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During the past few decades, the gradual merger of Discrete Geometry and the newer discipline of Computational Geometry has provided enormous impetus to mathematicians and computer scientists interested in geometric problems. This volume, which contains 32 papers on a broad range of topics of current interest in the field, is an outgrowth of that synergism.It includes surveys and research articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension. ... Read more

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The book "Computational Error and Complexity in Science and Engineering" pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologists. Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will tell us how much computation/computational effort has been spent to achieve that quality of result. Anyone who wants the specified physical problem to be solved has every right to know the quality of the solution as well as the resources spent for the solution. The computed error as well as the complexity provide the scientific convincing answer to these questions.
Specifically some of the disciplines in which the book will be readily useful are (i) Computational Mathematics, (ii) Applied Mathematics/Computational Engineering, Numerical and Computational Physics, Simulation and Modelling. Operations Research (both deterministic and stochastic), Computing Methodologies, Computer Applications, and Numerical Methods in Engineering.

Key Features:

- Describes precisely ready-to-use computational error and complexity
- Includes simple easy-to-grasp examples wherever necessary.
- Presents error and complexity in error-free, parallel, and probabilistic methods.
- Discusses deterministic and probabilistic methods with error and complexity.
- Points out the scope and limitation of mathematical error-bounds.
- Provides a comprehensive up-to-date bibliography after each chapter.

· Describes precisely ready-to-use computational error and complexity
· Includes simple easy-to-grasp examples wherever necessary.
· Presents error and complexity in error-free, parallel, and probabilistic methods.
· Discusses deterministic and probabilistic methods with error and complexity.
· Points out the scope and limitation of mathematical error-bounds.
· Provides a comprehensive up-to-date bibliography after each chapter. ... Read more

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This book is for readers with backgrounds in science engineering who have experience in computer programming but who lack a training in software engineering. The treatment is centered around a case study in software development in "e-Science'' using the Java™ programming language. A graphical front-end for browsing and visualising scientific waveform data is progressively refactored using important design patterns for object-oriented software. The final product is ready for porting onto the Grid. Object-oriented design patterns are taught in a real-world context which is relevant to computational science. A comprehensive CD of the case study accompanies the book.

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The finite-element method was originally developed by engineers in the 1950s to analyze large structural systems for aircraft. Aimed at advanced level undergraduates of engineering and fluid mechanics and researchers, engineers and scientists in fluid mechanics, mechanical and chemical engineering, this text derives, develops and applies finite-element solution methodology directly to the differential equation systems governing distinct and practical problem classes in fluid mechanics. It is principally a text on fluid mechanics and the theory of its computational simulation, for those with a basic interest in fluid mechanics. ... Read more

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Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined plasmas in modern magnetic fusion experiments and future magnetic fusion reactors. Largely self-contained, the text presents the basic concepts necessary for the numerical solution of partial differential equations.

Along with discussing numerical stability and accuracy, the author explores many of the algorithms used today in enough depth so that readers can analyze their stability, efficiency, and scaling properties. He focuses on mathematical models where the plasma is treated as a conducting fluid, since this is the most mature plasma model and most applicable to experiments. The book also emphasizes toroidal confinement geometries, particularly the tokamak—a very successful configuration for confining a high-temperature plasma. Many of the basic numerical techniques presented are also appropriate for equations encountered in a higher-dimensional phase space.

One of the most challenging research areas in modern science is to develop suitable algorithms that lead to stable and accurate solutions that can span relevant time and space scales. This book provides an excellent working knowledge of the algorithms used by the plasma physics community, helping readers on their way to more advanced study.

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Presents discretization methods on non-matching triangulations and iterative solvers with emphasis on mortar fine elements, Schwartz methods, and multigrid techniques. Also emphasizes the role of trace theorems, dual norms and weak interface conditions. Softcover. ... Read more

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All over the world sport plays a prominent role in society: as a leisure activity for many, as an ingredient of culture, as a business and as a matter of national prestige in such major events as the World Cup in soccer or the Olympic Games. Hence, it is not surprising that science has entered the realm of sports, and, in particular, that computer simulation has become highly relevant in recent years. This is explored in this book by choosing five different sports as examples, demonstrating that computational science and engineering (CSE) can make essential contributions to research on sports topics on both the fundamental level and, eventually, by supporting athletes’ performance.

