This Computer Algebra Handbook gives a comprehensive snapshot of this field at the intersection of mathematics and computer science with applications in physics, engineering and education. It contains both theory, systems and practice of the discipline of symbolic computation and computer algebra. With the wide angle of a "lense" of about 200 contributors it shows the state of computer algebra research and applications in the last decade of the twentieth century. Aside from discussing the foundations of computer algebra, the handbook describes 67 software systems and packages that perform tasks in symbolic computation. In addition, the handbook offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education. The book is accompanied by a CD-ROM, containing demo versions for most of the computer algebra systems treated in the book, as well as links to further information on some of these. This book will be very useful as a reference to graduate students and researchers in symbolic computation and computer algebra.

This two-volume handbook presents a collection of novel methodologies with applications and illustrative examples in the areas of data-driven computational social sciences. Throughout this handbook, the focus is kept specifically on business and consumer-oriented applications with interesting sections ranging from clustering and network analysis, meta-analytics, memetic algorithms, machine learning, recommender systems methodologies, parallel pattern mining and data mining to specific applications in market segmentation, travel, fashion or entertainment analytics. A must-read for anyone in data-analytics, marketing, behavior modelling and computational social science, interested in the latest applications of new computer science methodologies. The chapters are contributed by leading experts in the associated fields.The chapters cover technical aspects at different levels, some of which are introductory and could be used for teaching. Some chapters aim at building a common understanding of the methodologies and recent application areas including the introduction of new theoretical results in the complexity of core problems. Business and marketing professionals may use the book to familiarize themselves with some important foundations of data science. The work is a good starting point to establish an open dialogue of communication between professionals and researchers from different fields. Together, the two volumes present a number of different new directions in Business and Customer Analytics with an emphasis in personalization of services, the development of new mathematical models and new algorithms, heuristics and metaheuristics applied to the challenging problems in the field. Sections of the book have introductory material to more specific and advanced themes in some of the chapters, allowing the volumes to be used as an advanced textbook. Clustering, Proximity Graphs, Pattern Mining, Frequent Itemset Mining, Feature Engineering, Network and Community Detection, Network-based Recommending Systems and Visualization, are some of the topics in the first volume. Techniques on Memetic Algorithms and their applications to Business Analytics and Data Science are surveyed in the second volume; applications in Team Orienteering, Competitive Facility-location, and Visualization of Products and Consumers are also discussed. The second volume also includes an introduction to Meta-Analytics, and to the application areas of Fashion and Travel Analytics. Overall, the two-volume set helps to describe some fundamentals, acts as a bridge between different disciplines, and presents important results in a rapidly moving field combining powerful optimization techniques allied to new mathematical models critical for personalization of services. Academics and professionals working in the area of business anyalytics, data science, operations research and marketing will find this handbook valuable as a reference. Students studying these fields will find this handbook useful and helpful as a secondary textbook.

The book presents in a mathematical clear way the fundamentals of algorithmic information theory and a few selected applications. This 2nd edition presents new and important results obtained in recent years: the characterization of computable enumerable random reals, the construction of an Omega Number for which ZFC cannot determine any digits, and the first successful attempt to compute the exact values of 64 bits of a specific Omega Number. Finally, the book contains a discussion of some interesting philosophical questions related to randomness and mathematical knowledge. "Professor Calude has produced a first-rate exposition of up-to-date work in information and randomness." D.S. Bridges, Canterbury University, co-author, with Errett Bishop, of Constructive Analysis "The second edition of this classic work is highly recommended to anyone interested in algorithmic information and randomness." G.J. Chaitin, IBM Research Division, New York, author of Conversations with a Mathematician "This book is a must for a comprehensive introduction to algorithmic information theory and for anyone interested in its applications in the natural sciences." K. Svozil, Technical University of Vienna, author of Randomness & Undecidability in Physics

This volume is the first of two containing selected papers from the International Conference on Advances in Mathematical Sciences (ICAMS), held at the Vellore Institute of Technology in December 2017. This meeting brought together researchers from around the world to share their work, with the aim of promoting collaboration as a means of solving various problems in modern science and engineering. The authors of each chapter present a research problem, techniques suitable for solving it, and a discussion of the results obtained. These volumes will be of interest to both theoretical- and application-oriented individuals in academia and industry. Papers in Volume I are dedicated to active and open areas of research in algebra, analysis, operations research, and statistics, and those of Volume II consider differential equations, fluid mechanics, and graph theory.

By developing object calculi in which objects are treated as primitives, the authors are able to explain both the semantics of objects and their typing rules, and also demonstrate how to develop all of the most important concepts of object-oriented programming languages: self, dynamic dispatch, classes, inheritance, protected and private methods, prototyping, subtyping, covariance and contravariance, and method specialization. An innovative and important approach to the subject for researchers and graduates.

