Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems.

This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation.

Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics.

A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.

The aim of this book is to summarize probabilistic safety assessment (PSA) of nuclear power plants (NPPs), and to demonstrate that NPPs can be considered a safe method of producing energy, even in light of the Fukushima accident. The book examines level 1 and 2 full power, low power and shutdown probabilistic safety assessment of WWER440 reactors, and summarizes the author s experience gained during the last 35 years. It provides useful examples taken from PSA training courses delivered by the author and organized by the International Atomic Energy Agency. Such training courses were organised in Argonne National Laboratory (Chicago, IL, USA), Abdus Salaam International Centre for Theoretical Physics (Trieste, Italy) in Malaysia, Vietnam and Jordan to support experts from developing countries.

The role of probabilistic safety assessment (PSA) for NPPs (nuclear power plants) is an estimation of the risks in absolute terms and in comparison with other risks of the technical and the natural world. Plant-specific PSAs are being prepared for the NPPs and being applied for detection of weaknesses, design improvement and backfitting, incident analysis, accident management, emergency preparedness, prioritization of research & development and support of regulatory activities.

There are three levels of PSA, being performed for full power and low power operation and shutdown operating modes of the plant: Level 1 PSA, Level 2 PSA and Level 3 PSA. The nuclear regulatory authorities do not require the level 3 PSA for NPPs in the member countries of the European Union. So, only limited number of NPPs has available the level 3 PSA in Europe. However, in the light of the Fukushima accident the performance of such analyses is strongly recommended in the future. This book is intended for professionals working in the nuclear industry, and researchers and students interested in nuclear research.

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The theory of stochastic processes, for science and engineering, can be considered as an extension of probability theory allowing modeling of the evolution of systems over time. The modern theory of Markov processes has its origins in the studies of A.A. Markov (1856-1922) on sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon Brownian motion. The theory of stochastic processes entered in a period of intensive development when the idea of Markov property was brought in. This book is a modern overall view of semi-Markov processes and its applications in reliability. It is accessible to readers with a first course in Probability theory (including the basic notions of Markov chain). The text contains many examples which aid in the understanding of the theoretical notions and shows how to apply them to concrete physical situations including algorithmic simulations. Many examples of the concrete applications in reliability are given. Features: * Processes associated to semi-Markov kernel for general and discrete state spaces * Asymptotic theory of processes and of additive functionals * Statistical estimation of semi-Markov kernel and of reliability function * Monte Carlo simulation * Applications in reliability and maintenance The book is a valuable resource for understanding the latest developments in Semi-Markov Processes and reliability. Practitioners, researchers and professionals in applied mathematics, control and engineering who work in areas of reliability, lifetime data analysis, statistics, probability, and engineering will find this book an up-to-date overview of the field.

Queueing network models have been widely applied as a powerful tool for modelling, performance evaluation, and prediction of discrete flow systems, such as computer systems, communication networks, production lines, and manufacturing systems. Queueing network models with finite capacity queues and blocking have been introduced and applied as even more realistic models of systems with finite capacity resources and with population constraints. In recent years, research in this field has grown rapidly. Analysis of Queueing Networks with Blocking introduces queueing network models with finite capacity and various types of blocking mechanisms. It gives a comprehensive definition of the analytical model underlying these blocking queueing networks. It surveys exact and approximate analytical solution methods and algorithms and their relevant properties. It also presents various application examples of queueing networks to model computer systems and communication networks. This book is organized in three parts. Part I introduces queueing networks with blocking and various application examples. Part II deals with exact and approximate analysis of queueing networks with blocking and the condition under which the various techniques can be applied. Part III presents a review of various properties of networks with blocking, describing several equivalence properties both between networks with and without blocking and between different blocking types. Approximate solution methods for the buffer allocation problem are presented.

