This fifth edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses. The book is both complete and careful, and it continues to maintain its emphasis on algorithms and applications. Excellent exercise sets allow students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-making this the ideal text for preparing students for advanced study.

Electric power systems have become much more complex in the past years, due to the integration of distributed generation including renewable energy sources and the challenges caused by intermittency of renewables. This complexity makes power systems potentially more vulnerable. However, use of computer-based protection methods (i.e., digital protection relays) supported by communication technology have helped in protecting electrical networks from faults to which they are subjected to. This second edition of the book covers a comprehensive introduction to the protection of electrical power systems using digital protective relays. The new edition offers a thorough revision and update, and comprehensive additional material. Chapters treat the mathematical background of protection algorithms including, sinusoidal-wave-based algorithms, Walsh function and S-Transform-based techniques, least squares and differential equation-based techniques, travelling wave-based protection, protection of transformers, digital line differential protection, a comparison between digital protection algorithms, and importantly, protection of networks with distributed generation including renewable energy resources. The book is written for researchers in electrical engineering and power engineering, in industry, utilities and universities, and for advanced students. The treatment is logically structured, covering mathematics and principles for the development and implementation of the major algorithms underlying different protection techniques. These techniques can be applied to protection of generator transformers, lines, switchgear and cable circuits: the main components of transmission and distribution systems with and without integrated distributed energy sources including renewables.

This book offers an introduction into quantum machine learning research, covering approaches that range from "near-term" to fault-tolerant quantum machine learning algorithms, and from theoretical to practical techniques that help us understand how quantum computers can learn from data. Among the topics discussed are parameterized quantum circuits, hybrid optimization, data encoding, quantum feature maps and kernel methods, quantum learning theory, as well as quantum neural networks. The book aims at an audience of computer scientists and physicists at the graduate level onwards. The second edition extends the material beyond supervised learning and puts a special focus on the developments in near-term quantum machine learning seen over the past few years.

The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year's special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.

Fuzzy cognitive maps (FCMs) have gained popularity in the scientific community due to their capabilities in modeling and decision making for complex problems.This book presents a novel algorithm called glassoFCM to enable automatic learning of FCM models from data. Specifically, glassoFCM is a combination of two methods, glasso (a technique originated from machine learning) for data modeling and FCM simulation for decision making. The book outlines that glassoFCM elaborates simple, accurate, and more stable models that are easy to interpret and offer meaningful decisions. The research results presented are based on an investigation related to a real-world business intelligence problem to evaluate characteristics that influence employee work readiness.Finally, this book provides readers with a step-by-step guide of the 'fcm' package to execute and visualize their policies and decisions through the FCM simulation process.

In this book the author presents some techniques for exploring trees and graphs. He illustrates the linear search technique and the backtracking technique, and as instances of tree exploration methods he presents various algorithms for parsing subclasses of context-free languages. He also illustrates some tree and graph exploration and manipulation methods by presenting, among others, algorithms for visiting trees, evaluating Boolean expressions, proving propositional formulas, computing paths in graphs, and performing string matching. This book has been used for advanced undergraduate and graduate courses on automata and formal languages, and assumes some prior exposure to the basic notions in that area. Sample programs are presented in Java and Prolog.

This revised textbook motivates and illustrates the techniques of applied probability by applications in electrical engineering and computer science (EECS). The author presents information processing and communication systems that use algorithms based on probabilistic models and techniques, including web searches, digital links, speech recognition, GPS, route planning, recommendation systems, classification, and estimation. He then explains how these applications work and, along the way, provides the readers with the understanding of the key concepts and methods of applied probability. Python labs enable the readers to experiment and consolidate their understanding. The book includes homework, solutions, and Jupyter notebooks. This edition includes new topics such as Boosting, Multi-armed bandits, statistical tests, social networks, queuing networks, and neural networks. For ancillaries related to this book, including examples of Python demos and also Python labs used in Berkeley, please email Mary James at [email protected]. This is an open access book.

Coinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.

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 features more than 20 papers that celebrate the work of Hajnal Andreka and Istvan Nemeti. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andreka and Istvan Nemeti at the end of the book describe an adventurous journey from electric engineering and Maxwell's equations to a complex system of computer programs for designing Hungary's electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself.

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.

