Discrete Optimization Algorithms

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and because of the discovery of surprising and powerful algorithms. As a consequence, algorithmic number theory has gradually emerged as an important and distinct field with connections to computer science and cryptography as well as other areas of mathematics. This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that cover the essential topics in this area, and in addition, there are contributions pointing in broader directions, including cryptography, computational class field theory, zeta functions and L-series, discrete logarithm algorithms, and quantum computing.

Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and because of the discovery of surprising and powerful algorithms. As a consequence, algorithmic number theory has gradually emerged as an important and distinct field with connections to computer science and cryptography as well as other areas of mathematics. This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that cover the essential topics in this area, and in addition, there are contributions pointing in broader directions, including cryptography, computational class field theory, zeta functions and L-series, discrete logarithm algorithms, and quantum computing.

Algorithmic Aspects of Graph Connectivity is the first comprehensive book on this central notion in graph and network theory, emphasizing its algorithmic aspects. Because of its wide applications in the fields of communication, transportation, and production, graph connectivity has made tremendous algorithmic progress under the influence of the theory of complexity and algorithms in modern computer science. The book contains various definitions of connectivity, including edge-connectivity and vertex-connectivity, and their ramifications, as well as related topics such as flows and cuts. The authors thoroughly discuss new concepts and algorithms that allow for quicker and more efficient computing, such as maximum adjacency ordering of vertices. Covering both basic definitions and advanced topics, this book can be used as a textbook in graduate courses in mathematical sciences, such as discrete mathematics, combinatorics, and operations research, and as a reference book for specialists i

Master the practical aspects of implementing deep learning solutions with PyTorch, using a hands-on approach to understanding both theory and practice. This updated edition will prepare you for applying deep learning to real world problems with a sound theoretical foundation and practical know-how with PyTorch, a platform developed by Facebook's Artificial Intelligence Research Group.You'll start with a perspective on how and why deep learning with PyTorch has emerged as an path-breaking framework with a set of tools and techniques to solve real-world problems. Next, the book will ground you with the mathematical fundamentals of linear algebra, vector calculus, probability and optimization. Having established this foundation, you'll move on to key components and functionality of PyTorch including layers, loss functions and optimization algorithms. You'll also gain an understanding of Graphical Processing Unit (GPU) based computation, which is essential for training deep learning models

This book provides a solid foundation and an extensive study for an important class of constrained optimization problems known as Mathematical Programs with Equilibrium Constraints (MPEC), which are extensions of bilevel optimization problems. The book begins with the description of many source problems arising from engineering and economics that are amenable to treatment by the MPEC methodology. Error bounds and parametric analysis are the main tools to establish a theory of exact penalisation, a set of MPEC constraint qualifications and the first-order and second-order optimality conditions. The book also describes several iterative algorithms such as a penalty-based interior point algorithm, an implicit programming algorithm and a piecewise sequential quadratic programming algorithm for MPECs. Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has

This book provides a solid foundation and an extensive study for an important class of constrained optimization problems known as Mathematical Programs with Equilibrium Constraints (MPEC), which are extensions of bilevel optimization problems. The book begins with the description of many source problems arising from engineering and economics that are amenable to treatment by the MPEC methodology. Error bounds and parametric analysis are the main tools to establish a theory of exact penalisation, a set of MPEC constraint qualifications and the first-order and second-order optimality conditions. The book also describes several iterative algorithms such as a penalty-based interior point algorithm, an implicit programming algorithm and a piecewise sequential quadratic programming algorithm for MPECs. Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has

Explore the frontier of device engineering by applying optimization to nanoscience and device design. This cutting-edge work shows how robust, manufacturable designs that meet previously unobtainable system specifications can be created using a combination of modern computer power, adaptive algorithms, and realistic device-physics models. Applying this method to nanoscience is a path to creating new devices with new functionality, and it could be the key design element in making nanoscience a practical technology. Basic introductory examples along with MATLAB code are included, through to more formal and sophisticated approaches, and specific applications and designs are examined. Essential reading for researchers and engineers in electronic devices, nanoscience, materials science, applied mathematics, and applied physics.

