The Conference on Traffic and Granular Flow brings together international researchers from different fields ranging from physics to computer science and engineering to discuss the latest developments in traffic-related systems. Originally conceived to facilitate new ideas by considering the similarities of traffic and granular flow, TGF'15, organised by Delft University of Technology, now covers a broad range of topics related to driven particle and transport systems. Besides the classical topics of granular flow and highway traffic, its scope includes data transport (Internet traffic), pedestrian and evacuation dynamics, intercellular transport, swarm behaviour and the collective dynamics of other biological systems. Recent advances in modelling, computer simulation and phenomenology are presented, and prospects for applications, for example to traffic control, are discussed. The conference explores the interrelations between the above-mentioned fields and offers the opportunity to stimulate interdisciplinary research, exchange ideas, and meet many experts in these areas of research.

This book covers all the relevant dictionary learning algorithms, presenting them in full detail and showing their distinct characteristics while also revealing the similarities. It gives implementation tricks that are often ignored but that are crucial for a successful program. Besides MOD, K-SVD, and other standard algorithms, it provides the significant dictionary learning problem variations, such as regularization, incoherence enforcing, finding an economical size, or learning adapted to specific problems like classification. Several types of dictionary structures are treated, including shift invariant; orthogonal blocks or factored dictionaries; and separable dictionaries for multidimensional signals. Nonlinear extensions such as kernel dictionary learning can also be found in the book. The discussion of all these dictionary types and algorithms is enriched with a thorough numerical comparison on several classic problems, thus showing the strengths and weaknesses of each algorithm. A few selected applications, related to classification, denoising and compression, complete the view on the capabilities of the presented dictionary learning algorithms. The book is accompanied by code for all algorithms and for reproducing most tables and figures. Presents all relevant dictionary learning algorithms - for the standard problem and its main variations - in detail and ready for implementation; Covers all dictionary structures that are meaningful in applications; Examines the numerical properties of the algorithms and shows how to choose the appropriate dictionary learning algorithm.

This book presents theory and latest application work in Bond Graph methodology with a focus on: * Hybrid dynamical system models, * Model-based fault diagnosis, model-based fault tolerant control, fault prognosis * and also addresses * Open thermodynamic systems with compressible fluid flow, * Distributed parameter models of mechanical subsystems. In addition, the book covers various applications of current interest ranging from motorised wheelchairs, in-vivo surgery robots, walking machines to wind-turbines.The up-to-date presentation has been made possible by experts who are active members of the worldwide bond graph modelling community. This book is the completely revised 2nd edition of the 2011 Springer compilation text titled Bond Graph Modelling of Engineering Systems - Theory, Applications and Software Support. It extends the presentation of theory and applications of graph methodology by new developments and latest research results. Like the first edition, this book addresses readers in academia as well as practitioners in industry and invites experts in related fields to consider the potential and the state-of-the-art of bond graph modelling.

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. In particular, it features mathematical methods and models of applied analysis, probability theory, differential equations, tensor analysis and computational modelling used in applications to important problems concerning electromagnetics, antenna technologies, fluid dynamics, material and continuum physics and financial engineering. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed.The book consists of contributed chapters covering research developed as a result of a focused international seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Malardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications.It serves as a source of inspiration for a broad spectrum of researchers and research students in applied mathematics, as well as in the areas of applications of mathematics considered in the book.

This book presents a systematic overview on partition function form games: a game form in cooperative game theory to integrate externalities for various applications. Cooperative game theory has been immensely useful to study a wide range of issues, but the standard approaches ignore the side effects of cooperation. Recently interest shifted to problems where externalities play the main roles such as models of cooperation in market competition or the shared use of public resources. Such problems require richer models that can explicitly evaluate the side-effects of cooperation. In partition function form games the value of cooperation depends on the outsiders' actions. A recent surge of interest driven by applications has made results very fragmented. This book offers an accessible, yet comprehensive and systematic study of properties, solutions and applications of partition function games surveying both theoretical results and their applications. It assembles a survey of existing research and smaller original results as well as original interpretations and comparisons. The book is self-contained and accessible for readers with little or no knowledge of cooperative game theory.