This volume explores the connections between mathematical modeling, computational methods, and high performance computing, and how recent developments in these areas can help to solve complex problems in the natural sciences and engineering. The content of the book is based on talks and papers presented at the conference Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST), held at Inderprastha Engineering College in Ghaziabad, India in January 2020. A wide range of both theoretical and applied topics are covered in detail, including the conceptualization of infinity, efficient domain decomposition, high capacity wireless communication, infectious disease modeling, and more. These chapters are organized around the following areas: Partial and ordinary differential equations Optimization and optimal control High performance and scientific computing Stochastic models and statistics Recent Trends in Mathematical Modeling and High Performance Computing will be of interest to researchers in both mathematics and engineering, as well as to practitioners who face complex models and extensive computations.

This book provides a comprehensive examination of preconditioners for boundary element discretisations of first-kind integral equations. Focusing on domain-decomposition-type and multilevel methods, it allows readers to gain a good understanding of the mechanisms and necessary techniques in the analysis of the preconditioners. These techniques are unique for the discretisation of first-kind integral equations since the resulting systems of linear equations are not only large and ill-conditioned, but also dense. The book showcases state-of-the-art preconditioning techniques for boundary integral equations, presenting up-to-date research. It also includes a detailed discussion of Sobolev spaces of fractional orders to familiarise readers with important mathematical tools for the analysis. Furthermore, the concise overview of adaptive BEM, hp-version BEM, and coupling of FEM-BEM provides efficient computational tools for solving practical problems with applications in science and engineering.

This eighteenth volume in the Poincare Seminar Series provides a thorough description of Information Theory and some of its most active areas, in particular, its relation to thermodynamics at the nanoscale and the Maxwell Demon, and the emergence of quantum computation and of its counterpart, quantum verification. It also includes two introductory tutorials, one on the fundamental relation between thermodynamics and information theory, and a primer on Shannon's entropy and information theory. The book offers a unique and manifold perspective on recent mathematical and physical developments in this field.

This volume gathers papers presented at the Workshop on Computational Diffusion MRI (CDMRI 2019), held under the auspices of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), which took place in Shenzhen, China on October 17, 2019. This book presents the latest advances in the rapidly expanding field of diffusion MRI. It shares new perspectives on the latest research challenges for those currently working in the field, but also offers a valuable starting point for anyone interested in learning about computational techniques in diffusion MRI. The book includes rigorous mathematical derivations, a wealth of rich, full-colour visualisations and extensive clinically relevant results. As such, it will be of interest to researchers and practitioners in the fields of computer science, MRI physics and applied mathematics. Readers will find contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation, to new computational methods and estimation techniques for the in vivo recovery of microstructural and connectivity features, as well as diffusion-relaxometry and frontline applications in research and clinical practice. This edition includes invited works from high-profile researchers with a specific focus on three new and important topics that are gaining momentum within the diffusion MRI community, including diffusion MRI signal acquisition and processing strategies, machine learning for diffusion MRI, and diffusion MRI outside the brain and clinical applications.

The book shows that the analytic combinatorics (AC) method encodes the combinatorial problems of multiple object tracking-without information loss-into the derivatives of a generating function (GF). The book lays out an easy-to-follow path from theory to practice and includes salient AC application examples. Since GFs are not widely utilized amongst the tracking community, the book takes the reader from the basics of the subject to applications of theory starting from the simplest problem of single object tracking, and advancing chapter by chapter to more challenging multi-object tracking problems. Many established tracking filters (e.g., Bayes-Markov, PDA, JPDA, IPDA, JIPDA, CPHD, PHD, multi-Bernoulli, MBM, LMBM, and MHT) are derived in this manner with simplicity, economy, and considerable clarity. The AC method gives significant and fresh insights into the modeling assumptions of these filters and, thereby, also shows the potential utility of various approximation methods that are well established techniques in applied mathematics and physics, but are new to tracking. These unexplored possibilities are reviewed in the final chapter of the book.

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc.
The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them.
In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes.
Self contained presentation of key issues in successful numerical simulationAccessible to scientists and engineers with diverse backgroundProvides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations

This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.