Quantum machine learning investigates how quantum computers can be used for data-driven prediction and decision making. The books summarises and conceptualises ideas of this relatively young discipline for an audience of computer scientists and physicists from a graduate level upwards. It aims at providing a starting point for those new to the field, showcasing a toy example of a quantum machine learning algorithm and providing a detailed introduction of the two parent disciplines. For more advanced readers, the book discusses topics such as data encoding into quantum states, quantum algorithms and routines for inference and optimisation, as well as the construction and analysis of genuine ``quantum learning models''. A special focus lies on supervised learning, and applications for near-term quantum devices.

Semidefinite programming (SDP) is one of the most exciting and active research areas in optimization. It has and continues to attract researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity has been prompted by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. The Handbook of Semidefinite Programming offers an advanced and broad overview of the current state of the field. It contains nineteen chapters written by the leading experts on the subject. The chapters are organized in three parts: Theory, Algorithms, and Applications and Extensions.

This book provides a survey on different kinds of Feistel ciphers, with their definitions and mathematical/computational properties. Feistel ciphers are widely used in cryptography in order to obtain pseudorandom permutations and secret-key block ciphers. In Part 1, we describe Feistel ciphers and their variants. We also give a brief story of these ciphers and basic security results. In Part 2, we describe generic attacks on Feistel ciphers. In Part 3, we give results on DES and specific Feistel ciphers. Part 4 is devoted to improved security results. We also give results on indifferentiability and indistinguishability.

The notion of Fuzziness stands as one of the really new concepts that have recently enriched the world of Science. Science grows not only through technical and formal advances on one side and useful applications on the other side, but also as consequence of the introduction and assimilation of new concepts in its corpus. These, in turn, produce new developments and applications. And this is what Fuzziness, one of the few new concepts arisen in the XX Century, has been doing so far. This book aims at paying homage to Professor Lotfi A. Zadeh, the "father of fuzzy logic" and also at giving credit to his exceptional work and personality. In a way, this is reflected in the variety of contributions collected in the book. In some of them the authors chose to speak of personal meetings with Lotfi; in others, they discussed how certain papers of Zadeh were able to open for them a new research horizon. Some contributions documented results obtained from the author/s after taking inspiration from a particular idea of Zadeh, thus implicitly acknowledging him. Finally, there are contributions of several "third generation fuzzysists or softies" who were firstly led into the world of Fuzziness by a disciple of Lotfi Zadeh, who, following his example, took care of opening for them a new road in science. Rudolf Seising is Adjoint Researcher at the European Centre for Soft Computing in Mieres, Asturias (Spain). Enric Trillas and Claudio Moraga are Emeritus Researchers at the European Centre for Soft Computing, Mieres, Asturias (Spain). Settimo Termini is Professor of Theoretical Computer Science at the University of Palermo, Italy and Affiliated Researcher at the European Centre for Soft Computing, Mieres, Asturias (Spain)

This three-volume work presents a coherent description of the theoretical and practical aspects of coloured Petri nets (CP-nets). The second volume contains a detailed presentation of the analysis methods for CP-nets. They allow the modeller to investigate dynamic properties of CP-nets.
The main ideas behind the analysis methods are described as well as the mathematics on which they are based and also how the methods are supported by computer tools. Some parts of the volume are theoretical while others are application oriented. The purpose of the volume is to teach the reader how to use the formal analysis methods, which does not require a deep understanding of the underlying mathematical theory.

3. 8 Problems . . . 66 4 ENABLING REUSE 69 4. 1 Concepts . . . . . . . . 69 4. 2 Exploiting commonality 70 4. 3 Reusable building blocks 71 4. 4 Allowing replaceable components 75 4. 5 Other replaceable entities 79 4. 6 Limiting flexibility . . . 82 4. 7 Other considerations . . 84 4. 8 Language fundamentals 85 4. 9 Problems . . . . . . . . 88 5 FUNCTIONS 91 5. 1 Concepts . . . . . . . . 91 5. 2 Introduction to functions 92 5. 3 An interpolation function 94 5. 4 Multiple return values 96 97 5. 5 Passing records as arguments 5. 6 Using extemal subroutines 100 5. 7 Language fundamentals 102 5. 8 Problems . . . . . . . . 110 6 USING ARRAYS 113 6. 1 Concepts . . . . . . . . . . . . . . . . . . 113 6. 2 Planetary motion: Arrays of components . . 113 6. 3 Simple ID heat transfer: Arrays of variables 120 6. 4 Using arrays with chemical systems 132 6. 5 Language fundamentals 143 6. 6 Problems . . . . . . . . . . . . . . 152 7 HYBRID MODELS 155 7. 1 Concepts . . . . . . . . 155 7. 2 Modeling digital circuits 155 7. 3 Bouncing ball . . . . . . 162 7. 4 Sensor modeling . . . . 166 7. 5 Language fundamentals 178 7. 6 Problems . . . . . . . . 186 8 EXPLORING NONLINEAR BEHAVIOR 189 8. 1 Concepts . . . 189 8. 2 An ideal diode 189 8. 3 Backlash . . . 193 8. 4 Thermal properties 199 Contents vii 8. 5 Hodgkin-Huxley nerve cell models 203 8. 6 Language fundamentals 206 8. 7 Problems . . . . . . . . . . . . . . 210 9 MISCELLANEOUS 213 9. 1 Lookup rules 213 9. 2 Annotations . . 225 Part II Effective Modelica 10 MULTI-DOMAIN MODELING 231 10. 1 Concepts . . . . . . . . . 231 231 10. 2 Conveyor system . . . . .

