Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. It can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory.
Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. The second edition adds two new chapters on asymptotic and numerical methods and an appendix that separates some of the more delicate mathematical theory from the steady flow of examples in the main text.
Besides the two new chapters, the second edition includes a more extensive list of exercises, many additions to the exposition of combinatorics, new material on rates of convergence to equilibrium in reversible Markov chains, a discussion of basic reproduction numbers in population modeling, and better coverage of Brownian motion. Because many chapters are nearly self-contained, mathematical scientists from a variety of backgrounds will find Applied Probability useful as a reference

This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantization and quantum group. The second part is devoted to the theory of hypergroups and Lie hypergroups, which is one of the most important generalizations of the classical concept of locally compact group and of Lie group. A natural harmonic analysis arises on hypergroups, while any abstract transformation of Fourier type is gen erated by some hypergroup (commutative or not). Part III contains papers on the geometry of homogeneous spaces, Lie algebras and Lie superalgebras. Classical problems of the representation theory for Lie groups, as well as for topological groups and semigroups, are discussed in the papers of Part IV. Finally, the last part of the collection relates to applications of the ideas of Sophus Lie to differential equations."

Recent years have been characterized by the increasing amountofpublications in the field ofso-called ill-posed problems. This is easilyunderstandable because we observe the rapid progress of a relatively young branch ofmathematics, ofwhich the first results date back to about 30 years ago. By now, impressive results have been achieved both in the theory ofsolving ill-posed problems and in the applicationsofalgorithms using modem computers. To mention just one field, one can name the computer tomography which could not possibly have been developed without modem tools for solving ill-posed problems. When writing this book, the authors tried to define the place and role of ill posed problems in modem mathematics. In a few words, we define the theory of ill-posed problems as the theory of approximating functions with approximately given arguments in functional spaces. The difference between well-posed and ill posed problems is concerned with the fact that the latter are associated with discontinuous functions. This approach is followed by the authors throughout the whole book. We hope that the theoretical results will be of interest to researchers working in approximation theory and functional analysis. As for particular algorithms for solving ill-posed problems, the authors paid general attention to the principles ofconstructing such algorithms as the methods for approximating discontinuous functions with approximately specified arguments. In this way it proved possible to define the limits of applicability of regularization techniques."

The first English edition of a well-known Russian monograph. This book presents the method of difference potentials first proposed by the author in 1969, and contains illustrative examples and new algorithms for solving applied problems of gas dynamics, diffraction, scattering theory, and active noise screening.

This volume contains twenty contributions of work, conducted since 1996 in the French- German Research Programme "Numerical Flow Simulation" of the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). The main purpose of this publication is to give an overview over the work conducted in this programme, and to make the results obtained available to the pUblic. The reports are grouped under the four headings "Development of Solution Techniques", "Crystal Growth and Melts", "Flows of Reacting Gases" and "Turbulent Flows". AIl contributions to this publica- tion were reviewed by a board consisting of T. Alziary de Roquefort (Poitiers, France), P. Bontoux (Marseille, France), JA Desideri (Sophia-Antipolis, France), W. Kordulla (G6t- tingen, Germany), R. Peyret (Nice, France), R. Rannacher (Heidelberg, Germany), G. War- necke (Magdeburg, ,Germany), and the editor. The responsibility for the contents of the reports nevertheless lies with the authors. E. H. Hirschel Editor Preface The Colloquium on "Numerical Simulation of Flows", Marseille, November 21 and 22, th 1997, was the 6 Joint CNRS-DFG Colloquium organized in the frame of the French- German Research Collaboration on Computational Fluid Dynamics. This Collaborative Program was elaborated progressively since 1991, when the two major research groups were brought together: the Priority Program "Flow Simulation with Super Computers" from the DFG in Germany and the Groupement de Recherche de "Mecanique des Fluides NumCrique" (GDR MFN) from the CNRS in France.

