The contributions gathered here provide an overview of current research projects and selected software products of the Fraunhofer Institute for Algorithms and Scientific Computing SCAI. They show the wide range of challenges that scientific computing currently faces, the solutions it offers, and its important role in developing applications for industry. Given the exciting field of applied collaborative research and development it discusses, the book will appeal to scientists, practitioners, and students alike. The Fraunhofer Institute for Algorithms and Scientific Computing SCAI combines excellent research and application-oriented development to provide added value for our partners. SCAI develops numerical techniques, parallel algorithms and specialized software tools to support and optimize industrial simulations. Moreover, it implements custom software solutions for production and logistics, and offers calculations on high-performance computers. Its services and products are based on state-of-the-art methods from applied mathematics and information technology.

This book introduces the ade4 package for R which provides multivariate methods for the analysis of ecological data. It is implemented around the mathematical concept of the duality diagram, and provides a unified framework for multivariate analysis. The authors offer a detailed presentation of the theoretical framework of the duality diagram and also of its application to real-world ecological problems. These two goals may seem contradictory, as they concern two separate groups of scientists, namely statisticians and ecologists. However, statistical ecology has become a scientific discipline of its own, and the good use of multivariate data analysis methods by ecologists implies a fair knowledge of the mathematical properties of these methods. The organization of the book is based on ecological questions, but these questions correspond to particular classes of data analysis methods. The first chapters present both usual and multiway data analysis methods. Further chapters are dedicated for example to the analysis of spatial data, of phylogenetic structures, and of biodiversity patterns. One chapter deals with multivariate data analysis graphs. In each chapter, the basic mathematical definitions of the methods and the outputs of the R functions available in ade4 are detailed in two different boxes. The text of the book itself can be read independently from these boxes. Thus the book offers the opportunity to find information about the ecological situation from which a question raises alongside the mathematical properties of methods that can be applied to answer this question, as well as the details of software outputs. Each example and all the graphs in this book come with executable R code.

Biological and biomedical studies have entered a new era over the past two decades thanks to the wide use of mathematical models and computational approaches. A booming of computational biology, which sheerly was a theoretician's fantasy twenty years ago, has become a reality. Obsession with computational biology and theoretical approaches is evidenced in articles hailing the arrival of what are va- ously called quantitative biology, bioinformatics, theoretical biology, and systems biology. New technologies and data resources in genetics, such as the International HapMap project, enable large-scale studies, such as genome-wide association st- ies, which could potentially identify most common genetic variants as well as rare variants of the human DNA that may alter individual's susceptibility to disease and the response to medical treatment. Meanwhile the multi-electrode recording from behaving animals makes it feasible to control the animal mental activity, which could potentially lead to the development of useful brain-machine interfaces. - bracing the sheer volume of genetic, genomic, and other type of data, an essential approach is, ?rst of all, to avoid drowning the true signal in the data. It has been witnessed that theoretical approach to biology has emerged as a powerful and st- ulating research paradigm in biological studies, which in turn leads to a new - search paradigm in mathematics, physics, and computer science and moves forward with the interplays among experimental studies and outcomes, simulation studies, and theoretical investigations.

Multiple criteria decision aid (MCDA) methods are illustrated in this book through theoretical and computational techniques utilizing Python. Existing methods are presented in detail with a step by step learning approach. Theoretical background is given for TOPSIS, VIKOR, PROMETHEE, SIR, AHP, goal programming, and their variations. Comprehensive numerical examples are also discussed for each method in conjunction with easy to follow Python code. Extensions to multiple criteria decision making algorithms such as fuzzy number theory and group decision making are introduced and implemented through Python as well. Readers will learn how to implement and use each method based on the problem, the available data, the stakeholders involved, and the various requirements needed. Focusing on the practical aspects of the multiple criteria decision making methodologies, this book is designed for researchers, practitioners and advanced graduate students in the applied mathematics, information systems, operations research and business administration disciplines, as well as other engineers and scientists oriented in interdisciplinary research. Readers will greatly benefit from this book by learning and applying various MCDM/A methods. (Adiel Teixeira de Almeida, CDSID-Center for Decision System and Information Development, Universidade Federal de Pernambuco, Recife, Brazil) Promoting the development and application of multicriteria decision aid is essential to ensure more ethical and sustainable decisions. This book is a great contribution to this objective. It is a perfect blend of theory and practice, providing potential users and researchers with the theoretical bases of some of the best-known methods as well as with the computing tools needed to practice, to compare and to put these methods to use. (Jean-Pierre Brans, Vrije Universiteit Brussel, Brussels, Belgium) This book is intended for researchers, practitioners and students alike in decision support who wish to familiarize themselves quickly and efficiently with multicriteria decision aiding algorithms. The proposed approach is original, as it presents a selection of methods from the theory to the practical implementation in Python, including a detailed example. This will certainly facilitate the learning of these techniques, and contribute to their effective dissemination in applications. (Patrick Meyer, IMT Atlantique, Lab-STICC, Univ. Bretagne Loire, Brest, France)