Expert testimony relying on scientific and other specialized evidence has come under increased scrutiny by the legal system. A trilogy of recent U.S. Supreme Court cases has assigned judges the task of assessing the relevance and reliability of proposed expert testimony. In conjunction with the Federal judiciary, the American Association for the Advancement of Science has initiated a project to provide judges indicating a need with their own expert. This concern with the proper interpretation of scientific evidence, especially that of a probabilistic nature, has also occurred in England, Australia and in several European countries. Statistical Science in the Courtroom is a collection of articles written by statisticians and legal scholars who have been concerned with problems arising in the use of statistical evidence. A number of articles describe DNA evidence and the difficulties of properly calculating the probability that a random individual's profile would "match" that of the evidence as well as the proper way to intrepret the result. In addition to the technical issues, several authors tell about their experiences in court. A few have become disenchanted with their involvement and describe the events that led them to devote less time to this application. Other articles describe the role of statistical evidence in cases concerning discrimination against minorities, product liability, environmental regulation, the appropriateness and fairness of sentences and how being involved in legal statistics has raised interesting statistical problems requiring further research.

The title High Dimensional Probability is an attempt to describe the many trib utaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970's. In each of these fields it is necessary to consider large classes of stochastic processes under minimal conditions. There are rewards in re search of this sort. One can often gain deep insights, even about familiar processes, by stripping away details that in hindsight turn out to be extraneous. Many of the problems that motivated researchers in the 1970's were solved. But the powerful new tools created for their solution, such as randomization, isoperimetry, concentration of measure, moment and exponential inequalities, chaining, series representations and decoupling turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new ap proach to the study of aspects of Levy processes and Markov processes in general. Papers on these topics as well as on the continuing study of Gaussian processes and probability in Banach are included in this volume."

This thesis presents a new method for following evolving interactions between coupled oscillatory systems of the kind that abound in nature. Examples range from the subcellular level, to ecosystems, through climate dynamics, to the movements of planets and stars. Such systems mutually interact, adjusting their internal clocks, and may correspondingly move between synchronized and non-synchronized states. The thesis describes a way of using Bayesian inference to exploit the presence of random fluctuations, thus analyzing these processes in unprecedented detail. It first develops the basic theory of interacting oscillators whose frequencies are non-constant, and then applies it to the human heart and lungs as an example. Their coupling function can be used to follow with great precision the transitions into and out of synchronization. The method described has the potential to illuminate the ageing process as well as to improve diagnostics in cardiology, anesthesiology and neuroscience, and yields insights into a wide diversity of natural processes.

This book covers all types of literature on existing trend analysis approaches, but more than 60% of the methodologies are developed here and some of them are reflected to scientific literature and others are also innovative versions, modifications or improvements. The suggested methodologies help to design, develop, manage and deliver scientific applications and training to meet the needs of interested staff in companies, industries and universities including students. Technical content and expertise are also provided from different theoretical and especially active roles in the design, development and delivery of science in particular and economics and business in general. It is also ensured that, wherever possible and technically appropriate, priority is given to the inclusion and integration of real life data, examples and processes within the book content. The time seems right, because available books just focus on special sectors (fashion, social, business). This book reviews all the available trend approaches in the present literature on rational and logical bases.

This volume gathers selected peer-reviewed papers presented at the XXVI International Joint Conference on Industrial Engineering and Operations Management (IJCIEOM), held on July 8-11, 2020 in Rio de Janeiro, Brazil. The respective chapters address a range of timely topics in industrial engineering, including operations and process management, global operations, managerial economics, data science and stochastic optimization, logistics and supply chain management, quality management, product development, strategy and organizational engineering, knowledge and information management, work and human factors, sustainability, production engineering education, healthcare operations management, disaster management, and more. These topics broadly involve fields like operations, manufacturing, industrial and production engineering, and management. Given its scope, the book offers a valuable resource for those engaged in optimization research, operations research, and practitioners alike.

Immediately implementable code, with extensive and varied illustrations of graph variants and layouts. Examples and exercises across a variety of real-life contexts including business, politics, education, social media and crime investigation. Dedicated chapter on graph visualization methods. Practical walkthroughs of common methodological uses: finding influential actors in groups, discovering hidden community structures, facilitating diverse interaction in organizations, detecting political alignment, determining what influences connection and attachment. Various downloadable data sets for use both in class and individual learning projects. Final chapter dedicated to individual or group project examples.