Over the past decades, the Boundary Element Method has emerged as a ver satile and powerful tool for the solution of engineering problems, presenting in many cases an alternative to the more widely used Finite Element Method. As with any numerical method, the engineer or scientist who applies it to a practical problem needs to be acquainted with, and understand, its basic principles to be able to apply it correctly and be aware of its limitations. It is with this intention that we have endeavoured to write this book: to give the student or practitioner an easy-to-understand introductory course to the method so as to enable him or her to apply it judiciously. As the title suggests, this book not only serves as an introductory course, but also cov ers some advanced topics that we consider important for the researcher who needs to be up-to-date with new developments. This book is the result of our teaching experiences with the Boundary Element Method, along with research and consulting activities carried out in the field. Its roots lie in a graduate course on the Boundary Element Method given by the authors at the university of Stuttgart. The experiences gained from teaching and the remarks and questions of the students have contributed to shaping the 'Introductory course' (Chapters 1-8) to the needs of the stu dents without assuming a background in numerical methods in general or the Boundary Element Method in particular."

"This book is concerned with a probabilistic approach for image analysis, mostly from the Bayesian point of view, and the important Markov chain Monte Carlo methods commonly used....This book will be useful, especially to researchers with a strong background in probability and an interest in image analysis. The author has presented the theory with rigor he doesn t neglect applications, providing numerous examples of applications to illustrate the theory." -- MATHEMATICAL REVIEWS"

The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson, Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within the framework of this theory, algorithmic properties of abstract models are investigated by constructing representations on the set of natural numbers and studying relations between algorithmic and structural properties of these models. This book is a very readable exposition of the modern theory of constructive models and describes methods and approaches developed by representatives of the Siberian school of algebra and logic and some other researchers (in particular, Nerode and his colleagues). The main themes are the existence of recursive models and applications to fields, algebras, and ordered sets (Ershov), the existence of decidable prime models (Goncharov, Harrington), the existence of decidable saturated models (Morley), the existence of decidable homogeneous models (Goncharov and Peretyat'kin), properties of the Ehrenfeucht theories (Millar, Ash, and Reed), the theory of algorithmic dimension and conditions of autostability (Goncharov, Ash, Shore, Khusainov, Ventsov, and others), and the theory of computable classes of models with various properties. Future perspectives of the theory of constructive models are also discussed. Most of the results in the book are presented in monograph form for the first time. The theory of constructive models serves as a basis for recursive mathematics. It is also useful in computer science, in particular, in the study of programming languages, higher level languages of specification, abstract data types, and problems of synthesis and verification of programs. Therefore, the book will be useful for not only specialists in mathematical logic and the theory of algorithms but also for scientists interested in the mathematical fundamentals of computer science. The authors are eminent specialists in mathematical logic. They have established fundamental results on elementary theories, model theory, the theory of algorithms, field theory, group theory, applied logic, computable numberings, the theory of constructive models, and the theoretical computer science.