This volume is composed of peer-reviewed papers that have developed from the First Conference of the International Society for NonParametric Statistics (ISNPS). This inaugural conference took place in Chalkidiki, Greece, June 15-19, 2012. It was organized with the co-sponsorship of the IMS, the ISI, and other organizations. M.G. Akritas, S.N. Lahiri, and D.N. Politis are the first executive committee members of ISNPS, and the editors of this volume. ISNPS has a distinguished Advisory Committee that includes Professors R.Beran, P.Bickel, R. Carroll, D. Cook, P. Hall, R. Johnson, B. Lindsay, E. Parzen, P. Robinson, M. Rosenblatt, G. Roussas, T. SubbaRao, and G. Wahba. The Charting Committee of ISNPS consists of more than 50 prominent researchers from all over the world. The chapters in this volume bring forth recent advances and trends in several areas of nonparametric statistics. In this way, the volume facilitates the exchange of research ideas, promotes collaboration among researchers from all over the world, and contributes to the further development of the field.The conference program included over 250 talks, including special invited talks, plenary talks, and contributed talks on all areas of nonparametric statistics. Out of these talks, some of the most pertinent ones have been refereed and developed into chapters that share both research and developments in the field.

This volume presents the latest advances and trends in nonparametric statistics, and gathers selected and peer-reviewed contributions from the 3rd Conference of the International Society for Nonparametric Statistics (ISNPS), held in Avignon, France on June 11-16, 2016. It covers a broad range of nonparametric statistical methods, from density estimation, survey sampling, resampling methods, kernel methods and extreme values, to statistical learning and classification, both in the standard i.i.d. case and for dependent data, including big data. The International Society for Nonparametric Statistics is uniquely global, and its international conferences are intended to foster the exchange of ideas and the latest advances among researchers from around the world, in cooperation with established statistical societies such as the Institute of Mathematical Statistics, the Bernoulli Society and the International Statistical Institute. The 3rd ISNPS conference in Avignon attracted more than 400 researchers from around the globe, and contributed to the further development and dissemination of nonparametric statistics knowledge.

This book presents various recently developed and traditional statistical techniques, which are increasingly being applied in social science research. The social sciences cover diverse phenomena arising in society, the economy and the environment, some of which are too complex to allow concrete statements; some cannot be defined by direct observations or measurements; some are culture- (or region-) specific, while others are generic and common. Statistics, being a scientific method - as distinct from a 'science' related to any one type of phenomena - is used to make inductive inferences regarding various phenomena. The book addresses both qualitative and quantitative research (a combination of which is essential in social science research) and offers valuable supplementary reading at an advanced level for researchers.

This book focuses on the application and development of information geometric methods in the analysis, classification and retrieval of images and signals. It provides introductory chapters to help those new to information geometry and applies the theory to several applications. This area has developed rapidly over recent years, propelled by the major theoretical developments in information geometry, efficient data and image acquisition and the desire to process and interpret large databases of digital information. The book addresses both the transfer of methodology to practitioners involved in database analysis and in its efficient computational implementation.

"We live in the age of data. In the last few years, the methodology of extracting insights from data or "data science" has emerged as a discipline in its own right. The R programming language has become one-stop solution for all types of data analysis. The growing popularity of R is due its statistical roots and a vast open source package library. The goal of "Beginning Data Science with R" is to introduce the readers to some of the useful data science techniques and their implementation with the R programming language. The book attempts to strike a balance between the how: specific processes and methodologies, and understanding the why: going over the intuition behind how a particular technique works, so that the reader can apply it to the problem at hand. This book will be useful for readers who are not familiar with statistics and the R programming language.

This book presents the R software environment as a key tool for oceanographic computations and provides a rationale for using R over the more widely-used tools of the field such as MATLAB. Kelley provides a general introduction to R before introducing the 'oce' package. This package greatly simplifies oceanographic analysis by handling the details of discipline-specific file formats, calculations, and plots. Designed for real-world application and developed with open-source protocols, oce supports a broad range of practical work. Generic functions take care of general operations such as subsetting and plotting data, while specialized functions address more specific tasks such as tidal decomposition, hydrographic analysis, and ADCP coordinate transformation. In addition, the package makes it easy to document work, because its functions automatically update processing logs stored within its data objects. Kelley teaches key R functions using classic examples from the history of oceanography, specifically the work of Alfred Redfield, Gordon Riley, J. Tuzo Wilson, and Walter Munk. Acknowledging the pervasive popularity of MATLAB, the book provides advice to users who would like to switch to R. Including a suite of real-life applications and over 100 exercises and solutions, the treatment is ideal for oceanographers, technicians, and students who want to add R to their list of tools for oceanographic analysis.