With the boom of big data and machine learning and the subsequent need for parallel processing technologies, fork-join queues are more relevant now than ever before. In this book, new estimates of the average response time in fork-join queues are proposed, which form the basis for new research opportunities. Analysis of Fork-Join Systems: Network of Queues with Precedence Constraints explores numerical approaches to estimate the average response time of fork-join queueing networks and offers never before published simple expressions for the mean response time as conjectures. Extensive experiments are included to demonstrate the remarkable accuracy of the conjectures and algorithms used in the estimation of the average response time. Graduate students, professors, and researchers in the fields of operations research, management science, industrial engineering, computer science, and electrical engineering will find this book very useful. Students, as well as researchers in both academia and industry, will also find this book of great help when looking for results related to fork-join queues

This book offers an overview on the main modern important topics in random variables, random processes, and decision theory for solving real-world problems. After an introduction to concepts of statistics and signals, the book introduces many essential applications to signal processing like denoising, texture classification, histogram equalization, deep learning, or feature extraction. The book uses MATLAB algorithms to demonstrate the implementation of the theory to real systems. This makes the contents of the book relevant to students and professionals who need a quick introduction but practical introduction how to deal with random signals and processes

Unique blend of asymptotic theory and small sample practice through simulation experiments and data analysis.

Novel reproducing kernel Hilbert space methods for the analysis of smoothing splines and local polynomials. Leading to uniform error bounds and honest confidence bands for the mean function using smoothing splines

Exhaustive exposition of algorithms, including the Kalman filter, for the computation of smoothing splines of arbitrary order.

Highly recommended by JASA, Technometrics, and other leading statistical journals, the first two editions of this bestseller showed how to easily perform complex linear mixed model (LMM) analyses via a variety of software programs. Linear Mixed Models: A Practical Guide Using Statistical Software, Third Edition continues to lead readers step-by-step through the process of fitting LMMs. The third edition provides a comprehensive update of the available tools for fitting linear mixed-effects models in the newest versions of SAS, SPSS, R, Stata, and HLM. All examples have been updated, with a focus on new tools for visualization of results and interpretation. New conceptual and theoretical developments in mixed-effects modeling have been included, and there is a new chapter on power analysis for mixed-effects models. Features:*Dedicates an entire chapter to the key theories underlying LMMs for clustered, longitudinal, and repeated measures data *Provides descriptions, explanations, and examples of software code necessary to fit LMMs in SAS, SPSS, R, Stata, and HLM *Contains detailed tables of estimates and results, allowing for easy comparisons across software procedures *Presents step-by-step analyses of real-world data sets that arise from a variety of research settings and study designs, including hypothesis testing, interpretation of results, and model diagnostics *Integrates software code in each chapter to compare the relative advantages and disadvantages of each package *Supplemented by a website with software code, datasets, additional documents, and updates Ideal for anyone who uses software for statistical modeling, this book eliminates the need to read multiple software-specific texts by covering the most popular software programs for fitting LMMs in one handy guide. The authors illustrate the models and methods through real-world examples that enable comparisons of model-fitting options and results across the software procedures.

This book contains the lectures given at the Conference on Dynamics and Randomness held at the Centro de Modelamiento Matematico of the Universidad de Chile from December 11th to 15th, 2000. This meeting brought together mathematicians, theoretical physicists and theoretical computer scientists, and graduate students interested in fields re lated to probability theory, ergodic theory, symbolic and topological dynam ics. We would like to express our gratitude to all the participants of the con ference and to the people who contributed to its organization. In particular, to Pierre Collet, Bernard Host and Mike Keane for their scientific advise. VVe want to thank especially the authors of each chapter for their well prepared manuscripts and the stimulating conferences they gave at Santiago. We are also indebted to our sponsors and supporting institutions, whose interest and help was essential to organize this meeting: ECOS-CONICYT, FONDAP Program in Applied Mathematics, French Cooperation, Fundacion Andes, Presidential Fellowship and Universidad de Chile. We are grateful to Ms. Gladys Cavallone for their excellent work during the preparation of the meeting as well as for the considerable task of unifying the typography of the different chapters of this book."