In Part I, the impact of an integro-differential operator on parity logic engines (PLEs) as a tool for scientific modeling from scratch is presented. Part II outlines the fuzzy structural modeling approach for building new linear and nonlinear dynamical causal forecasting systems in terms of fuzzy cognitive maps (FCMs). Part III introduces the new type of autogenetic algorithms (AGAs) to the field of evolutionary computing. Altogether, these PLEs, FCMs, and AGAs may serve as conceptual and computational power tools.

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.

Looking back at the years that have passed since the realization of the very first electronic, multi-purpose computers, one observes a tremendous growth in hardware and software performance. Today, researchers and engi neers have access to computing power and software that can solve numerical problems which are not fully understood in terms of existing mathemati cal theory. Thus, computational sciences must in many respects be viewed as experimental disciplines. As a consequence, there is a demand for high quality, flexible software that allows, and even encourages, experimentation with alternative numerical strategies and mathematical models. Extensibil ity is then a key issue; the software must provide an efficient environment for incorporation of new methods and models that will be required in fu ture problem scenarios. The development of such kind of flexible software is a challenging and expensive task. One way to achieve these goals is to in vest much work in the design and implementation of generic software tools which can be used in a wide range of application fields. In order to provide a forum where researchers could present and discuss their contributions to the described development, an International Work shop on Modern Software Tools for Scientific Computing was arranged in Oslo, Norway, September 16-18, 1996. This workshop, informally referred to as Sci Tools '96, was a collaboration between SINTEF Applied Mathe matics and the Departments of Informatics and Mathematics at the Uni versity of Oslo."

This volume provides a survey of the subject in the form of a collection of articles written by experts, that together provides a comprehensive guide to research. The editors'aim has been to provide an accessible description of the current stae of complexity theory, and to demonstrate the breadth of techniques and results that make this subject so exciting. Thus, papers run the gamut from sublogarithmic space to exponential time, and from new combinatorial techniques to interactive proof systems.

Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science. The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs. The book contains chapter and section summaries, detailed proofs and many end-of-section exercises -- key to the learning process. The book is suitable for undergraduate and graduate students, and although the treatment focuses on areas with frequent applications in computer science, the book is also suitable for students of mathematics and engineering.

Numerical computation, knowledge discovery and statistical data analysis integrated with powerful 2D and 3D graphics for visualization are the key topics of this book. The Python code examples powered by the Java platform can easily be transformed to other programming languages, such as Java, Groovy, Ruby and BeanShell. This book equips the reader with a computational platform which, unlike other statistical programs, is not limited by a single programming language.The author focuses on practical programming aspects and covers a broad range of topics, from basic introduction to the Python language on the Java platform (Jython), to descriptive statistics, symbolic calculations, neural networks, non-linear regression analysis and many other data-mining topics. He discusses how to find regularities in real-world data, how to classify data, and how to process data for knowledge discoveries. The code snippets are so short that they easily fit into single pages. Numeric Computation and Statistical Data Analysis on the Java Platform is a great choice for those who want to learn how statistical data analysis can be done using popular programming languages, who want to integrate data analysis algorithms in full-scale applications, and deploy such calculations on the web pages or computational servers regardless of their operating system. It is an excellent reference for scientific computations to solve real-world problems using a comprehensive stack of open-source Java libraries included in the DataMelt (DMelt) project and will be appreciated by many data-analysis scientists, engineers and students.

Faithful communication is a necessary precondition for large-scale quantum information processing and networking, irrespective of the physical platform. Thus, the problems of quantum-state transfer and quantum-network engineering have attracted enormous interest over the last years, and constitute one of the most active areas of research in quantum information processing. The present volume introduces the reader to fundamental concepts and various aspects of this exciting research area, including links to other related areas and problems. The implementation of state-transfer schemes and the engineering of quantum networks are discussed in the framework of various quantum optical and condensed matter systems, emphasizing the interdisciplinary character of the research area. Each chapter is a review of theoretical or experimental achievements on a particular topic, written by leading scientists in the field. The volume aims at both newcomers as well as experienced researchers.

