 Maximum Entropy, Equilibrium, and Stability 174 11.6 Mixing 178 Problems 184 12. Thermodynamic Potentials 185 12.1 Internal Energy 185 12.2 Free Energies 186 12.3 Properties From Potentials 188 12.4 Systems in Contact with a Heat Reservoir 193 12.5 Minimum Free Energy 194 Problems 197 Appendix 12.A. Derivatives of Potentials 197 13. Phase Transitions and Open Systems 201 13.1 Two-Phase Equilibrium 201 13.2 Chemical Potential 206 13.3 Multi-Component Systems 211 13.4 Gibbs Phase Rule 214 13.5 Chemical Reactions 215 Problems 217 14. Dielectric and Magnetic Systems 219 14.1 Dielectrics 219 14.2 Magnetic Materials 224 14.3 Critical Phenomena 229 Problems 233 Part III Statistical Thermodynamics 235 15. Molecular Models 237 15.1 Microscopic Descriptions 237 15.2 Gas Pressure 238 15.3 Equipartition of Energy 243 15.4 Internal Energy of Solids 246 15.5 Inactive Degrees of Freedom 247 15.6 Microscopic Significance of Heat 248 Problems 253 16. Kinetic Theory of Gases 255 16.1 Velocity Distribution 255 16.2 Combinatorics 256 16.3 Method of Undetermined Multipliers 258 16.4 Maxwell Distribution 260 16.5 Mean-Free-Path 265 Problems 267 Appendix 16.A. Quantum Distributions 267 17. Microscopic Significance of Entropy 273 17.1 Boltzmann Entropy 273 17.2 Ideal Gas 274 17.3 Statistical Interpretation 278 17.4 Thermodynamic Properties 279 17.5 Boltzmann Factors 284 Problems 286 Appendix 17.A. Evaluation of I3N 286 Part IV Statistical Mechanics I 289 18. Ensembles 291 18.1 Probabilities and Averages 291 18.2 Two-Level Systems 293 18.3 Information Theory 295 18.4 Equilibrium Ensembles 298 18.5 Canonical Thermodynamics 302 18.6 Composite Systems 305 Problems 308 Appendix 18.A. Uniqueness Theorem 308 19. Partition Function 311 19.1 Hamiltonians and Phase Space 311 19.2 Model Hamiltonians 312 19.3 Classical Canonical Ensemble 316 19.4 Thermodynamic Properties and Averages 318 19.5 Ideal Gases 322 19.6 Harmonic Solids 326 Problems 328 20. Quantum Systems 331 20.1 Energy Eigenstates 331 20.2 Quantum Canonical Ensemble 333 20.3 Ideal Gases 334 20.4 Einstein Model 337 20.5 Classical Approximation 341 Problems 344 Appendix 20.A. Ideal Gas Eigenstates 344 21. Independent Particles and Paramagnetism 349 21.1 Averages 349 21.2 Statistical Independence 351 21.3 Classical Systems 353 21.4 Paramagnetism 357 21.5 Spin Systems 360 21.6 Classical Dipoles 365 Problems 367 Appendix 21.A. Negative Temperature 367 22. Fluctuations and Energy Distributions 371 22.1 Standard Deviation 371 22.2 Energy Fluctuations 375 22.3 Gibbs Paradox 376 22.4 Microcanonical Ensemble 380 22.5 Comparison of Ensembles 386 Problems 391 23. Generalizations and Diatomic Gases 393 23.1 Generalized Coordinates 393 23.2 Diatomic Gases 397 23.3 Quantum Effects 402 23.4 Density Matrices 405 23.5 Canonical Ensemble 408 Problems 410 Appendix 23.A. Classical Approximation 410 Part V Statistical Mechanics II 415 24. Photons and Phonons 417 24.1 Plane Wave Eigenstates 417 24.2 Photons 421 24.3 Harmonic Approximation 425 24.4 Phonons 429 Problems 434 25. Grand Canonical Ensemble 435 25.1 Thermodynamics of Open Systems 435 25.2 Grand Canonical Ensemble 437 25.3 Properties and Fluctuations 438 25.4 Ideal Gases 441 Problems 443 26. Fermions and Bosons 445 26.1 Identical Particles 445 26.2 Exchange Symmetry 447 26.3 Fermi–Dirac and Bose–Einstein Statistics 452 Problems 456 Appendix 26.A. Fermions in the Canonical Ensemble 457 27. Fermi and Bose Gases 461 27.1 Ideal Gases 461 27.2 Fermi Gases 465 27.3 Low Temperature Heat Capacity 466 27.4 Bose Gases 469 Problems 472 28. Interacting Systems 475 28.1 Ising Model 475 28.2 Nonideal Gases 481 Problems 487 29. Computer Simulations 489 29.1 Averages 489 29.2 Virial Formula for Pressure 490 29.3 Simulation Algorithms 496 A. Mathematical Relations, Constants, and Properties 501 A.1 Partial Derivatives 501 A.2 Integrals and Series 501 A.3 Taylor Series 502 A.4 Hyperbolic Functions 502 A.5 Fundamental Constants 503 A.6 Conversion Factors 503 A.7 Useful Formulas 503 A.8 Properties of Water 504 A.9 Properties of Materials 504 Answers to Problems 505 Index 509

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Book SynopsisThis text presents the two complementary aspects of thermal physics as an integrated theory of the properties of matter. Conceptual understanding is promoted by thorough development of basic concepts. In contrast to many texts, statistical mechanics, including discussion of the required probability theory, is presented first. This provides a statistical foundation for the concept of entropy, which is central to thermal physics. A unique feature of the book is the development of entropy based on Boltzmann''s 1877 definition; this avoids contradictions or ad hoc corrections found in other texts. Detailed fundamentals provide a natural grounding for advanced topics, such as black-body radiation and quantum gases. An extensive set of problems (solutions are available for lecturers through the OUP website), many including explicit computations, advance the core content by probing essential concepts. The text is designed for a two-semester undergraduate course but can be adapted for one-semeTrade ReviewIn his innovative new text, Carnegie Mellon University physics professor Robert Swendsen presents the foundations of statistical mechanics with, as he puts it, a detour through thermodynamics. That's a desirable strategy because the statistical approach is more fundamental than the classical thermodynamics approach and has many applications to current research problems. [] The mathematical notation is carefully introduced and useful; the selected mathematical techniques are clearly explained in a conversational style that both graduate and advanced undergraduate students will find easy to follow. The author's subject organization and conceptual viewpoint address some of the shortcomings of conventional developments of thermal physics and will be helpful to students and researchers seeking a deep appreciation of statistical physics. * Physics Today *Bob Swendsen's book is very well thought out, educationally sound, and more original than other texts. * Jan Tobochnik, Kalamazoo College, USA *Robert Swendsen is a well-respected researcher who has developed many novel algorithms that illustrate his deep understanding of statistical mechanics. His textbook reflects his deep understanding and will likely have a major impact on the way statistical mechanics and thermodynamics is taught. Particularly noteworthy is Swendsen's treatment of entropy, following Boltzmann's original definition in terms of probability, and his comprehensive discussion of the fundamental principles and applications of statistical mechanics and thermodynamics. Students and instructors will enjoy reading the book as much as Swendsen obviously enjoyed writing it. * Harvey Gould, Clark University, USA *In this reader-friendly, excellent text, the author provides a unique combination of the best of two worlds: traditional thermodynamics (following Callen's footsteps) and modern statistical mechanics (including VPython codes for simulations). * Royce Zia, Virginia Polytechnic Institute and State University, USA *Swendsen is famous for developing Monte Carlo algorithms which dramatically speed up the simulation of many systems near a phase transition. The ideas for those algorithms required deep understanding of statistical mechanics, an understanding which is now fully applied to this excellent textbook. * Peter Young, University of California, USA *Table of ContentsI ENTROPY; II INTRODUCTION TO THERMODYNAMICS; III CLASSICAL STATISTICAL MECHANICS; IV QUANTUM STATISTICAL MECHANICS