Originally published in 1940, this book was aimed at students of science who had not previously been acquainted with algebra and the core mathematical principles. 'It is quite wrong that science students, particularly biology students, should go to their universities without having been made aware of even the existence of a side of mathematics whose importance is becoming more and more apparent'. The book caters for students who wish to develop their mathematical and reasoning skills, necessary to progress in the sciences. Chapters are broad in scope, detailed and varied; chapter titles include, 'The theory of quadratic equations', 'Probability' and 'Statistics'. A multitude of examples are included throughout to reinforce learning and answers can be found at the back. Providing an overview of algebra for school students before entering undergraduate science, this book will be of significant value to anyone with an interest in mathematics and the history of education.

This collection of selected papers presented at the 11th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in St. Wolfgang, Austria, in 2016, showcases the state of the art in SCEE. The aim of the SCEE 2016 conference was to bring together scientists from academia and industry, mathematicians, electrical engineers, computer scientists, and physicists, and to promote intensive discussions on industrially relevant mathematical problems, with an emphasis on the modeling and numerical simulation of electronic circuits and devices, electromagnetic fields, and coupled problems. The focus in methodology was on model order reduction and uncertainty quantification. This extensive reference work is divided into six parts: Computational Electromagnetics, Circuit and Device Modeling and Simulation, Coupled Problems and Multi-Scale Approaches in Space and Time, Mathematical and Computational Methods Including Uncertainty Quantification, Model Order Reduction, and Industrial Applications. Each part starts with a general introduction, followed by the respective contributions. This book will appeal to mathematicians and electrical engineers. Further, it introduces algorithm and program developers to recent advances in the other fields, while industry experts will be introduced to new programming tools and mathematical methods.

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

This stimulating textbook presents a broad and accessible guide to the fundamentals of discrete mathematics, highlighting how the techniques may be applied to various exciting areas in computing. The text is designed to motivate and inspire the reader, encouraging further study in this important skill. Features: provides an introduction to the building blocks of discrete mathematics, including sets, relations and functions; describes the basics of number theory, the techniques of induction and recursion, and the applications of mathematical sequences, series, permutations, and combinations; presents the essentials of algebra; explains the fundamentals of automata theory, matrices, graph theory, cryptography, coding theory, language theory, and the concepts of computability and decidability; reviews the history of logic, discussing propositional and predicate logic, as well as advanced topics; examines the field of software engineering, describing formal methods; investigates probability and statistics.

This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications.

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

In this book, physics in its many aspects (thermodynamics, mechanics, electricity, fluid dynamics) is the guiding light on a fascinating journey through biological systems, providing ideas, examples and stimulating reflections for undergraduate physics, chemistry and life-science students, as well as for anyone interested in the frontiers between physics and biology. Rather than introducing a lot of new information, it encourages young students to use their recently acquired knowledge to start seeing the physics behind the biology. As an undergraduate textbook in introductory biophysics, it includes the necessary background and tools, including exercises and appendices, to form a progressive course. In this case, the chapters can be used in the order proposed, possibly split between two semesters. The book is also an absorbing read for researchers in the life sciences who wish to refresh or go deeper into the physics concepts gleaned in their early years of scientific training. Less physics-oriented readers might want to skip the first chapter, as well as all the "gray boxes" containing the more formal developments, and create their own a-la-carte menu of chapters.

