This textbook offers an algorithmic introduction to the field of computer algebra. A leading expert in the field, the author guides readers through numerous hands-on tutorials designed to build practical skills and algorithmic thinking. This implementation-oriented approach equips readers with versatile tools that can be used to enhance studies in mathematical theory, applications, or teaching. Presented using Mathematica code, the book is fully supported by downloadable sessions in Mathematica, Maple, and Maxima. Opening with an introduction to computer algebra systems and the basics of programming mathematical algorithms, the book goes on to explore integer arithmetic. A chapter on modular arithmetic completes the number-theoretic foundations, which are then applied to coding theory and cryptography. From here, the focus shifts to polynomial arithmetic and algebraic numbers, with modern algorithms allowing the efficient factorization of polynomials. The final chapters offer extensions into more advanced topics: simplification and normal forms, power series, summation formulas, and integration. Computer Algebra is an indispensable resource for mathematics and computer science students new to the field. Numerous examples illustrate algorithms and their implementation throughout, with online support materials to encourage hands-on exploration. Prerequisites are minimal, with only a knowledge of calculus and linear algebra assumed. In addition to classroom use, the elementary approach and detailed index make this book an ideal reference for algorithms in computer algebra.

This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science. "Mathematicians have never been comfortable handling infinities... But an entirely new type of mathematics looks set to by-pass the problem... Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem... " MIT Technology Review "These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used." A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing. "I am sure that the new approach ... will have a very deep impact both on Mathematics and Computer Science." D. Trigiante, Computational Management Science. "Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural". R. Gangle, G. Caterina, F. Tohme, Soft Computing. "The computational features offered by the Infinity Computer allow us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort." P. Amodio, L. Brugnano, F. Iavernaro & F. Mazzia, Soft Computing

The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable normalization, are discussed, the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family, the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures, in particular, the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed, when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Wald's test, their relationship with the likelihood ratio test and Karl Pearson's chi-square test. An important finding is that, while testing any hypothesis about the parameters of a multinomial distribution, a score test statistic and Karl Pearson's chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions, various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter, to motivate students towards solving these exercises and to enable digestion of the underlying concepts. The concepts from asymptotic inference are crucial in modern statistics, but are difficult to grasp in view of their abstract nature. To overcome this difficulty, keeping up with the recent trend of using R software for statistical computations, the book uses it extensively, for illustrating the concepts, verifying the properties of estimators and carrying out various test procedures. The last section of the chapters presents R codes to reveal and visually demonstrate the hidden aspects of different concepts and procedures. Augmenting the theory with R software is a novel and a unique feature of the book. The book is designed primarily to serve as a text book for a one semester introductory course in asymptotic statistical inference, in a post-graduate program, such as Statistics, Bio-statistics or Econometrics. It will also provide sufficient background information for studying inference in stochastic processes. The book will cater to the need of a concise but clear and student-friendly book introducing, conceptually and computationally, basics of asymptotic inference.

The richly illustrated Interactive Web-Based Data Visualization with R, plotly, and shiny focuses on the process of programming interactive web graphics for multidimensional data analysis. It is written for the data analyst who wants to leverage the capabilities of interactive web graphics without having to learn web programming. Through many R code examples, you will learn how to tap the extensive functionality of these tools to enhance the presentation and exploration of data. By mastering these concepts and tools, you will impress your colleagues with your ability to quickly generate more informative, engaging, and reproducible interactive graphics using free and open source software that you can share over email, export to pdf, and more. Key Features: Convert static ggplot2 graphics to an interactive web-based form Link, animate, and arrange multiple plots in standalone HTML from R Embed, modify, and respond to plotly graphics in a shiny app Learn best practices for visualizing continuous, discrete, and multivariate data Learn numerous ways to visualize geo-spatial data This book makes heavy use of plotly for graphical rendering, but you will also learn about other R packages that support different phases of a data science workflow, such as tidyr, dplyr, and tidyverse. Along the way, you will gain insight into best practices for visualization of high-dimensional data, statistical graphics, and graphical perception. The printed book is complemented by an interactive website where readers can view movies demonstrating the examples and interact with graphics.

This book is a text for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics. Prerequisites are a first course in the theory of ODEs and a survey course in numerical analysis, in addition to specific programming experience, preferably in MATLAB, and knowledge of elementary matrix theory. Professionals will also find that this useful concise reference contains reviews of technical issues and realistic and detailed examples. The programs for the examples are supplied on the accompanying web site and can serve as templates for solving other problems. Each chapter begins with a discussion of the "facts of life" for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understaning the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.