Developed from the Second International Congress on Actuarial Science and Quantitative Finance, this volume showcases the latest progress in all theoretical and empirical aspects of actuarial science and quantitative finance. Held at the Universidad de Cartagena in Cartegena, Colombia in June 2016, the conference emphasized relations between industry and academia and provided a platform for practitioners to discuss problems arising from the financial and insurance industries in the Andean and Caribbean regions. Based on invited lectures as well as carefully selected papers, these proceedings address topics such as statistical techniques in finance and actuarial science, portfolio management, risk theory, derivative valuation and economics of insurance.

1. 1 Introduction This book is written in four major divisions. The first part is the introductory chapters consisting of Chapters 1 and 2. In part two, Chapters 3-11, we develop fuzzy estimation. For example, in Chapter 3 we construct a fuzzy estimator for the mean of a normal distribution assuming the variance is known. More details on fuzzy estimation are in Chapter 3 and then after Chapter 3, Chapters 4-11 can be read independently. Part three, Chapters 12- 20, are on fuzzy hypothesis testing. For example, in Chapter 12 we consider the test Ho : /1 = /10 verses HI : /1 f=- /10 where /1 is the mean of a normal distribution with known variance, but we use a fuzzy number (from Chapter 3) estimator of /1 in the test statistic. More details on fuzzy hypothesis testing are in Chapter 12 and then after Chapter 12 Chapters 13-20 may be read independently. Part four, Chapters 21-27, are on fuzzy regression and fuzzy prediction. We start with fuzzy correlation in Chapter 21. Simple linear regression is the topic in Chapters 22-24 and Chapters 25-27 concentrate on multiple linear regression. Part two (fuzzy estimation) is used in Chapters 22 and 25; and part 3 (fuzzy hypothesis testing) is employed in Chapters 24 and 27. Fuzzy prediction is contained in Chapters 23 and 26. A most important part of our models in fuzzy statistics is that we always start with a random sample producing crisp (non-fuzzy) data.

This volume highlights Prof. Hira Koul's achievements in many areas of Statistics, including Asymptotic theory of statistical inference, Robustness, Weighted empirical processes and their applications, Survival Analysis, Nonlinear time series and Econometrics, among others. Chapters are all original papers that explore the frontiers of these areas and will assist researchers and graduate students working in Statistics, Econometrics and related areas. Prof. Hira Koul was the first Ph.D. student of Prof. Peter Bickel. His distinguished career in Statistics includes the receipt of many prestigious awards, including the Senior Humbolt award (1995), and dedicated service to the profession through editorial work for journals and through leadership roles in professional societies, notably as the past president of the International Indian Statistical Association. Prof. Hira Koul has graduated close to 30 Ph.D. students, and made several seminal contributions in about 125 innovative research papers. The long list of his distinguished collaborators is represented by the contributors to this volume.

The Palm theory and the Loynes theory of stationary systems are the two pillars of the modern approach to queuing. This book, presenting the mathematical foundations of the theory of stationaryqueuing systems, contains a thorough treatment of both of these.

This approach helps to clarify the picture, in that it separates the task of obtaining the key system formulas from that of proving convergence to a stationary state and computing its law.

The theory is constantly illustrated by classical results and models: Pollaczek-Khintchin and Tacacs formulas, Jackson and Gordon-Newell networks, multiserver queues, blocking queues, loss systems etc., but it also contains recent and significant examples, where the tools developed turn out to be indispensable.

Several other mathematical tools which are useful within this approach are also presented, such as the martingale calculus for point processes, or stochastic ordering for stationary recurrences.

This thoroughly revised second edition contains substantial additions - in particular, exercises and their solutions - rendering this now classic reference suitable for use as a textbook.

This book explores all relevant aspects of net scoring, also known as uplift modeling: a data mining approach used to analyze and predict the effects of a given treatment on a desired target variable for an individual observation. After discussing modern net score modeling methods, data preparation, and the assessment of uplift models, the book investigates software implementations and real-world scenarios. Focusing on the application of theoretical results and on practical issues of uplift modeling, it also includes a dedicated chapter on software solutions in SAS, R, Spectrum Miner, and KNIME, which compares the respective tools. This book also presents the applications of net scoring in various contexts, e.g. medical treatment, with a special emphasis on direct marketing and corresponding business cases. The target audience primarily includes data scientists, especially researchers and practitioners in predictive modeling and scoring, mainly, but not exclusively, in the marketing context.

