Galton used quantiles more than a hundred years ago in describing data. Tukey and Parzen used them in the 60s and 70s in describing populations. Since then, the authors of many papers, both theoretical and practical, have used various aspects of quantiles in their work. Until now, however, no one put all the ideas together to form what turns out to be a general approach to statistics. Statistical Modelling with Quantile Functions does just that. It systematically examines the entire process of statistical modelling, starting with using the quantile function to define continuous distributions. The author shows that by using this approach, it becomes possible to develop complex distributional models from simple components. A modelling kit can be developed that applies to the whole model - deterministic and stochastic components - and this kit operates by adding, multiplying, and transforming distributions rather than data. Statistical Modelling with Quantile Functions adds a new dimension to the practice of statistical modelling that will be of value to anyone faced with analyzing data. Not intended to replace classical approaches but to supplement them, it will make some of the traditional topics easier and clearer, and help readers build and investigate models for their own practical statistical problems.

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.

During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing applications. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematical tools required for applications can be intimidating. Potential end users often get the impression that jump and Lévy processes are beyond their reach.

Financial Modelling with Jump Processes demonstrates that this is not so. It provides a self-contained overview of the theoretical, numerical, and empirical aspects of using jump processes in financial modeling, and does so in terms well within the grasp of nonspecialists. With clear-sighted explanations, the authors motivate the use of the various mathematical tools used in the modelling process, and while giving an intuitive understanding of proofs, provide precise mathematical statements of the results. They illustrate the mathematical concepts with many numerical and empirical examples and provide the details of numerical implementation of pricing and calibration algorithms.

This book clearly shows that the concepts and tools necessary for understanding and implementing these models can be much more accessible and intuitive that those involved in the Black Scholes and diffusion models. If you have even a basic familiarity with quantitative methods in finance, Financial Modelling with Jump Processes will give you a valuable new set of tools for modelling market fluctuations.

Hidden Markov models have become a widely used class of statistical models with applications in diverse areas such as communications engineering, bioinformatics, finance and many more. This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces, which allow for exact algorithms for filtering, estimation etc. and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Simulation in hidden Markov models is addressed in five different chapters that cover both Markov chain Monte Carlo and sequential Monte Carlo approaches. Many examples illustrate the algorithms and theory. The book also carefully treats Gaussian linear state-space models and their extensions and it contains a chapter on general Markov chain theory and probabilistic aspects of hidden Markov models. This volume will suit anybody with an int background, while the more theoretical parts require knowledge of probability theory at the measure-theoretical level.

The International Conference on Computational Fluid Dynamics (ICCFD) is the merger of the International Conference on Numerical Methods in Fluid Dynamics (ICNMFD) and the International Symposium on Computational Fluid Dynamics (ISCFD). It is held every two years and brings together physicists, mathematicians and engineers to review and share recent advances in mathematical and computational techniques for modeling fluid dynamics. The proceedings of the 2004 conference held in Toronto, Canada, contain a selection of refereed contributions and are meant to serve as a source of reference for all those interested in the state of the art in computational fluid dynamics.

This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.

This book reports on advanced theories and methods in three related fields of research: applied physics, system science and computers. It is organized in two main parts, the first of which covers applied physics topics, including lasers and accelerators; condensed matter, soft matter and materials science; nanoscience and quantum engineering; atomic, molecular, optical and plasma physics; as well as nuclear and high-energy particle physics. It also addresses astrophysics, gravitation, earth and environmental science, as well as medical and biological physics. The second part focuses on advances in system science and computers, exploring automatic circuit control, power systems, computer communication, fluid mechanics, simulation and modeling, software engineering, data structures and applications of artificial intelligence among other areas. Offering a collection of contributions presented at the 1st International Conference on Applied Physics, System Science and Computers (APSAC 2016), the book bridges the gap between applied physics and electrical engineering. It not only to presents new methods, but also promotes collaborations between different communities working on related topics at the interface between physics and engineering, with a special focus on communication, data modeling and visualization, quantum information, applied mechanics as well as bio and geophysics.

This book describes a system of mathematical models and methods that can be used to analyze real economic and managerial decisions and to improve their effectiveness. Application areas include: management of development and operation budgets, assessment and management of economic systems using an energy entropy approach, equation of exchange rates and forecasting foreign exchange operations, evaluation of innovative projects, monitoring of governmental programs, risk management of investment processes, decisions on the allocation of resources, and identification of competitive industrial clusters. The proposed methods and models were tested on the example of Kazakhstan's economy, but the generated solutions will be useful for applications at other levels and in other countries. Regarding your book "Mathematical Methods and Models in Economics", I am impressed because now it is time when "econometrics" is becoming more appreciated by economists and by schools that are the hosts or employers of modern economists. ... Your presented results really impressed me. John F. Nash, Jr., Princeton University, Nobel Memorial Prize in Economic Sciences The book is within my scope of interest because of its novelty and practicality. First, there is a need for realistic modeling of complex systems, both natural and artificial that conclude computer and economic systems. There has been an ongoing effort in developing models dealing with complexity and incomplete knowledge. Consequently, it is clear to recognize the contribution of Mutanov to encapsulate economic modeling with emphasis on budgeting and innovation. Secondly, the method proposed by Mutanov has been verified by applying to the case of the Republic of Kazakhstan, with her vibrant emerging economy. Thirdly, Chapter 5 of the book is of particular interest for the computer technology community because it deals with innovation. In summary, the book of Mutanov should become one of the outstanding recognized pragmatic guides for dealing with innovative systems. Andrzej Rucinski, University of New Hampshire This book is unique in its theoretical findings and practical applicability. The book is an illuminating study based on an applied mathematical model which uses methods such as linear programming and input-output analysis. Moreover, this work demonstrates the author's great insight and academic brilliance in the fields of finance, technological innovations and marketing vis-a-vis the market economy. From both theoretical and practical standpoint, this work is indeed a great achievement. Yeon Cheon Oh, President of Seoul National University