Six Sigma has arisen in the last two decades as a breakthrough Quality Management Methodology. With Six Sigma, we are solving problems and improving processes using as a basis one of the most powerful tools of human development: the scientific method. For the analysis of data, Six Sigma requires the use of statistical software, being R an Open Source option that fulfills this requirement. R is a software system that includes a programming language widely used in academic and research departments. Nowadays, it is becoming a real alternative within corporate environments. The aim of this book is to show how R can be used as the software tool in the development of Six Sigma projects. The book includes a gentle introduction to Six Sigma and a variety of examples showing how to use R within real situations. It has been conceived as a self contained piece. Therefore, it is addressed not only to Six Sigma practitioners, but also to professionals trying to initiate themselves in this management methodology. The book may be used as a text book as well.

The first part of this title contained all statistical tests that are relevant for starters on SPSS, and included standard parametric and non-parametric tests for continuous and binary variables, regression methods, trend tests, and reliability and validity assessments of diagnostic tests. The current part 2 of this title reviews multistep methods, multivariate models, assessments of missing data, performance of diagnostic tests, meta-regression, Poisson regression, confounding and interaction, and survival analyses using log tests and segmented time-dependent Cox regression. Methods for assessing non linear models, data seasonality, distribution free methods, including Monte Carlo methods and artificial intelligence, and robust tests are also covered.

Each method of testing is explained using a data example from clinical practice, including every step in SPSS, and a text with interpretations of the results and hints convenient for data reporting. In order to facilitate the use of this cookbook the data files of the examples is made available by the editor through extras.springer.com.

Both part 1 and 2 of this title contain a minima amount of text and maximal technical details, but we believe that this property will not refrain students from mastering the SPSS software systematics, and that, instead, it will be a help to that aim. Yet, we recommend that it will used together with the textbook "Statistics Applied to Clinical Trials" (5th edition, Springer, Dordrecht 2012) and the e-books "Statistics on a Pocket Calculator Part 1 and 2 (Springer, Dordrecht, 2011 and 2012) from the same authors.

Stata is the most flexible and extensible data analysis package available from a commercial vendor. R is a similarly flexible free and open source package for data analysis, with over 3,000 add-on packages available. This book shows you how to extend the power of Stata through the use of R. It introduces R using Stata terminology with which you are already familiar. It steps through more than 30 programs written in both languages, comparing and contrasting the two packages' different approaches. When finished, you will be able to use R in conjunction with Stata, or separately, to import data, manage and transform it, create publication quality graphics, and perform basic statistical analyses.

A glossary defines over 50 R terms using Stata jargon and again using more formal R terminology. The table of contents and index allow you to find equivalent R functions by looking up Stata commands and vice versa. The example programs and practice datasets for both R and Stata are available for download.

Bayesian statistical methods have become widely used for data analysis and modelling in recent years, and the BUGS software has become the most popular software for Bayesian analysis worldwide. Authored by the team that originally developed this software, The BUGS Book provides a practical introduction to this program and its use. The text presents complete coverage of all the functionalities of BUGS, including prediction, missing data, model criticism, and prior sensitivity. It also features a large number of worked examples and a wide range of applications from various disciplines. The book introduces regression models, techniques for criticism and comparison, and a wide range of modelling issues before going into the vital area of hierarchical models, one of the most common applications of Bayesian methods. It deals with essentials of modelling without getting bogged down in complexity. The book emphasises model criticism, model comparison, sensitivity analysis to alternative priors, and thoughtful choice of prior distributions-all those aspects of the "art" of modelling that are easily overlooked in more theoretical expositions. More pragmatic than ideological, the authors systematically work through the large range of "tricks" that reveal the real power of the BUGS software, for example, dealing with missing data, censoring, grouped data, prediction, ranking, parameter constraints, and so on. Many of the examples are biostatistical, but they do not require domain knowledge and are generalisable to a wide range of other application areas. Full code and data for examples, exercises, and some solutions can be found on the book's website.

