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Statistical Mechanics of Neural Networks
by Haiping HuangThis book highlights a comprehensive introduction to the fundamental statistical mechanics underneath the inner workings of neural networks. The book discusses in details important concepts and techniques including the cavity method, the mean-field theory, replica techniques, the Nishimori condition, variational methods, the dynamical mean-field theory, unsupervised learning, associative memory models, perceptron models, the chaos theory of recurrent neural networks, and eigen-spectrums of neural networks, walking new learners through the theories and must-have skillsets to understand and use neural networks. The book focuses on quantitative frameworks of neural network models where the underlying mechanisms can be precisely isolated by physics of mathematical beauty and theoretical predictions. It is a good reference for students, researchers, and practitioners in the area of neural networks.
Statistical Meso-Mechanics of Damage and Failure: Series Publication of Multiscale Mechanics
by Yilong Bai Mengfen Xia Fujiu KeThis book introduces a trans-scale framework necessary for the physical understanding of breakdown behaviors and presents some new paradigm to clarify the mechanisms underlying the trans-scale processes. The book, which is based on the interaction of mechanics and statistical physics, will help to deepen the understanding of how microdamage induces disaster and benefit the forecasting of the occurrence of catastrophic rupture. It offers notes and problems in each part as interesting background and illustrative exercises.Readers of the book would be graduate students, researchers, engineers working on civil, mechanical and geo-engineering, etc. However, people with various background but interested in disaster reduction and forecasting, like applied physics, geophysics, seismology, etc., may also be interested in the book.
Statistical Methods and Modeling of Seismogenesis
by Nikolaos Limnios Eleftheria Papadimitriou George TsaklidisThe study of earthquakes is a multidisciplinary field, an amalgam of geodynamics, mathematics, engineering and more. The overriding commonality between them all is the presence of natural randomness. Stochastic studies (probability, stochastic processes and statistics) can be of different types, for example, the black box approach (one state), the white box approach (multi-state), the simulation of different aspects, and so on. This book has the advantage of bringing together a group of international authors, known for their earthquake-specific approaches, to cover a wide array of these myriad aspects. A variety of topics are presented, including statistical nonparametric and parametric methods, a multi-state system approach, earthquake simulators, post-seismic activity models, time series Markov models with regression, scaling properties and multifractal approaches, selfcorrecting models, the linked stress release model, Markovian arrival models, Poisson-based detection techniques, change point detection techniques on seismicity models, and, finally, semi-Markov models for earthquake forecasting.
Statistical Methods and the Geographer
by S GregoryFirst published in 1978. Routledge is an imprint of Taylor & Francis, an informa company.
Statistical Methods for Climate Scientists
by Timothy DelSole Michael TippettA comprehensive introduction to the most commonly used statistical methods relevant in atmospheric, oceanic and climate sciences. Each method is described step-by-step using plain language, and illustrated with concrete examples, with relevant statistical and scientific concepts explained as needed. Particular attention is paid to nuances and pitfalls, with sufficient detail to enable the reader to write relevant code. Topics covered include hypothesis testing, time series analysis, linear regression, data assimilation, extreme value analysis, Principal Component Analysis, Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. The specific statistical challenges that arise in climate applications are also discussed, including model selection problems associated with Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. Requiring no previous background in statistics, this is a highly accessible textbook and reference for students and early-career researchers in the climate sciences.
Statistical Methods for Field and Laboratory Studies in Behavioral Ecology (Chapman & Hall/CRC Applied Environmental Statistics)
by Scott Pardo Michael PardoStatistical Methods for Field and Laboratory Studies in Behavioral Ecology focuses on how statistical methods may be used to make sense of behavioral ecology and other data. It presents fundamental concepts in statistical inference and intermediate topics such as multiple least squares regression and ANOVA. The objective is to teach students to recognize situations where various statistical methods should be used, understand the strengths and limitations of the methods, and to show how they are implemented in R code. Examples are based on research described in the literature of behavioral ecology, with data sets and analysis code provided. Features: This intermediate to advanced statistical methods text was written with the behavioral ecologist in mind Computer programs are provided, written in the R language. Datasets are also provided, mostly based, at least to some degree, on real studies. Methods and ideas discussed include multiple regression and ANOVA, logistic and Poisson regression, machine learning and model identification, time-to-event modeling, time series and stochastic modeling, game-theoretic modeling, multivariate methods, study design/sample size, and what to do when things go wrong. It is assumed that the reader has already had exposure to statistics through a first introductory course at least, and also has sufficient knowledge of R. However, some introductory material is included to aid the less initiated reader. Scott Pardo, Ph.D., is an accredited professional statistician (PStat®) by the American Statistical Association. Michael Pardo is a Ph.D. is a candidate in behavioral ecology at Cornell University, specializing in animal communication and social behavior.