fEt moi, . . . . sifavait sucommenten rcvenir, One service mathematics has rendered the jen'yseraispointall: human race. It hasput rommon senseback JulesVerne whereit belongs, on the topmost shelf next tothedustycanisterlabelled'discardednon Theseriesis divergent; thereforewemaybe sense'. ahletodosomethingwithit. EricT. Bell O. Heaviside Mathematicsisatoolforthought. Ahighlynecessarytoolinaworldwherebothfeedbackandnon linearitiesabound. Similarly, allkindsofpartsofmathematicsserveastoolsforotherpartsandfor othersciences. Applyinga simplerewritingrule to thequoteon theright aboveonefinds suchstatementsas: 'One service topology hasrenderedmathematicalphysics . . . '; 'Oneservicelogichasrenderedcom puterscience . . . ';'Oneservicecategorytheoryhasrenderedmathematics . . . '. Allarguablytrue. And allstatementsobtainablethiswayformpartoftheraisond'etreofthisseries. This series, Mathematics and Its Applications, started in 1977. Now that over one hundred volumeshaveappeareditseemsopportunetoreexamineitsscope. AtthetimeIwrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by puttingforth new branches. It also happens, quiteoften in fact, that branches which were thought to becompletely disparatearesuddenly seento berelated. Further, thekindandlevelofsophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially)in regionaland theoretical economics; algebraic geometryinteractswithphysics; theMinkowskylemma, codingtheoryandthestructure of water meet one another in packing and covering theory; quantum fields, crystal defectsand mathematicalprogrammingprofit from homotopy theory; Liealgebras are relevanttofiltering; andpredictionandelectricalengineeringcanuseSteinspaces. And in addition to this there are such new emerging subdisciplines as 'experimental mathematics', 'CFD', 'completelyintegrablesystems', 'chaos, synergeticsandlarge-scale order', whicharealmostimpossibletofitintotheexistingclassificationschemes. They drawuponwidelydifferentsectionsofmathematics. " By andlarge, all this stillapplies today. Itis still truethatatfirst sightmathematicsseemsrather fragmented and that to find, see, and exploit the deeper underlying interrelations more effort is neededandsoarebooks thatcanhelp mathematiciansand scientistsdoso. Accordingly MIA will continuetotry tomakesuchbooksavailable. If anything, the description I gave in 1977 is now an understatement."

The first edition of this book entitled Analysis on Riemannian Manifolds and Some Problems of Mathematical Physics was published by Voronezh Univer sity Press in 1989. For its English edition, the book has been substantially revised and expanded. In particular, new material has been added to Sections 19 and 20. I am grateful to Viktor L. Ginzburg for his hard work on the transla tion and for writing Appendix F, and to Tomasz Zastawniak for his numerous suggestions. My special thanks go to the referee for his valuable remarks on the theory of stochastic processes. Finally, I would like to acknowledge the support of the AMS fSU Aid Fund and the International Science Foundation (Grant NZBOOO), which made possible my work on some of the new results included in the English edition of the book. Voronezh, Russia Yuri Gliklikh September, 1995 Preface to the Russian Edition The present book is apparently the first in monographic literature in which a common treatment is given to three areas of global analysis previously consid ered quite distant from each other, namely, differential geometry and classical mechanics, stochastic differential geometry and statistical and quantum me chanics, and infinite-dimensional differential geometry of groups of diffeomor phisms and hydrodynamics. The unification of these topics under the cover of one book appears, however, quite natural, since the exposition is based on a geometrically invariant form of the Newton equation and its analogs taken as a fundamental law of motion."

This book is a revised edition of the monograph which appeared under the same title in the series Research Notes in Theoretical Computer Science, Pit man, in 1986. In addition to a general effort to improve typography, English, and presentation, the main novelty of this second edition is the integration of some new material. Part of it is mine (mostly jointly with coauthors). Here is brief guide to these additions. I have augmented the account of categorical combinatory logic with a description of the confluence properties of rewriting systems of categor ical combinators (Hardin, Yokouchi), and of the newly developed cal culi of explicit substitutions (Abadi, Cardelli, Curien, Hardin, Levy, and Rios), which are similar in spirit to the categorical combinatory logic, but are closer to the syntax of A-calculus (Section 1.2). The study of the full abstraction problem for PCF and extensions of it has been enriched with a new full abstraction result: the model of sequential algorithms is fully abstract with respect to an extension of PCF with a control operator (Cartwright, Felleisen, Curien). An order extensional model of error-sensitive sequential algorithms is also fully abstract for a corresponding extension of PCF with a control operator and errors (Sections 2.6 and 4.1). I suggest that sequential algorithms lend themselves to a decomposition of the function spaces that leads to models of linear logic (Lamarche, Curien), and that connects sequentiality with games (Joyal, Blass, Abramsky) (Sections 2.1 and 2.6)."