An introduction to computational modeling for cognitive neuroscientists, covering both foundational work and recent developments. Cognitive neuroscientists need sophisticated conceptual tools to make sense of their field’s proliferation of novel theories, methods, and data. Computational modeling is such a tool, enabling researchers to turn theories into precise formulations. This book offers a mathematically gentle and theoretically unified introduction to modeling cognitive processes. Theoretical exercises of varying degrees of difficulty throughout help readers develop their modeling skills. After a general introduction to cognitive modeling and optimization, the book covers models of decision making; supervised learning algorithms, including Hebbian learning, delta rule, and backpropagation; the statistical model analysis methods of model parameter estimation and model evaluation; the three recent cognitive modeling approaches of reinforcement learning, unsupervised learning, and

Discover scalable, dependable, and intelligent solutions to the challenges of integrating complex networked microgrids with this definitive guide to the development of cutting-edge power and data systems. Includes advanced fault management control and optimization to enable enhanced microgrid penetration without compromising reliability. Features SDN-based architectures and techniques to enable secure, reliable and fault-tolerant algorithms for resilient networked systems. Provides reachability techniques to facilitate a deeper understanding of microgrid resilience in areas with high penetration of renewables. Combining resilient control, fast programmable networking, reachability analysis, and cyber-physical security, this is essential reading for researchers, professional engineers, and graduate students interested in creating the next generation of data-intensive self-configurable networked microgrid systems, smart communities, and smart infrastructure.

Providing key background material together with advanced topics, this self-contained book is written in an easy-to-read style and is ideal for newcomers to multicarrier systems. Early chapters provide a review of basic digital communication, starting from the equivalent discrete time channel and including a detailed review of the MMSE receiver. Later chapters then provide extensive performance analysis of OFDM and DMT systems, with discussions of many practical issues such as implementation and power spectrum considerations. Throughout, theoretical analysis is presented alongside practical design considerations, whilst the filter bank transceiver representation of OFDM and DMT systems opens up possibilities for further optimization such as minimum bit error rate, minimum transmission power, and higher spectral efficiency. With plenty of insightful real-world examples and carefully designed end-of-chapter problems this is an ideal single-semester textbook for senior undergraduate and gr

This self-contained introduction to machine learning, designed from the start with engineers in mind, will equip students with everything they need to start applying machine learning principles and algorithms to real-world engineering problems. With a consistent emphasis on the connections between estimation, detection, information theory, and optimization, it includes: an accessible overview of the relationships between machine learning and signal processing, providing a solid foundation for further study; clear explanations of the differences between state-of-the-art techniques and more classical methods, equipping students with all the understanding they need to make informed technique choices; demonstration of the links between information-theoretical concepts and their practical engineering relevance; reproducible examples using Matlab, enabling hands-on student experimentation. Assuming only a basic understanding of probability and linear algebra, and accompanied by lecture slide

This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the now-famous Schramm–Loewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourier-analytic set-up, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging.

This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the now-famous Schramm–Loewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourier-analytic set-up, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging.

By the time students have done some programming in one or two languages and have learnt the common ways of representing information in a computer, they will want to embark upon further study of theoretical or applied topics in computer science. Most will encounter problems that require for their solution one or more of the techniques described in this book: for example problems depending upon the formation and solution of different equations; the task of making lists of possible alternatives and of answering questions about them; or the search for discrete optima. Written by the same authors as the highly successful Information Representation and Manipulation in a Computer, this book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus. Numerous exercises are provided, with hints to their solutions.

Application of Artificial Intelligence in Hybrid Electric Vehicle Energy Management presents the state-of-the-art in hybrid electric vehicle system modelling and management. With a focus on learning-based energy management strategies, the book provides detailed methods, mathematical models, and strategies designed to optimize the energy management of the energy supply module of a hybrid vehicle.The book first addresses the underlying problems in Hybrid Electric Vehicle (HEV) modeling, and then introduces several artificial intelligence-based energy management strategies of HEV systems, including those based on fuzzy control with driving pattern recognition, multi objective optimization, fuzzy Q-learning and Deep Deterministic Policy Gradient (DDPG) algorithms. To help readers apply these management strategies, the book also introduces State of Charge and State of Health prediction methods and real time driving pattern recognition. For each application, the detailed experimental process