Statistical Methods in Hydrology and Hydroclimatology (Springer Transactions in Civil and Environmental Engineering)
by Rajib MaityThis book focuses on the application of statistical methods in the field of hydrology and hydroclimatology. Among the latest theories being used in these fields, the book introduces the theory of copulas and its applications in this context. The purpose is to develop an understanding and illustrate the usefulness of the statistical techniques with detailed theory and numerous worked out examples. Apart from this, MATLAB-based codes and solutions of some worked out examples are also provided to assist the readers to handle real life data. This book presents a comprehensive knowledge of statistical techniques combining the basics of probability and the current advances in stochastic hydrology. Besides serving as a textbook for graduate courses on stochastic modeling in hydrology and related disciplines, the book offers valuable resources for researchers and professionals involved in the field of hydrology and climatology.
Statistical Modeling Using Bayesian Latent Gaussian Models: With Applications in Geophysics and Environmental Sciences
by Birgir HrafnkelssonThis book focuses on the statistical modeling of geophysical and environmental data using Bayesian latent Gaussian models. The structure of these models is described in a thorough introductory chapter, which explains how to construct prior densities for the model parameters, how to infer the parameters using Bayesian computation, and how to use the models to make predictions. The remaining six chapters focus on the application of Bayesian latent Gaussian models to real examples in glaciology, hydrology, engineering seismology, seismology, meteorology and climatology. These examples include: spatial predictions of surface mass balance; the estimation of Antarctica’s contribution to sea-level rise; the estimation of rating curves for the projection of water level to discharge; ground motion models for strong motion; spatial modeling of earthquake magnitudes; weather forecasting based on numerical model forecasts; and extreme value analysis of precipitation on a high-dimensional grid. The book is aimed at graduate students and experts in statistics, geophysics, environmental sciences, engineering, and related fields.
Statistical Optimal Transport: École d'Été de Probabilités de Saint-Flour XLIX – 2019 (Lecture Notes in Mathematics #2364)
by Sinho Chewi Jonathan Niles-Weed Philippe RigolletThis monograph aims to offer a concise introduction to optimal transport, quickly transitioning to its applications in statistics and machine learning. It is primarily tailored for students and researchers in these fields, yet it remains accessible to a broader audience of applied mathematicians and computer scientists. Each chapter is complemented with exercises for the reader to test their understanding. As such, this monograph is suitable for a graduate course on the topic of statistical optimal transport.
Statistical Physics
by Josef HonerkampThe application of statistical methods to physics is essential. This unique book on statistical physics offers an advanced approach with numerous applications to the modern problems students are confronted with. Therefore the text contains more concepts and methods in statistics than the student would need for statistical mechanics alone. Methods from mathematical statistics and stochastics for the analysis of data are discussed as well. The book is divided into two parts, focusing first on the modeling of statistical systems and then on the analysis of these systems. Problems with hints for solution help the students to deepen their knowledge. The third edition has been updated and enlarged with new sections deepening the knowledge about data analysis. Moreover, a customized set of problems with solutions is accessible on the Web at extras. springer. com.