Scientific Data Analysis using Jython Scripting and Java presents practical approaches for data analysis using Java scripting based on Jython, a Java implementation of the Python language. The chapters essentially cover all aspects of data analysis, from arrays and histograms to clustering analysis, curve fitting, metadata and neural networks. A comprehensive coverage of data visualisation tools implemented in Java is also included. Written by the primary developer of the jHepWork data-analysis framework, the book provides a reliable and complete reference source laying the foundation for data-analysis applications using Java scripting. More than 250 code snippets (of around 10-20 lines each) written in Jython and Java, plus several real-life examples help the reader develop a genuine feeling for data analysis techniques and their programming implementation. This is the first data-analysis and data-mining book which is completely based on the Jython language, and opens doors to scripting using a fully multi-platform and multi-threaded approach. Graduate students and researchers will benefit from the information presented in this book.

later versions. In addition, the CD-ROM contains a complete solutions manual that includes detailed solutions to all the problems in the book. If the reader does not wish to consult these solutions, then a brief list of answers is provided in printed form at the end of the book. Iwouldliketothankmyfamilymembersfortheirhelpandcontinuedsupportwi- out which this book would not have been possible. I would also like to acknowledge the help of the editior at Springer-Verlag (Dr. Thomas Ditzinger) for his assistance in bringing this book out in its present form. Finally, I would like to thank my brother, Nicola, for preparing most of the line drawings in both editions. In this edition, I am providing two email addresses for my readers to contact me (pkattan@tedata. net. jo and pkattan@lsu. edu). The old email address that appeared in the ?rst edition was cancelled in 2004. December 2006 Peter I. Kattan PrefacetotheFirstEdition 3 This is a book for people who love ?nite elements and MATLAB . We will use the popular computer package MATLAB as a matrix calculator for doing ?nite element analysis. Problems will be solved mainly using MATLAB to carry out the tedious and lengthy matrix calculations in addition to some manual manipulations especially when applying the boundary conditions. In particular the steps of the ?nite element method are emphasized in this book. The reader will not ?nd ready-made MATLAB programsforuseasblackboxes. Insteadstep-by-stepsolutionsof?niteelementpr- lems are examined in detail using MATLAB.

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come.

The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation; the founder of the Research Institute for Symbolic Computation (RISC) and its chairman from 1987-2000; the founder in 1990 of the Softwarepark Hagenberg, Austria, and since then its director.

More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essays by leading authorities, on such topics as mathematical foundations from the perspective of computer verification; a symbolic-computational philosophy and methodology for mathematics; the role of logic and algebra in software engineering; and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically interested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computer science and logic.

Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchberger s successor as director of the Research Institute for Symbolic Computation.

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This volume features selected contributions on a variety of topics related to linear statistical inference. The peer-reviewed papers from the International Conference on Trends and Perspectives in Linear Statistical Inference (LinStat 2016) held in Istanbul, Turkey, 22-25 August 2016, cover topics in both theoretical and applied statistics, such as linear models, high-dimensional statistics, computational statistics, the design of experiments, and multivariate analysis. The book is intended for statisticians, Ph.D. students, and professionals who are interested in statistical inference.

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

Mathematics is undoubtedly the key to state-of-the-art high technology. It is aninternationaltechnicallanguageandprovestobeaneternallyyoungscience to those who have learned its ways. Long an indispensable part of research thanks to modeling and simulation, mathematics is enjoying particular vit- ity now more than ever. Nevertheless, this stormy development is resulting in increasingly high requirements for students in technical disciplines, while general interest in mathematics continues to wane at the same time. This book and its appendices on the Internet seek to deal with this issue, helping students master the di?cult transition from the receptive to the productive phase of their education. The author has repeatedly held a three-semester introductory course - titled Higher Mathematics at the University of Stuttgart and used a series of "handouts" to show further aspects, make the course contents more motiv- ing, and connect with the mechanics lectures taking place at the same time. One part of the book has more or less evolved from this on its own. True to the original objective, this part treats a variety of separate topics of varying degrees of di?culty; nevertheless, all these topics are oriented to mechanics. Anotherpartofthisbookseekstoo?eraselectionofunderstandablereal- ticmodelsthatcanbeimplementeddirectlyfromthemultitudeofmathema- calresources.TheauthordoesnotattempttohidehispreferenceofNumerical Mathematics and thus places importance on careful theoretical preparation.