There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

This authoritative account of electronic and optoelectronic devices operating at frequencies greater than 1 GHz covers the concepts and fundamental principles of operation, and, uniquely, their circuit applications too. Key features include: • a comprehensive coverage of electron devices, such as MESFET, HEMT, RF MOSFET, BJT and HBT, and their models • discussions of semiconductor devices fabricated in a variety of material systems, such as Si, III-V compound semiconductors, and Si-Ge • a description of light-emitting diodes, semiconductor lasers and photodetectors • plentiful real-world examples • end-of-chapter problems to test understanding of the material covered From crystal structure to atomic bonding, recombination and radiation in semiconductors to p-n junctions and heterojunctions, a wide range of critical topics is covered. Optimization algorithms, such as simulated annealing and neural network applications, are also discussed. Graduate students in electrical engineering, in

This Element presents a unified computational fluid dynamics framework from rarefied to continuum regimes. The framework is based on the direct modelling of flow physics in a discretized space. The mesh size and time step are used as modelling scales in the construction of discretized governing equations. With the variation-of-cell Knudsen number, continuous modelling equations in different regimes have been obtained, and the Boltzmann and Navier-Stokes equations become two limiting equations in the kinetic and hydrodynamic scales. The unified algorithms include the discrete velocity method (DVM)–based unified gas-kinetic scheme (UGKS), the particlebased unified gas-kinetic particle method (UGKP), and the wave and particle–based unified gas-kinetic wave-particle method (UGKWP). The UGKWP is a multi-scale method with the particle for non-equilibrium transport and wave for equilibrium evolution. The particle dynamics in the rarefied regime and the hydrodynamic flow solver in the continuu

Data structures are the fundamental building blocks of any computer program, used for storing, representing and manipulating data in a computer. This text presents the basic concepts of data structures as part of the art of writing computer programs. The author concentrates on the fundamentals of what should be done to solve a problem efficiently rather than technical implementation details. The text includes pseudocode and covers all the most common data structures, such as queues, stacks, trees, heaps, and hash tables, along with the basics of searching, sorting, and coding. This book can supplement any undergraduate algorithms or discrete math course and will also be accessible to students and researchers in other quantitative disciplines. No prerequisites beyond introductory programming and basic mathematics are required, and the accessible, conceptual presentation will appeal to undergraduates in many quantitative fields. Carefully designed problem sets with selected solutions wil

Data structures are the fundamental building blocks of any computer program, used for storing, representing and manipulating data in a computer. This text presents the basic concepts of data structures as part of the art of writing computer programs. The author concentrates on the fundamentals of what should be done to solve a problem efficiently rather than technical implementation details. The text includes pseudocode and covers all the most common data structures, such as queues, stacks, trees, heaps, and hash tables, along with the basics of searching, sorting, and coding. This book can supplement any undergraduate algorithms or discrete math course and will also be accessible to students and researchers in other quantitative disciplines. No prerequisites beyond introductory programming and basic mathematics are required, and the accessible, conceptual presentation will appeal to undergraduates in many quantitative fields. Carefully designed problem sets with selected solutions wil

Numerical analysis deals with the manipulation of numbers to solve a particular problem. This book discusses in detail the creation, analysis and implementation of algorithms to solve the problems of continuous mathematics. An input is provided in the form of numerical data or it is generated as required by the system to solve a mathematical problem. Subsequently, this input is processed through arithmetic operations together with logical operations in a systematic manner and an output is produced in the form of numbers. Covering the fundamentals of numerical analysis and its applications in one volume, this book offers detailed discussion on relevant topics including difference equations, Fourier series, discrete Fourier transforms and finite element methods. In addition, the important concepts of integral equations, Chebyshev Approximation and Eigen Values of Symmetric Matrices are elaborated upon in separate chapters. The book will serve as a suitable textbook for undergraduate stud

Peak signal power is an important factor in the implementation of multicarrier (MC) modulation schemes, like OFDM, in wireless and wireline communication systems. This 2007 book describes tools necessary for analyzing and controlling the peak-to-average power ratio in MC systems, and how these techniques are applied in practical designs. The author starts with an overview of multicarrier signals and basic tools and algorithms, before discussing properties of MC signals in detail: discrete and continuous maxima; statistical distribution of peak power; codes with constant peak-to-average power ratio are all covered, concluding with methods to decrease peak power in MC systems. Current knowledge, problems, methods and definitions are summarized using rigorous mathematics, with an overview of the tools for the engineer. The book is aimed at graduate students and researchers in electrical engineering, computer science and applied mathematics, and practitioners in the telecommunications indu