Metrics are a hot topic. Executive leadership, boards of directors, management, and customers are all asking for data-based decisions. As a result, many managers, professionals, and change agents are asked to develop metrics, but have no clear idea of how to produce meaningful ones. Wouldn't it be great to have a simple explanation of how to collect, analyze, report, and use measurements to improve your organization? Metrics: How to Improve Key Business Results provides that explanation and the tools you'll need to make your organization more effective. Not only does the book explain the why of metrics, but it walks you through a step-by-step process for creating a report card that provides a clear picture of organizational health and how well you satisfy customer needs. Metrics will help you to measure the right things, the right way - the first time. No wasted effort, no chasing data. The report card provides a simple tool for viewing the health of your organization, from the outside in.You will learn how to measure the key components of the report card and thereby improve real measures of business success, like repeat customers, customer loyalty, and word-of-mouth advertising.This book: * Provides a step-by-step guide for building an organizational effectiveness report card * Takes you from identifying key services and products and using metrics, to determining business strategy * Provides examples of how to identify, collect, analyze, and report metrics that will be immediately useful for improving all aspects of the enterprise, including IT What you'll learn * Understand the difference between data, measures, information, and metrics * Identify root performance questions to ensure you build the right metrics * Develop meaningful and accurate metrics using concrete, easy-to-follow instructions * Avoid the high risks that come with collecting, analyzing, reporting, and using complex data * Formulate practical answers to data-based questions * Select and use the proper tools for creating, implementing, and using metrics * Learn one of the most powerful methods yet invented for improving organizational results Who this book is for Metrics: How to Improve Key Business Results was written for senior managers who need to improve key results.Equally, the book is for the department heads, middle managers, analysts, IT professionals, and change agents responsible for collecting, analyzing, and reporting metrics. Finally, it's for those who have to chase data and find meaningful answers to the interesting questions executives ponder. Table of Contents * Introduction: Who, What, Where, When, Why, and How You Use Metrics * Establishing a Common Language * Where to Begin: Planning a Good Metric * Using Metrics as Indicators * Using the Answer Key * Start with Effectiveness * Triangulation: Essential to Creating Effective Metrics * Expectations: How to View Data in a Meaningful Way * Creating and Interpreting the Metrics Report Card * Final Product: the Metrics Report Card * Employing Advanced Metrics * Creating the Service Catalog * Establishing Standards and Benchmarks * Respecting the Power of Metrics * Avoiding the Research Trap * Embracing Your Organization's Uniqueness * Appendix: Metrics Tools to Use and Useful Resources

Computational inference is based on an approach to statistical methods that uses modern computational power to simulate distributional properties of estimators and test statistics. This book describes computationally intensive statistical methods in a unified presentation, emphasizing techniques, such as the PDF decomposition, that arise in a wide range of methods.

This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.

Data mining is the art and science of intelligent data analysis. By building knowledge from information, data mining adds considerable value to the ever increasing stores of electronic data that abound today. In performing data mining many decisions need to be made regarding the choice of methodology, the choice of data, the choice of tools, and the choice of algorithms. Throughout this book the reader is introduced to the basic concepts and some of the more popular algorithms of data mining. With a focus on the hands-on end-to-end process for data mining, Williams guides the reader through various capabilities of the easy to use, free, and open source Rattle Data Mining Software built on the sophisticated R Statistical Software. The focus on doing data mining rather than just reading about data mining is refreshing. The book covers data understanding, data preparation, data refinement, model building, model evaluation, and practical deployment. The reader will learn to rapidly deliver a data mining project using software easily installed for free from the Internet. Coupling Rattle with R delivers a very sophisticated data mining environment with all the power, and more, of the many commercial offerings.

Advanced R helps you understand how R works at a fundamental level. It is designed for R programmers who want to deepen their understanding of the language, and programmers experienced in other languages who want to understand what makes R different and special. This book will teach you the foundations of R; three fundamental programming paradigms (functional, object-oriented, and metaprogramming); and powerful techniques for debugging and optimising your code. By reading this book, you will learn: The difference between an object and its name, and why the distinction is important The important vector data structures, how they fit together, and how you can pull them apart using subsetting The fine details of functions and environments The condition system, which powers messages, warnings, and errors The powerful functional programming paradigm, which can replace many for loops The three most important OO systems: S3, S4, and R6 The tidy eval toolkit for metaprogramming, which allows you to manipulate code and control evaluation Effective debugging techniques that you can deploy, regardless of how your code is run How to find and remove performance bottlenecks The second edition is a comprehensive update: New foundational chapters: "Names and values," "Control flow," and "Conditions" comprehensive coverage of object oriented programming with chapters on S3, S4, R6, and how to choose between them Much deeper coverage of metaprogramming, including the new tidy evaluation framework use of new package like rlang (http://rlang.r-lib.org), which provides a clean interface to low-level operations, and purr (http://purrr.tidyverse.org/) for functional programming Use of color in code chunks and figures Hadley Wickham is Chief Scientist at RStudio, an Adjunct Professor at Stanford University and the University of Auckland, and a member of the R Foundation. He is the lead developer of the tidyverse, a collection of R packages, including ggplot2 and dplyr, designed to support data science. He is also the author of R for Data Science (with Garrett Grolemund), R Packages, and ggplot2: Elegant Graphics for Data Analysis.