Inverse problems such as imaging or parameter identification deal with the recovery of unknown quantities from indirect observations, connected via a model describing the underlying context. While traditionally inverse problems are formulated and investigated in a static setting, we observe a significant increase of interest in time-dependence in a growing number of important applications over the last few years. Here, time-dependence affects a) the unknown function to be recovered and / or b) the observed data and / or c) the underlying process. Challenging applications in the field of imaging and parameter identification are techniques such as photoacoustic tomography, elastography, dynamic computerized or emission tomography, dynamic magnetic resonance imaging, super-resolution in image sequences and videos, health monitoring of elastic structures, optical flow problems or magnetic particle imaging to name only a few. Such problems demand for innovation concerning their mathematical description and analysis as well as computational approaches for their solution.

Sparse grids are a popular tool for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different flavors, are frequently the method of choice. This volume of LNCSE presents selected papers from the proceedings of the fifth workshop on sparse grids and applications, and demonstrates once again the importance of this numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including uncertainty quantification, plasma physics simulations, and computational chemistry, to name but a few.

This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of nonlinearity is a universal feature in mathematics, physics, chemistry and biology, and is used to characterize systems whose behavior does not amount to a superposition of simple building blocks, but rather features complex and often chaotic patterns and phenomena. Each chapter of the book features a synopsis that not only recaps the recent progress in each field but also charts the challenges that lie ahead. This interdisciplinary book presents contributions from a diverse group of experts from various fields to provide an overview of each field's past, present and future. It will appeal to both beginners and seasoned researchers in nonlinear science, numerous areas of physics (optics, quantum physics, biophysics), and applied mathematics (ODEs, PDEs, dynamical systems, machine learning) as well as engineering.

This textbook introduces major topics that include quantum bits, superposition, entanglement, logic gates, quantum search algorithm, quantum Fourier transform, inverse quantum Fourier transform, Shor's order-finding algorithm and phase estimation. Everyone can write algorithms and programs in the cloud making using IBM's quantum computers that support IBM Q Experience which contains the composer, open quantum assembly language, simulators and real quantum devices. Furthermore, this book teaches you how to use open quantum assembly language to write quantum programs for dealing with complex problems. Through numerous examples and exercises, readers will learn how to write a quantum program with open quantum assembly language for solving any problem from start to complete. This book includes six main chapters: *Quantum Bits and Quantum Gates-learn what quantum bits are, how to declare and measure them, what quantum gates are and how they work on a simulator or a real device in the cloud. *Boolean Algebra and its Applications-learn how to decompose CCNOT gate into six CNOT gates and nine gates of one bit and how to use NOT gates, CNOT gates and CCNOT gates to implement logic operations including NOT, OR, AND, NOR, NAND, Exclusive-OR (XOR) and Exclusive-NOR (XNOR). *Quantum Search Algorithm and its Applications-learn core concepts of quantum search algorithm and how to write quantum programs to implement core concepts of quantum search algorithm for solving two famous NP-complete problems that are the satisfiability problem in n Boolean variables and m clauses and the clique problem in a graph with n vertices and q edges. *Quantum Fourier Transform and its Applications-learn core concepts of quantum Fourier transform and inverse quantum Fourier transform and how to write quantum programs to implement them for solving two real applications that are to compute the period and the frequency of two given oracular functions. *Order-Finding and Factoring-learn core concepts of Shor's order-finding algorithm and how to write quantum programs to implement Shor's order-finding algorithm for completing the prime factorization to 15. Phase Estimation and its Applications-learn core concepts of phase estimation and quantum counting and how to write quantum programs to implement them to compute the number of solution(s) in the independent set problem in a graph with two vertices and one edge.

This book provides an overview of state-of-the-art implementations of quantum random number generators (QRNGs), and especially examines their relation to classical statistical randomness models and numerical techniques for computing random numbers. The reader - who ideally has a background in classical statistics, computer science, or cryptography - is introduced to the world of quantum bits step by step, and explicit relations between QRNGs and their classical counterparts are identified along the way. Random number generation is a major pillar of cryptography. Capitalizing on the randomness inherent in quantum phenomena is a rapidly evolving branch of quantum cryptography with countless applications for the future. The value of quantum randomness for cryptographic purposes is empirically demonstrated in statistical evaluations of QRNGs' performance compared to classical techniques for true and pseudorandom number generation. The book then provides an overview of technical implementations of QRNGs, before a concluding discussion of major achievements and remaining obstacles in the field rounds out the coverage, while also opening the door for future research directions.