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory. This edition now includes over 150 new exercises, ranging from the routine to the challenging, that flesh out the material presented in the body of the text, and which further develop the theory and present new applications. The material has also been reorganized to improve clarity of exposition and presentation. Ideal as a textbook for introductory courses in number theory and algebra, especially those geared t

Peak signal power is an important factor in the implementation of multicarrier (MC) modulation schemes, like OFDM, in wireless and wireline communication systems. This 2007 book describes tools necessary for analyzing and controlling the peak-to-average power ratio in MC systems, and how these techniques are applied in practical designs. The author starts with an overview of multicarrier signals and basic tools and algorithms, before discussing properties of MC signals in detail: discrete and continuous maxima; statistical distribution of peak power; codes with constant peak-to-average power ratio are all covered, concluding with methods to decrease peak power in MC systems. Current knowledge, problems, methods and definitions are summarized using rigorous mathematics, with an overview of the tools for the engineer. The book is aimed at graduate students and researchers in electrical engineering, computer science and applied mathematics, and practitioners in the telecommunications indu

A practical, accessible guide to optimization problems with discrete or integer variablesInteger Programming stands out from other textbooks by explaining in clear and simple terms how to construct cu

《離散粒子群優化算法及其應用》主要闡述離散粒子群優化（Discrete Particle Swarm Optimization，DPSO）算法的具體構建及其在各種組合優化問題中的應用等。 全書分為11章，各章節內容具體安排如下：第1章主要介紹丁基本PSO算法的原理機制及其發展現狀，并著重介紹了PSO算法的三種常見離散化策略，闡述了DPSO算法的應用成果；第2章主要介紹了PSO算法在tsp優化問題

"This book considers the foremost optimization algorithms in several applications. It deals primarily with methods and approaches that include meta-heuristics for further systems improvements. It gran

Many machine learning algorithms require real-valued feature vectors of data instances as inputs. By projecting data into vector spaces, representation learning techniques have achieved promising performance in many areas such as computer vision and natural language processing. There is also a need to learn representations for discrete relational data, namely networks or graphs. Network Embedding (NE) aims at learning vector representations for each node or vertex in a network to encode the topologic structure. Due to its convincing performance and efficiency, NE has been widely applied in many network applications such as node classification and link prediction.This book provides a comprehensive introduction to the basic concepts, models, and applications of network representation learning (NRL). The book starts with an introduction to the background and rising of network embeddings as a general overview for readers. Then it introduces the development of NE techniques by presenting se

衝突多目標優化問題在現實世界中廣泛存在，這類多目標優化問題(multi-objective optimization problems,MOP)不存在單個最優解使所有目標均達到最優，理論上只能尋求多個衝突目標的權衡優化解。相較于傳統的數學優化方法而言，基於種群優化的多目標演化算法(multi-objective evolutionary algorithms,MOEA)則能更好地權衡多個衝突目標的優化。近年來，針對具有超多目標、大規模決策變量、約束條件、數據驅動及不確定性魯棒性等特性的複雜多目標優化問題，MOEA已成為研究熱點並受到廣泛關注，各類新方法與新技術不斷湧現。與此同時，隨著智能計算技術的發展，將MOEA與各種先進智能計算方法相結合，推動著更有效地解決一系列複雜的多目標優化問題，這成為非常有前景的研究方向。本書主要內容為作者在上述研究領域內過去近十年中的主要相關研究成果的總結。全書共14章，大致分為四個部分：第一部分(第1章)對智能計算進行簡要概述；第二部分(第2～3章)比較全面地介紹各類複雜的MOPs及複雜多目標演化優化的基礎知識；第三部分(第4～10章)介紹求解各類複雜的MOPs所提出的各種先進的MOEAs，並涉及利用智能計算技術輔助的一系列理論成果；第四部分(第11～14章)圍繞MOEA與智能計算的進一步聯繫，介紹將MOEA應用于求解機器學習、深度學習中複雜MOP的前沿理論成果。