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Book SynopsisThis textbook brings together the fundamentals of the macroscopic and microscopic aspects of thermal physics by presenting thermodynamics and statistical mechanics as complementary theories based on small numbers of postulates.Table of ContentsPreface xiii Part I Elements of Thermal Physics 1 1. Fundamentals 3 1.1 PVT Systems 3 1.2 Equilibrium States 6 1.3 Processes and Heat 10 1.4 Temperature 12 1.5 Size Dependence 13 1.6 Heat Capacity and Specific Heat 14 Problems 17 2. First Law of Thermodynamics 19 2.1 Work 19 2.2 Heat 21 2.3 The First Law 21 2.4 Applications 22 Problems 26 3. Properties and Partial Derivatives 27 3.1 Conventions 27 3.2 Equilibrium Properties 28 3.3 Relationships between Properties 34 3.4 Series Expansions 40 3.5 Summary 41 Problems 42 4. Processes in Gases 45 4.1 Ideal Gases 45 4.2 Temperature Change with Elevation 48 4.3 Cyclic Processes 50 4.4 Heat Engines 52 Problems 58 5. Phase Transitions 61 5.1 Solids, Liquids, and Gases 61 5.2 Latent Heats 65 5.3 Van der Waals Model 67 5.4 Classification of Phase Transitions 70 Problems 72 6. Reversible and Irreversible Processes 75 6.1 Idealization and Reversibility 75 6.2 Nonequilibrium Processes and Irreversibility 76 6.3 Electrical Systems 79 6.4 Heat Conduction 82 Problems 86 Part II Foundations of Thermodynamics 89 7. Second Law of Thermodynamics 91 7.1 Energy, Heat, and Reversibility 91 7.2 Cyclic Processes 93 7.3 Second Law of Thermodynamics 95 7.4 Carnot Cycles 98 7.5 Absolute Temperature 100 7.6 Applications 103 Problems 107 8. Temperature Scales and Absolute Zero 109 8.1 Temperature Scales 109 8.2 Uniform Scales and Absolute Zero 111 8.3 Other Temperature Scales 114 Problems 115 9. State Space and Differentials 117 9.1 Spaces 117 9.2 Differentials 121 9.3 Exact Versus Inexact Differentials 123 9.4 Integrating Differentials 127 9.5 Differentials in Thermodynamics 129 9.6 Discussion and Summary 134 Problems 136 10. Entropy 139 10.1 Definition of Entropy 139 10.2 Clausius’ Theorem 142 10.3 Entropy Principle 145 10.4 Entropy and Irreversibility 148 10.5 Useful Energy 151 10.6 The Third Law 155 10.7 Unattainability of Absolute Zero 156 Problems 158 Appendix 10.A. Entropy Statement of the Second Law 158 11. Consequences of Existence of Entropy 165 11.1 Differentials of Entropy and Energy 165 11.2 Ideal Gases 167 11.3 Relationships Between CV, CP, BT , BS, and αV 170 11.4 Clapeyron’s Equation 172 11.5 Maximum Entropy, Equilibrium, and Stability 174 11.6 Mixing 178 Problems 184 12. Thermodynamic Potentials 185 12.1 Internal Energy 185 12.2 Free Energies 186 12.3 Properties From Potentials 188 12.4 Systems in Contact with a Heat Reservoir 193 12.5 Minimum Free Energy 194 Problems 197 Appendix 12.A. Derivatives of Potentials 197 13. Phase Transitions and Open Systems 201 13.1 Two-Phase Equilibrium 201 13.2 Chemical Potential 206 13.3 Multi-Component Systems 211 13.4 Gibbs Phase Rule 214 13.5 Chemical Reactions 215 Problems 217 14. Dielectric and Magnetic Systems 219 14.1 Dielectrics 219 14.2 Magnetic Materials 224 14.3 Critical Phenomena 229 Problems 233 Part III Statistical Thermodynamics 235 15. Molecular Models 237 15.1 Microscopic Descriptions 237 15.2 Gas Pressure 238 15.3 Equipartition of Energy 243 15.4 Internal Energy of Solids 246 15.5 Inactive Degrees of Freedom 247 15.6 Microscopic Significance of Heat 248 Problems 253 16. Kinetic Theory of Gases 255 16.1 Velocity Distribution 255 16.2 Combinatorics 256 16.3 Method of Undetermined Multipliers 258 16.4 Maxwell Distribution 260 16.5 Mean-Free-Path 265 Problems 267 Appendix 16.A. Quantum Distributions 267 17. Microscopic Significance of Entropy 273 17.1 Boltzmann Entropy 273 17.2 Ideal Gas 274 17.3 Statistical Interpretation 278 17.4 Thermodynamic Properties 279 17.5 Boltzmann Factors 284 Problems 286 Appendix 17.A. Evaluation of I3N 286 Part IV Statistical Mechanics I 289 18. Ensembles 291 18.1 Probabilities and Averages 291 18.2 Two-Level Systems 293 18.3 Information Theory 295 18.4 Equilibrium Ensembles 298 18.5 Canonical Thermodynamics 302 18.6 Composite Systems 305 Problems 308 Appendix 18.A. Uniqueness Theorem 308 19. Partition Function 311 19.1 Hamiltonians and Phase Space 311 19.2 Model Hamiltonians 312 19.3 Classical Canonical Ensemble 316 19.4 Thermodynamic Properties and Averages 318 19.5 Ideal Gases 322 19.6 Harmonic Solids 326 Problems 328 20. Quantum Systems 331 20.1 Energy Eigenstates 331 20.2 Quantum Canonical Ensemble 333 20.3 Ideal Gases 334 20.4 Einstein Model 337 20.5 Classical Approximation 341 Problems 344 Appendix 20.A. Ideal Gas Eigenstates 344 21. Independent Particles and Paramagnetism 349 21.1 Averages 349 21.2 Statistical Independence 351 21.3 Classical Systems 353 21.4 Paramagnetism 357 21.5 Spin Systems 360 21.6 Classical Dipoles 365 Problems 367 Appendix 21.A. Negative Temperature 367 22. Fluctuations and Energy Distributions 371 22.1 Standard Deviation 371 22.2 Energy Fluctuations 375 22.3 Gibbs Paradox 376 22.4 Microcanonical Ensemble 380 22.5 Comparison of Ensembles 386 Problems 391 23. Generalizations and Diatomic Gases 393 23.1 Generalized Coordinates 393 23.2 Diatomic Gases 397 23.3 Quantum Effects 402 23.4 Density Matrices 405 23.5 Canonical Ensemble 408 Problems 410 Appendix 23.A. Classical Approximation 410 Part V Statistical Mechanics II 415 24. Photons and Phonons 417 24.1 Plane Wave Eigenstates 417 24.2 Photons 421 24.3 Harmonic Approximation 425 24.4 Phonons 429 Problems 434 25. Grand Canonical Ensemble 435 25.1 Thermodynamics of Open Systems 435 25.2 Grand Canonical Ensemble 437 25.3 Properties and Fluctuations 438 25.4 Ideal Gases 441 Problems 443 26. Fermions and Bosons 445 26.1 Identical Particles 445 26.2 Exchange Symmetry 447 26.3 Fermi–Dirac and Bose–Einstein Statistics 452 Problems 456 Appendix 26.A. Fermions in the Canonical Ensemble 457 27. Fermi and Bose Gases 461 27.1 Ideal Gases 461 27.2 Fermi Gases 465 27.3 Low Temperature Heat Capacity 466 27.4 Bose Gases 469 Problems 472 28. Interacting Systems 475 28.1 Ising Model 475 28.2 Nonideal Gases 481 Problems 487 29. Computer Simulations 489 29.1 Averages 489 29.2 Virial Formula for Pressure 490 29.3 Simulation Algorithms 496 A. Mathematical Relations, Constants, and Properties 501 A.1 Partial Derivatives 501 A.2 Integrals and Series 501 A.3 Taylor Series 502 A.4 Hyperbolic Functions 502 A.5 Fundamental Constants 503 A.6 Conversion Factors 503 A.7 Useful Formulas 503 A.8 Properties of Water 504 A.9 Properties of Materials 504 Answers to Problems 505 Index 509

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Book SynopsisThis undergraduate textbook provides students with a statistical mechanical foundation to the classical laws of thermodynamics through a comprehensive treatment of the basics of classical thermodynamics, equilibrium statistical mechanics, irreversible thermodynamics, and statistical mechanics of non-equilibrium phenomena.Trade Review“Summing Up: Recommended. Upper-division undergraduates.” (Choice, 1 March 2014) “The best choice is finally that the entropy is uncertainty commodified". The reviewer believes that the aim of the book is evident and it is worthwhile to make a detailed study of it from time to time.” (Zentralblatt MATH, 1 October 2013)Table of ContentsPreface xiii 1. Disorder or Uncertainty? 1 2. Classical Thermodynamics 5 2.1 The Classical Laws of Thermodynamics 5 2.2 Macroscopic State Variables and Thermodynamic Processes 6 2.3 Properties of the Ideal Classical Gas 8 2.4 Thermodynamic Processing of the Ideal Gas 10 2.5 Entropy of the Ideal Gas 13 2.6 Entropy Change in Free Expansion of an Ideal Gas 15 2.7 Entropy Change due to Nonquasistatic Heat Transfer 17 2.8 Cyclic Thermodynamic Processes, the Clausius Inequality and Carnot’s Theorem 19 2.9 Generality of the Clausius Expression for Entropy Change 21 2.10 Entropy Change due to Nonquasistatic Work 23 2.11 Fundamental Relation of Thermodynamics 25 2.12 Entropy Change due to Nonquasistatic Particle Transfer 28 2.13 Entropy Change due to Nonquasistatic Volume Exchange 30 2.14 General Thermodynamic Driving 31 2.15 Reversible and Irreversible Processes 32 2.16 Statements of the Second Law 33 2.17 Classical Thermodynamics: the Salient Points 35 Exercises 35 3. Applications of Classical Thermodynamics 37 3.1 Fluid Flow and Throttling Processes 37 3.2 Thermodynamic Potentials and Availability 39 3.2.1 Helmholtz Free Energy 40 3.2.2 Why Free Energy? 43 3.2.3 Contrast between Equilibria 43 3.2.4 Gibbs Free Energy 44 3.2.5 Grand Potential 46 3.3 Maxwell Relations 47 3.4 Nonideal Classical Gas 48 3.5 Relationship between Heat Capacities 49 3.6 General Expression for an Adiabat 50 3.7 Determination of Entropy from a Heat Capacity 50 3.8 Determination of Entropy from an Equation of State 51 3.9 Phase Transitions and Phase Diagrams 52 3.9.1 Conditions for Coexistence 53 3.9.2 Clausius–Clapeyron Equation 55 3.9.3 The Maxwell Equal Areas Construction 57 3.9.4 Metastability and Nucleation 59 3.10 Work Processes without Volume Change 59 3.11 Consequences of the Third Law 60 3.12 Limitations of Classical Thermodynamics 61 Exercises 62 4. Core Ideas of Statistical Thermodynamics 65 4.1 The Nature of Probability 65 4.2 Dynamics of Complex Systems 68 4.2.1 The Principle of Equal a Priori Probabilities 68 4.2.2 Microstate Enumeration 71 4.3 Microstates and Macrostates 72 4.4 Boltzmann’s Principle and the Second Law 75 4.5 Statistical Ensembles 77 4.6 Statistical Thermodynamics: the Salient Points 78 Exercises 79 5. Statistical Thermodynamics of a System of Harmonic Oscillators 81 5.1 Microstate Enumeration 81 5.2 Microcanonical Ensemble 83 5.3 Canonical Ensemble 84 5.4 The Thermodynamic Limit 88 5.5 Temperature and the Zeroth Law of Thermodynamics 91 5.6 Generalisation 91 Exercises 92 6. The Boltzmann Factor and the Canonical Partition Function 95 6.1 Simple Applications of the Boltzmann Factor 95 6.1.1 Maxwell–Boltzmann Distribution 95 6.1.2 Single Classical Oscillator and the Equipartition Theorem 97 6.1.3 Isothermal Atmosphere Model 98 6.1.4 Escape Problems and Reaction Rates 99 6.2 Mathematical Properties of the Canonical Partition Function 99 6.3 Two-Level Paramagnet 101 6.4 Single Quantum Oscillator 103 6.5 Heat Capacity of a Diatomic Molecular Gas 104 6.6 Einstein Model of the Heat Capacity of Solids 105 6.7 Vacancies in Crystals 106 Exercises 108 7. The Grand Canonical Ensemble and Grand Partition Function 111 7.1 System of Harmonic Oscillators 111 7.2 Grand Canonical Ensemble for a General System 115 7.3 Vacancies in Crystals Revisited 116 Exercises 117 8. Statistical Models of Entropy 119 8.1 Boltzmann Entropy 119 8.1.1 The Second Law of Thermodynamics 120 8.1.2 The Maximum Entropy Macrostate of Oscillator Spikiness 122 8.1.3 The Maximum Entropy Macrostate of Oscillator Populations 122 8.1.4 The Third Law of Thermodynamics 126 8.2 Gibbs Entropy 127 8.2.1 Fundamental Relation of Thermodynamics and Thermodynamic Work 129 8.2.2 Relationship to Boltzmann Entropy 130 8.2.3 Third Law Revisited 131 8.3 Shannon Entropy 131 8.4 Fine and Coarse Grained Entropy 132 8.5 Entropy at the Nanoscale 133 8.6 Disorder and Uncertainty 134 Exercises 135 9. Statistical Thermodynamics of the Classical Ideal Gas 137 9.1 Quantum Mechanics of a Particle in a Box 137 9.2 Densities of States 138 9.3 Partition Function of a One-Particle Gas 140 9.4 Distinguishable and Indistinguishable Particles 141 9.5 Partition Function of an N -Particle Gas 145 9.6 Thermal Properties and Consistency with Classical Thermodynamics 146 9.7 Condition for Classical Behaviour 147 Exercises 149 10. Quantum Gases 151 10.1 Spin and Wavefunction Symmetry 151 10.2 Pauli Exclusion Principle 152 10.3 Phenomenology of Quantum Gases 153 Exercises 154 11. Boson Gas 155 11.1 Grand Partition Function for Bosons in a Single Particle State 155 11.2 Bose–Einstein Statistics 156 11.3 Thermal Properties of a Boson Gas 158 11.4 Bose–Einstein Condensation 161 11.5 Cooper Pairs and Superconductivity 166 Exercises 167 12. Fermion Gas 169 12.1 Grand Partition Function for Fermions in a Single Particle State 169 12.2 Fermi–Dirac Statistics 170 12.3 Thermal Properties of a Fermion Gas 171 12.4 Maxwell–Boltzmann Statistics 173 12.5 The Degenerate Fermion Gas 176 12.6 Electron Gas in Metals 177 12.7 White Dwarfs and the Chandrasekhar Limit 179 12.8 Neutron Stars 182 12.9 Entropy of a Black Hole 183 Exercises 184 13. Photon Gas 187 13.1 Electromagnetic Waves in a Box 187 13.2 Partition Function of the Electromagnetic Field 189 13.3 Thermal Properties of a Photon Gas 191 13.3.1 Planck Energy Spectrum of Black-Body Radiation 191 13.3.2 Photon Energy Density and Flux 193 13.3.3 Photon Pressure 193 13.3.4 Photon Entropy 194 13.4 The Global Radiation Budget and Climate Change 195 13.5 Cosmic Background Radiation 197 Exercises 198 14. Statistical Thermodynamics of Interacting Particles 201 14.1 Classical Phase Space 201 14.2 Virial Expansion 203 14.3 Harmonic Structures 206 14.3.1 Triatomic Molecule 207 14.3.2 Einstein Solid 208 14.3.3 Debye Solid 209 Exercises 211 15. Thermodynamics away from Equilibrium 213 15.1 Nonequilibrium Classical Thermodynamics 213 15.1.1 Energy and Particle Currents and their Conjugate Thermodynamic Driving Forces 213 15.1.2 Entropy Production in Constrained and Evolving Systems 218 15.2 Nonequilibrium Statistical Thermodynamics 220 15.2.1 Probability Flow and the Principle of Equal a Priori Probabilities 220 15.2.2 The Dynamical Basis of the Principle of Entropy Maximisation 222 Exercises 223 16. The Dynamics of Probability 225 16.1 The Discrete Random Walk 225 16.2 Master Equations 226 16.2.1 Solution to the Random Walk 228 16.2.2 Entropy Production during a Random Walk 229 16.3 The Continuous Random Walk and the Fokker–Planck Equation 230 16.3.1 Wiener Process 232 16.3.2 Entropy Production in the Wiener Process 233 16.4 Brownian Motion 235 16.5 Transition Probability Density for a Harmonic Oscillator 236 Exercises 238 17. Fluctuation Relations 241 17.1 Forward and Backward Path Probabilities: a Criterion for Equilibrium 241 17.2 Time Asymmetry of Behaviour and a Definition of Entropy Production 243 17.3 The Relaxing Harmonic Oscillator 245 17.4 Entropy Production Arising from a Single Random Walk 247 17.5 Further Fluctuation Relations 249 17.6 The Fundamental Basis of the Second Law 253 Exercises 253 18. Final Remarks 255 Further Reading 261 Index 263