Scientists today collect samples of curves and other functional observations. This monograph presents many ideas and techniques for such data. Included are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drwan from growth analysis, meterology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, to applied data analysts, and to experienced researchers; it will have value both within statistics and across a broad spectrum of other fields. Much of the material is based on the authors' own work, some of which appears here for the first time. Jim Ramsay is Professor of Psychology at McGill University and is an international authority on many aspects of multivariate analysis. He draws on his collaboration with researchers in speech articulation, motor control, meteorology, psychology, and human physiology to illustrate his technical contributions to functional data analysis in a wide range of statistical and application journals. Bernard Silverman, author of the highly regarded "Density Estimation for Statistics and DataAnalysis," and coauthor of "Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach," is Professor of Statistics at Bristol University. His published work on smoothing methods and other aspects of applied, computational, and theoretical statistics has been recognized by the Presidents' Award of the Committee of Presidents of Statistical Societies, and the award of two Guy Medals by the Royal Statistical Society.

This volume begins with a description of Alladi Ramakrishnan's remarkable scientific career and his grand vision that led to the creation of The Institute of Mathematical Sciences (MATSCIENCE), in Madras (now Chennai), India, in 1962. The lists of his research publications, his PhD students, and other relevant facts relating to his eventful career are included. The inclusion of both research and survey articles by leading mathematicians, statisticians, and physicists who got to know Alladi Ramakrishnan over the years and admired his significant contributions to research and to the scientific profession, have been written and dedicated in this volume to Ramakrishnan's memory.

Resonances are ubiquitous in dynamical systems with many degrees of freedom. They have the basic effect of introducing slow-fast behavior in an evolutionary system which, coupled with instabilities, can result in highly irregular behavior. This book gives a unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, a general finite dimensional theory of homoclinic jumping is developed and illustrated with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context. Previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds are described. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics. The theory is further used to study resonances in Hamiltonian systems with applications to molecular dynamics and rigid body motion. The final chapter contains an infinite dimensional extension of the finite dimensional theory, with application to the perturbed nonlinear Schrodinger equation and coupled NLS equations."

The intersection of probability and physics has been a rich and explosive area of growth in the past two decades, specifically covering such subjects as percolation theory, random walks, interacting particle systems, and various topics related to statistical mechanics. In the last several years, substantial progress has been made in a number of directions: fluctuations of 2-dimensional growth processes, Wulf constructions in higher dimensions for percolation, Potts and Ising models, classification of random walks in random environments, the introduction of the stochastic Loewner equation, the rigorous proof of intersection exponents for planar Brownian motion, and finally the proof of conformal invariance for critical percolation on the triangular lattice. This volume consists of a collection of invited articles, written by some of the most distinguished probabilists in the above-mentioned areas, most of whom were personally responsible for advances in the various subfields of probability. All of the articles are an outgrowth of the Fourth Brazilian School of Probability, held in Mambucaba, Brazil, August 2000. Contributors: K. Alexander * J.M. AzaAs * J. van den Berg * T. Bodineau * F. Camia * N. Cancrini * G. Grimmett * P. Hiemer * A.E. Holroyd * H. Kesten * G.F. Lawler * T.M. Liggett * J. Lorinczi * F. Martinelli * C. M. Newman * J. Quastel * C.-E. Pfister * M. PrAhofer * C. Roberto * O. Schramm * V. Sidoravicius * H. Spohn * A. Toom * B. TA3th * D. Ueltschi * W. Werner * M. Wschebor * M. WA1/4thrich Graduate students and researchers in probability theory and math physics will find this book a useful reference.

This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. It is based on lectures given at the international conference Fourier Analysis and Pseudo-Differential Operators, June 25 30, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series Fourier Analysis and Partial Differential Equations. "