This unique text/reference provides an overview of crossbar-based interconnection networks, offering novel perspectives on these important components of high-performance, parallel-processor systems. A particular focus is placed on solutions to the blocking and scalability problems. Topics and features: introduces the fundamental concepts in interconnection networks in multi-processor systems, including issues of blocking, scalability, and crossbar networks; presents a classification of interconnection networks, and provides information on recognizing each of the networks; examines the challenges of blocking and scalability, and analyzes the different solutions that have been proposed; reviews a variety of different approaches to improve fault tolerance in multistage interconnection networks; discusses the scalable crossbar network, which is a non-blocking interconnection network that uses small-sized crossbar switches as switching elements. This invaluable work will be of great benefit to students, researchers and practitioners interested in computer networks, parallel processing and reliability engineering. The text is also essential reading for course modules on interconnection network design and reliability.

This unique text/reference presents a fresh look at nonlinear processing through nonlinear eigenvalue analysis, highlighting how one-homogeneous convex functionals can induce nonlinear operators that can be analyzed within an eigenvalue framework. The text opens with an introduction to the mathematical background, together with a summary of classical variational algorithms for vision. This is followed by a focus on the foundations and applications of the new multi-scale representation based on non-linear eigenproblems. The book then concludes with a discussion of new numerical techniques for finding nonlinear eigenfunctions, and promising research directions beyond the convex case. Topics and features: introduces the classical Fourier transform and its associated operator and energy, and asks how these concepts can be generalized in the nonlinear case; reviews the basic mathematical notion, briefly outlining the use of variational and flow-based methods to solve image-processing and computer vision algorithms; describes the properties of the total variation (TV) functional, and how the concept of nonlinear eigenfunctions relate to convex functionals; provides a spectral framework for one-homogeneous functionals, and applies this framework for denoising, texture processing and image fusion; proposes novel ways to solve the nonlinear eigenvalue problem using special flows that converge to eigenfunctions; examines graph-based and nonlocal methods, for which a TV eigenvalue analysis gives rise to strong segmentation, clustering and classification algorithms; presents an approach to generalizing the nonlinear spectral concept beyond the convex case, based on pixel decay analysis; discusses relations to other branches of image processing, such as wavelets and dictionary based methods. This original work offers fascinating new insights into established signal processing techniques, integrating deep mathematical concepts from a range of different fields, which will be of great interest to all researchers involved with image processing and computer vision applications, as well as computations for more general scientific problems.

The state of the art in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics Modeling is presented in this new second edition book. It shows how advanced physical and mathematical methods can expand classical models in order to cover heterogeneous drug-biological processes and therapeutic effects in the body. The book is divided into four parts; the first deals with the fundamental principles of fractals, diffusion and nonlinear dynamics; the second with drug dissolution, release, and absorption; the third with epirical, compartmental, and stochastic pharmacokinetic models, with two new chapters, one on fractional pharmacokinetics and one on bioequivalence; and the fourth mainly with classical and nonclassical aspects of pharmacodynamics. The classical models that have relevance and application to these sciences are also considered throughout. This second edition has new information on reaction limited models of dissolution, non binary biopharmaceutic classification system, time varying models, and interface models. Many examples are used to illustrate the intrinsic complexity of drug administration related phenomena in the human, justifying the use of advanced modeling methods. This book will appeal to graduate students and researchers in pharmacology, pharmaceutical sciences, bioengineering, and physiology. Reviews of the first edition: "This book presents a novel modelling approach to biopharmaceutics, pharmacokinetics and pharmacodynamic phenomena. This state-of-the-art volume will be helpful to students and researchers in pharmacology, bioengineering, and physiology. This book is a must for pharmaceutical researchers to keep up with recent developments in this field." (P. R. Parthasarathy, Zentralblatt MATH, Vol. 1103 (5), 2007) "These authors are the unique (or sole) contributors in this area that are working on these questions and bring a special expertise to the field that is now being recognized as essential to understanding biological system and kinetic/dynamic characteristics in drug development...This text is an essential primer for those who would envision the incorporation of heterogeneous approaches to systems where homogeneous approaches are not sufficient to describe the system." (Robert R. Bies, Journal of Clinical Pharmacology, Vol. 46, 2006)

