The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects.

The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.

Continuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics. Developed over the last two decades, it is based on the mathematical theory of nonlinear thermoelasticity, in which a new viewpoint on material symmetry, motivated by molecular theories, plays a central role.

This is the first organized presentation of a nonlinear elastic approach to twinning and displacive phase transition in crystalline solids. The authors develop geometry, kinematics, and energy invariance in crystals in strong connection and with the purpose of investigating the actual mechanical aspects of the phenomena, particularly in an elastostatics framework based on the minimization of a thermodynamic potential. Interesting for both mechanics and mathematical analysis, the new theory offers the possibility of investigating the formation of microstructures in materials undergoing martensitic phase transitions, such as shape-memory alloys.

Although phenomena such as twinning and phase transitions were once thought to fall outside the range of elastic models, research efforts in these areas have proved quite fruitful. Relevant to a variety of disciplines, including mathematical physics, continuum mechanics, and materials science, Continuum Models for Phase Transitions and Twinning in Crystals is your opportunity to explore these current research methods and topics.

Many methods for analyzing clustered data exist, all with advantages and limitations in particular applications. Compiled from the contributions of leading specialists in the field, Topics in Modelling of Clustered Data describes the tools and techniques for modelling the clustered data often encountered in medical, biological, environmental, and social science studies. It focuses on providing a comprehensive treatment of marginal, conditional, and random effects models using, among others, likelihood, pseudo-likelihood, and generalized estimating equations methods.

The authors motivate and illustrate all aspects of these models in a variety of real applications. They discuss several variations and extensions, including individual-level covariates and combined continuous and discrete outcomes. Flexible modelling with fractional and local polynomials, omnibus lack-of-fit tests, robustification against misspecification, exact, and bootstrap inferential procedures all receive extensive treatment. The applications discussed center primarily, but not exclusively, on developmental toxicity, which leads naturally to discussion of other methodologies, including risk assessment and dose-response modelling.

Clearly written, Topics in Modelling of Clustered Data offers a practical, easily accessible survey of important modelling issues. Overview models give structure to a multitude of approaches, figures help readers visualize model characteristics, and a generous use of examples illustrates all aspects of the modelling process.

In this book, a number of experts from various disciplines take a look at three different strands in learning to model. They examine the activity of modeling from disparate theoretical standpoints, taking into account the individual situation of the individuals involved. The chapters seek to bridge the modeling of communication and the modeling of particular scientific domains. In so doing, they seek to throw light on the educational communication that goes on in conceptual learning.
Taken together, the chapters brought together in this volume illustrate the diversity and vivacity of research on a relatively neglected, yet crucially important aspect of education across disciplines: learning to model. A common thread across the research presented is the view that communication and interaction, as fundamental to most educational practices and as a repository of conceptual understanding and a learning mechanism in itself, is intimately linked to elaborating meaningful, coherent, and valid representations of the world.
The editors hope this volume will contribute to both the fundamental research in its field and ultimately provide results that can be of practical value in designing new situations for teaching and learning modeling, particularly those involving computers.

A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers. Members of the editorial board of this series consists of following prominent economists and mathematicians: Managing Editors: S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.) Editors: R. Anderson (U.C.Berkeley), C. Castaing (Univ. Montpellier), F. H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeleyer), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J. -M. Grandmont (CREST-CNRS), N. Hirano (Yokohama National Univ.), L. Hurwicz (Univ. of Minnesota), T. Ichiishi (Ohio State Univ.), A. Ioffe (Israel Institute of Technology), S. Iwamoto (Kyushu Univ.), K. Kamiya (Univ. Tokyo), K. Kawamata (Keio Univ.), N. Kikuchi (Keio Univ.), H. Matano (Univ. Tokyo), K. Nishimura (Kyoto Univ.), M. K. Richter (Univ. Minnesota), Y. Takahashi (Kyoto Univ.), M. Valadier (Univ. Montpellier II), M. Yano (Keio Univ).

Particle methods have seen increasing use in several engineering and scientific fields, both because of their unique modelling capabilities and the availability of the necessary computational power. This title focuses on their theory and application.

Mathematical modeling is becoming increasingly versatile and multi-disciplinary. This text demonstrates the broadness of this field as the authors consider the principles of model construction and use common approaches to build models from a range of subject areas. The book reflects the interests and experiences of the authors, but it explores mathematical modeling across a wide range of applications, from mechanics to social science. A general approach is adopted, where ideas and examples are favored over rigorous mathematical procedures. This insightful book will be of interest to specialists, teachers, and students across a wide range of disciplines..