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Mathematical models in the social sciences have become increasingly sophisticated and widespread in the last decade.This period has also seen many critiques, most lamenting the sacrifices incurred in pursuit of mathematical perfection. If, as critics argue, our ability to understand the world has not improved during the mathematization of the social sciences, we might want to adopt a different paradigm.This book examines the three main fields of mathematical modeling--game theory, statistics, and computational methods--and proposes a new framework for modeling. ... Read more

Customer Reviews (1)

Review From Public Choice
Imagine that you're out for a relaxing dinner at your neighborhood bistro. Your waiter, a lanky young lad named Trey, sidles up to your table and describes the evening's specials beginning with a free range, grilled, Sonoma chicken bathed in a white wine and balsamic reduction and peppered with bits of black truffle.You think that the dish sounds wonderful and accept it for consumption with no revisions.

After reading this book, I can only guess that Scott de Marchi's reaction would be a little different.He'd point out that grilling was just one of many options. Alternatively, the chef could have fried it, baked it, braised it, seared it, roasted it, or even cooked it at low temperature in a Ziplock bag.Why did the chef choose grilling? And, oh by the way, why free range Sonoma chicken?Why not organic chicken - wouldn't its stronger taste hold up better to the wine and balsamic reduction? Heck, why not go all out and get one of those chickens that was hand-fed corn mash by Italian monks who gave it daily massages and hour long walks thru Tuscan valleys?And what about the number of possible spice and sauce combinations?Why black truffles?

The chicken entrée suffers from a curse of dimensionality.By modifying our choices on each dimension, we can create enough chicken variations to awe even the late Carl Sagan. Gourmands benefit from the curse - we can expect an original special every week.Social scientists - historians, theorists and empiricists alike - take the curse on the chin.It obliges a rethinking of how we construct and evaluate a model, or so says Scott de Marchi in this fascinating and challenging new book.To feel the effects of the curse, suppose that you're writing an empirical model of why countries go to war. In choosing variables for your regression, you pick ten from a set of twenty.You then toss in an interaction term, chosen with great care from the forty-five possible pairs.You then choose a model specification - linear, log linear, non parametric, or whatever.When you step back and look at the process of creating your empirical model, you realize that you have as many possible regressions as the bistro's chef has chicken entrees.

Suppose instead that you're writing a game theory model of first strikes.Professor de Marchi has a few questions to ask:Is the game one shot or repeated?Are moves sequential or simultaneous?Is information asymmetric?Are the players risk averse?Are preferences separable?

Given the billions of possible model specifications, the task of finding significant coefficients or proving (wink-wink) a general theorem suddenly doesn't look so impressive.Even combining the two: integrating a theoretical model and empirical analysis (EITM anyone?) looks about as hard as cooking up a little Bonferroni chicken to go with that Oregon Coast Pinot Noir. Once aware of the existence of the curse, we can see no shortage of naked emperors (some of whom de Marchi reveals with some relish).We can also try to get around it, to conjure up a counter hex.

The counter hex proposed by de Marchi consists of three parts. First, he wants us to split our data into training sets and testing sets -- a good idea, but it comes with a cost.A little math shows that dividing the data results in data sets that are, on average, only half as big, so we'll need a lot more wars for IR to have any hope of finding statistical significance.

Second, he wants us to analyze classes of models and not individual models with idiosyncratic (and possibly brittle) assumptions.In demanding that we consider classes of models, de Marchi implicitly charges some mathematical theorists with selling magic beans in the form of theorems that rely on specific functional forms.Results for a single functional form do not a general theorem make.The difference between a three person, three alternative example of a Condercet Cycle and Arrow's Possibility Theorem is the difference between predicting that a falling apple will hit the ground and formulating the theory of gravity.But proving general results is not easy.In fact, few general results exist.So why not be honest about the lack of generality rather than cooking up specific models that give the desired result?

The proposed solution, to create a feature space (dimensions on which we make various assumptions) and explore all of the models within that space, sounds good but it creates a problem unless we can increase the birth rates in Pasadena and Rochester. We still have too many models to explore. To get around the problem of too many models and too little time, de Marchi has a novel solution: use computational methods to explore the space of possible models. If we're using specific functional forms anyway, we might as well simulate them and not bother with formal proofs.Simulation is quicker.By simulating within feature space, we can distinguish robust findings from brittle examples.This approach requires combining art and science.We must constrain the feature space so that we're merely stunned and not cursed by the dimensionality.