"LISREL: Issues, Debates, and Strategies" examines issues of concern to researchers already familiar with the basics of structural equation modeling. Building on his earlier work in "Structural Equation Modeling in LISREL," Leslie Hayduk explains procedures that maximize researchers' control over the meanings of their concepts and integrates the modeling of single and multiple indicators. The constraints and deceptions of the factor model are used to highlight measurement issues and the debate over whether one should estimate a measurement model prior to estimating a structural model is reviewed, extended, and evaluated.

For sociologists, political scientists, psychologists, and researchers in science, medicine, and education, "LISREL" offers a wealth of useful information:

A loop-equivalent to the standard recursive model is presented as grounding an interpretation style that can be used to challenge any or all the effect estimates from recursive models. (Loop-equivalent provide an appealing alternative conceptualization of longitudinal processes.)

Models with acceptable negative "R2"'s are discussed and "LAR2" is introduced as a more appropriate indication of error variance for variables touching reciprocal relationships or loops. The logic connecting partial correlations, tetrads, equivalent models, and LISREL is presented and recent advances in this area are reviewed.

Phantom variables and a modeling trick combine to illustrate how stacked models based on differing sets of indicator variables can be used: to identify otherwise unidentified models, to control for unmeasured variables, and to integrate models based on diverse data sets.

A more appropriate Monte-Carlo-test model is proposed and a brief review of the recent literature is provided.

This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schroedinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell's inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.

Originally published in 1984. Since the logic underlying economic theory can only be grasped fully by a thorough understanding of the mathematics, this book will be invaluable to economists wishing to understand vast areas of important research. It provides a basic introduction to the fundamental mathematical ideas of topology and calculus, and uses these to present modern singularity theory and recent results on the generic existence of isolated price equilibria in exchange economies.

"Multiscale Signal Analysis and Modeling" presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representation/transmission, coding, nonparametric statistical signal processing, and statistical learning theory.

Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February 2016 conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM). The conference gathered research communities across disciplines to share ideas and problems in their fields and formed small research groups made up of graduate students, postdoctoral researchers, junior faculty, and group leaders who designed and led the projects. Peer reviewed and revised, each of this volume's five papers achieves the conference's goal of using algebraic geometry to address a problem in either coding theory or cryptography. Proposed variants of the McEliece cryptosystem based on different constructions of codes, constructions of locally recoverable codes from algebraic curves and surfaces, and algebraic approaches to the multicast network coding problem are only some of the topics covered in this volume. Researchers and graduate-level students interested in the interactions between algebraic geometry and both coding theory and cryptography will find this volume valuable.

Hormones as Tokens of Selection addresses deep questions in biology: How are biological systems controlled? How can one formulate general theories of homeostasis and control and instantiate such theories in mathematical models? How can one use evolutionary arguments to guide our answers to these questions, recognising that the control mechanisms themselves are a product of evolution? Biological systems are exceptionally varied and extremely difficult to understand, because they are complex and experimentation remains limited relative to the challenges at hand. Moreover, biological phenomena occur at a wide range of temporal and spatial scales. Such a deeply convoluted subject calls for a unifying and coherent theoretical foundation - one which recognises and departs from the primary importance of mathematical modelling and key physicochemical principles to theory formation in the life sciences. This Focus monograph proposes and outlines such a foundation, departing from the deceptively simple proposition that hormones are tokens of evolutionary pressures. Features Provides a coherent and unified approach to a multifaceted problem Pays close attention to both the biological and mathematical modelling aspects of the subject matter, exploring the philosophical background where appropriate Written in a concise and innovative style

This textbook gives an introduction to fluid dynamics based on flows for which analytical solutions exist, like individual vortices, vortex streets, vortex sheets, accretions disks, wakes, jets, cavities, shallow water waves, bores, tides, linear and non-linear free-surface waves, capillary waves, internal gravity waves and shocks. Advanced mathematical techniques ("calculus") are introduced and applied to obtain these solutions, mostly from complex function theory (Schwarz-Christoffel theorem and Wiener-Hopf technique), exterior calculus, singularity theory, asymptotic analysis, the theory of linear and nonlinear integral equations and the theory of characteristics. Many of the derivations, so far contained only in research journals, are made available here to a wider public.