This book examines how individuals behave across time and to what degree that behavior changes, fluctuates, or remains stable.

It features the most current methods on modeling repeated measures data as reported by a distinguished group of experts in the field. The goal is to make the latest techniques used to assess intraindividual variability accessible to a wide range of researchers. Each chapter is written in a "user-friendly" style such that even the "novice" data analyst can easily apply the techniques.

Each chapter features:

• a minimum discussion of mathematical detail;
• an empirical example applying the technique; and
• a discussion of the software related to that technique.

Content highlights include analysis of mixed, multi-level, structural equation, and categorical data models. It is ideal for researchers, professionals, and students working with repeated measures data from the social and behavioral sciences, business, or biological sciences.

The authors of this monograph have developed a large and important class of survival analysis models that generalize most of the existing models. In a unified, systematic presentation, this monograph fully details those models and explores areas of accelerated life testing usually only touched upon in the literature.

Accelerated Life Models: Modeling and Statistical Analysis presents models, methods of data collection, and statistical analysis for failure-time regression data in accelerated life testing and for degradation data with explanatory variables. In addition to the classical results, the authors devote considerable attention to models with time-varying explanatory variables and to methods of semiparametric estimation. They also examine the simultaneous analysis of degradation and failure-time data when the intensities of failure in different modes depend on the level of degradation and the values of explanatory variables.

The authors avoid technical details by explaining the ideas and referring to resources where thorough analysis can be found. Whether used for teaching, research or general reference, Accelerated Life Models: Modeling and Statistical Analysis provides new and known models and modern methods of accelerated life data analysis.

This book is a unique combination of a basic guide to general analog circuit simulation and a SPICE OPUS software manual, which may be used as a textbook or self-study reference. The book is divided into three parts: mathematical theory of circuit analysis, a crash course on SPICE OPUS, and a complete SPICE OPUS reference guide. All simulations as well as the free simulator software may be directly downloaded from the SPICE OPUS homepage: www.spiceopus.si.

Circuit Simulation with SPICE OPUS is intended for a wide audience of undergraduate and graduate students, researchers, and practitioners in electrical and systems engineering, circuit design, and simulation development.

Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.

The articles collected in this volume represent the contributions presented at the IMA workshop on "Dynamics of Algorithms" which took place in November 1997. The workshop was an integral part of the 1997 -98 IMA program on "Emerging Applications of Dynamical Systems." The interaction between algorithms and dynamical systems is mutually beneficial since dynamical methods can be used to study algorithms that are applied repeatedly. Convergence, asymptotic rates are indeed dynamical properties. On the other hand, the study of dynamical systems benefits enormously from having efficient algorithms to compute dynamical objects.

This monograph on measurement error and misclassification covers a broad range of problems and emphasizes unique features in modeling and analyzing problems arising from medical research and epidemiological studies. Many measurement error and misclassification problems have been addressed in various fields over the years as well as with a wide spectrum of data, including event history data (such as survival data and recurrent event data), correlated data (such as longitudinal data and clustered data), multi-state event data, and data arising from case-control studies. Statistical Analysis with Measurement Error or Misclassification: Strategy, Method and Application brings together assorted methods in a single text and provides an update of recent developments for a variety of settings. Measurement error effects and strategies of handling mismeasurement for different models are closely examined in combination with applications to specific problems. Readers with diverse backgrounds and objectives can utilize this text. Familiarity with inference methods-such as likelihood and estimating function theory-or modeling schemes in varying settings-such as survival analysis and longitudinal data analysis-can result in a full appreciation of the material, but it is not essential since each chapter provides basic inference frameworks and background information on an individual topic to ease the access of the material. The text is presented in a coherent and self-contained manner and highlights the essence of commonly used modeling and inference methods. This text can serve as a reference book for researchers interested in statistical methodology for handling data with measurement error or misclassification; as a textbook for graduate students, especially for those majoring in statistics and biostatistics; or as a book for applied statisticians whose interest focuses on analysis of error-contaminated data. Grace Y. Yi is Professor of Statistics and University Research Chair at the University of Waterloo. She is the 2010 winner of the CRM-SSC Prize, an honor awarded in recognition of a statistical scientist's professional accomplishments in research during the first 15 years after having received a doctorate. She is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute.

