Algorithms

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Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries. For a century, these images barely existed outside the imagination of mathematicians. However, in the 1980s, the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

生產與運輸協同調度:模型與算法(英文版)》是作者精心為廣大讀者朋友們編寫而成的此書，可以讓更多的讀者朋友們從書中了解到更多的知識，從而提升讀者朋友們自身的知識水平。《生產與運輸協同調度:模型與算法(英文版)》圍繞擠壓廠的連續批處理機加工過程，系統性分析了多種情形下的多階段生產運輸協同調度問題。

The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. Enables students, researchers, and engineers to learn the BEM and fast multipole method from a s

Originally published in 1976, this book introduced a series of mathematical models of urban phenomena relevant to scientists and planners attempting to understand and predict the form of cities and regions. Dr Batty organises the book around the main theme of designing and using such models in practical situations and develops a family of static and dynamic models dealing with the location of land use and economic activities. He describes the models both as urban theories and as computer algorithms, and thoroughly explores the process of calibrating or 'tuning' the models to reflect reality. Problems concerning the definition of the spatial systems to which these models refer are examined, as are other practical difficulties such as data organisation. The quasi-experimental approach which characterises this style of computer model-building extends to using the models in conditional prediction and Dr Batty discusses their role in the planning process, with their use in testing the impac

Welcome to the second International Symposium on Parallel Architectures, Al-gorithms and Programming （PAAP 2009）. The symposium is sponsored andorganized by University of Science and Technology of Chi

The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. Enables students, researchers, and engineers to learn the BEM and fast multipole method from a s

On-line learning is one of the most powerful and commonly used techniques for training large layered networks and has been used successfully in many real-world applications. Traditional analytical methods have been recently complemented by ones from statistical physics and Bayesian statistics. This powerful combination of analytical methods provides more insight and deeper understanding of existing algorithms and leads to novel and principled proposals for their improvement. This book presents a coherent picture of the state-of-the-art in the theoretical analysis of on-line learning. An introduction relates the subject to other developments in neural networks and explains the overall picture. Surveys by leading experts in the field combine new and established material and enable non-experts to learn more about the techniques and methods used. This book, the first in the area, provides a comprehensive view of the subject and will be welcomed by mathematicians, scientists and engineers,

The sign-solvability of a linear system implies that the signs of the entries of the solution are determined solely on the basis of the signs of the coefficients of the system. That it might be worthwhile and possible to investigate such linear systems was recognised by Samuelson in his classic book Foundations of Economic Analysis. Sign-solvability is part of a larger study which seeks to understand the special circumstances under which an algebraic, analytic or geometric property of a matrix can be determined from the combinatorial arrangement of the positive, negative and zero elements of the matrix. The large and diffuse body of literature connected with sign-solvability is presented as a coherent whole for the first time in this book, displaying it as a beautiful interplay between combinatorics and linear algebra. One of the features of this book is that algorithms that are implicit in many of the proofs have been explicitly described and their complexity has been commented on.

本書主要著重於那些隱藏在演算法設計和分析背後的主要觀念。 在書中分別分析非遞迴演算法和遞迴演算法兩種方法之效率。 第二章中特別介紹演算法實證分析以及演算法之可視化。 書中有系統地為讀者精心設計一些問題，希望引起讀者的注意與更進一步的思考。 每一章結束時都會對本章最重要的概念和結論做一個總結。 本書包含大約600道習題，並且都附有提示。其中，謎題類的習題均以特殊的圖示加以標註。

Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. In this way, all the key ideas are covered without getting involved in the complications of more advanced systems, but concentrating rather on the principles that make the theory work in practice. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm which lies at the heart of every such system. Also featured are two other interesting algorithms that have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making the book at a level which can be used as an introduction to type theory for comp

Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries. For a century, these images barely existed outside the imagination of mathematicians. However, in the 1980s, the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.