This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms. Another feature of the book is that it emphasizes what model underlies a procedure and what objective function is optimized for fitting the model to data. The author believes that the matrix-based learning of such models and objective functions is the fastest way to comprehend multivariate data analysis. The text is arranged so that readers can intuitively capture the purposes for which multivariate analysis procedures are utilized: plain explanations of the purposes with numerical examples precede mathematical descriptions in almost every chapter. This volume is appropriate for undergraduate students who already have studied introductory statistics. Graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis will also find the book useful, as it is based on modern matrix formulations with a special emphasis on singular value decomposition among theorems in matrix algebra. The book begins with an explanation of fundamental matrix operations and the matrix expressions of elementary statistics, followed by the introduction of popular multivariate procedures with advancing levels of matrix algebra chapter by chapter. This organization of the book allows readers without knowledge of matrices to deepen their understanding of multivariate data analysis.

Who was Nicolas Rashevsky? To answer that question, this book draws on Rashevsky's unexplored personal archival papers and shares interviews with his family, students and friends, as well as discussions with biologists and mathematical biologists, to flesh out and complete the picture. "Most modern-day biologists have never heard of Rashevsky. Why?" In what constitutes the first detailed biography of theoretical physicist Nicolas Rashevsky (1899-1972), spanning key aspects of his long scientific career, the book captures Rashevsky's ways of thinking about the place mathematical biology should have in biology and his personal struggle for the acceptance of his views. It brings to light the tension between mathematicians, theoretical physicists and biologists when it comes to the introduction of physico-mathematical tools into biology. Rashevsky's successes and failures in his efforts to establish mathematical biology as a subfield of biology provide an important test case for understanding the role of theory (in particular mathematics) in understanding the natural world. With the biological sciences moving towards new vistas of inter- and multi-disciplinary collaborations and research programs, the book will appeal to a wide readership ranging from historians, sociologists, and ethnographers of American science and culture to students and general readers with an interest in the history of the life sciences, mathematical biology and the social construction of science.

This book presents the first "How To" guide to the use of radial basis functions (RBF). It provides a clear vision of their potential, an overview of ready-for-use computational tools and precise guidelines to implement new engineering applications of RBF. Radial basis functions (RBF) are a mathematical tool mature enough for useful engineering applications. Their mathematical foundation is well established and the tool has proven to be effective in many fields, as the mathematical framework can be adapted in several ways. A candidate application can be faced considering the features of RBF: multidimensional space (including 2D and 3D), numerous radial functions available, global and compact support, interpolation/regression. This great flexibility makes RBF attractive - and their great potential has only been partially discovered. This is because of the difficulty in taking a first step toward RBF as they are not commonly part of engineers' cultural background, but also due to the numerical complexity of RBF problems that scales up very quickly with the number of RBF centers. Fast RBF algorithms are available to alleviate this and high-performance computing (HPC) can provide further aid. Nevertheless, a consolidated tradition in using RBF in engineering applications is still missing and the beginner can be confused by the literature, which in many cases is presented with language and symbolisms familiar to mathematicians but which can be cryptic for engineers. The book is divided in two main sections. The first covers the foundations of RBF, the tools available for their quick implementation and guidelines for facing new challenges; the second part is a collection of practical RBF applications in engineering, covering several topics, including response surface interpolation in n-dimensional spaces, mapping of magnetic loads, mapping of pressure loads, up-scaling of flow fields, stress/strain analysis by experimental displacement fields, implicit surfaces, mesh to cad deformation, mesh morphing for crack propagation in 3D, ice and snow accretion using computational fluid dynamics (CFD) data, shape optimization for external aerodynamics, and use of adjoint data for surface sculpting. For each application, the complete path is clearly and consistently exposed using the systematic approach defined in the first section.

This is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials. The mathematical part of the book is a new approach to integrability structures that allows to treat all of them in a unified way. The software is an official package of Reduce. Reduce is free software, so everybody can download it and make experiments using the programs available at our website.