The prolonged boom in the US and European stock markets has led to increased interest in the mathematics of security markets, most notably in the theory of stochastic integration. This text gives a rigorous development of the theory of stochastic integration as it applies to the valuation of derivative securities. It includes all the tools necessary for readers to understand how the stochastic integral is constructed with respect to a general continuous martingale.

The author develops the stochastic calculus from first principles, but at a relaxed pace that includes proofs that are detailed, but streamlined to applications to finance. The treatment requires minimal prerequisites-a basic knowledge of measure theoretic probability and Hilbert space theory-and devotes an entire chapter to application in finances, including the Black Scholes market, pricing contingent claims, the general market model, pricing of random payoffs, and interest rate derivatives.

Continuous Stochastic Calculus with Application to Finance is your first opportunity to explore stochastic integration at a reasonable and practical mathematical level. It offers a treatment well balanced between aesthetic appeal, degree of generality, depth, and ease of reading.

Designed for undergraduate and graduate students interested in learning basic soil physics and its application to environment, soil health, water quality and productivity, this book provides readers with a clear coverage of the basic principles of water and solute transport through vadose zone, the theory behind transport and step-by-step guidance on how to use current computer models in the public domain along with soil erosion and contaminant remediation. Students will develop a deeper understanding of the fundamental processes within the soil profile that control water infiltration, redistribution, evapotranspiration, drainage, and erosion. The updated second edition features two new chapters, highlighting new problems, new computer models, and remediation. Features Serves as the most up-to-date textbook on soil physics available. Includes two new chapters and many new numerical examples. Offers mathematical descriptions supported by simplified explanations. Provides case studies and step-by-step guidance on how to use public domain computer models. Covers all principles and processes in an easy-to-understand format with numerous illustrations and sample problems. Students studying in the fields of Soil Science, Environment Science, Natural Resources, Agriculture Engineering, Civil Engineering, Environmental Engineering, Range Sciences, Horticulture, Crop Sciences, and Forestry, will find this book provides a solid foundation for their studies. Professionals, researchers, academicians, and companies working in fields related to Environmental Science, Soil Physics, Hydrology, and irrigation, will find this book is a great reference tool as it is the most up to date in its field.

Almost all materials posses a microstructure, which cannot be accounted for in detail in structural engineering calculations. Instead, effective material properties are used. These are obtained by homogenization methods. This book provides

Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.

Statistical inference carries great significance in model building from both the theoretical and the applications points of view. Its applications to engineering and economic systems, financial economics, and the biological and medical sciences have made statistical inference for stochastic processes a well-recognized and important branch of statistics and probability.
The class of semimartingales includes a large class of stochastic processes, including diffusion type processes, point processes, and diffusion type processes with jumps, widely used for stochastic modeling. Until now, however, researchers have had no single reference that collected the research conducted on the asymptotic theory for semimartingales.

Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for stochastic processes. The author brings together into one volume the state-of-the-art in the inferential aspect for such processes. The topics discussed include:

· Asymptotic likelihood theory
· Quasi-likelihood
· Likelihood and efficiency
· Inference for counting processes
· Inference for semimartingale regression models

The author addresses a number of stochastic modeling applications from engineering, economic systems, financial economics, and medical sciences. He also includes some of the new and challenging statistical and probabilistic problems facing today's active researchers working in the area of inference for stochastic processes.

Practical Handbook of Genetic Algorithms, Volume 3: Complex Coding Systems contains computer-code examples for the development of genetic algorithm systems - compiling them from an array of practitioners in the field.
Each contribution of this singular resource includes:
unique code segments
documentation
description of the operations performed
rationale for the chosen approach
problems the code overcomes or addresses
Practical Handbook of Genetic Algorithms, Volume 3: Complex Coding Systems complements the first two volumes in the series by offering examples of computer code. The first two volumes dealt with new research and an overview of the types of applications that could be taken with GAs. This volume differs from its predecessors by specifically concentrating on specific functions in genetic algorithms, serving as the only compilation of useful and usable computer code in the field.

Anti-scientific misinformation has become a serious problem on many fronts, including vaccinations and climate change. One of these fronts is the persistence of anti-evolutionism, which has recently been given a superficially professional gloss in the form of the intelligent design movement. Far from solely being of interest to researchers in biology, anti-evolutionism must be recognized as part of a broader campaign with a conservative religious and political agenda. Much of the rhetorical effectiveness of anti-evolutionism comes from its reliance on seemingly precise mathematical arguments. This book, the first of its kind to be written by a mathematician, discusses and refutes these arguments. Along the way, it also clarifies common misconceptions about both biology and mathematics. Both lay audiences and professionals will find the book to be accessible and informative.