Third, de Marchi wants our models to be more realistic.(Who doesn't?) But, how do we achieve realism and yet maintain a limited feature space that we explore in depth?Can we be realistic and remain within or at least comfortably near Chris Achen's three-variable world?de Marchi believes that we can, provided that we start simple and build up toward realism.Thus, we have complicated models as the sum of lots of simple models, all of which we understand fully as a result of exploring their feature spaces.As an example of a realistic model, he goes outside of social science and looks at machine chess programs.These programs don't just apply to chess in some metaphorical sense, as in "the Colonel Blotto game captures the essence of chess."They actually play chess and play better than people do.Having a model that plays chess produces a further advantage: the modeler can use real data from games.

Let's suppose we take a vote between continuing with the status quo and accepting de Marchi's vision of the future. The status quo consists of unrealistic, narrow models that we test using all of our data with substantial freedom over what control variables we include. de Marchi's alternative consists of cumulative realistic models (as well as nearby models to make sure that our theory is robust) that are calibrated on training sets and tested on separate data. The vote would be Roosevelt-Landon 1936 all over again.Apart from some holdouts in Vermont and Maine, de Marchi would win everywhere.However, in this election, we don't just pull levers.We have to vote with our heads, which can be thick and slow to respond.

The path de Marchi would like us to take requires nontrivial changes in how we build models and how we test them. Sure we can learn to split our data sets in two.But will we learn Perl?Will we take the time to construct a feature space?And what if that feature space reveals brittleness? Will we bail out and write a paper with quasi-linear preferences or with a one-dimensional preference space?Not only does he require that we learn new tools, he's asking us to change our standards. Rather than bestow awards on books that consist of (a) a captivating anecdote from history (b) a narrow specific functional form model that provides the key intuition (c) an empirical test with ten control variables and one interactive term that demonstrates validity of key intuition and (d) a rich case study that fills in all the gaps, we might see these books as cursed by problems of dimensionality. With so much history, so many models, and so many variables to choose from, these books should be as easy to make as the Chicken Marbella from The Silver Palate.

This critique of the status quo may get under the skin of some readers. Sure, your average PhD student can choose from among thousands of theoretical models and econometric specifications, but finding two that align -- where the econometrics support what the theory predicts - is not as easy as he makes it sound. If it were, we'd have many more papers that met this standard, and we wouldn't have summer courses sponsored by the NSF teaching students how to integrate these methods taught by (among others) Scott de Marchi.Furthermore, the models in these award-winning books aren't all that brittle.They do meet qualitative robustness criteria. Most theorists and econometricians can sniff out rigged models.We can tell a universal insight from a unicorn. When we see a model with quasi-linear preferences or the monotone likelihood ratio property, we know the rabbit has been placed in the hat, and we take the author to task accordingly.

Given that we're all aware of the curse, and we're qualitatively mindful of it when evaluating research, de Marchi's claims seem less provocative, and at the same time, more reasonable.He's advocating that we supplement our reasoned judgment with a scientific approach based on feature spaces and computational models.Any time we can replace subjective criteria with more objective, scientific criteria, we move science forward, which this book urges us to do.

Some critiques may complain that this book explains how to do it, but it doesn't actually do it. True, the book would be stronger if it took us on a complete tour of the shiny new city on the hill that it constructs. A short chapter on how de Marchi built a model (and critics may say an unrealistic one - ouch!) along with a smidgen of Perl code won't sway the masses. The book would be more convincing if had a six hundred page companion volume that took on a puzzle, defined and explored a feature space, tested the robust conclusions out of sample, and then built on the model cumulatively to create a skin tight fit to data.It doesn't.That's because neither he, nor anyone else for that matter, quite knows how to do what he'd like us to do. We're not there, at least not yet, though I suspect that midnight oil burns in Durham.

At present, we have is this slim volume, full of good ideas, deep insights, and practical advice for how to do sound methodological work and how not to do it.Given these strengths, this book should earn a cultish following among graduate students who possess a methodological bent. The book should also become standard reading in introductory methodology courses, at least in those that aren't spineless. (I mean those that don't rely on books.)If it doesn't, the discipline misses an opportunity to improve methodological training.

