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Clustering has been around for many decades and located itself in a uniquepositionasafundamentalconceptualandalgorithmiclandmark of data analysis. Almost since the very inception of fuzzy sets, the role and potential of these information granules in revealing and describing structureindatawasfullyacknowledgedandappreciated.Asamatter of fact, with the rapid growth of volumes of digital information, the role of clustering becomes even more visible and critical. Furthermore given the anticipated human centricity of the majority of artifacts of digitaleraandacontinuousbuildupofmountainsofdata,onebecomes fully cognizant of the growing role and an enormous potential of fuzzy sets and granular computing in the design of intelligent systems. In therecentyearsclusteringhasundergoneasubstantialmetamorphosis. Frombeinganexclusivelydata drivenpursuit,ithastransformeditself into a vehicle whose data centricity has been substantially augmented by the incorporation of domain knowledge thus giving rise to the next generation of knowledge-oriented and collaborative clustering. Interestingly enough, fuzzy clustering exhibits a dominant role in many developments of the technology of fuzzy sets including fuzzy modeling, fuzzy control, data mining, pattern recognition, and image processing. When browsing through numerous papers on fuzzy m- eling we can witness an important trend of a substantial reliance on fuzzy clustering being regarded as the general development tool. The same central position of fuzzy clustering becomes visible in pattern classi?ers and neurofuzzy systems. All in all, it becomes evident that further progress in fuzzy clustering is of vital relevance and bene?t to the overall progress of the area of fuzzy sets and their applications.

This volume presents results of the International Meshing Roundtable conference organized by Sandia National Laboratories held in September 2005. The conference is held annually and since its inception eleven years ago has become widely recognized as a major forum for the exchange of ideas in this field. The papers of this proceedings are devoted to mesh generation and adaptation which has applications to finite element simulation as well as to computational geometry and computer graphics. This book introduces theoretical and novel ideas with practical potential as well as technical applications from industrial researchers, bringing together renowned specialists from engineering, computer science and mathematics.

The 1990 CIME course on Mathematical Modelling of Industrial Processes set out to illustrate some advances in questions of industrial mathematics, i.e.of the applications of mathematics (with all its'academic'rigour) to real-life problems. The papers describe the genesis of the models and illustrate their relevant mathematical characteristics. Among the themesdealt with are: thermally controlled crystal growth, thermal behaviour of a high-pressure gas-discharge lamp, the sessile-drop problem, etching processes, the batch-coil- annealing process, inverse problems in classical dynamics, image representation and dynamical systems, scintillation in rear projections screens, identification of semiconductor properties,pattern recognition with neural networks. CONTENTS: H.K. Kuiken: Mathematical Modelling of Industrial Processes.- B. Forte: Inverse Problems in Mathematics for Industry.- S. Busenberg: Case Studies in Industrial Mathematics.

The IMA Hot Topics workshop on compatible spatialdiscretizations was held May 11-15, 2004 at the University of Minnesota. The purpose of the workshop was to bring together scientists at the forefront of the research in the numerical solution of PDEs to discuss recent advances and novel applications of geometrical and homological approaches to discretization. This volume contains original contributions based on the material presented at the workshop. A unique feature of the collection is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Compatible spatial discretizations are those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. The papers in the volume offer a snapshot of the current trends and developments in compatible spatial discretizations. The reader will find valuable insights on spatial compatibility from several different perspectives and important examples of applications compatible discretizations in computational electromagnetics, geosciences, linear elasticity, eigenvalue approximations and MHD. The contributions collected in this volume will help to elucidate relations between different methods and concepts and to generally advance our understanding of compatible spatial discretizations for PDEs. Abstracts and presentation slides from the workshop can be accessed at http://www.ima.umn.edu/talks/workshops/5-11-15.2004/.

I think the next century will be the century of complexity. We have already discovered the basic laws that govern matter and understand all the normal situations. We don't know how the laws?t together, and what happens under extreme conditions. But I expect we will?nd a complete uni?ed theory sometime this century. There is no limit to the complexity that we can build using those basic laws. Stephen Hawking, January 2000. We don't know what we are talking about. Many of us believed that string theory was a very dramatic break with our previous notions of quantum theory. But now we learn that string theory, well, is not that much of a break. The state of physics today is like it was when we were mysti?ed by radioactivity. They were missing something absolutely fundamental. We are missing perhaps something as profound as they were back then. Nobel Laureate David Gross, December 2005. This volume is essentially a compilation of papers presented at the Int- national Workshop on Mathematics and Physics of Complex and Nonlinear Systems that was held at Indian Institute of Technology Kanpur, March 14 – 26, 2004 on the theme ChaNoXity: The Nonlinear Dynamics of Nature.