On-line learning is one of the most powerful and commonly used techniques for training large layered networks and has been used successfully in many real-world applications. Traditional analytical methods have been recently complemented by ones from statistical physics and Bayesian statistics. This powerful combination of analytical methods provides more insight and deeper understanding of existing algorithms and leads to novel and principled proposals for their improvement. This book presents a coherent picture of the state-of-the-art in the theoretical analysis of on-line learning. An introduction relates the subject to other developments in neural networks and explains the overall picture. Surveys by leading experts in the field combine new and established material and enable non-experts to learn more about the techniques and methods used. This book, the first in the area, provides a comprehensive view of the subject and will be welcomed by mathematicians, scientists and engineers,

Beginning with a brief introduction to algorithms and diophantine equations, this volume aims to provide a coherent account of the methods used to find all the solutions to certain diophantine equations, particularly those procedures which have been developed for use on a computer. The study is divided into three parts, the emphasis throughout being on examining approaches with a wide range of applications. The first section considers basic techniques including local methods, sieving, descent arguments and the LLL algorithm. The second section explores problems which can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves, mainly focusing on rational and integral points on elliptic curves. Each chapter concludes with a useful set of exercises. A detailed bibliography is included. This book will appeal to graduate students and research workers, with a basic knowledge of number theory, who are interested in solving diop

Beginning with a brief introduction to algorithms and diophantine equations, this volume aims to provide a coherent account of the methods used to find all the solutions to certain diophantine equations, particularly those procedures which have been developed for use on a computer. The study is divided into three parts, the emphasis throughout being on examining approaches with a wide range of applications. The first section considers basic techniques including local methods, sieving, descent arguments and the LLL algorithm. The second section explores problems which can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves, mainly focusing on rational and integral points on elliptic curves. Each chapter concludes with a useful set of exercises. A detailed bibliography is included. This book will appeal to graduate students and research workers, with a basic knowledge of number theory, who are interested in solving diop

Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. In this way, all the key ideas are covered without getting involved in the complications of more advanced systems, but concentrating rather on the principles that make the theory work in practice. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm which lies at the heart of every such system. Also featured are two other interesting algorithms that have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making the book at a level which can be used as an introduction to type theory for comp

This book presents a comprehensive and coherent account of the theory of quantum fields on a lattice, an essential technique for the study of the strong and electroweak nuclear interactions. Quantum field theory describes basic physical phenomena over an extremely wide range of length or energy scales. Quantum fields exist in space and time, which can be approximated by a set of lattice points. This approximation allows the application of powerful analytical and numerical techniques, and has provided a powerful tool for the study of both the strong and the electroweak interaction. After introductory chapters on scalar fields, gauge fields and fermion fields, the book studies quarks and gluons in QCD and fermions and bosons in the electroweak theory. The last chapter is devoted to numerical simulation algorithms which have been used in recent large-scale numerical simulations. The book will be valuable for graduate students and researchers in theoretical physics, elementary particle phy

The sign-solvability of a linear system implies that the signs of the entries of the solution are determined solely on the basis of the signs of the coefficients of the system. That it might be worthwhile and possible to investigate such linear systems was recognised by Samuelson in his classic book Foundations of Economic Analysis. Sign-solvability is part of a larger study which seeks to understand the special circumstances under which an algebraic, analytic or geometric property of a matrix can be determined from the combinatorial arrangement of the positive, negative and zero elements of the matrix. The large and diffuse body of literature connected with sign-solvability is presented as a coherent whole for the first time in this book, displaying it as a beautiful interplay between combinatorics and linear algebra. One of the features of this book is that algorithms that are implicit in many of the proofs have been explicitly described and their complexity has been commented on.

Diophantine equations over number fields have formed one of the most important and fruitful areas of mathematics throughout civilisation. In recent years increasing interest has been aroused in the analogous area of equations over function fields. However, although considerable progress has been made by previous authors, none has attempted the central problem of providing methods for the actual solution of such equations. The latter is the purpose and achievement of this volume: algorithms are provided for the complete resolution of various families of equations, such as those of Thue, hyperelliptic and genus one type. The results are achieved by means of an original fundamental inequality, first announced by the author in 1982. Several specific examples are included as illustrations of the general method and as a testimony to its efficiency. Furthermore, bounds are obtained on the solutions which improve on those obtained previously by other means. Extending the equality to a differen