This book provides state-of-the-art results and theories in homogeneous turbulence, including anisotropy and compressibility effects with extension to quantum turbulence, magneto-hydodynamic turbulence and turbulence in non-newtonian fluids. Each chapter is devoted to a given type of interaction (strain, rotation, shear, etc.), and presents and compares experimental data, numerical results, analysis of the Reynolds stress budget equations and advanced multipoint spectral theories. The role of both linear and non-linear mechanisms is emphasized. The link between the statistical properties and the dynamics of coherent structures is also addressed. Despite its restriction to homogeneous turbulence, the book is of interest to all people working in turbulence, since the basic physical mechanisms which are present in all turbulent flows are explained. The reader will find a unified presentation of the results and a clear presentation of existing controversies. Special attention is given to bridge the results obtained in different research communities. Mathematical tools and advanced physical models are detailed in dedicated chapters.

This guide provides a comprehensive overview of High Performance Computing (HPC) to equip students with a full skill set including cluster setup, network selection, and a background of supercomputing competitions. It covers the system, architecture, evaluating approaches, and other practical supercomputing techniques. As the world's largest supercomputing hackathon, the ASC Student Supercomputer Challenge has attracted a growing number of new talent to supercomputing and has greatly promoted communications in the global HPC community. Enclosed in this book, readers will also find how to analyze and optimize supercomputing systems and applications in real science and engineering cases.

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

This volume presents the latest developments in the highly active and rapidly growing field of diffusion MRI. The reader will find numerous contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation, to new computational methods and estimation techniques for the in-vivo recovery of microstructural and connectivity features, as well as frontline applications in neuroscience research and clinical practice. These proceedings contain the papers presented at the 2017 MICCAI Workshop on Computational Diffusion MRI (CDMRI'17) held in Quebec, Canada on September 10, 2017, sharing new perspectives on the most recent research challenges for those currently working in the field, but also offering a valuable starting point for anyone interested in learning computational techniques in diffusion MRI. This book includes rigorous mathematical derivations, a large number of rich, full-colour visualisations and clinically relevant results. As such, it will be of interest to researchers and practitioners in the fields of computer science, MRI physics and applied mathematics.

This book summarizes a number of fundamental developments at the interface of granular crystals and the mathematical and computational analysis of some of their key localized nonlinear wave solutions. The subject presents a blend of the appeal of granular crystals as a prototypical engineering tested for a variety of diverse applications, the novelty in the nonlinear physics of its coherent structures, and the tractability of a series of mathematical and computational techniques to analyse them. While the focus is on principal one-dimensional solutions such as shock waves, traveling waves, and discrete breathers, numerous extensions of the discussed patterns, e.g., in two dimensions, chains with defects, heterogeneous settings, and other recent developments are discussed. The emphasis on the subject was motivated by models in condensed matter physics, ferroelectrics, high energy physics, and statistical mechanics, leading to developments in mathematical analysis, numerical computation and insights on the physical aspects of the model. The book appeals to researchers in the field, as well as for graduate and advanced undergraduate students. It will be of interest to mathematicians, physicists and engineers alike.

This book is a collection of papers presented at the 'Forum "Math-for-Industry" 2016 ' (FMfl2016), held at Queensland University of Technology, Brisbane, Australia, on November 21-23, 2016. The theme for this unique and important event was "Agriculture as a Metaphor for Creativity in All Human Endeavors", and it brought together leading international mathematicians and active researchers from universities and industry to discuss current challenging topics and to promote interactive collaborations between mathematics and industry. The success of agricultural practice relies fundamentally on its interconnections with and dependence on biology and the environment. Both play essential roles, including the biological adaption to cope with environmental challenges of biotic and abiotic stress and global warming. The book highlights the development of mathematics within this framework that successful agricultural practice depends upon and exploits.