The World Wide Web is growing in size at a remarkable rate.  It is a huge evolving system and its data are rife with uncertainties.  Probability and statistics are the fundamental mathematical tools that enable us to model, reason and infer meaningful results from such data.  Modelling the Internet and the Web covers the most important aspects of modeling the Web using a modern mathematical and probabilistic treatment.  It focuses on the information and application layers, as well as some of the merging properties of the Internet.

• Provides a comprehensive introduction to the modeling of the Internet and Web at the information  level.
• Takes a modern approach based on mathematical, probabilistic and graphical modeling.
• Provides an integrated presentation of theory, examples, exercies and applications.
• Covers key topics such as text analysis, link analysis, crawling techniques, human behaviour, and commerce on the Web.

Interdisciplinary in nature, Modeling the Internet and the Web will be of interest to students and researchers from a variety of disciplines including computer science, machine learning, engineering, statistics, economics, business and the social sciences.

Dynamic management of systems development is a precondition for the realization of sustainable system development. This approach allows for the usage of systems theory methods that take into consideration the interaction of decisions made over time and space. A characteristic feature of this kind of method is that the process of sophisticated object development over time is examined for optimal decision selection. This requires the application of modelling methods that represent properties of the developing objects, high speed calculation methods for the estimation of technical and economic characteristics, as well as effective optimization methods. Dynamic Management of Sustainable Development presents a concise summary of the authors' research in the area of dynamic methods analysis of technical systems development. Along with systematic illustration of mathematical methods, considerable attention is drawn to practical realization and applications. Dynamic Management of Sustainable Development will be helpful for scientists involved in the mathematical modelling of large technical systems development and for engineers working in the area of large technical systems planning.

7. 1. 1 Background Uncertainty can be considered as the lack of adequate information to make a decision. It is important to quantify uncertainties in mathematical models used for design and optimization of nondeterministic engineering systems. In general, - certainty can be broadly classi?ed into three types (Bae et al. 2004; Ha-Rok 2004; Klir and Wierman 1998; Oberkampf and Helton 2002; Sentz 2002). The ?rst one is aleatory uncertainty (also referred to as stochastic uncertainty or inherent - certainty) - it results from the fact that a system can behave in random ways. For example, the failure of an engine can be modeled as an aleatory uncertaintybecause the failure can occur at a random time. One cannot predict exactly when the engine will fail even if a large quantity of failure data is gathered (available). The second one is epistemic uncertainty (also known as subjective uncertainty or reducible - certainty) - it is the uncertainty of the outcome of some random event due to lack of knowledge or information in any phase or activity of the modeling process. By gaining information about the system or environmental factors, one can reduce the epistemic uncertainty. For example, a lack of experimental data to characterize new materials and processes leads to epistemic uncertainty.

Anti-scientific misinformation has become a serious problem on many fronts, including vaccinations and climate change. One of these fronts is the persistence of anti-evolutionism, which has recently been given a superficially professional gloss in the form of the intelligent design movement. Far from solely being of interest to researchers in biology, anti-evolutionism must be recognized as part of a broader campaign with a conservative religious and political agenda. Much of the rhetorical effectiveness of anti-evolutionism comes from its reliance on seemingly precise mathematical arguments. This book, the first of its kind to be written by a mathematician, discusses and refutes these arguments. Along the way, it also clarifies common misconceptions about both biology and mathematics. Both lay audiences and professionals will find the book to be accessible and informative.

Analyzing and Modeling Rank Data is the first single-source volume to fully address this prevalent practice in both its analytical and modeling aspects. The information discussed presents the use of data consisting of rankings in such diverse fields as psychology, animal science, educational testing, sociology, economics, and biology. This book systematically presents the basic models and methods for analyzing data in the form of ranks. Integrating material from a wide range of fields, this book applies graphical, numerical, and modeling techniques to data sets, uncovering fascinating structures in the rank data. Topics examined include unified treatment of numerical summaries and statistical tests for analyzing and comparing samples; graphical projections for exploring permutation polytypes; extensive coverage of models for rank data; and examples from numerous fields illustrating the use of the techniques. Providing the most extensive coverage of the subject found in statistical literature, this book will be a welcomed reference to statisticians. In addition, this volume is also accessible to people in all areas of quantitative research. Researchers in psychology and consumer preference will discover a valuable resource; and sociologists, biologists, political and animal scientists will also benefit. As a text, it will be ideal for graduate students in courses on statistics and other quantitative disciplines.