Geometric properties and relations play central roles in the description and processing of spatial data. The properties and relations studied by mathematicians usually have precise definitions, but verbal descriptions often involve imprecisely defined concepts such as elongatedness or proximity. The methods used in soft computing provide a framework for formulating and manipulating such concepts. This volume contains eight papers on the soft definition and manipulation of spatial relations and gives a comprehensive summary on the subject.

Traditional Artificial Intelligence (AI) systems adopted symbolic processing as their main paradigm. Symbolic AI systems have proved effective in handling problems characterized by exact and complete knowledge representation. Unfortunately, these systems have very little power in dealing with imprecise, uncertain and incomplete data and information which significantly contribute to the description of many real world problems, both physical systems and processes as well as mechanisms of decision making. Moreover, there are many situations where the expert domain knowledge (the basis for many symbolic AI systems) is not sufficient for the design of intelligent systems, due to incompleteness of the existing knowledge, problems caused by different biases of human experts, difficulties in forming rules, etc. In general, problem knowledge for solving a given problem can consist of an explicit knowledge (e.g., heuristic rules provided by a domain an implicit, hidden knowledge "buried" in past-experience expert) and numerical data. A study of huge amounts of these data (collected in databases) and the synthesizing of the knowledge "encoded" in them (also referred to as knowledge discovery in data or data mining), can significantly improve the performance of the intelligent systems designed."

Faced with the challenge of solving the hard optimization problems that abound in the real world, existing methods often encounter great difficulties. Important applications in business, engineering or economics cannot be tackled by the techniques that have formed the predominant focus of academic research throughout the past three decades. Exact and heuristic approaches are dramatically changing our ability to solve problems of practical significance and are extending the frontier of problems that can be handled effectively. This monograph details state-of-the-art optimization methods, both exact and heuristic, for the LOP. The authors employ the LOP to illustrate contemporary optimization technologies as well as how to design successful implementations of exact and heuristic procedures. Therefore, they do not limit the scope of this book to the LOP, but on the contrary, provide the reader with the background and practical strategies in optimization to tackle different combinatorial problems.

Biometrics, the science of using physical traits to identify individuals, is playing an increasing role in our security-conscious society and across the globe. Biometric authentication, or bioauthentication, systems are being used to secure everything from amusement parks to bank accounts to military installations. Yet developments in this field have not been matched by an equivalent improvement in the statistical methods for evaluating these systems. Compensating for this need, this unique text/reference provides a basic statistical methodology for practitioners and testers of bioauthentication devices, supplying a set of rigorous statistical methods for evaluating biometric authentication systems. This framework of methods can be extended and generalized for a wide range of applications and tests. This is the first single resource on statistical methods for estimation and comparison of the performance of biometric authentication systems. The book focuses on six common performance metrics: for each metric, statistical methods are derived for a single system that incorporates confidence intervals, hypothesis tests, sample size calculations, power calculations and prediction intervals. These methods are also extended to allow for the statistical comparison and evaluation of multiple systems for both independent and paired data. Topics and features: * Provides a statistical methodology for the most common biometric performance metrics: failure to enroll (FTE), failure to acquire (FTA), false non-match rate (FNMR), false match rate (FMR), and receiver operating characteristic (ROC) curves * Presents methods for the comparison of two or more biometric performance metrics * Introduces a new bootstrap methodology for FMR and ROC curve estimation * Supplies more than 120 examples, using publicly available biometric data where possible * Discusses the addition of prediction intervals to the bioauthentication statistical toolset * Describes sample-size and power calculations for FTE, FTA, FNMR and FMR Researchers, managers and decisions makers needing to compare biometric systems across a variety of metrics will find within this reference an invaluable set of statistical tools. Written for an upper-level undergraduate or master's level audience with a quantitative background, readers are also expected to have an understanding of the topics in a typical undergraduate statistics course. Dr. Michael E. Schuckers is Associate Professor of Statistics at St. Lawrence University, Canton, NY, and a member of the Center for Identification Technology Research.