This is the rare book that suffers from brevity - the examples could be worked out in greater detail. It's not perfect.The argument is flawed in places.For example, not all theory has to be immediately tested to be useful.All of that preference theory comes in handy when he writes his separable preference model, yet little of it was written to be testable.Yes, the light it shines is harsh in places, but overall, the book must be seen as a huge success.It's both deep and approachable.de Marchi manages not to dull our senses with an abundance of jargon or notation.To the contrary, the reader wants even more detail, especially about computational models.

Computational modelers like de Marchi want space at the conferences and in the journals.They want to be taken as seriously as the mathematical modelers. Surely, de Marchi has advanced that cause. As his book makes clear, the existence of computational models provides an opportunity to improve social science. Computational modelers have a powerful technology and they're building a science. They've gained footholds in physics, chemistry, biology, and (egad) mathematics.Social scientists would do far better to be accepting than to be skeptical.

In sum, de Marchi's provocative, incisive, and at times brilliant introduction to computational methods can be thought analogous to one of those early maps of North America.We might quibble with the depiction of the coastline, but we cannot deny the existence of the continent.




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Product Description

Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.

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This book focuses on the computational and theoretical approaches to the coupling of fluid mechanics and solids mechanics. In particular, nonlinear dynamical systems are introduced to the handling of complex fluid-solid interaction systems, For the past few decades, many terminologies have been introduced to this field, namely, flow-induced vibration, aeroelasticity, hydroelasticity, fluid-structure interaction, fluid-solid interaction, and more recently multi-physics problems. Moreover, engineering applications are distributed within different disciplines, such as nuclear, civil, aerospace, ocean, chemical, electrical, and mechanical engineering. Regrettably, while each particular subject is by itself very extensive, it has been difficult for a single book to cover in a reasonable depth and in the mean time to connect various topics. In light of the current multidisciplinary research need in nanotechnology and bioengineering, there is an urgent need for books to provide such a linkage and to lay a foundation for more specialized fields.

- Interdisciplinary across all types of engineering
- Comprehensive study of fluid-solid interaction
- Discusses complex system dynamics derived from interactive systems
- Provides mathematic modeling of biological systems ... Read more

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The boundary element method (BEM), also known as the boundary integral equation method (BIEM), is a modern numerical technique which has enjoyed increasing popularity over the past two decades. It is now an established alternative to traditional computational methods of engineering analysis. The main advantage of the BEM is its unique ability to provide a complete solution in terms of boundary values only, with substantial savings in modeling effort. This book is designed to provide readers with a comprehensive and up-to-date account of the method and its application to problems in engineering and science. Each chapter provides a brief description of historical development, followed by basic theory, derivation and examples. ... Read more

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This book is based on the author's Ph.D. thesis which was selected as the winning thesis of the 1999 ACM Doctoral Dissertation Competition. Dieter van Melkebeek did his Ph.D. work at the University of Chicago with Lance Fortnow as thesis advisor. This work studies some central issues in computational complexity: the relative power of time, space, and randomness in computing and verification. The author develops techniques for separating complexity classes by isolating structural differences between their complete problems. He presents several approaches based on such diverse concepts as density, redundancy, and frequency of occurrence. ... Read more

Product Description
This book considers recent developments in numerical error estimation and adaptive discretization for finite element and finite volume methods with particular attention given to discretization methods used frequently in computational fluid dynamics. The volume consists of six detailed articles by leading specialists covering a range of topics including a posteriori error estimation of functionals, one- and two-sided error bounds, error indicators for ad aptivity, and nd geometrical aspects of adaptive mesh refinement. This book should be of interest to readers actively working in the field as well as readers seeking a comprehensive introduction to the topic. ... Read more

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Dealing with the volume, complexity, and diversity of data currently being generated by scientific experiments and simulations often causes scientists to waste productive time. Scientific Data Management: Challenges, Technology, and Deployment describes cutting-edge technologies and solutions for managing and analyzing vast amounts of data, helping scientists focus on their scientific goals.

The book begins with coverage of efficient storage systems, discussing how to write and read large volumes of data without slowing the simulation, analysis, or visualization processes. It then focuses on the efficient data movement and management of storage spaces and explores emerging database systems for scientific data. The book also addresses how to best organize data for analysis purposes, how to effectively conduct searches over large datasets, how to successfully automate multistep scientific process workflows, and how to automatically collect metadata and lineage information.

This book provides a comprehensive understanding of the latest techniques for managing data during scientific exploration processes, from data generation to data analysis. Enhanced by numerous detailed color images, it includes real-world examples of applications drawn from biology, ecology, geology, climatology, and more.