This beginner's introduction to MATLAB teaches a sufficient subset of the functionality and gives the reader practical experience on how to find more information. A forty-page appendix contains unique user-friendly summaries and tables of MATLAB functions enabling the reader to find appropriate functions, understand their syntax and get a good overview. The large number of exercises, tips, and solutions mean that the course can be followed with or without a computer. Recent development in MATLAB to advance programming is described using realistic examples in order to prepare students for larger programming projects.  Revolutionary step by step 'guided tour' eliminates the steep learning curve encountered in learning new programming languages. Each chapter corresponds to an actual engineering course, where examples in MATLAB illustrate the typical theory, providing a practical understanding of these courses. Complementary homepage contains exercises, a take-home examination, and an automatic marking that grades the solution. End of chapter exercises with selected solutions in an appendix. The development of MATLAB programming and the rapid increase in the use of MATLAB in engineering courses makes this a valuable self-study guide for both engineering students and practising engineers. Readers will find that this time-less material can be used throughout their education and into their career.

Over the past 80 years, the way that citation frequency was counted and analyzed changed dramatically from the early manual transcribing and statistical computation of citation data to computer-based citation data creation and its manipulation.""Author Cocitation Analysis: Quantitative Methods for Mapping the Intellectual Structure of an Academic Discipline"" provides a blueprint for researchers to follow in a wide variety of investigations. Pertinent to faculty, researchers, and graduate students in any academic field, this book introduces an alternative approach to conducting author cocitation analysis (ACA) without relying on commercial citation databases.

Given the explosion of interest in mathematical methods for solving problems in finance and trading, a great deal of research and development is taking place in universities, large brokerage firms, and in the supporting trading software industry. Mathematical advances have been made both analytically and numerically in finding practical solutions.

This book provides a comprehensive overview of existing and original material, about what mathematics when allied with Mathematica can do for finance. Sophisticated theories are presented systematically in a user-friendly style, and a powerful combination of mathematical rigor and Mathematica programming. Three kinds of solution methods are emphasized: symbolic, numerical, and Monte-- Carlo. Nowadays, only good personal computers are required to handle the symbolic and numerical methods that are developed in this book.

Key features: * No previous knowledge of Mathematica programming is required * The symbolic, numeric, data management and graphic capabilities of Mathematica are fully utilized * Monte--Carlo solutions of scalar and multivariable SDEs are developed and utilized heavily in discussing trading issues such as Black--Scholes hedging * Black--Scholes and Dupire PDEs are solved symbolically and numerically * Fast numerical solutions to free boundary problems with details of their Mathematica realizations are provided * Comprehensive study of optimal portfolio diversification, including an original theory of optimal portfolio hedging under non-Log-Normal asset price dynamics is presented

The book is designed for the academic community of instructors and students, and most importantly, will meet the everyday trading needs of quantitatively inclined professional and individual investors.

The Model-Free Prediction Principle expounded upon in this monograph is based on the simple notion of transforming a complex dataset to one that is easier to work with, e.g., i.i.d. or Gaussian. As such, it restores the emphasis on observable quantities, i.e., current and future data, as opposed to unobservable model parameters and estimates thereof, and yields optimal predictors in diverse settings such as regression and time series. Furthermore, the Model-Free Bootstrap takes us beyond point prediction in order to construct frequentist prediction intervals without resort to unrealistic assumptions such as normality. Prediction has been traditionally approached via a model-based paradigm, i.e., (a) fit a model to the data at hand, and (b) use the fitted model to extrapolate/predict future data. Due to both mathematical and computational constraints, 20th century statistical practice focused mostly on parametric models. Fortunately, with the advent of widely accessible powerful computing in the late 1970s, computer-intensive methods such as the bootstrap and cross-validation freed practitioners from the limitations of parametric models, and paved the way towards the `big data' era of the 21st century. Nonetheless, there is a further step one may take, i.e., going beyond even nonparametric models; this is where the Model-Free Prediction Principle is useful. Interestingly, being able to predict a response variable Y associated with a regressor variable X taking on any possible value seems to inadvertently also achieve the main goal of modeling, i.e., trying to describe how Y depends on X. Hence, as prediction can be treated as a by-product of model-fitting, key estimation problems can be addressed as a by-product of being able to perform prediction. In other words, a practitioner can use Model-Free Prediction ideas in order to additionally obtain point estimates and confidence intervals for relevant parameters leading to an alternative, transformation-based approach to statistical inference.

This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC'2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23-24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.