Computer-aided-design (CAD) of semiconductor microtransducers is relatively new in contrast to their counterparts in the integrated circuit world. Integrated silicon microtransducers are realized using microfabrication techniques similar to those for standard integrated circuits (ICs). Unlike IC devices, however, microtransducers must interact with their environment, so their numerical simulation is considerably more complex. While the design of ICs aims at suppressing "parasitic effects, microtransducers thrive on optimizing the one or the other such effect. The challenging quest for physical models and simulation tools enabling microtransducer CAD is the topic of this book. It is intended as a text for graduate students in Electrical Engineering and Physics and as a reference for CAD engineers in the microsystems industry. This text evolved from a series of courses offered to graduate students from Electrical Engineering and Physics. Much of the material in the book can be presented in about 40 hours of lecture time. The book starts with an illustrative example which highlights the goals and benefits of microtransducer CAD. This follows with a summary of model equations describing electrical transport in semiconductor devices and microtransducers in the absence of external fields. Models treating the effects of the external radiant, magnetic, thermal, and mechanical fields on electrical transport are then systematically introduced. To enable a smooth transition into modeling of mechanical systems, an abridged version of solid structural and fluid mechanics is presented, whereby the focus is on pertinent model equations and boundary conditions. This follows with model equations and boundary conditions relevant to various types of mechanical microactuators including electrostatic, thermal, magnetic, piezoelectric, and electroacoustic. The book concludes with a glimpse into SPICE simulation of the mixed-signal microsystem, i.e., microtransducer plus circuitry. Where possible, the model equations are supplemented with tables and/or graphs of process-dependent material data to enable the CAD engineer to carry out simulations even when reliable material models are not available. IVZ LANG: Introduction: Modeling and Simulation of Microtransducers; Illustrative Example; Progress in Microtransducer Modeling; References.- Basic Electronic Transport: Poisson s Equation; Continuity Equations; Carrier Transport in Crystalline Materials and Isothermal Behavior; Electrical Conductivity and Isothermal Behavior in Polycrystalline Materials; Electrical Conductivity and Isothermal Behavior in Metals; Boundary and Interface Conditions; The External Fields What Do They Influence?; References.- Radiation Effects on Carrier Transport: Reflection and Transmission of Optical Signals; Modeling Optical Absorption in Intrinsic Semiconductors; Absorption in Heavily-Doped Semiconductors; Optical Generation Rate and Quantum Efficiency; Low Energy Interactions with Insulators and Metals; High Energy Interactions and Monte Carlo Simulations; Model Equations for Radiant Sensor Simulation; Illustrative Simulation Example Color Sensor; References.- Magnetic-Field Effects on Carrier Transport: Galvanomagnetic Transport Equation; Galvanomagnetic Transport Coefficients; Equations and Boundary Conditions for Magnetic Sensor Simulation; Illustrative Simulation Example Micromachined Magnetic Vector Probe; References.- Thermal Non-Uniformity Effects on Carrier Transport: Non-Isothermal Effects; Electrothermal Transport Model; Electrical and Thermal Transport Coefficients; Electro-Thermo-Magnetic Interactions; Heat Transfer in Thermal Microstructures; Summary of Equations and Computational Procedure; Illustrative Simulation Example Micro Pirani Gauge; References.- Mechanical Effects on Carrier Transport: Piezoresistive Effect; Strain and Electron Transport; Strain and Hole Transport; Piezojunction Effect; Effects of Stress Gradients; Galvano-Piezo-Magnetic Effects; The Piezo Drift-Diffusion Transport Model; Illustrative Simulation Example Stress Effects on Hall Sensors; References.- Mechanical and Fluidic Signals: Definitions; Model Equations for Mechanical Analysis; Model Equations for Analysis of Fluid Transport; Illustrative Simulation Example Analysis of Flow Channels; References.- Micro-Actuation: Transduction Principles; State-of-the-Art and Preview; Electrostatic Actuation; Thermal Actuation; Magnetic Actuation; Piezoelectric Actuation; Electroacoustic Transducers; Computational Procedure and Coupling; Illustrative Example CMOS Micromirror.- Microsystem Simulation: Electrical Analogues for Mixed-Signals and Historical Developments; Circuit Modeling and Implementation Considerations; Lumped Analysis: Illustrative Example Electrostatic Micromirror; Distributed Analysis: Illustrative Example Flow Microsensor; References.- Subject Index."