Recently, a variety ofresults on the complexitystatusofthegraph isomorphism problem has been obtained. These results belong to the so-called structural part of Complexity Theory. Our idea behind this book is to summarize such results which might otherwise not be easily accessible in the literature, and also, to give the reader an understanding of the aims and topics in Structural Complexity Theory, in general. The text is basically self contained; the only prerequisite for reading it is some elementary knowledge from Complexity Theory and Probability Theory. It can be used to teach a seminar or a monographic graduate course, but also parts of it (especially Chapter 1) provide a source of examples for a standard graduate course on Complexity Theory. Many people have helped us in different ways III the process of writing this book. Especially, we would like to thank V. Arvind, R.V. Book, E. May ordomo, and the referee who gave very constructive comments. This book project was especially made possible by a DAAD grant in the "Acciones In tegrada" program. The third author has been supported by the ESPRIT project ALCOM-II."

This text provides an introduction to the numerical solution of initial and boundary value problems in ordinary differential equations on a firm theoretical basis. The book strictly presents numerical analysis as part of the more general field of scientific computing. Important algorithmic concepts are explained down to questions of software implementation. For initial value problems a dynamical systems approach is used to develop Runge-Kutta, extrapolation, and multistep methods. For boundary value problems including optimal control problems both multiple shooting and collocation methods are worked out in detail. Graduate students and researchers in mathematics, computer science, and engineering will find this book useful. Chapter summaries, detailed illustrations, and exercises are contained throughout the book with many interesting applications taken from a rich variety of areas.Peter Deuflhard is founder and president of the Zuse Institute Berlin (ZIB) and full professor of scientific computing at the Free University of Berlin, department of mathematics and computer science.Folkmar Bornemann is full professor of scientific computing at the Center of Mathematical Sciences, Technical University of Munich.

This book describes in detail the current, state-of-the-art numerical treatment and simulation of multiphase flows in porous media. The porous media considered range from ordinary to fractured and deformable media, the models treated from single-phase compressible flow to multiphase multicomponent flow with mass interchange, while the computational algorithms encompass everything from classical iterative solvers to modern multigrid and domain decomposition approaches. Addressing many problems originating from the applied geosciences, the book focuses on their common mathematical and computational aspects. It will serve as an excellent research reference for all geoscientists, mathematicians, physicists, and engineers who work in the mathematical modeling and numerical simulation of multiphase flows in porous media.

This book starts with the basic concepts of fuzzy sets and progresses througha normative view on possibility distributions and OWA operators in multiple criteria decisions.

Five applications (that all build on experience from solving complex real world problems)of possibility distributions to strategic decisions about closing/not closinga production plant using fuzzy real options, portfolio selection with imprecise future data, predictive probabilities and possibilities for risk assessment in grid computing, fuzzy ontologies for process industry, and design (and implementation) of mobile value servicesare presented and carefully discussed. It can be useful for researchers and students workingin soft computing, real options, fuzzy decision making, grid computing, knowledge mobilization andmobile value services."

This book contains leading survey papers on the various aspects of Abduction, both logical and numerical approaches. Abduction is central to all areas of applied reasoning, including artificial intelligence, philosophy of science, machine learning, data mining and decision theory, as well as logic itself.

The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), held every 2 years, provides a forum for discussing recent advances in and aspects of numerical mathematics and scientific and industrial applications. The previous ENUMATH meetings took place in Paris (1995), Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011) and Lausanne (2013). This book presents a selection of invited and contributed lectures from the ENUMATH 2015 conference, which was organised by the Institute of Applied Mathematics (IAM), Middle East Technical University, Ankara, Turkey, from September 14 to 18, 2015. It offers an overview of central recent developments in numerical analysis, computational mathematics, and applications in the form of contributions by leading experts in the field.

The correlations between physical systems provide significant information about their collective behaviour - information that is used as a resource in many applications, e.g. communication protocols. However, when it comes to the exploitation of such correlations in the quantum world, identification of the associated 'resource' is extremely challenging and a matter of debate in the quantum community. This dissertation describes three key results on the identification, detection, and quantification of quantum correlations. It starts with an extensive and accessible introduction to the mathematical and physical grounds for the various definitions of quantum correlations. It subsequently focusses on introducing a novel unified picture of quantum correlations by taking a modern resource-theoretic position. The results show that this novel concept plays a crucial role in the performance of collaborative quantum computations that is not captured by the standard textbook approaches. Further, this new perspective provides a deeper understanding of the quantum-classical boundary and paves the way towards establishing a resource theory of quantum computations.