The series of Online World Conferences on Soft Computing (WSC) is organized by the World Federation of Soft Computing (WFSC) and has become an established annual event in the academic calendar and was already held for the 8th time in 2003. Starting as a small workshop held at Nagoya University, Japan in 1994 it has - tured to the premier online event on soft computing in industrial applications. It has been hosted by the universities of Granada, Spain, Fraunhofer Gesellschaft, Berlin, Cran?eld University, Helsinki University of Technology and Nagoya University. The goal of WFSC is to promote soft computing across the world, by using the internet as a forum for virtual technical discussion and publishing at no cost to authors and participants. The of?cial journal of the World Federation on Soft Computing is the journal Applied Soft Computing. The 8th WSC Conference (WSC8) took place from September 29th to October 10th, 2003. Registered participants had the opportunity to follow and discuss the online presentations of authors from all over the world. Out of more than 60 subm- sions the program committee had accepted 27 papers for?nal presentation at WSC8.

Peter Kall and János Mayer are distinguished scholars and professors of Operations Research and their research interest is particularly devoted to the area of stochastic optimization. Stochastic Linear Programming: Models, Theory, and Computation is a definitive presentation and discussion of the theoretical properties of the models, the conceptual algorithmic approaches, and the computational issues relating to the implementation of these methods to solve problems that are stochastic in nature. The application area of stochastic programming includes portfolio analysis, financial optimization, energy problems, random yields in manufacturing, risk analysis, etc. In this book, models in financial optimization and risk analysis are discussed as examples, including solution methods and their implementation. Stochastic programming is a fast developing area of optimization and mathematical programming. Numerous papers and conference volumes, and several monographs have been published in the area; however, the Kall and Mayer book will be particularly useful in presenting solution methods including their solid theoretical basis and their computational issues, based in many cases on implementations by the authors. The book is also suitable for advanced courses in stochastic optimization.

We are proud to introduce the proceedings of the Seventh International C- ference on Parallel Problem Solving from Nature, PPSN VII, held in Granada, Spain, on 7–11 September 2002. PPSN VII was organized back-to-back with the Foundations of Genetic Algorithms (FOGA) conference, which took place in Torremolinos, Malaga, Spain, in the preceding week. ThePPSNseriesofconferencesstartedinDortmund,Germany[1].Fromthat pioneering meeting, the event has been held biennially, in Brussels, Belgium [2], Jerusalem, Israel [3], Berlin, Germany [4], Amsterdam, The Netherlands [5], and Paris, France [6]. During the Paris conference, several bids to host PPSN 2002 were put forward; it was decided that the conference would be held in Granada with Juan J. Merelo Guerv´ os as General Chairman. The scienti?c content of the PPSN conference focuses on problem-solving paradigms gleaned from natural models, with an obvious emphasis on those that display an innate parallelism, such as evolutionary algorithms and ant-colony optimization algorithms. The majority of the papers, however, concentrate on evolutionary and hybrid algorithms, as is shown in the contents of this book and itspredecessors.Thiseditionoftheconferenceproceedingshasalargesectionon applications,betheytoclassicalproblemsortoreal-worldengineeringproblems, which shows how bioinspired algorithms are extending their use in the realms of business and enterprise.

In March 1997, we launched the Japan Association for Evolutionary Economics {JAFEE) to gather the academic minds that, out of dissatisfaction with established dynamic approaches, were separately searching for new approaches to economics. To our surprise and joy,as many as 500members, including graduate students,joined us. Later that year Prof. Horst Hanusch, then President of the International [oseph A. Schumpeter Society, remarked that such a start would take a couple of decades in Europe to prepare for. Since then we have been developing our activities incessantly not only in terms of the number of members, but also in terms of the intensity of international academic exchange. Originally the planning of this book came about as the successful outcome of our fourth annual conference organized as an international one, JAFEE 2000.Incorporat­ ing other international contributions related to our preceding conferences, this book has eventually turned out to be one of the most enterprising anthologies on evolu­ tionary economics ever published. Specifically, it contains excellent papers on such topics as streams of evolutionary economics, evolutionary nonlinear dynamics, experimental economics and evolution, multiagent systems and complexity, new frontiers for evolutionary economics, and economic heresies. In short, this book will provide a vivid and full-fledged picture of up-to-date evolutionary economics.

'Whatever regrets may be, we have done our best.'(Sir Ernest Shack­ 0 leton, turning back on 9 January 1909 at 88 23'South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth­ ods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretical nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered con­ secutively in each section and indicate, in addition, the section number. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by'author'plus'year'in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.