Check out Dr. Shoshani discuss the book during an interview with International Science Grid This Week (iSGTW): http://www.isgtw.org/?pid=1002259

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The focus of this book deals with a cross cutting issue affecting all transport disciplines, whether it be photon, neutron, charged particle or neutrino transport. That is, verification and validation (V&V). In other words, are the equations being solved correctly and are the correct equations being solved? Verification and validation assures a scientist, engineer or mathematician that a simulation code is a mirror of reality and not just an expensive computer game. In this book, we will learn what the astrophysicist, atmospheric scientist, mathematician or nuclear engineer do to assess the accuracy of their code. What convergence studies, what error analysis, what problems do each field use to benchmark ascertain the accuracy of their transport simulations. Is there a need for new benchmark problems? Are there experiments that can be used to help validate the simulation results? If not, are there new experiments that could address these issues? These are all questions raised in this proceedings of the Second Computational Methods in Transport Workshop.

Product Description

Describes most popular computational methods used to solve problems in electromagnetics

Matlab code is included throughout, so that the reader can implement the various techniques discussed

Exercises included

Customer Reviews (1)

Review of "Computational Electromagnetics"
This is an excellent introduction to the field of computational electromagnetics, from a reasonably mathematical perspective - but in a very readable form, well suited to electronic engineers. It's obviously a book on a specialist topic; assuming you want to understand the mathematics behind finite approximations of Maxwell's equations (FEM, FDTD, Mom) - at least at introductory level - this is certainly one of the best to start with. As the authors state, although there are a number of books covering one of these methods in detail, only a couple of others (in particular, those by Sadiku, and myself) -and of course this text - cover all three of these methods. Strongly recommended. ... Read more

Customer Reviews (1)

Up to the point
This survey precludes a solid dive in to the world of analysis, yet manages to maitain an overview to this vast field. The chapter 1 summaries on BASIC and FORTRAN(-an excellent language for the engineering domain-) are particularly concise and welcome. It's a standard text, but one that excells on certain areas. ... Read more

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Computational modelling allows researchers to combine the rich detail of qualitative research with the rigour of quantitative and formal research, as well as to represent complex structures and processes within a theoretical model.

After an introduction to modelling, the authors discuss the role of computational methods in the social sciences. They treat computational methods, including dynamic simulation, knowledge-based models and machine learning, as a single broad class of research tools and develop a framework for incorporating them within established traditions of social science research. They provide a concise description of each method and a variety of social science illustrations, including four detailed examples. ... Read more

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This book treats the numerical analysis of finite element computational fluid dynamics. Assuming minimal background, the text covers finite element methods; the derivation, behavior, analysis, and numerical analysis of Navier Stokes equations; and turbulence and turbulence models used in simulations. Each chapter on theory is followed by a numerical analysis chapter that expands on the theory. The chapters contain numerous exercises.

Introduction to the Numerical Analysis of Incompressible Viscous Flows provides the foundation for understanding the interconnection of the physics, mathematics, and numerics of the incompressible case, which is essential for progressing to the more complex flows not addressed in this book (e.g., viscoelasticity, plasmas, compressible flows, coating flows, flows of mixtures of fluids, and bubbly flows). With mathematical rigor and physical clarity, the book progresses from the mathematical preliminaries of energy and stress to finite element computational fluid dynamics in a format manageable in one semester.

Audience: This unified treatment of fluid mechanics, analysis, and numerical analysis is intended for graduate students in mathematics, engineering, physics, and the sciences who are interested in understanding the foundations of methods commonly used for flow simulations. ... Read more

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This volume contains selected papers that were presented at theInternational Conference `Computational Finance' held at the LondonBusiness School. Formerly known as Neural Networks in the CapitalMarkets (NNCM), this series of meetings has emerged as a trulymulti-disciplinary international conference and provided aninternational focus for innovative research on the application of amultiplicity of advanced decision technologies to many areas offinancial engineering. It has drawn upon theoretical advances infinancial economics and robust methodological developments in thestatistical, econometric and computer sciences. To reflect itsmulti-disciplinary nature, the NNCM conference has adopted the newtitle `Computational Finance'.
The papers in this volume are organised in six parts: Market Dynamicsand Risk, Trading and Arbitrage strategies, Volatility and Options,Term-Structure and Factor Models, Corporate Distress Models, andAdvances in Methodology. ... Read more