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Book SynopsisA comprehensive text and reference bringing together advances in the theory of probability and statistics and relating them to applications.Table of ContentsUnivariate Nonlinear Regression. Univariate Nonlinear Regression: Special Situations. A Unified Asymptotic Theory for Nonlinear Models with RegressionStructure. Univariate Nonlinear Regression: Asymptotic Theory. Multivariate Nonlinear Regression. Nonlinear Simultaneous Equations Models. A Unified Asymptotic Theory for Dynamic Nonlinear Models. References. Index.

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Book SynopsisMoving beyond purely theoretical models, the author applies methods supported by empirical research of equity and foreign exchange markets to show how daily and more frequent asset prices, and the prices of option contracts, can be used to construct and assess predictions about future prices, their volatility, and their probability distributions.Trade ReviewWinner of the 2005 BestBook Award, Riskbook.com "This book provides thorough, well-presented and concise coverage of asset price dynamics and manages to combine new developments, established issues, theory and application in a practical and refreshing manner. It is well illustrated with time series graphs and tables and has a good balance between theoretical concepts and their practical applications with a mathematical treatment that is not too specialized."--Anthony F. Gyles, RSSTable of ContentsPreface xiii Chapter 1: Introduction 1 1.1 Asset Price Dynamics 1 1.2 Volatility 1 1.3 Prediction 2 1.4 Information 2 1.5 Contents 3 1.6 Software 5 1.7 Web Resources 6 PART I: Foundations 7 Chapter 2: Prices and Returns 9 2.1 Introduction 9 2.2 Two Examples of Price Series 9 2.3 Data-Collection Issues 10 2.4 Two Returns Series 13 2.5 Definitions of Returns 14 2.6 Further Examples of Time Series of Returns 19 Chapter 3: Stochastic Processes: Definitions and Examples 23 3.1 Introduction 23 3.2 Random Variables 24 3.3 Stationary Stochastic Processes 30 3.4 Uncorrelated Processes 33 3.5 ARMA Processes 36 3.6 Examples of ARMA 1 1 Specifications 44 3.7 ARIMA Processes 46 3.8 ARFIMA Processes 46 3.9 Linear Stochastic Processes 48 3.10 Continuous-Time Stochastic Processes 49 3.11 Notation for Random Variables and Observations 50 Chapter 4: Stylized Facts for Financial Returns 51 4.1 Introduction 51 4.2 Summary Statistics 52 4.3 Average Returns and Risk Premia 53 4.4 Standard Deviations 57 4.5 Calendar Effects 59 4.6 Skewness and Kurtosis 68 4.7 The Shape of the Returns Distribution 69 4.8 Probability Distributions for Returns 73 4.9 Autocorrelations of Returns 76 4.10 Autocorrelations of Transformed Returns 82 4.11 Nonlinearity of the Returns Process 92 4.12 Concluding Remarks 93 4.13 Appendix: Autocorrelation Caused by Day-of-the-Week Effects 94 4.14 Appendix: Autocorrelations of a Squared Linear Process 95 PART II: Conditional Expected Returns 97 Chapter 5: The Variance-Ratio Test of the Random Walk Hypothesis 99 5.1 Introduction 99 5.2 The Random Walk Hypothesis 100 5.3 Variance-Ratio Tests 102 5.4 An Example of Variance-Ratio Calculations 105 5.5 Selected Test Results 107 5.6 Sample Autocorrelation Theory 112 5.7 Random Walk Tests Using Rescaled Returns 115 5.8 Summary 120 Chapter 6: Further Tests of the Random Walk Hypothesis 121 6.1 Introduction 121 6.2 Test Methodology 122 6.3 Further Autocorrelation Tests 126 6.4 Spectral Tests 130 6.5 The Runs Test 133 6.6 Rescaled Range Tests 135 6.7 The BDS Test 136 6.8 Test Results for the Random Walk Hypothesis 138 6.9 The Size and Power of Random Walk Tests 144 6.10 Sources of Minor Dependence in Returns 148 6.11 Concluding Remarks 151 6.12 Appendix: the Correlation between Test Values for Two Correlated Series 153 6.13 Appendix: Autocorrelation Induced by Rescaling Returns 154 Chapter 7: Trading Rules and Market Efficiency 157 7.1 Introduction 157 7.2 Four Trading Rules 158 7.3 Measures of Return Predictability 163 7.4 Evidence about Equity Return Predictability 166 7.5 Evidence about the Predictability of Currency and Other Returns 168 7.6 An Example of Calculations for the Moving-Average Rule 172 7.7 Efficient Markets: Methodological Issues 175 7.8 Breakeven Costs for Trading Rules Applied to Equities 176 7.9 Trading Rule Performance for Futures Contracts 179 7.10 The Efficiency of Currency Markets 181 7.11 Theoretical Trading Profits for Autocorrelated Return Processes 184 7.12 Concluding Remarks 186 PART III: Volatility Processes 187 Chapter 8: An Introduction to Volatility 189 8.1 Definitions of Volatility 189 8.2 Explanations of Changes in Volatility 191 8.3 Volatility and Information Arrivals 193 8.4 Volatility and the Stylized Facts for Returns 195 8.5 Concluding Remarks 196 Chapter 9: ARCH Models: Definitions and Examples 197 9.1 Introduction 197 9.2 ARCH(1) 198 9.3 GARCH 1 1 199 9.4 An Exchange Rate Example of the GARCH 1 1 Model 205 9.5 A General ARCH Framework 212 9.6 Nonnormal Conditional Distributions 217 9.7 Asymmetric Volatility Models 220 9.8 Equity Examples of Asymmetric Volatility Models 222 9.9 Summary 233 Chapter 10: ARCH Models: Selection and Likelihood Methods 235 10.1 Introduction 235 10.2 Asymmetric Volatility: Further Specifications and Evidence 235 10.3 Long Memory ARCH Models 242 10.4 Likelihood Methods 245 10.5 Results from Hypothesis Tests 251 10.6 Model Building 256 10.7 Further Volatility Specifications 261 10.8 Concluding Remarks 264 10.9 Appendix: Formulae for the Score Vector 265 Chapter 11: Stochastic Volatility Models 267 11.1 Introduction 267 11.2 Motivation and Definitions 268 11.3 Moments of Independent SV Processes 270 11.4 Markov Chain Models for Volatility 271 11.5 The Standard Stochastic Volatility Model 278 11.6 Parameter Estimation for the Standard SV Model 283 11.7 An Example of SV Model Estimation for Exchange Rates 288 11.8 Independent SV Models with Heavy Tails 291 11.9 Asymmetric Stochastic Volatility Models 293 11.10 Long Memory SV Models 297 11.11 Multivariate Stochastic Volatility Models 298 11.12 ARCH versus SV 299 11.13 Concluding Remarks 301 11.14 Appendix: Filtering Equations 301 PART IV: High-Frequency Methods 303 Chapter 12: High-Frequency Data and Models 305 12.1 Introduction 305 12.2 High-Frequency Prices 306 12.3 One Day of High-Frequency Price Data 309 12.4 Stylized Facts for Intraday Returns 310 12.5 Intraday Volatility Patterns 316 12.6 Discrete-Time Intraday Volatility Models 321 12.7 Trading Rules and Intraday Prices 325 12.8 Realized Volatility: Theoretical Results 327 12.9 Realized Volatility: Empirical Results 332 12.10 Price Discovery 342 12.11 Durations 343 12.12 Extreme Price Changes 344 12.13 Daily High and Low Prices 346 12.14 Concluding Remarks 348 12.15 Appendix: Formulae for the Variance of the Realized Volatility Estimator 349 PART V: Inferences from Option Prices 351 Chapter 13: Continuous-Time Stochastic Processes 353 13.1 Introduction 353 13.2 The Wiener Process 354 13.3 Diffusion Processes 355 13.4 Bivariate Diffusion Processes 359 13.5 Jump Processes 361 13.6 Jump-Diffusion Processes 363 13.7 Appendix: a Construction of the Wiener Process 366 Chapter 14: Option Pricing Formulae 369 14.1 Introduction 369 14.2 Definitions, Notation, and Assumptions 370 14.3 Black-Scholes and Related Formulae 372 14.4 Implied Volatility 378 14.5 Option Prices when Volatility Is Stochastic 383 14.6 Closed-Form Stochastic Volatility Option Prices 388 14.7 Option Prices for ARCH Processes 391 14.8 Summary 394 14.9 Appendix: Heston's Option Pricing Formula 395 Chapter 15: Forecasting Volatility 397 15.1 Introduction 397 15.2 Forecasting Methodology 398 15.3 Two Measures of Forecast Accuracy 401 15.4 Historical Volatility Forecasts 403 15.5 Forecasts from Implied Volatilities 407 15.6 ARCH Forecasts that Incorporate Implied Volatilities 410 15.7 High-Frequency Forecasting Results 414 15.8 Concluding Remarks 420 Chapter 16: Density Prediction for Asset Prices 423 16.1 Introduction 423 16.2 Simulated Real-World Densities 424 16.3 Risk-Neutral Density Concepts and Definitions 428 16.4 Estimation of Implied Risk-Neutral Densities 431 16.5 Parametric Risk-Neutral Densities 435 16.6 Risk-Neutral Densities from Implied Volatility Functions 446 16.7 Nonparametric RND Methods 448 16.8 Towards Recommendations 450 16.9 From Risk-Neutral to Real-World Densities 451 16.10 An Excel Spreadsheet for Density Estimation 458 16.11 Risk Aversion and Rational RNDs 461 16.12 Tail Density Estimates 464 16.13 Concluding Remarks 465 Symbols 467 References 473 Author Index 503 Subject Index 513