Statistical Physics: A Probabilistic Approach
by Bernard H. LavendaSuitable for graduate students in chemical physics, statistical physics, and physical chemistry, this text develops an innovative, probabilistic approach to statistical mechanics. The treatment employs Gauss's principle and incorporates Bose-Einstein and Fermi-Dirac statistics to provide a powerful tool for the statistical analysis of physical phenomena. The treatment begins with an introductory chapter on entropy and probability that covers Boltzmann's principle and thermodynamic probability, among other topics. Succeeding chapters offer a case history of black radiation, examine quantum and classical statistics, and discuss methods of processing information and the origins of the canonical distribution. The text concludes with explorations of statistical equivalence, radiative and material phase transitions, and the kinetic foundations of Gauss's error law. Bibliographic notes complete each chapter.
Statistical Physics
by Nicolas Sator Nicolas Pavloff Lenaic CouedelThis book presents an introduction to the main concepts of statistical physics, followed by applications to specific problems and more advanced concepts, selected for their pedagogical or practical interest. Particular attention has been devoted to the presentation of the fundamental aspects, including the foundations of statistical physics, as well as to the discussion of important physical examples. Comparison of theoretical results with the relevant experimental data (with illustrative curves) is present through the entire textbook. This aspect is facilitated by the broad range of phenomena pertaining to statistical physics, providing example issues from domains as varied as the physics of classical and quantum liquids, condensed matter, liquid crystals, magnetic systems, astrophysics, atomic and molecular physics, superconductivity and many more. This textbook is intended for graduate students (MSc and PhD) and for those teaching introductory or advanced courses on statistical physics. Key Features: A rigorous and educational approach of statistical physics illustrated with concrete examples. A clear presentation of fundamental aspects of statistical physics. Many exercises with detailed solutions. Nicolas Sator is Associate Professor at Sorbonne University, Paris, France. He is a member of the Laboratory of Theoretical Physics of Condensed Matter (LPTMC) and his research focuses on the physics of liquids. Nicolas Pavloff is Professor at Paris-Saclay University, France. He is a member of Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS) and his domain of research is quantum fluid theory. Lénaïc Couëdel is Professor at the University of Sasktchewan, Saskatoon, Canada and researcher at CNRS, France. His research area is plasma physics with a focus on complex plasma crystals.
Statistical Physics for Biological Matter (Graduate Texts in Physics)
by Wokyung SungThis book aims to cover a broad range of topics in statistical physics, including statistical mechanics (equilibrium and non-equilibrium), soft matter and fluid physics, for applications to biological phenomena at both cellular and macromolecular levels. It is intended to be a graduate level textbook, but can also be addressed to the interested senior level undergraduate. The book is written also for those involved in research on biological systems or soft matter based on physics, particularly on statistical physics.Typical statistical physics courses cover ideal gases (classical and quantum) and interacting units of simple structures. In contrast, even simple biological fluids are solutions of macromolecules, the structures of which are very complex. The goal of this book to fill this wide gap by providing appropriate content as well as by explaining the theoretical method that typifies good modeling, namely, the method of coarse-grained descriptions that extract the most salient features emerging at mesoscopic scales. The major topics covered in this book include thermodynamics, equilibrium statistical mechanics, soft matter physics of polymers and membranes, non-equilibrium statistical physics covering stochastic processes, transport phenomena and hydrodynamics. Generic methods and theories are described with detailed derivations, followed by applications and examples in biology. The book aims to help the readers build, systematically and coherently through basic principles, their own understanding of nonspecific concepts and theoretical methods, which they may be able to apply to a broader class of biological problems.