In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets.

The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations.

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"The book as a whole is awell-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in therecently developed methods. The book, reflecting the currentstate of the art, can also be used for teaching special courses."
(Mathematical Reviews)"

Polynomial optimization have been a hot research topic for the past few years and its applications range from Operations Research, biomedical engineering, investment science, to quantum mechanics, linear algebra, and signal processing, among many others. In this brief the authors discuss some important subclasses of polynomial optimization models arising from various applications, with a focus on approximations algorithms with guaranteed worst case performance analysis. The brief presents a clear view of the basic ideas underlying the design of such algorithms and the benefits are highlighted by illustrative examples showing the possible applications.

This timely treatise will appeal to researchers and graduate students in the fields of optimization, computational mathematics, Operations Research, industrial engineering, and computer science."

This book offers a mathematical update of the state of the art of the research in the field of mathematical and numerical models of the circulatory system. It is structured into different chapters, written by outstanding experts in the field. Many fundamental issues are considered, such as: the mathematical representation of vascular geometries extracted from medical images, modelling blood rheology and the complex multilayer structure of the vascular tissue, and its possible pathologies, the mechanical and chemical interaction between blood and vascular walls, and the different scales coupling local and systemic dynamics. All of these topics introduce challenging mathematical and numerical problems, demanding for advanced analysis and efficient simulation techniques, and pay constant attention to applications of relevant clinical interest. This book is addressed to graduate students and researchers in the field of bioengineering, applied mathematics and medicine, wishing to engage themselves in the fascinating task of modeling the cardiovascular system or, more broadly, physiological flows.

This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method.

This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps that determine the global atmospheric model design. They encompass the choice of the equation set, computational grids on the sphere, horizontal and vertical discretizations, time integration methods, filtering and diffusion mechanisms, conservation properties, tracer transport, and considerations for designing models for massively parallel computers. A reader interested in applied numerical methods but also the many facets of atmospheric modeling should find this book of particular relevance.

This brief provides guidance for the application of cohesive models to determine damage and fracture in materials and structural components. This can be done for configurations with or without a pre-existing crack. Although the brief addresses structural behaviour, the methods described herein may also be applied to any deformation induced material damage and failure, e.g. those occurring during manufacturing processes. The methods described are applicable to the behaviour of ductile metallic materials and structural components made thereof. Hints are also given for applying the cohesive model to other materials.

Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student in applied mathematics and engineering, this text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation.
Prerequisites suggested for using this book in a course might include at least one semester of partial differential equations and some programming capability. The author stresses the use of technology throughout the text, allowing the student to utilize it as much as possible. The use of graphics for both illustration and analysis is emphasized, and algebraic manipulators are used when convenient. This is the second volume of a two-part book.

In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011. The selected articles present recent advances in the mathematical understanding and analysis of sparse grid discretization. Aspects arising from applications are given particular attention.

This book constitutes the thoroughly refereed post-conference proceedings of the 20th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2013, held in Ischia, Italy, in July 2013. The 28 revised full papers presented were carefully reviewed and selected from 67 submissions. SIROCCO is devoted to the study of communication and knowledge in distributed systems. Special emphasis is given to innovative approaches and fundamental understanding, in addition to efforts to optimize current designs. The typical areas include distributed computing, communication networks, game theory, parallel computing, social networks, mobile computing (including autonomous robots), peer to peer systems, communication complexity, fault tolerant graph theories and randomized/probabilistic issues in networks.