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Book SynopsisA thoroughly modern graduate-level introduction to the theory of critical behaviour.Trade Review' … a short but very intelligible textbook well equilibrated by a variety of material.' V. Zagrebnov, Zentralblatt Math'Supported with interesting exercises at the end of each chapter, Cardy's book is likely to prove a popular introduction to this demanding but extraordinarily successful method for probing many complex phenomena.' Robert Matthews New ScientistTable of ContentsPreface; 1. Phase transitions in simple systems; 2. Mean field theory; 3. The renormalization group idea; 4. Phase diagrams and fixed points; 5. The perturbative renormalization group; 6. Near two dimensions; 7. Surface critical behaviour; 8. Random systems; 9. Polymer statistics; 10. Critical dynamics; 11. Conformal symmetry; Appendix: Gaussian integration; Selected bibliography; Index.

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Book SynopsisThe Fourth Edition of Statistics: A Gentle Introduction shows students that an introductory statistics class doesn’t need to be difficult or dull. This text minimizes students’ anxieties about math by explaining the concepts of statistics in plain language first, before addressing the math. Each formula within the text has a step-by-step example to demonstrate the calculation so students can follow along. Only those formulas that are important for final calculations are included in the text so students can focus on the concepts, not the numbers. A wealth of real-world examples and applications gives a context for statistics in the real world and how it helps us solve problems and make informed choices. New to the Fourth Edition are sections on working with big data, new coverage of alternative non-parametric tests, beta coefficients, and the "nocebo effect," discussions of p values in the context of research, an expanded discussion of confidence intervals, and more exercises and homework options under the new feature "Test Yourself." Included with this title: The password-protected Instructor Resource Site (formally known as SAGE Edge) offers access to all text-specific resources, including a test bank and editable, chapter-specific PowerPoint® slides.Trade ReviewStatistics is generally not a dynamic topic. But Coolidge is able to break it down in a way that is manageable. His discussion of each type of analyses is easily accessed by the table of contents and accurately depicted in the index. This is especially important for this generation of learners who want easy access to the specific information that is necessary without waiting through extraneous concepts. Coolidge also describes contemporary and specific examples of how miss use of data can have an impact in real world circumstances. This is beneficial because it makes a true connection with the power that a statistical researcher holds. -- Dr. Lynn DeSpainIt is the only book on the market that covers important advanced techniques such as repeated measures ANOVA and multiple regressions, using SPSS. -- Abby Heckman CoatsThe book is written to address a broad range of student ability. It is helpful to students without a strong background in mathematics. -- Andrew ZekeriTable of ContentsPreface Acknowledgments About the Author Chapter 1: A Gentle Introduction How Much Math Do I Need to Do Statistics? The General Purpose of Statistics: Understanding the World What Is a Statistician? Liberal and Conservative Statisticians Descriptive and Inferential Statistics Experiments Are Designed to Test Theories and Hypotheses Oddball Theories Bad Science and Myths Eight Essential Questions of Any Survey or Study On Making Samples Representative of the Population Experimental Design and Statistical Analysis as Controls The Language of Statistics On Conducting Scientific Experiments The Dependent Variable and Measurement Operational Definitions Measurement Error Measurement Scales: The Difference Between Continuous and Discrete Variables Types of Measurement Scales Rounding Numbers and Rounding Error Statistical Symbols Summary History Trivia: Achenwall to Nightingale Key Terms Chapter 1 Practice Problems Chapter 1 Test Yourself Questions SPSS Lesson 1 Chapter 2: Descriptive Statistics: Understanding Distributions of Numbers The Purpose of Graphs and Tables: Making Arguments and Decisions A Summary of the Purpose of Graphs and Tables Graphical Cautions Frequency Distributions Shapes of Frequency Distributions Grouping Data Into Intervals Advice on Grouping Data Into Intervals The Cumulative Frequency Distribution Cumulative Percentages, Percentiles, and Quartiles Stem-and-Leaf Plot Non-normal Frequency Distributions On the Importance of the Shapes of Distributions Additional Thoughts About Good Graphs Versus Bad Graphs History Trivia: De Moivre to Tukey Key Terms Chapter 2 Practice Problems Chapter 2 Test Yourself Questions SPSS Lesson 2 Chapter 3: Statistical Parameters: Measures of Central Tendency and Variation Measures of Central Tendency Choosing Among Measures of Central Tendency Klinkers and Outliers Uncertain or Equivocal Results Measures of Variation Correcting for Bias in the Sample Standard Deviation How the Square Root of x2 Is Almost Equivalent to Taking the Absolute Value of x The Computational Formula for Standard Deviation The Variance The Sampling Distribution of Means, the Central Limit Theorem, and the Standard Error of the Mean The Use of the Standard Deviation for Prediction Practical Uses of the Empirical Rule: As a Definition of an Outlier Practical Uses of the Empirical Rule: Prediction and IQ Tests Some Further Comments History Trivia: Fisher to Eels Key Terms Chapter 3 Practice Problems Chapter 3 Test Yourself Questions SPSS Lesson 3 Chapter 4: Standard Scores, the z Distribution, and Hypothesis Testing Standard Scores The Classic Standard Score: The z Score and the z Distribution Calculating z Scores More Practice on Converting Raw Data Into z Scores Converting z Scores to Other Types of Standard Scores The z Distribution Interpreting Negative z Scores Testing the Predictions of the Empirical Rule With the z Distribution Why Is the z Distribution So Important? How We Use the z Distribution to Test Experimental Hypotheses More Practice With the z Distribution and T Scores Summarizing Scores Through Percentiles History Trivia: Karl Pearson to Egon Pearson Key Terms Chapter 4 Practice Problems Chapter 4 Test Yourself Questions SPSS Lesson 4 Chapter 5: Inferential Statistics: The Controlled Experiment, Hypothesis Testing, and the z Distribution Hypothesis Testing in the Controlled Experiment Hypothesis Testing: The Big Decision How the Big Decision Is Made: Back to the z Distribution The Parameter of Major Interest in Hypothesis Testing: The Mean Nondirectional and Directional Alternative Hypotheses A Debate: Retain the Null Hypothesis or Fail to Reject the Null Hypothesis The Null Hypothesis as a Nonconservative Beginning The Four Possible Outcomes in Hypothesis Testing Significance Levels Significant and Nonsignificant Findings Trends, and Does God Really Love the .05 Level of Significance More Than the .06 Level? Directional or Nondirectional Alternative Hypotheses: Advantages and Disadvantages Did Nuclear Fusion Occur? Baloney Detection Conclusions About Science and Pseudoscience The Most Critical Elements in the Detection of Baloney in Suspicious Studies and Fraudulent Claims Can Statistics Solve Every Problem? Probability History Trivia: Egon Pearson to Karl Pearson Key Terms Chapter 5 Practice Problems Chapter 5 Test Yourself Questions SPSS Lesson 5 Chapter 6: An Introduction to Correlation and Regression Correlation: Use and Abuse A Warning: Correlation Does Not Imply Causation Another Warning: Chance Is Lumpy Correlation and Prediction The Four Common Types of Correlation The Pearson Product–Moment Correlation Coefficient Testing for the Significance of a Correlation Coefficient Obtaining the Critical Values of the t Distribution If the Null Hypothesis Is Rejected Representing the Pearson Correlation Graphically: The Scatterplot Fitting the Points With a Straight Line: The Assumption of a Linear Relationship Interpretation of the Slope of the Best-Fitting Line The Assumption of Homoscedasticity The Coefficient of Determination: How Much One Variable Accounts for Variation in Another Variable—The Interpretation of r2 Quirks in the Interpretation of Significant and Nonsignificant Correlation Coefficients Linear Regression Reading the Regression Line Final Thoughts About Multiple Regression Analyses: A Warning About the Interpretation of the Significant Beta Coefficients Spearman’s Correlation Significance Test for Spearman’s r Ties in Ranks Point-Biserial Correlation Testing for the Significance of the Point-Biserial Correlation Coefficient Phi (F) Correlation Testing for the Significance of Phi History Trivia: Galton to Fisher Key Terms Chapter 6 Practice Problems Chapter 6 Test Yourself Questions SPSS Lesson 6 Chapter 7: The t Test for Independent Groups The Statistical Analysis of the Controlled Experiment One t Test but Two Designs Assumptions of the Independent t Test The Formula for the Independent t Test You Must Remember This! An Overview of Hypothesis Testing With the t Test What Does the t Test Do? Components of the t Test Formula What If the Two Variances Are Radically Different From One Another? A Computational Example Marginal Significance The Power of a Statistical Test Effect Size The Correlation Coefficient of Effect Size Another Measure of Effect Size: Cohen’s d Confidence Intervals Estimating the Standard Error History Trivia: Gosset and Guinness Brewery Key Terms Chapter 7 Practice Problems Chapter 7 Test Yourself Questions SPSS Lesson 7 Chapter 8: The t Test for Dependent Groups Variations on the Controlled Experiment Assumptions of the Dependent t Test Why the Dependent t Test May Be More Powerful Than the Independent t Test How to Increase the Power of a t Test Drawbacks of the Dependent t Test Designs One-Tailed or Two-Tailed Tests of Significance Hypothesis Testing and the Dependent t Test: Design 1 Design 1 (Same Participants or Repeated Measures): A Computational Example Design 2 (Matched Pairs): A Computational Example Design 3 (Same Participants and Balanced Presentation): A Computational Example History Trivia: Fisher to Pearson Key Terms Chapter 8 Practice Problems Chapter 8 Test Yourself Questions SPSS Lesson 8 Chapter 9: Analysis of Variance (ANOVA): One-Factor Completely Randomized Design A Limitation of Multiple t Tests and a Solution The Equally Unacceptable Bonferroni Solution The Acceptable Solution: An Analysis of Variance The Null and Alternative Hypotheses in ANOVA The Beauty and Elegance of the F Test Statistic The F Ratio How Can There Be Two Different Estimates of Within-Groups Variance? ANOVA Designs ANOVA Assumptions Pragmatic Overview What a Significant ANOVA Indicates A Computational Example Degrees of Freedom for the Numerator Degrees of Freedom for the Denominator Determining Effect Size in ANOVA: Omega Squared (w2) Another Measure of Effect Size: Eta (h) History Trivia: Gosset to Fisher Key Terms Chapter 9 Practice Problems Chapter 9 Test Questions Chapter 9 Test Yourself Questions SPSS Lesson 9 Chapter 10: After a Significant ANOVA: Multiple Comparison Tests Conceptual Overview of Tukey’s Test Computation of Tukey’s HSD Test What to Do If the Number of Error Degrees of Freedom Is Not Listed in the Table of Tukey’s q Values Determining What It All Means Warning! On the Importance of Nonsignificant Mean Differences Final Results of ANOVA Quirks in Interpretation Tukey’s With Unequal Ns Key Terms Chapter 10 Practice Problems Chapter 10 Test Yourself Questions SPSS Lesson 10 Chapter 11: Analysis of Variance (ANOVA): One-Factor Repeated-Measures Design The Repeated-Measures ANOVA Assumptions of the One-Factor Repeated-Measures ANOVA Computational Example Determining Effect Size in ANOVA Key Terms Chapter 11 Practice Problems Chapter 11 Test Yourself Questions SPSS Lesson 11 Chapter 12: Factorial ANOVA: Two-Factor Completely Randomized Design Factorial Designs The Most Important Feature of a Factorial Design: The Interaction Fixed and Random Effects and In Situ Designs The Null Hypotheses in a Two-Factor ANOVA Assumptions and Unequal Numbers of Participants Computational Example Key Terms Chapter 12 Practice Problems Chapter 12 Test Yourself Problems SPSS Lesson 12 Chapter 13: Post Hoc Analysis of Factorial ANOVA Main Effect Interpretation: Gender Why a Multiple Comparison Test Is Unnecessary for a Two-Level Main Effect, and When Is a Multiple Comparison Test Necessary? Main Effect: Age Levels Multiple Comparison Test for the Main Effect for Age Warning: Limit Your Main Effect Conclusions When the Interaction Is Significant Multiple Comparison Tests Interpretation of the Interaction Effect Final Summary Writing Up the Results Journal Style Language to Avoid Exploring the Possible Outcomes in a Two-Factor ANOVA Determining Effect Size in a Two-Factor ANOVA History Trivia: Fisher and Smoking Key Terms Chapter 13 Practice Problems Chapter 13 Test Yourself Questions SPSS Lesson 13 Chapter 14: Factorial ANOVA: Additional Designs The Split-Plot Design Overview of the Split-Plot ANOVA Computational Example Two-Factor ANOVA: Repeated Measures on Both Factors Design Overview of the Repeated-Measures ANOVA Computational Example Key Terms and Definitions Chapter 14 Practice Problems Chapter 14 Test Yourself Questions SPSS Lesson 14 Chapter 15: Nonparametric Statistics: The Chi-Square Test and Other Nonparametric Tests Overview of the Purpose of Chi-Square Overview of Chi-Square Designs Chi-Square Test: Two-Cell Design (Equal Probabilities Type) The Chi-Square Distribution Assumptions of the Chi-Square Test Chi-Square Test: Two-Cell Design (Different Probabilities Type) Interpreting a Significant Chi-Square Test for a Newspaper Chi-Square Test: Three-Cell Experiment (Equal Probabilities Type) Chi-Square Test: Two-by-Two Design What to Do After a Chi-Square Test Is Significant When Cell Frequencies Are Less Than 5 Revisited Other Nonparametric Tests History Trivia: Pearson and Biometrika Key Terms Chapter 15 Practice Problems Chapter 15 Test Yourself Questions SPSS Lesson 15 Chapter 16: Other Statistical Topics, Parameters, and Tests Big Data Health Science Statistics Additional Statistical Analyses and Multivariate Statistics A Summary of Multivariate Statistics Coda Key Terms Chapter 16 Practice Problems Chapter 16 Test Yourself Questions Appendix A: z Distribution Appendix B: t Distribution Appendix C: Spearman’s Correlation Appendix D: Chi-Square ?2 Distribution Appendix E: F Distribution Appendix F: Tukey’s Table Appendix G: Mann–Whitney U Critical Values Appendix H: Wilcoxon Signed-Rank Test Critical Values Appendix I: Answers to Odd-Numbered Test Yourself Questions Glossary References Index

