This book provides practical applications of doubly classified models by using R syntax to generate the models. It also presents these models in symbolic tables so as to cater to those who are not mathematically inclined, while numerous examples throughout the book illustrate the concepts and their applications. For those who are not aware of this modeling approach, it serves as a good starting point to acquire a basic understanding of doubly classified models. It is also a valuable resource for academics, postgraduate students, undergraduates, data analysts and researchers who are interested in examining square contingency tables.

This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.

This book presents a set theoretical development for the foundations of the theory of atomic and finitely supported structures. It analyzes whether a classical result can be adequately reformulated by replacing a 'non-atomic structure' with an 'atomic, finitely supported structure'. It also presents many specific properties, such as finiteness, cardinality, connectivity, fixed point, order and uniformity, of finitely supported atomic structures that do not have non-atomic correspondents. In the framework of finitely supported sets, the authors analyze the consistency of various forms of choice and related results. They introduce and study the notion of 'cardinality' by presenting various order and arithmetic properties. Finitely supported partially ordered sets, chain complete sets, lattices and Galois connections are studied, and new fixed point, calculability and approximation properties are presented. In this framework, the authors study the finitely supported L-fuzzy subsets of a finitely supported set and the finitely supported fuzzy subgroups of a finitely supported group. Several pairwise non-equivalent definitions for the notion of 'infinity' (Dedekind infinity, Mostowski infinity, Kuratowski infinity, Tarski infinity, ascending infinity) are introduced, compared and studied in the new framework. Relevant examples of sets that satisfy some forms of infinity while not satisfying others are provided. Uniformly supported sets are analyzed, and certain surprising properties are presented. Finally, some variations of the finite support requirement are discussed. The book will be of value to researchers in the foundations of set theory, algebra and logic.

This book discusses the elementary ideas and tools needed for open quantum systems in a comprehensive manner. The emphasis is given to both the traditional master equation as well as the functional (path) integral approaches. It discusses the basic paradigm of open systems, the harmonic oscillator and the two-level system in detail. The traditional topics of dissipation and tunneling, as well as the modern field of quantum information, find a prominent place in the book. Assuming a basic background of quantum and statistical mechanics, this book will help readers familiarize with the basic tools of open quantum systems. Open quantum systems is the study of quantum dynamics of the system of interest, taking into account the effects of the ambient environment. It is ubiquitous in the sense that any system could be envisaged to be surrounded by its environment which could naturally exert its influence on it. Open quantum systems allows for a systematic understanding of irreversible processes such as decoherence and dissipation, of the essence in order to have a correct understanding of realistic quantum dynamics and also for possible implementations. This would be essential for a possible development of quantum technologies.

The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.

This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.

Wagman gives a broad, structured, and detailed account of advancing intellectual developments in both psychological and computational theories of the nature of problem- solving. Known for originating the PLATO computer-based Dilemma Counseling System, psychologist Wagman is the author of 17 books, including "Scientific Discovery Processes in Humans and Computers "(Praeger, 2000).

In this book, Professor Emeritus Morton Wagman gives a broad, structured, and detailed account of advancing intellectual developments in both psychological and computational theories of the nature of problem solving. Known for originating the PLATO computer-based Dilemma Counseling System, psychologist Wagman is the author of 17 books, including "Scientific Discovery Processes in Humans and Computers, "(Praeger, 2000)

Of special interest to readers will be Wagman's conclusion that artificial intelligence problem-solving systems are deepening and broadening theories of human problem solving from scientific to everyday approaches. Scholars and professionals in psychology, artificial intelligence, and cognitive science will consider this a volume a valuable addition to their collections.

This book introduces new models based on R-calculus and theories of belief revision for dealing with large and changing data. It extends R-calculus from first-order logic to propositional logic, description logics, modal logic and logic programming, and from minimal change semantics to subset minimal change, pseudo-subformula minimal change and deduction-based minimal change (the last two minimal changes are newly defined). And it proves soundness and completeness theorems with respect to the minimal changes in these logics. To make R-calculus computable, an approximate R-calculus is given which uses finite injury priority method in recursion theory. Moreover, two applications of R-calculus are given to default theory and semantic inheritance networks. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.