The investigation of the role of mechanical and mechano-chemical interactions in cellular processes and tissue development is a rapidly growing research field in the life sciences and in biomedical engineering. Quantitative understanding of this important area in the study of biological systems requires the development of adequate mathematical models for the simulation of the evolution of these systems in space and time. Since expertise in various fields is necessary, this calls for a multidisciplinary approach. This edited volume connects basic physical, biological, and physiological concepts to methods for the mathematical modeling of various materials by pursuing a multiscale approach, from subcellular to organ and system level. Written by active researchers, each chapter provides a detailed introduction to a given field, illustrates various approaches to creating models, and explores recent advances and future research perspectives. Topics covered include molecular dynamics simulations of lipid membranes, phenomenological continuum mechanics of tissue growth, and translational cardiovascular modeling. Modeling Biomaterials will be a valuable resource for both non-specialists and experienced researchers from various domains of science, such as applied mathematics, biophysics, computational physiology, and medicine.

• Plenty of examples and case studies utilize Mathematica 7's newest tools, such as dynamic manipulations and adaptive three-dimensional plotting.
• Emphasizes the breadth of Mathematica and the impressive results of combining techniques from different areas.
• Whenever possible, the book shows how Mathematica can be used to discover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, and new and surprising formulas for p.
• Visualization is emphasized throughout, with finely crafted graphics in each chapter.
• All Mathematica code is included on a CD, saving the reader hours of typing.

BRIDGES THE GAP BETWEEN SAS AND R, ALLOWING USERS TRAINED IN ONE LANGUAGE TO EASILY LEARN THE OTHER SAS and R are widely-used, very different software environments. Prized for its statistical and graphical tools, R is an open-source programming language that is popular with statisticians and data miners who develop statistical software and analyze data. SAS (Statistical Analysis System) is the leading corporate software in analytics thanks to its faster data handling and smaller learning curve. SAS for R Users enables entry-level data scientists to take advantage of the best aspects of both tools by providing a cross-functional framework for users who already know R but may need to work with SAS. Those with knowledge of both R and SAS are of far greater value to employers, particularly in corporate settings. Using a clear, step-by-step approach, this book presents an analytics workflow that mirrors that of the everyday data scientist. This up-to-date guide is compatible with the latest R packages as well as SAS University Edition. Useful for anyone seeking employment in data science, this book: Instructs both practitioners and students fluent in one language seeking to learn the other Provides command-by-command translations of R to SAS and SAS to R Offers examples and applications in both R and SAS Presents step-by-step guidance on workflows, color illustrations, sample code, chapter quizzes, and more Includes sections on advanced methods and applications Designed for professionals, researchers, and students, SAS for R Users is a valuable resource for those with some knowledge of coding and basic statistics who wish to enter the realm of data science and business analytics.

Computational techniques based on simulation have now become an essential part of the statistician's toolbox. It is thus crucial to provide statisticians with a practical understanding of those methods, and there is no better way to develop intuition and skills for simulation than to use simulation to solve statistical problems. Introducing Monte Carlo Methods with R covers the main tools used in statistical simulation from a programmer's point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison. While this book constitutes a comprehensive treatment of simulation methods, the theoretical justification of those methods has been considerably reduced, compared with Robert and Casella (2004). Similarly, the more exploratory and less stable solutions are not covered here.