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Book SynopsisThis book is a collective volume authored by leading scientists in the field of stochastic modelling, associated statistical topics and corresponding applications. The main classes of stochastic processes for dependent data investigated throughout this book are Markov, semi-Markov, autoregressive and piecewise deterministic Markov models. The material is divided into three parts corresponding to: (i) Markov and semi-Markov processes, (ii) autoregressive processes and (iii) techniques based on divergence measures and entropies. A special attention is payed to applications in reliability, survival analysis and related fields.Table of ContentsPreface xiVlad Stefan BARBU and Nicolas VERGNE Part 1. Markov and Semi-Markov Processes 1 Chapter 1. Variable Length Markov Chains, Persistent Random Walks: A Close Encounter 3Peggy CÉNAC, Brigitte CHAUVIN, Frédéric PACCAUT and Nicolas POUYANNE 1.1. Introduction 3 1.2. VLMCs: definition of the model 6 1.3. Definition and behavior of PRWs 9 1.3.1. PRWs in dimension one 9 1.3.2. PRWs in dimension two 13 1.4. VLMC: existence of stationary probability measures 15 1.5. Where VLMC and PRW meet 19 1.5.1. Semi-Markov chains and Markov additive processes 19 1.5.2. PRWs induce semi-Markov chains 20 1.5.3. Semi-Markov chain of the α-LIS in a stable VLMC 22 1.5.4. The meeting point 23 1.6. References 27 Chapter 2. Bootstraps of Martingale-difference Arrays Under the Uniformly Integrable Entropy 29Salim BOUZEBDA and Nikolaos LIMNIOS 2.1. Introduction and motivation 29 2.2. Some preliminaries and notation 30 2.3. Main results 35 2.4. Application for the semi-Markov kernel estimators 36 2.5. Proofs 41 2.6. References 45 Chapter 3. A Review of the Dividend Discount Model: From Deterministic to Stochastic Models 47Guglielmo D’AMICO and Riccardo DE BLASIS 3.1. Introduction 47 3.2. General model 48 3.3. Gordon growth model and extensions 50 3.3.1. Gordon model 50 3.3.2. Two-stage model 51 3.3.3. H model 52 3.3.4. Three-stage model 52 3.3.5. N-stage model 53 3.3.6. Other extensions 53 3.4. Markov chain stock models 54 3.4.1. Hurley and Johnson model 54 3.4.2. Yao model 56 3.4.3. Markov stock model 57 3.4.4. Multivariate Markov chain stock model 61 3.5. Conclusion 64 3.6. References 65 Chapter 4. Estimation of Piecewise-deterministic Trajectories in a Quantum Optics Scenario 69Romain AZAЇS and Bruno LEGGIO 4.1. Introduction 69 4.1.1. The postulates of quantum mechanics 69 4.1.2. Dynamics of open quantum Markovian systems 71 4.1.3. Stochastic wave function: quantum dynamics as PDPs 74 4.1.4. Estimation for PDPs 76 4.2. Problem formulation 77 4.2.1. Atom-field interaction 77 4.2.2. Piecewise-deterministic trajectories 78 4.2.3. Measures 80 4.3. Estimation procedure 80 4.3.1. Strategy 80 4.3.2. Least-square estimators 82 4.3.3. Numerical experiments 83 4.4. Physical interpretation 86 4.5. Concluding remarks 87 4.6. References 88 Chapter 5. Identification of Patterns in a Semi-Markov Chain 91Brenda Ivette GARCIA-MAYA and Nikolaos LIMNIOS 5.1. Introduction 91 5.2. The prefix chain 93 5.3. The semi-Markov setting 94 5.4. The hitting time of the pattern 100 5.5. A genomic application 102 5.6. Concluding remarks 106 5.7. References 106 Part 2. Autoregressive Processes 109 Chapter 6. Time Changes and Stationarity Issues for Continuous Time Autoregressive Processes of Order p 111Valérie GIRARDIN and Rachid SENOUSSI 6.1. Introduction 111 6.2. Basics 112 6.3. Stationary AR processes 114 6.3.1. Formulas for the two first-order moments 114 6.3.2. Examples 116 6.3.3. Conditions for stationarity of CAR1(p) processes 118 6.4. Time transforms 125 6.4.1. Properties of time transforms 125 6.4.2. MS processes 131 6.5. Conclusion 132 6.6. Appendix 133 6.7. References 136 Chapter 7. Sequential Estimation for Non-parametric Autoregressive Models 139Ouerdia ARKOUN, Jean-Yves BRUA and Serguei PERGAMENCHTCHIKOV 7.1. Introduction 139 7.2. Main conditions 141 7.3. Pointwise estimation with absolute error risk 142 7.3.1. Minimax approach 142 7.3.2. Adaptive minimax approach 144 7.3.3. Non-adaptive procedure 145 7.3.4. Sequential kernel estimator 148 7.3.5. Adaptive sequential procedure 151 7.4. Estimation with quadratic integral risk 153 7.4.1. Passage to a discrete time regression model 155 7.4.2. Model selection 159 7.4.3. Main results 161 7.5. References 164 Part 3. Divergence Measures and Entropies 167 Chapter 8. Inference in Parametric and Semi-parametric Models: The Divergence-based Approach 169Michel BRONIATOWSKI 8.1. Introduction 169 8.1.1. Csiszár divergences, variational form 170 8.1.2. Dual form of the divergence and dual estimators in parametric models 172 8.1.3. Decomposable discrepancies 178 8.2. Models and selection of statistical criteria 183 8.3. Non-regular cases: the interplay between the model and the criterion 184 8.3.1. Test statistics 185 8.4. References 187 Chapter 9. Dynamics of the Group Entropy Maximization Processes and of the Relative Entropy Group Minimization Processes Based on the Speed-gradient Principle 189Vasile PREDA and Irina BĂNCESCU 9.1. Introduction 190 9.1.1. The SG principle 191 9.1.2. Entropy groups 193 9.2. Group entropies and the SG principle 196 9.2.1. Total energy constraint 199 9.3. Relative entropy group and the SG principle 202 9.3.1. Equilibrium stability 205 9.3.2. Total energy constraint 205 9.4. A new (G, a) power relative entropy group and the SG principle 206 9.5. Conclusion 210 9.6. References 210 Chapter 10. Inferential Statistics Based on Measures of Information and Divergence 215Alex KARAGRIGORIOU and Christos MESELIDIS 10.1. Introduction 215 10.2. Divergence measures 216 10.2.1. ϕ-Divergences 216 10.2.2. α-Divergences 217 10.2.3. Bregman divergences 218 10.3. Properties of divergence measures 219 10.4. Model selection criteria 220 10.5. Goodness of fit tests 222 10.5.1. Simple null hypothesis 222 10.5.2. Composite null hypothesis 223 10.6. Simulation study 227 10.7. References 231 Chapter 11. Goodness-of-Fit Tests Based on Divergence Measures for Frailty Models 235Filia VONTA 11.1. Introduction 235 11.2. The proposed goodness-of-fit test 236 11.3. Main results 240 11.4. Frailty models 243 11.5. Simulations 244 11.5.1. Linear models for the estimation of critical values 247 11.5.2. Size of the test 248 11.6. References 250 List of Authors 253 Index 257