Statistical Physics of Complex Systems
by Eric BertinThis course-tested primer 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. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting units, and on the other to predict the macroscopic, collective behavior of the system considered from the perspective of the microscopic laws governing the dynamics of the individual entities. These two goals are essentially also shared by what is now called 'complex systems science,' and as such, systems studied in the framework of statistical physics may be considered to be among the simplest examples of complex systems - while also offering a rather well developed mathematical treatment. The second edition has been significantly revised and expanded, featuring in particular three new chapters addressing 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. Yet, the original spirit of the book - to remain accessible to a broad, non-specialized readership - has been kept throughout: 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. From the reviews of the first edition: ". . . a good introduction to basic concepts of statistical physics and complex systems for students and researchers with an interest in complex systems in other fields . . . . " Georg Hebermehl, Zentralblatt MATH, Vol. 1237, 2012 ". . . this short text remains very refreshing for the mathematician. " Dimitri Petritis, Mathematical Reviews, Issue 2012k
Statistical Physics of Fields
by Mehran KardarWhile many scientists are familiar with fractals, fewer are familiar with scale-invariance and universality which underly the ubiquity of their shapes. These properties may emerge from the collective behaviour of simple fundamental constituents, and are studied using statistical field theories. Initial chapters connect the particulate perspective developed in the companion volume, to the coarse grained statistical fields studied here. Based on lectures taught by Professor Kardar at MIT, this textbook demonstrates how such theories are formulated and studied. Perturbation theory, exact solutions, renormalization groups, and other tools are employed to demonstrate the emergence of scale invariance and universality, and the non-equilibrium dynamics of interfaces and directed paths in random media are discussed. Ideal for advanced graduate courses in statistical physics, it contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set available to lecturers at www. cambridge. org/9780521873413.
The Statistical Physics of Fixation and Equilibration in Individual-Based Models
by Peter AshcroftThis thesis explores several interdisciplinary topics at the border of theoretical physics and biology, presenting results that demonstrate the power of methods from statistical physics when applied to neighbouring disciplines. From birth-death processes in switching environments to discussions on the meaning of quasi-potential landscapes in high-dimensional spaces, this thesis is a shining example of the efficacy of interdisciplinary research. The fields advanced in this work include game theory, the dynamics of cancer, and invasion of mutants in resident populations, as well as general contributions to the theory of stochastic processes. The background material provides an intuitive introduction to the theory and applications of stochastic population dynamics, and the use of techniques from statistical physics in their analysis. The thesis then builds on these foundations to address problems motivated by biological phenomena.
Statistical Physics of Nanoparticles in the Gas Phase (Springer Series on Atomic, Optical, and Plasma Physics #73)
by Klavs HansenThermal processes are ubiquitous and an understanding of thermal phenomena is essential for a complete description of the physics of nanoparticles, both for the purpose of modeling the dynamics of the particles and for the correct interpretation of experimental data.The second edition of this book follows the logic of first edition, with an emphasis on presentation of literature results and to guide the reader through derivations. Several topics have been added to the repertoire, notably magnetism, a fuller exposition of aggregation and the related area of nucleation theory. Also a new chapter has been added on the transient hot electron phenomenon. The book remains focused on the fundamental properties of nanosystems in the gas phase. Each chapter is enriched with additional new exercises and three Appendices provide additional useful material.
Statistical Physics of Non-Thermal Phase Transitions
by Sergey G. AbaimovThis book addresses the application of methods used in statistical physics to complex systems--from simple phenomenological analogies to more complex aspects, such as correlations, fluctuation-dissipation theorem, the concept of free energy, renormalization group approach and scaling. Statistical physics contains a well-developed formalism that describes phase transitions. It is useful to apply this formalism for damage phenomena as well. Fractals, the Ising model, percolation, damage mechanics, fluctuations, free energy formalism, renormalization group, and scaling, are some of the topics covered in Statistical Physics of Phase Transitions.
Statistical Physics of Particles
by Mehran KardarStatistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www. cambridge. org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.
Statistical Physics of Synchronization (SpringerBriefs in Complexity)
by Shamik Gupta Alessandro Campa Stefano RuffoThis book introduces and discusses the analysis of interacting many-body complex systems exhibiting spontaneous synchronization from the perspective of nonequilibrium statistical physics. While such systems have been mostly studied using dynamical system theory, the book underlines the usefulness of the statistical physics approach to obtain insightful results in a number of representative dynamical settings. Although it is intractable to follow the dynamics of a particular initial condition, statistical physics allows to derive exact analytical results in the limit of an infinite number of interacting units. Chapter one discusses dynamical characterization of individual units of synchronizing systems as well as of their interaction and summarizes the relevant tools of statistical physics. The latter are then used in chapters two and three to discuss respectively synchronizing systems with either a first- or a second-order evolution in time. This book provides a timely introduction to the subject and is meant for the uninitiated as well as for experienced researchers working in areas of nonlinear dynamics and chaos, statistical physics, and complex systems.