This book takes a foundational approach to the semantics of probabilistic programming. It elaborates a rigorous Markov chain semantics for the probabilistic typed lambda calculus, which is the typed lambda calculus with recursion plus probabilistic choice. The book starts with a recapitulation of the basic mathematical tools needed throughout the book, in particular Markov chains, graph theory and domain theory, and also explores the topic of inductive definitions. It then defines the syntax and establishes the Markov chain semantics of the probabilistic lambda calculus and, furthermore, both a graph and a tree semantics. Based on that, it investigates the termination behavior of probabilistic programs. It introduces the notions of termination degree, bounded termination and path stoppability and investigates their mutual relationships. Lastly, it defines a denotational semantics of the probabilistic lambda calculus, based on continuous functions over probability distributions as domains. The work mostly appeals to researchers in theoretical computer science focusing on probabilistic programming, randomized algorithms, or programming language theory.

This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory: The theory of automorphic forms and their associated L-functions Arithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varieties The emerging applications of number theory in information technology Kumar Murty has been a substantial influence in these topics, and the two conferences were aimed at honoring his many contributions to number theory, arithmetic geometry, and information technology.

This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest's research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism-the thesis that there exist true but inconsistent sentences-and paraconsistency-an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest's work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest's work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest's work and attest to its continued relevance and topicality. The book also includes Priest's responses to the contributors, providing a further layer to the development of these themes .

Mathematical logic is essentially related to computer science. This book describes the aspects of mathematical logic that are closely related to each other, including classical logic, constructive logic, and modal logic. This book is intended to attend to both the peculiarities of logical systems and the requirements of computer science.In this edition, the revisions essentially involve rewriting the proofs, increasing the explanations, and adopting new terms and notations.

This book is aimed at researchers, graduate students and engineers who would like to be initiated to Piecewise Deterministic Markov Processes (PDMPs). A PDMP models a deterministic mechanism modified by jumps that occur at random times. The fields of applications are numerous : insurance and risk, biology, communication networks, dependability, supply management, etc. Indeed, the PDMPs studied so far are in fact deterministic functions of CSMPs (Completed Semi-Markov Processes), i.e. semi-Markov processes completed to become Markov processes. This remark leads to considerably broaden the definition of PDMPs and allows their properties to be deduced from those of CSMPs, which are easier to grasp. Stability is studied within a very general framework. In the other chapters, the results become more accurate as the assumptions become more precise. Generalized Chapman-Kolmogorov equations lead to numerical schemes. The last chapter is an opening on processes for which the deterministic flow of the PDMP is replaced with a Markov process. Marked point processes play a key role throughout this book.

This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to present it in their lively and humorous style, interspersing core content with funny quotations and tongue-in-cheek explanations.

Genetic Algorithms in Molecular Modeling is the first book available on the use of genetic algorithms in molecular design. This volume marks the beginning of an ew series of books, Principles in Qsar and Drug Design, which will be an indispensible reference for students and professionals involved in medicinal chemistry, pharmacology, (eco)toxicology, and agrochemistry. Each comprehensive chapter is written by a distinguished researcher in the field.
Through its up to the minute content, extensive bibliography, and essential information on software availability, this book leads the reader from the theoretical aspects to the practical applications. It enables the uninitiated reader to apply genetic algorithms for modeling the biological activities and properties of chemicals, and provides the trained scientist with the most up to date information on the topic.
. Extremely topical and timely
. Sets the foundations for the development of
computer-aided tools for solving numerous
problems in QSAR and drug design
. Written to be accessible without prior direct
experience in genetic algorithms

Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form more complex ones. Coming historically from algebraic topology, operads intervene now as important objects in computer science and in combinatorics. A lot of operads involving combinatorial objects highlight some of their properties and allow to discover new ones. This book portrays the main elements of this theory under a combinatorial point of view and exposes the links it maintains with computer science and combinatorics. Examples of operads appearing in combinatorics are studied. The modern treatment of operads consisting in considering the space of formal power series associated with an operad is developed. Enrichments of nonsymmetric operads as colored, cyclic, and symmetric operads are reviewed.

Numerical partial differential equations (PDEs) are an important part of numerical simulation, the third component of the modern methodology for science and engineering, besides the traditional theory and experiment. This volume contains papers that originated with the collaborative research of the teams that participated in the IMA Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations and Scientific Computing in August 2014.