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Book SynopsisThis book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levTrade Review' … there is no other treatment coming close in terms of comprehensiveness and readability … it is indispensable for anybody working on dynamical systems in almost any context, and even experts will find interesting new proofs, insights and historical references throughout the book.' Monatshefte für Mathematik'… contains detailed discussion … presents many recent results … The text is carefully written and is accompanied by many excercises.' European Mathematical Society Newsletter'This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline.' L'Enseignement MathématiqueTable of ContentsPart I. Examples and Fundamental Concepts; Introduction; 1. First examples; 2. Equivalence, classification, and invariants; 3. Principle classes of asymptotic invariants; 4. Statistical behavior of the orbits and introduction to ergodic theory; 5. Smooth invariant measures and more examples; Part II. Local Analysis and Orbit Growth; 6. Local hyperbolic theory and its applications; 7. Transversality and genericity; 8. Orbit growth arising from topology; 9. Variational aspects of dynamics; Part III. Low-Dimensional Phenomena; 10. Introduction: What is low dimensional dynamics; 11. Homeomorphisms of the circle; 12. Circle diffeomorphisms; 13. Twist maps; 14. Flows on surfaces and related dynamical systems; 15. Continuous maps of the interval; 16. Smooth maps of the interval; Part IV. Hyperbolic Dynamical Systems; 17. Survey of examples; 18. Topological properties of hyperbolic sets; 19. Metric structure of hyperbolic sets; 20. Equilibrium states and smooth invariant measures; Part V. Sopplement and Appendix; 21. Dynamical systems with nonuniformly hyperbolic behavior Anatole Katok and Leonardo Mendoza.

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Book SynopsisThis book is a general introduction to the statistical analysis of networks, and can serve both as a research monograph and as a textbook. Numerous fundamental tools and concepts needed for the analysis of networks are presented, such as network modeling, community detection, graph-based semi-supervised learning and sampling in networks. The description of these concepts is self-contained, with both theoretical justifications and applications provided for the presented algorithms.Researchers, including postgraduate students, working in the area of network science, complex network analysis, or social network analysis, will find up-to-date statistical methods relevant to their research tasks. This book can also serve as textbook material for courses related to thestatistical approach to the analysis of complex networks.In general, the chapters are fairly independent and self-supporting, and the book could be used for course composition “à la carte”. Nevertheless, Chapter 2 is needed to a certain degree for all parts of the book. It is also recommended to read Chapter 4 before reading Chapters 5 and 6, but this is not absolutely necessary. Reading Chapter 3 can also be helpful before reading Chapters 5 and 7. As prerequisites for reading this book, a basic knowledge in probability, linear algebra and elementary notions of graph theory is advised. Appendices describing required notions from the above mentioned disciplines have been added to help readers gain further understanding.Trade ReviewThis is an interesting book. Models are introduced in the first chapter, and then centralities in the second. Community detection is certainly a popular topic, especially among those working in complex network analysis. And the author is certainly correct that community detection in dynamic networks has received comparatively less exposure. There are models for dynamic networks and extensions of characterizations (like centrality and otherwise) for dynamic networks. Finally, the chapter on sampling is of interest, and not something that is usually covered in network texts. In my opinion the book should have good market appeal. Eric D. Kolaczyk, Boston University, USA -- Eric D. KolaczykThe book proposed is a worthwhile one. Network analysis is an active area with a huge amount of work being produced in recent years. The subject of network analysis spans mathematics, probability, statistics, physics and computer science, amongst others. The book focusses on the topics of community detection, dynamic graphs and sampling on graphs. These are all topics of interest to researchers in network analysis and people who analyse network data. Community detection is hugely relevant in applications of network analysis. The book would be useful in providing a formal treatment of many topics of interest to people who use network analysis. The book also focusses on centrality measures which are important, are a full chapter in the book, but downplayed in the description; they should also be emphasised. Brendan Murphy, University College Dublin, Ireland -- Brendan MurphyTable of Contents 1. Introduction 2. Random Graph Models 3. Network Centrality Indices 4. Community Detection in Networks 5. Graph-based Semi-Supervised Learning 6. Community Detection in Temporal Networks 7. Sampling in Networks 8. Appendices

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Book SynopsisThis book offers an introduction to statistical mechanics, special relativity, and quantum physics. It is based on the lecture notes prepared for the one-semester course of "Quantum Physics" belonging to the Bachelor of Science in Material Sciences at the University of Padova.The first chapter briefly reviews the ideas of classical statistical mechanics introduced by James Clerk Maxwell, Ludwig Boltzmann, Willard Gibbs, and others. The second chapter is devoted to the special relativity of Albert Einstein. In the third chapter, it is historically analyzed the quantization of light due to Max Planck and Albert Einstein, while the fourth chapter discusses the Niels Bohr quantization of the energy levels and the electromagnetic transitions. The fifth chapter investigates the Schrodinger equation, which was obtained by Erwin Schrodinger from the idea of Louis De Broglie to associate to each particle a quantum wavelength. Chapter Six describes the basic axioms of quantum mechanics, which were formulated in the seminal books of Paul Dirac and John von Neumann. In chapter seven, there are several important application of quantum mechanics: the quantum particle in a box, the quantum particle in the harmonic potential, the quantum tunneling, the stationary perturbation theory, and the time-dependent perturbation theory. Chapter Eight is devoted to the study of quantum atomic physics with special emphasis on the spin of the electron, which needs the Dirac equation for a rigorous theoretical justification. In the ninth chapter, it is explained the quantum mechanics of many identical particles at zero temperature, while in Chapter Ten the discussion is extended to many quantum particles at finite temperature by introducing and using the quantum statistical mechanics. The four appendices on Dirac delta function, complex numbers, Fourier transform, and differential equations are a useful mathematical aid for the reader.Table of ContentsTable of Contents1 Classical Statistical Mechanics1.1 Kinetic Theory of Gases 1.1.1 Maxwell Distribution of Velocities1.1.2 Maxwell-Boltzmann Distribution of Energies 1.1.3 Single-Particle Density of States 1.2 Statistical Ensembles of Gibbs 1.2.1 Microcanonical Ensemble 1.2.2 Canonical Ensemble 1.2.3 Grand Canonical Ensemble 1.2.4 Many-Particle Density of States 2 Special Relativity 2.1 Lorentz Transformations 2.2 Einstein Postulates 2.2.1 Gedanken Experiment of Einstein 2.3 Relativistic Mechanics 2.3.1 Relativistic Kinematics 2.3.2 Relativistic Dynamics 3 Quantum Properties of Light 3.1 Black-Body Radiation 3.1.1 Ideal Black Body 3.1.2 Derivation of the Planck Law 3.2 Photoelectric E ect 3.2.1 Experimental Data 3.2.2 Theoretical Explanation 3.3 Energy and Linear Momentum of a Photon 3.4 Compton E ect 3.4.1 Theoretical Explanation 4 Quantum Energy Levels of Atoms 4.1 Energy Spectra 4.1.1 Energy Spectrum of Hydrogen Atom 4.2 Hydrogen Atom of Bohr4.2.1 Derivation of the Bohr Results 4.3 Energy Levels and Photons 4.4 Electromagnetic Transitions 5 Wave Properties of Matter 5.1 De Broglie Wavelength 5.1.1 Explaining the Bohr Quantization 5.2 Experiment of Davisson and Germer 5.3 Double-Slit Experiment with Light5.4 Double-Slit Experiment with Electrons 5.5 Old Quantum Mechanics of Bohr, Wilson and Sommerfeld5.6 Matrix Quantum Mechanics of Heisenberg, Born and Jordan 5.7 Wave Quantum Mechanics of Schrodinger 5.7.1 Derivation of the Schr odinger Equation 5.8 Formal Quantization Rules5.8.1 Schrodinger Equation for a Free Particle 5.8.2 Schrodinger Equation for a Particle in an External Potential 5.9 Stationary Schr odinger Equation6 Axioms of Quantum Mechanics 6.1 Matrix Mechanics 6.2 Axioms of Quantum Mechanics7 Applications of Quantum Mechanics 7.1 Quantum Particle in a One-Dimensional Box Potential7.2 Quantum Particle in a One-Dimensional Harmonic Potential8 Quantum Physics of Atoms 8.1 Quantum Particle in a Separable Potential 8.1.1 Quantum Particle in the Harmonic Potential 8.2 Dirac Notation for a Quantum State8.3 Electron in the Hydrogen Atom 8.3.1 Schrodinger Equation in Spherical Polar Coordinates 8.3.2 Selection Rules 8.4 Pauli Exclusion Principle and the Spin8.5 Semi-Integer and Integer Spin: Fermions and Bosons8.6 The Dirac Equation 8.6.1 The Pauli Equation and the Spin8.6.2 Dirac Equation with a Central Potential 8.6.3 Relativistic Hydrogen Atom and Fine Splitting 8.6.4 Relativistic Corrections to the Schrodinger Hamiltonian9 Quantum Mechanics of Many-Body Systems 9.1 Identical Quantum Particles 9.1.1 Spin-Statistics Theorem9.2 Non-Interacting Identical Particles9.2.1 Atomic Shell Structure and the Periodic Table of the Elements 9.3 Interacting Identical Particles9.3.1 Variational Principle9.3.2 Electrons in Atoms and Molecules10 Quantum Statistical Mechanics 10.1 Quantum Statistical Ensembles 10.1.1 Quantum Microcanonical Ensemble 10.1.2 Quantum Canonical Ensemble 10.1.3 Quantum Grand Canonical Ensemble 10.2 Bosons and Fermions at Finite Temperature 10.2.1 Gas of Photons at Thermal Equlibrium10.2.2 Gas of Massive Bosons at Thermal Equlibrium 10.2.3 Gas of Non-Interacting Fermions at Zero TemperatureAppendix A Dirac Delta Function A.1 The Heaviside Step Function A.2 The Strange Function of Dirac A.2.1 Dirac Function and the Integrals A.3 Dirac Function in D Spatial Dimensions Appendix B Complex Numbers B.1 Set of Complex Numbers B.2 Gauss Plane B.2.1 Polar Representation B.3 Euler Formula B.3.1 Proof of the Euler Formula B.3.2 De Moivre FormulaB.4 Fundamental Theorem of Algebra B.5 Complex Functions Appendix C Fourier Transform C.1 Geometric and Taylor SeriesC.2 Fourier Series .C.2.1 Complex Representation of the Fourier Series C.3 Fourier Integral C.3.1 Properties of the Fourier Transform C.3.2 Fourier Transform and Uncertanty TheoremC.4 Fourier Transform of Space-Time FunctionsAppendix D Di erential equations D.1 First-Order Ordinary Di erential EquationsD.1.1 Separation of Variables D.2 Second-Order Ordinary Di erential Equations D.3 Newton Law as a Second-Order ODE D.4 Partial Di erential Equations D.4.1 Wave Equation D.4.2 Di usion Equation Bibliography