Statistical Physics of Wave Interactions
by Fabrizio AntenucciThis thesis reveals the utility of pursuing a statistical physics approach in the description of wave interactions in multimode optical systems. To that end, the appropriate Hamiltonian models are derived and their limits of applicability are discussed. The versatility of the framework allows the characterization of ordered and disordered lasers in open and closed cavities in a unified scheme, from standard mode-locking to random lasers. With the use of replica method and Monte Carlo simulations, the models are categorized on the basis of universal properties, and nontrivial predictions of experimental relevance are obtained. In particular, the approach makes it possible to nonperturbatively treat the interplay between disorder and nonlinearity and to envisage novel and fascinating physical phenomena such as glassy random lasers, providing a novel way to experimentally investigate replica symmetry breaking.
Statistical Rock Physics (Earth and Environmental Sciences Library)
by Gabor KorvinThe book is the first systematic and comprehensive treatise of stochastic models and computational tools that have emerged in rock-physics in the last 20 years. The field of statistical rock-physics is a part of rock-physics (Petrophysics). Its concepts, methods and techniques are borrowed from stochastic geometry and statistical physics. This discipline describes the interior geometry of rocks; derives their effective physical properties based on their random composition and the random arrangement of their constituents; and builds models to simulate the past geological processes that had formed the rock. The aim of the book is to help the readers to understand the claims, techniques and published results of this new field and—most importantly—to teach them in order to creatively apply stochastic geometry and statistical physics in their own research tasks. For this purpose, the underlying mathematics will be discussed in all sections of the book; numerical solutions will be highlighted; a full set of references will be provided; and theory will go hand-in-hand with practical applications to hydraulic permeability, electric conduction, rock failure, NMR, mechanics of random grain packings, as well as the compaction of shale.
Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences (Manchester Physics Series #29)
by R. J. BarlowThe Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A.C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Written by a physicist, Statistics is tailored to the needs of physical scientists, containing and explaining all they need to know. It concentrates on parameter estimation, especially the methods of Least Squares and Maximum Likelihood, but other techniques, such as hypothesis testing, Bayesian statistics and non-parametric methods are also included. Intended for reasonably numerate scientists it contains all the basic formulae, their derivations and applications, together with some more advanced ones. Statistics features: * Comprehensive coverage of the essential techniques physical scientists are likely to need. * A wealth of examples, and problems with their answers. * Flexible structure and organisation allows it to be used as a course text and a reference. * A review of the basics, so that little prior knowledge is required.
Statistics and Analysis of Scientific Data
by Massimiliano BonamenteStatistics and Analysis of Scientific Data covers the foundations of probability theory and statistics, and a number of numerical and analytical methods that are essential for the present-day analyst of scientific data. Topics covered include probability theory, distribution functions of statistics, fits to two-dimensional datasheets and parameter estimation, Monte Carlo methods and Markov chains. Equal attention is paid to the theory and its practical application, and results from classic experiments in various fields are used to illustrate the importance of statistics in the analysis of scientific data. The main pedagogical method is a theory-then-application approach, where emphasis is placed first on a sound understanding of the underlying theory of a topic, which becomes the basis for an efficient and proactive use of the material for practical applications. The level is appropriate for undergraduates and beginning graduate students, and as a reference for the experienced researcher. Basic calculus is used in some of the derivations, and no previous background in probability and statistics is required. The book includes many numerical tables of data, as well as exercises and examples to aid the students' understanding of the topic.
Statistics for Geography and Environmental Science
by Richard Harris Claire JarvisStatistics are important tools for validating theory, making predictions and engaging in policy research. They help to provide informed commentary about social and environmental issues, and to make the case for change. Knowledge of statistics is therefore a necessary skill for any student of geography or environmental science. This textbook is aimed at students on a degree course taking a module in statistics for the first time. It focuses on analysing, exploring and making sense of data in areas of core interest to physical and human geographers, and to environmental scientists. It covers the subject in a broadly conventional way from descriptive statistics, through inferential statistics to relational statistics but does so with an emphasis on applied data analysis throughout.