Now, for the first time, publication of the landmark work in backpropagation Scientists, engineers, statisticians, operations researchers, and other investigators involved in neural networks have long sought direct access to Paul Werbos's groundbreaking, much-cited 1974 Harvard doctoral thesis, The Roots of Backpropagation, which laid the foundation of backpropagation. Now, with the publication of its full text, these practitioners can go straight to the original material and gain a deeper, practical understanding of this unique mathematical approach to social studies and related fields. In addition, Werbos has provided three more recent research papers, which were inspired by his original work, and a new guide to the field. Originally written for readers who lacked any knowledge of neural nets, The Roots of Backpropagation firmly established both its historical and continuing significance as it:
* Demonstrates the ongoing value and new potential of backpropagation
* Creates a wealth of sound mathematical tools useful across disciplines
* Sets the stage for the emerging area of fast automatic differentiation
* Describes new designs for forecasting and control which exploit backpropagation
* Unifies concepts from Freud, Jung, biologists, and others into a new mathematical picture of the human mind and how it works
* Certifies the viability of Deutsch's model of nationalism as a predictive tool--as well as the utility of extensions of this central paradigm
"What a delight it was to see Paul Werbos rediscover Freud's version of 'back-propagation.' Freud was adamant (in The Project for a Scientific Psychology) that selective learning could only take place if the presynaptic neuron was as influenced as is the postsynaptic neuron during excitation. Such activation of both sides of the contact barrier (Freud's name for the synapse) was accomplished by reducing synaptic resistance by the absorption of 'energy' at the synaptic membranes. Not bad for 1895 But Werbos 1993 is even better." --Karl H. Pribram Professor Emeritus, Stanford University

This book explores internet applications in which a crucial role is played by classification, such as spam filtering, recommender systems, malware detection, intrusion detection and sentiment analysis. It explains how such classification problems can be solved using various statistical and machine learning methods, including K nearest neighbours, Bayesian classifiers, the logit method, discriminant analysis, several kinds of artificial neural networks, support vector machines, classification trees and other kinds of rule-based methods, as well as random forests and other kinds of classifier ensembles. The book covers a wide range of available classification methods and their variants, not only those that have already been used in the considered kinds of applications, but also those that have the potential to be used in them in the future. The book is a valuable resource for post-graduate students and professionals alike.

An essential contribution to the study of the history of computers, this work identifies the computer's impact on the physical, biological, cognitive, and medical sciences. References fundamental to the understudied area of the history of scientific computing also document the significant role of the sciences in helping to shape the development of computer technology. More broadly, the many resources on scientific computing help demonstrate how the computer was the most significant scientific instrument of the 20th century.

The only guide of its kind covering the use and impact of computers on the the physical, biological, medical, and cognitive sciences, it contains more than 1,000 annotated citations to carefully selected secondary and primary resources. Historians of technology and science will find this a very useful resource. Computer scientists, physicians, biologists, chemists, and geologists will also benefit from this extensive bibliography on the history of computer applications and the sciences.

This book presents covert, semi-covert and overt techniques for communication over printed media by modifying images, texts or barcodes within the document. Basic and advanced techniques are discussed aimed to modulate information into images, texts and barcodes. Conveying information over printed media can be useful for content authentication, author copyright, information and piracy product deterrent, side information for marketing, among other applications. Practical issues are discussed and experiments are provided to evaluate competitive approaches for hard-copy communication. This book is a useful resource for researchers, practitioners and graduate students in the field of hard-copy communication by providing the fundamentals, basic and advanced techniques as examples of approaches to address the hard-copy media distortions and particularities.

This textbook provides concise coverage of the basics of linear and integer programming which, with megatrends toward optimization, machine learning, big data, etc., are becoming fundamental toolkits for data and information science and technology. The authors' approach is accessible to students from almost all fields of engineering, including operations research, statistics, machine learning, control system design, scheduling, formal verification and computer vision. The presentations enables the basis for numerous approaches to solving hard combinatorial optimization problems through randomization and approximation. Readers will learn to cast various problems that may arise in their research as optimization problems, understand the cases where the optimization problem will be linear, choose appropriate solution methods and interpret results appropriately.

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

Written by the pioneer and foremost authority on the subject, this new book is both a comprehensive university textbook and professional/research reference on the finite-difference time-domain (FD-TD) computational solution method for Maxwell's equations. It presents in-depth discussions of: The revolutionary Berenger PML absorbing boundary condition; FD-TD modelling of nonlinear, dispersive, and gain optical materials used in lasers and optical microchips; unstructured FD-TD meshes for modelling of complex systems; 2.5-dimensional body-of-revolution FD-TD algorithms; Linear and nonlinear electronic circuit models, including a seamless tie-in to SPICE; Digital signal postprocessing of FD-TD data; FD-TD modelling of microlaser cavities; and FD-TD software development for the latest Intel and Cray massively parallel computers.

Creativity in Computing and DataFlow Supercomputing, the latest release in the Advances in Computers series published since 1960, presents detailed coverage of innovations in computer hardware, software, theory, design, and applications. In addition, it provides contributors with a medium in which they can explore topics in greater depth and breadth than journal articles typically allow. As a result, many articles have become standard references that continue to be of significant, lasting value in this rapidly expanding field.