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Book SynopsisA visually intuitive approach to statistical data analysis Visual Statistics brings the most complex and advanced statistical methods within reach of those with little statistical training by using animated graphics of the data. Using ViSta: The Visual Statistics System-developed by Forrest Young and Pedro Valero-Mora and available free of charge on the Internet-students can easily create fully interactive visualizations from relevant mathematical statistics, promoting perceptual and cognitive understanding of the data''s story. An emphasis is placed on a paradigm for understanding data that is visual, intuitive, geometric, and active, rather than one that relies on convoluted logic, heavy mathematics, systems of algebraic equations, or passive acceptance of results. A companion Web site complements the book by further demonstrating the concept of creating interactive and dynamic graphics. The book provides users with the opportunity to view the graphics in a Trade Review"With contributions by highly regarded professionals in the field, Visual Statistics not only improves a student's understanding of statistics, but also builds condence to overcome problems that may have previously been intimidating." (Zentralblatt MATH 2016) "A good book about a great software system." (Psychometrika, March 2008) "The people who would benefit most from this book are those who teach courses in statistics." (AstA Advances in Statistical Analysis, 2008) "... the book admirably guides readers through the process of exploring and analyzing a variety of types of data." (The American Statistician, August 2007) "A technically well-produced book, significant in that it documents efforts these psychometrics faculty made in using visual approaches to analyze data." (CHOICE, March 2007) "... covers its subject matter skillfully, and provides great insight into the world of the dynamic visualization of statistical data." (Journal of Applied Statistics, 2007) "Forrest Young has been a leading light in developing dynamic interactive graphics for decades... so [I] am delighted to see this book appear." (Short Book Reviews, December 2006) "... the book not only improves a student's understanding of statistics, but also builds confidence to overcome problems that may have previously been intimidating... an excellent textbook" (Computing Reviews.com, November 16, 2006)Table of ContentsPart I Introduction 1 Introduction 1.1 Visual Statistics 6 1.2 Dynamic Interactive Graphies 7 1.2.1 An Analogy 7 1.2.2 Why Use Dynamic Graphies? 8 1.2.3 The Four Respects 8 1.3 Three Examples 9 1.3.1 Nonrandom Numbers 9 1.3.2 Automobile Efficiency 11 1.3.3 Fidelity and Marriage 14 1.4 History of Statistical Graphics 18 1.4.1 1600-1699: Measurement and Theory 18 1.4.2 1700-1799: New Graphic Forms and Data 19 1.4.3 1800-1899: Modern Graphics and the Golden Age 20 1.4.4 1900-1950: The Dark Ages of Statistical Graphics—The Golden Age of Mathematical Statistics 21 1.4.5 1950-1975: Rebirth of Statistical Graphics 22 1.4.6 1975-2000: Statistical Graphics Comes of Age 23 1.5 About Software 24 1.5.1 XLisp-Stat 25 1.5.2 Commercial Systems 26 1.5.3 Noncommercial Systems 26 1.5.4 ViSta 27 1.6 About Data 29 1.6.1 Essential Characteristics 30 1.6.2 Datatypes 32 1.6.3 Datatype Examples 34 1.7 About This Book 34 1.7.1 What This Book Is—and Isn't 34 1.7.2 Organization 34 1.7.3 Who Our Audience Is—and Isn't 37 1.7.4 Comics 38 1.7.5 Thumb-Powered Dynamic Graphics 39 1.8 Visual Statistics and the Graphical User Interface 40 1.9 Visual Statistics and the Scientific Method 40 1.9.1 A Paradigm for Seeing Data 41 1.9.2 About Statistical Data Analysis: Visual or Otherwise 42 2 Examples 45 2.1 Random Numbers 47 2.2 Medical Diagnosis 52 2.3 Fidelity and Marriage 59 Part II See Data—The Process 3 Interfaces and Environments 73 3.1 Objects 77 3.2 User Interfaces for Seeing Data 78 3.3 Character-Based Statistical Interface Objects 79 3.3.1 Command Line 79 3.3.2 Calculator 80 3.3.3 Program Editor 80 3.3.4 Report Generator 81 3.4 Graphics-Based Statistical Interfaces 81 3.4.1 Datasheets 81 3.4.2 Variable Window 82 3.4.3 Desktop 82 3.4.4 Workmap 83 3.4.5 Selector 87 3.5 Plots 88 3.5.1 Look of Plots 89 3.5.2 Feel of Plots 91 3.5.3 Impact of Plot Look and Feel 93 3.6 Spreadplots 94 3.6.1 Layout 96 3.6.2 Coordination 98 3.6.3 SpreadPlots 100 3.6.4 Look of Spreadplots 102 3.6.5 Feel of Spreadplots 104 3.6.6 Look and Feel of Statistical Data Analysis 104 3.7 Environments for Seeing Data 111 3.8 Sessions and Projects 114 3.9 The Next Reality 114 3.9.1 The Fantasy 114 3.9.2 The Reality 116 3.9.3 Reality Check 118 4 Tools and Techniques 119 4.1 Types of Controls 123 4.1.1 Buttons 123 4.1.2 Palettes 125 4.1.3 Menus and Menu Items 125 4.1.4 Dialog Boxes 125 4.1.5 Sliders 126 4.1.6 Control Panels 127 4.1.7 The Plot Itself 127 4.1.8 Hyperlinking 127 4.2 Datasheets 128 4.3 Plots 129 4.3.1 Activating Plot Objects 131 4.3.2 Manipulating Plot Objects 132 4.3.3 Manipulating Plot Dimensions 138 4.3.4 Adding Graphical Elements 141 Part III Seeing Data—Objects 5 Seeing Frequency Data 145 5.1 Data 148 5.1.1 Automobile Efficiency: 148 5.1.2 Berkeley Admissions Data 148 5.1.3 Tables of Frequency data 150 5.1.4 Working at the Categories Level 151 5.1.5 Working at the Variables Level 153 5.2 Frequency Plots 157 5.2.1 Mosaic Displays 157 5.2.2 Dynamic Mosaic Displays 159 5.3 Visual Fitting of Log-Linear Models 164 5.3.1 Log-Linear Spreadplot 165 5.3.2 Specifying Log-Linear Models and the Model Builder Window 166 5.3.3 Evaluating the Global Fit of Models and Their History 170 5.3.4 Visualizing Fitted and Residual Values with Mosaic Displays 174 5.3.5 Interpreting the Parameters of the Model 176 5.4 Conclusions 179 6 Seeing Univariate Data 181 6.1 Introduction 183 6.2 Data: Automobile Efficiency 185 6.2.1 Looking at the Numbers 186 6.2.2 What Can Unidimensional Methods Reveal? 186 6.3 Univariate Plots 190 6.3.1 Dotplots 190 6.3.2 Boxplots 193 6.3.3 Cumulative Distribution Plots 196 6.3.4 Histograms and Frequency Polygons 199 6.3.5 Ordered Series Plots 208 6.3.6 Namelists 209 6.4 Visualization for Exploring Univariate Data 209 6.5 What Do We See in MPG1 212 7 Seeing Bivariate Data 215 7.1 Introduction 217 7.1.1 Plots About Relationships 217 7.1.2 Chapter Preview 220 7.2 Data: Automobile Efficiency 221 7.2.1 What the Data Seem to Say 222 7.3 Bivariate Plots 224 7.3.1 Scatterplots 224 7.3.2 Distribution Comparison Plots 233 7.3.3 Parallel-Coordinates Plots and Parallel Boxplots 236 7.4 Multiple Bivariate Plots 236 7.4.1 Scatterplot Plot Matrix 2377.4.2 Quantile Plot Matrix 238 7.4.3 Numerical Plot-matrix 238 7.4.4 BoxPlot Plot Matrix 239 7.5 Bivariate Visualization Methods 241 7.6 Visual Exploration 242 7.6.1 Two Bivariate Data Visualizations 243 7.6.2 Using These Visualizations 245 7.7 Visual Transformation: Box-Cox 247 7.7.1 The Transformation Visualization 249 7.7.2 Using Transformation Visualization 251 7.7.3 The Box-Cox Power Transformation 255 7.8 Visual Fitting: Simple Regression 256 7.9 Conclusions 260 8 Seeing Multivariate Data 263 8.1 Data: Medical Diagnosis 266 8.2 Three Families of Multivariate Plots 270 8.3 Parallel-Axes Plots 272 8.3.1 Parallel-Coordinates Plot 272 8.3.2 Parallel-Comparisons Plot 276 8.3.3 Parallel Univariate Plots 277 8.4 Orthogonal-Axes Plots 279 8.4.1 Spinplot 280 8.4.2 Orbitplot 283 8.4.3 BiPlot 286 8.4.4 Wiggle-Worm (Multivariable Comparison) Plot 291 8.5 Paired-Axes Plots 292 8.5.1 Spinplot Plot Matrix 293 8.5.2 Parallel-Coordinates Plot Matrix 294 8.6 Multivariate Visualization 295 8.6.1 Variable Visualization 295 8.6.2 Principal Components Analysis 296 8.6.3 Fit Visualization 298 8.6.4 Principal Components Visualization 300 8.6.5 One More Step - Discriminant Analysis 302 8.7 Summary 304 8.7.1 What Did We See? Clusters! 304 8.7.2 How Did We See It? 304 8.7.3 How Do We Interpret It? With Diagnostic Groups! 305 8.8 Conclusion 306 9 Seeing Missing Values 309 9.1 Introduction 312 9.2 Data: Sleep in Mammals 314 9.3 Missing Data Visualization Tools 315 9.3.1 Missing Values Bar Charts 316 9.3.2 Histograms and Bar Charts 316 9.3.3 Boxplots 316 9.3.4 Scatterplots 316 9.4 Visualizing Imputed Values 317 9.4.1 Marking the Imputed Values 318 9.4.2 Single Imputation 320 9.4.3 Multiple Imputation 325 9.4.4 Summary of Imputation 327 9.5 Missing Data Patterns 327 9.5.1 Patterns and Number of Cases 328 9.5.2 The Mechanisms Leading to Missing Data 329 9.5.3 Visualizing Dynamically the Patterns of Missing Data 331 9.6 Conclusions 337 References 339 Author Index 351 Subject Index 355

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Book SynopsisData 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.Table of Contents1. Prologue: linking 'The Future' with the present; 2. A data assimilation reminder; 3. Remembrance of things path; 4. SDA variational principles; Euler–Lagrange equations and Hamiltonian formulation; 5. Using waveform information; 6. Annealing in the model precision Rf; 7. Discrete time integration in data assimilation variational principles; Lagrangian and Hamiltonian formulations; 8. Monte Carlo methods; 9. Machine learning and its equivalence to statistical data assimilation; 10. Two examples of the practical use of data assimilation; 11. Unfinished business; Bibliography; Index.