★今天的數據科學家正扮演著古代神諭和中世紀占星師的角色，掌控著社會資源的分配。★本書將揭露 AI 如何透過「預測」來誘導行為，最終讓我們活成演算法設定好的樣子。★在這個監視資本主義時代，我們該如何拒絕被標籤化，重新拿回對自己生活的主導權？【權力不在未來，而在於誰「定義」了未來】從古代神諭到當代 AI：一場橫跨三千年的預測爭奪戰。為什麼銀行能決定你是否能貸款？為什麼演算法能預判你何時會辭職？我們以為預測是為了避開風險，但牛津大學教授 Carissa Véliz 尖銳地指出：「預測」從來不是為了預知未來，而是為了「控制」人類。From an award-winning University of Oxford professor comes a brilliant, urgent new look at prophecies—the predictions that determine our lives, from our personal finances and the quality of our healthcare to the news and social media we consume and the products foisted upon us.Today’s computer scientists play the same role as the oracles of the ancient world and the astrologers of the Middle Ages. Modern predictions not only advise on war, crop output, and marriages, but algorithms and statisticians also now determine whether we can get a loan, a job, an apartment, or an organ transplant. And when we cede ground to these predictions, we lose control of our own lives.In this powerful, refreshing new look at the many ways predic

A book from the stand-up mathematician that makes math fun again!Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it’s als

This book focuses on the design methods for reconfigurable computing processors for cryptographic algorithms. It covers the dynamic reconfiguration analysis of cryptographic algorithms, hardware archi

Make confident, evidence-based decisions in everyday critical care practice with Critical Care Medicine: An Algorithmic Approach. This first-of-its-kind decision making tool provides concise, practical guidance on key aspects of critical care in the form of easy-to-follow diagnostic and treatment algorithms, diagrams, and tables. The unique format saves you time as it guides you through best practices and reliable data to improve patient outcomes in the ICU.Chapters cover a particular organ system and are organized by disorder for easy reference. Each chapter includes a brief overview of the disorder, diagnostic algorithms, treatment algorithms, potential complications and strategies for overcoming them, and supporting references. Helpful mnemonics and advice from critical care experts are provided throughout. Key topics include ventilatory failure: asthma and COPD; ABG analysis; pleural effusion; acute respiratory failure; infectious disease; psychiatric aspects of critical care; ARDS

Algorithmic graph theory has been expanding at an extremely rapid rate since the middle of the twentieth century, in parallel with the growth of computer science and the accompanying utilization of computers, where efficient algorithms have been a prime goal. This book presents material on developments on graph algorithms and related concepts that will be of value to both mathematicians and computer scientists, at a level suitable for graduate students, researchers and instructors. The fifteen expository chapters, written by acknowledged international experts on their subjects, focus on the application of algorithms to solve particular problems. All chapters were carefully edited to enhance readability and standardize the chapter structure as well as the terminology and notation. The editors provide basic background material in graph theory, and a chapter written by the book's Academic Consultant, Martin Charles Golumbic (University of Haifa, Israel), provides background material on al

This textbook introduces advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for

Classical and Recent Aspects of Power System Optimization presents conventional and meta-heuristic optimization methods and algorithms for power system studies. The classic aspects of optimization in

Mapping and localization are two essential tasks in autonomous mobile robotics. Due to the unavoidable noise that sensors present, mapping algorithms usually rely on loop closure detection techniques,

This important text/reference presents a comprehensive review of techniques for taxonomy matching, discussing matching algorithms, analyzing matching systems, and comparing matching evaluation approac

"This book presents applications of heuristic and metaheuristic algorithms in manufacturing systems. This book discusses the main heuristic and metaheuristic methods to manage and optimize the problem

"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

This book describes the revolutionary capabilities of new shock fitting algorithms; a great improvement in computational fluid dynamics (CFD) for high-speed numerical simulations. Shock fitting method

Advanced Electromagnetic Computation with MATLAB® discusses commercial electromagnetic software, widely used in the industry. Algorithms of Finite Differences, Moment method, Finite Element method and

This book presents spectrum sharing efforts between cellular systems and radars. The book addresses coexistence algorithms for radar and communication systems. Topics include radar and cellular system

This revised and extended second edition covers problems concerning the design and realization of digital control algorithms for power electronics circuits using digital signal processing (DSP) method

Computer software and its structures, devices and processes are woven into our everyday life. Their significance is not just technical: the algorithms, programming languages, abstractions and metadata

Computer software and its structures, devices and processes are woven into our everyday life. Their significance is not just technical: the algorithms, programming languages, abstractions and metadata