This book does not require a preliminary exposure to the R programming language or to Monte Carlo methods, nor an advanced mathematical background. While many examples are set within a Bayesian framework, advanced expertise in Bayesian statistics is not required. The book covers basic random generation algorithms, Monte Carlo techniques for integration and optimization, convergence diagnoses, Markov chain Monte Carlo methods, including Metropolis {Hastings and Gibbs algorithms, and adaptive algorithms. All chapters include exercises and all R programs are available as an R package called mcsm. The book appeals to anyone with a practical interest in simulation methods but no previous exposure. It is meant to be useful for students and practitioners in areas such as statistics, signal processing, communications engineering, control theory, econometrics, finance and more. The programming parts are introduced progressively to be accessible to any reader.

There has been dramatic growth in the development and application of Bayesian inference in statistics. Berger (2000) documents the increase in Bayesian activity by the number of published research articles, the number of books, andtheextensivenumberofapplicationsofBayesianarticlesinapplied disciplines such as science and engineering. One reason for the dramatic growth in Bayesian modeling is the availab- ity of computational algorithms to compute the range of integrals that are necessary in a Bayesian posterior analysis. Due to the speed of modern c- puters, it is now possible to use the Bayesian paradigm to 't very complex models that cannot be 't by alternative frequentist methods. To 't Bayesian models, one needs a statistical computing environment. This environment should be such that one can: write short scripts to de?ne a Bayesian model use or write functions to summarize a posterior distribution use functions to simulate from the posterior distribution construct graphs to illustrate the posterior inference An environment that meets these requirements is the R system. R provides a wide range of functions for data manipulation, calculation, and graphical d- plays. Moreover, it includes a well-developed, simple programming language that users can extend by adding new functions. Many such extensions of the language in the form of packages are easily downloadable from the Comp- hensive R Archive Network (CRAN)

Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi-Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi-Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry. Driven by data and written in an informal style, The Calabi-Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.

R is a language and environment for data analysis and graphics. It may be considered an implementation of S, an award-winning language initially - veloped at Bell Laboratories since the late 1970s. The R project was initiated by Robert Gentleman and Ross Ihaka at the University of Auckland, New Zealand, in the early 1990s, and has been developed by an international team since mid-1997. Historically, econometricians have favored other computing environments, some of which have fallen by the wayside, and also a variety of packages with canned routines. We believe that R has great potential in econometrics, both for research and for teaching. There are at least three reasons for this: (1) R is mostly platform independent and runs on Microsoft Windows, the Mac family of operating systems, and various ?avors of Unix/Linux, and also on some more exotic platforms. (2) R is free software that can be downloaded and installed at no cost from a family of mirror sites around the globe, the Comprehensive R Archive Network (CRAN); hence students can easily install it on their own machines. (3) R is open-source software, so that the full source code is available and can be inspected to understand what it really does, learn from it, and modify and extend it. We also like to think that platform independence and the open-source philosophy make R an ideal environment for reproducible econometric research.

New statistical tools are changing the ways in which scientists analyze and interpret data and models. Many of these are emerging as a result of the wide availability of inexpensive, high speed computational power. In particular, hierarchical Bayes and Markov Chain Monte Carlo methods for anyalsis provide consistent framework for inference and prediction where information is heterogeneous and uncertain, processes are complex, and responses depend on scale. Nowhere are these methods more promising than in the environmental sciences. Models have developed rapidly, and there is now a requirement for a clear exposition of the methodology through to application for a range of environmental challenges.

This volume contains selected papers presented at two joint German-Japanese symposia on data analysis and related elds. The articles substantially extend and further develop material presented at the two symposia organized on the basis of longstanding and close relationships which have been cultivated in the last couple of decades between the two classi cation societies: the German Class- cation Society (Gesellschaft fu ]r Klassi kation e. V.) and the Japanese Classi cation Society. These symposia have been very helpful in exchanging ideas, views, and knowledge between the two societies and have served as a spring board for more extensive and closer co-operation between the societies as well as among their individual members. The scienti c program of the rst Joint Japanese-German Symposium (Tokyo 2005)included23presentations;forthesecondJointGerman-JapaneseSymposium (Berlin 2006) 27 presentations were scheduled. This volume presents 21 peer refereed papers, which are grouped into three parts: 1. Part 1 Clustering and Visualization (eight papers) 2. Part 2 Methods in Fields (nine papers) 3. Part 3 Applications in Clustering and Visualization (four papers) The concept of having a joint symposium of the two classi cation societies came from the talks with Hans-Hermann and Wolfgang when Akinori attended the 28th Annual Conference of the German Classi cation Society held in Dortmund in March 2004."