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Book SynopsisIn this book, the authors treat macroeconomic models as composed of large numbers of micro-units or agents of several types and explicitly discuss stochastic dynamic and combinatorial aspects of interactions among them. In mainstream macroeconomics sound microfoundations for macroeconomics have meant incorporating sophisticated intertemporal optimization by representative agents into models. Optimal growth theory, once meant to be normative, is now taught as a descriptive theory in mainstream macroeconomic courses. In neoclassical equilibria flexible prices led the economy to the state of full employment and marginal productivities are all equated. Professors Aoki and Yoshikawa contrariwise show that such equilibria are not possible in economies with a large number of agents of heterogeneous types. They employ a set of statistical dynamical tools via continuous-time Markov chains and statistical distributions of fractions of agents by types available in the new literature of combinatorTrade ReviewReviews of the hardback: 'Thoughtful macroeconomists are uncomfortably aware that consumers, firms, and workers vary widely in their local environments, perceptions, and beliefs. Ignoring this heterogeneity, as 'modern macro' does, is a likely source of systematic error. Aoki and Yoshikawa propose to repair this failure by modeling the macroeconomy explicitly as a cloud of interacting particles. The goal is to deduce the distributions of economic characteristics that describe the system as a whole. There are already some surprising beginning results, including a novel treatment of aggregate demand, and one can expect more when their approach is combined with standard economic reasoning. This is the start, not the finish, of a potentially far-reaching research program. It should excite the curiosity of all those thoughtful macroeconomists.' Robert M. Solow, Massachusetts Institute of Technology'This book is a bold and daring challenge to the growing influence of neoclassical equilibrium theory in the field of modern macroeconomics. Not simply an approach to traditional Keynesian theory that attempts to refine it and make it more accurate, the treatment makes use of a new methodology in statistical physics and combinatorial stochastic processes to mount a direct challenge to real business cycle theory and rational expectations theory. Professor Aoki has made important contributions to the application of statistical physics to economics, and Professor Yoshikawa is a leading Japanese economist who has done outstanding work in the fields of both theoretical and empirical economics. This book is the superb product of the optimum combination of these two scholars' different talents.' Ryuzo Sato, New York University and University of Tokyo'Masanao Aoki and Hiroshi Yoshikawa have written no less than the foundation of a new approach (and I believe the right one) to the core problem of macroeconomics, which is to aggregate behaviors by stressing the importance of the heterogeneity and variability of real economic agents. Getting inspiration from and adapting the concepts and tools of statistical physics, they masterfully derive important and novel insights on the most crucial problems of the field: the principle of effective demand, role of uncertainty, sticky prices/wages, and the endogenous business cycle. This book is perhaps the first successful effort to develop macroeconomics as a real science on par with physics, with falsifiable hypotheses underpinned by sound micro-principles and testable predictions.' Didier Sornette, Swiss Federal Institute of Technology, Zurich'This book shows the impossibility of efficient equilibria in economics with market clearing mainstream hypotheses when such an economy is populated by a large number of heterogenous agents. In such a case, Aoki and Yoshikawa show that, through combined stochastic processes, a new approach to macroeconomics is not only possible: it is real and this book shows how to reach it.' Mauro Gallegati, Università Politechnia delle Marche'Reconstructing Macroeconomics is an ambitious, informative, challenging … book that addresses fundamental questions of economic theory on many levels. In my view mainstream macroeconomists can only benefit by becoming familiar with the point of view Aoki and Yoshikawa represent so ably here … Those who aspire to create a new macroeconomics, including the various schools of 'heterodox' economics, can also learn a lot from this book.' Journal of Economic Behavior and OrganizationTable of ContentsPreface 1 Masanao Aoki; Preface 2 Hiroshi Yoshikawa; 1. Introduction - a new approach to macroeconomics; 2. The methods - jump Markov processes and random partitions; 3. Equilibrium as distribution - the role of demand in macroeconomics; 4. Uncertainty trap - policy ineffectiveness and long stagnation of the macroeconomy; 5. Slow dynamics of the macro system - no mystery of inflexible prices; 6. Business cycles - an endogenous stochastic approach; 7. Labor market dynamics - a new look at natural unemployment and Okun's law; 8. Demand saturation - creation and economic growth; 9. The types of investors and volatility in financial markets - analyzing clusters of heterogeneous agents; 10. Stock prices and the real macroeconomy - power-law versus exponential distributions.

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Book SynopsisStatistical mechanics is one of the most important areas of physics, and it also has applications to subjects as diverse as economics, social behavior, algorithmic theory, and evolutionary biology. This bokk introduces important developments in classical statistical mechanics, and guides readers to the very threshold of research.Trade Review"Unlike typical textbooks ... [Statistical Mechanics in a Nutshell] presents statistical mechanics as a more general theory with broader applications... A graduate student or researcher who wants to explore the applications of statistical mechanics would be very well served by this book."--Choice "Peliti's Statistical Mechanics in a Nutshell is a fantastic reference for those who know the subject, teach it, or need a quick technical reminder, especially on the topic of phase transitions, which are consistently featured in modern-day discussions... Statistical Mechanics in a Nutshell provides the more general overview, with topics such as the renormalization group method. It includes a good mix of fundamental thermodynamics, phase behaviour, and other key subjects."--Physics TodayTable of ContentsPreface to the English Edition xi Preface xiii Chapter 1: Introduction 1 1.1 The Subject Matter of Statistical Mechanics 1 1.2 Statistical Postulates 3 1.3 An Example: The Ideal Gas 3 1.4 Conclusions 7 Recommended Reading 8 Chapter 2: Thermodynamics 9 2.1 Thermodynamic Systems 9 2.2 Extensive Variables 11 2.3 The Central Problem of Thermodynamics 12 2.4 Entropy 13 2.5 Simple Problems 14 2.6 Heat and Work 18 2.7 The Fundamental Equation 23 2.8 Energy Scheme 24 2.9 Intensive Variables and Thermodynamic Potentials 26 2.10 Free Energy and Maxwell Relations 30 2.11 Gibbs Free Energy and Enthalpy 31 2.12 The Measure of Chemical Potential 33 2.13 The Koenig Born Diagram 35 2.14 Other Thermodynamic Potentials 36 2.15 The Euler and Gibbs-Duhem Equations 37 2.16 Magnetic Systems 39 2.17 Equations of State 40 2.18 Stability 41 2.19 Chemical Reactions 44 2.20 Phase Coexistence 45 2.21 The Clausius-Clapeyron Equation 47 2.22 The Coexistence Curve 48 2.23 Coexistence of Several Phases 49 2.24 The Critical Point 50 2.25 Planar Interfaces 51 Recommended Reading 54 Chapter 3: The Fundamental Postulate 55 3.1 Phase Space 55 3.2 Observables 57 3.3 The Fundamental Postulate: Entropy as Phase-Space Volume 58 3.4 Liouville's Theorem 59 3.5 Quantum States 63 3.6 Systems in Contact 66 3.7 Variational Principle 67 3.8 The Ideal Gas 68 3.9 The Probability Distribution 70 3.10 Maxwell Distribution 71 3.11 The Ising Paramagnet 71 3.12 The Canonical Ensemble 74 3.13 Generalized Ensembles 77 3.14 The p-T Ensemble 80 3.15 The Grand Canonical Ensemble 82 3.16 The Gibbs Formula for the Entropy 84 3.17 Variational Derivation of the Ensembles 86 3.18 Fluctuations of Uncorrelated Particles 87 Recommended Reading 88 Chapter 4: Interaction-Free Systems 89 4.1 Harmonic Oscillators 89 4.2 Photons and Phonons 93 4.3 Boson and Fermion Gases 102 4.4 Einstein Condensation 112 4.5 Adsorption 114 4.6 Internal Degrees of Freedom 116 4.7 Chemical Equilibria in Gases 123 Recommended Reading 124 Chapter 5: Phase Transitions 125 5.1 Liquid-Gas Coexistence and Critical Point 125 5.2 Van der Waals Equation 127 5.3. Other Singularities 129 5.4 Binary Mixtures 130 5.5 Lattice Gas 131 5.6 Symmetry 133 5.7 Symmetry Breaking 134 5.8 The Order Parameter 135 5.9 Peierls Argument 137 5.10 The One-Dimensional Ising Model 140 5.11 Duality 142 5.12 Mean-Field Theory 144 5.13 Variational Principle 147 5.14 Correlation Functions 150 5.15 The Landau Theory 153 5.16 Critical Exponents 156 5.17 The Einstein Theory of Fluctuations 157 5.18 Ginzburg Criterion 160 5.19 Universality and Scaling 161 5.20 Partition Function of the Two-Dimensional Ising Model 165 Recommended Reading 170 Chapter 6: Renormalization Group 173 6.1 Block Transformation 173 6.2 Decimation in the One-Dimensional Ising Model 176 6.3 Two-Dimensional Ising Model 179 6.4 Relevant and Irrelevant Operators 183 6.5 Finite Lattice Method 187 6.6 Renormalization in Fourier Space 189 6.7 Quadratic Anisotropy and Crossover 202 6.8 Critical Crossover 203 6.9 Cubic Anisotrophy 208 6.10 Limit n 209 6.11 Lower and Upper Critical Dimensions 213 Recommended Reading 214 Chapter 7: Classical Fluids 215 7.1 Partition Function for a Classical Fluid 215 7.2 Reduced Densities 219 7.3 Virial Expansion 227 7.4 Perturbation Theory 244 7.5 Liquid Solutions 246 Recommended Reading 249 Chapter 8: Numerical Simulation 251 8.1 Introduction 251 8.2 Molecular Dynamics 253 8.3 Random Sequences 259 8.4 Monte Carlo Method 261 8.5 Umbrella Sampling 272 8.6 Discussion 274 Recommended Reading 275 Chapter 9: Dynamics 277 9.1 Brownian Motion 277 9.2 Fractal Properties of Brownian Trajectories 282 9.3 Smoluchowski Equation 285 9.4 Diffusion Processes and the Fokker-Planck Equation 288 9.5 Correlation Functions 289 9.6 Kubo Formula and Sum Rules 292 9.7 Generalized Brownian Motion 293 9.8 Time Reversal 296 9.9 Response Functions 296 9.10 Fluctuation-Dissipation Theorem 299 9.11 Onsager Reciprocity Relations 301 9.12 Affinities and Fluxes 303 9.13 Variational Principle 306 9.14 An Application 308 Recommended Reading 310 Chapter 10: Complex Systems 311 10.1 Linear Polymers in Solution 312 10.2 Percolation 321 10.3 Disordered Systems 338 Recommended Reading 356 Appendices 357 Appendix A Legendre Transformation 359 A.1 Legendre Transform 359 A.2 Properties of the Legendre Transform 360 A.3 Lagrange Multipliers 361 Appendix B Saddle Point Method 364 B.1 Euler Integrals and the Saddle Point Method 364 B.2 The Euler Gamma Function 366 B.3 Properties of N-Dimensional Space 367 B.4 Integral Representation of the Delta Function 368 Appendix C A Probability Refresher 369 C.1 Events and Probability 369 C.2 Random Variables 369 C.3 Averages and Moments 370 C.4 Conditional Probability: Independence 371 C.5 Generating Function 372 C.6 Central Limit Theorem 372 C.7 Correlations 373 Appendix D Markov Chains 375 D.1 Introduction 375 D.2 Definitions 375 D.3 Spectral Properties 376 D.4 Ergodic Properties 377 D.5 Convergence to Equilibrium 378 Appendix E Fundamental Physical Constants 380 Bibliography 383 Index 389

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