This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.

Recent interest in nanotechnology is challenging the community to analyse, develop and design nanometer to micrometer-sized devices for applications in new generations of computer, electronics, photonics and drug delivery systems. To successfully design and fabricate novel nanomaterials and nanosystems, we must necessarily bridge the gap in our understanding of mechanical properties and processes at length scales ranging from 100 nanometers (where atomistic simulations are currently possible) to a micron (where continuum mechanics is experimentally validated). For this purpose the difficulties and complexity originate in the substantial differences in philosophy and viewpoints between conventional continuum mechanics and quantum theories. The challenge lies in how to establish the relationship between a continuum mechanical system and its atomistic counterpart in order to define continuum variables that are calculable within an atomic system.

Modeling and Simulation have become endeavors central to all disciplines of Science and Engineering. They are used in the analysis of physical systems where they help us gain a better understanding of the functioning of our physical world. They are also important to the design of new engineering systems where they enable us to predict the behavior of a system before it is ever actually built. Modeling and Simulation are the only techniques available that allow us to analyze arbitrarily non-linear sys- tems accurately and under varying experimental conditions. Modeling and Simulation of Continuous Systems introduces the student to an important subclass of these techniques. They deal with the analysis of systems described through a set of ordinary or partial differential equations or through a set of difference equations. This volume introduces concepts of modeling physical systems through a set of differential and/or difference equations. The purpose is twofold: it enhances the scientific understanding of our physical world by codifying (organizing) knowledge about this world, and it supports engineering design by allowing us to assess the consequences of a particular design alternative before it is actually built. This text has a flavor of the mathematical discipline of dynamical systems, and is strongly oriented towards Newtonian physical science.

Providing an introduction to major topics in macroeconomic theory, this book offers the reader three keys for comparing different models. The first key is a mathematical reformulation of Say's Law. The second key is the use of the income velocity of the circulation of money as a behavioural function in accordance with the Friedman tradition. The third is the use of the Phillips curve to represent the labour market. The book also deals with rationing equilibria and some extensions. It provides a neo-Walrasian synthesis of Patinkin's suggestions and new perspectives on Keynesian criticism of neoclassical theory.

The book is mainly addressed to young graduate students in engineering and natural sciences who start to face numerical simulation, either at a research level or in the field of industrial applications. The main subjects covered are: Biomechanics, Stochastic Calculus, Geophysical flow simulation and Shock-Capturing numerical methods for Hyperbolic Systems of Partial Differential Equations. The book can also be useful to researchers or even technicians working at an industrial environment, who are interested in the state-of-the-art numerical techniques in these fields. Moreover, it gives an overview of the researchdeveloped at the French and Spanish universities and in some European scientific institutions. This book can be also useful as a textbook at master courses in Mathematics, Physics or Engineering."

Volume I of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. The chapters are thematically organized into the following main areas: cellular biophysics, regulatory networks, developmental biology, biomedical applications, data analysis and model validation.

The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.

This monograph is devoted to recent mathematical theories on the bottom up self-organization observed in closed and isolated thermo-dynamical systems. Its main features include:

This book covers pattern recognition techniques applied to various areas of biomedicine, including disease diagnosis and prognosis, and several problems of classification, with a special focus on-but not limited to-pattern recognition modeling of biomedical signals and images. Multidisciplinary by definition, the book's topic blends computing, mathematics and other technical sciences towards the development of computational tools and methodologies that can be applied to pattern recognition processes. In this work, the efficacy of such methods and techniques for processing medical information is analyzed and compared, and auxiliary criteria for determining the correct diagnosis and treatment strategies are recommended and applied. Researchers in applied mathematics, the computer sciences, engineering and related fields with a focus on medical applications will benefit from this book, as well as professionals with a special interest in state-of-the-art pattern recognition techniques as applied to biomedicine.

This monograph explores the application of the potential method to three-dimensional problems of the mathematical theories of elasticity and thermoelasticity for multi-porosity materials. These models offer several new possibilities for the study of important problems in engineering and mechanics involving multi-porosity materials, including geological materials (e.g., oil, gas, and geothermal reservoirs); manufactured porous materials (e.g., ceramics and pressed powders); and biomaterials (e.g., bone and the human brain). Proceeding from basic to more advanced material, the first part of the book begins with fundamental solutions in elasticity, followed by Galerkin-type solutions and Green's formulae in elasticity and problems of steady vibrations, quasi-static, and pseudo-oscillations for multi-porosity materials. The next part follows a similar format for thermoelasticity, concluding with a chapter on problems of heat conduction for rigid bodies. The final chapter then presents a number of open research problems to which the results presented here can be applied. All results discussed by the author have not been published previously and offer new insights into these models. Potential Method in Mathematical Theories of Multi-Porosity Media will be a valuable resource for applied mathematicians, mechanical, civil, and aerospace engineers, and researchers studying continuum mechanics. Readers should be knowledgeable in classical theories of elasticity and thermoelasticity.