Algorithms

The most comprehensive overview of signal detection available. This is a thorough, up-to-date introduction to optimizing detection algorithms for implementation on digital computers. It focuses extensively on real-world signal processing applications, including state-of-the-art speech and communications technology as well as traditional sonar/radar systems. Start with a quick review of the fundamental issues associated with mathematical detection, as well as the most important probability density functions and their properties. Next, review Gaussian, Chi-Squared, F, Rayleigh, and Rician PDFs, quadratic forms of Gaussian random variables, asymptotic Gaussian PDFs, and Monte Carlo Performance Evaluations. Three chapters introduce the basics of detection based on simple hypothesis testing, including the Neyman-Pearson Theorem, handling irrelevant data, Bayes Risk, multiple hypothesis testing, and both deterministic and random signals. The author then presents exceptionally detailed covera

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

Paul Erdös was one of the greatest mathematicians of this century, known the world over for his brilliant ideas and stimulating questions. On the date of his 80th birthday a conference was held in his honour at Trinity College, Cambridge. Many leading combinatorialists attended. Their subsequent contributions are collected here. The areas represented range from set theory and geometry, through graph theory, group theory and combinatorial probability, to randomised algorithms and statistical physics. Erdös himself was able to give a survey of recent progress made on his favourite problems. Consequently this volume, consisting of in-depth studies at the frontier of research, provides a valuable panorama across the breadth of combinatorics as it is today.

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

Studying the dynamics of a large number of particles interacting through long-range forces, commonly referred to as the 'N-body problem', is a central aspect of many different branches of physics. In recent years, significant advances have been made in the development of fast N-body algorithms to deal efficiently with such complex problems. This book is the first to give a thorough introduction to these so-called 'tree methods', setting out the basic principles and giving many practical examples of their use. No prior specialist knowledge is assumed, and the techniques are illustrated throughout with reference to a broad range of applications. The book will be of great interest to graduate students and researchers working on the modelling of systems in astrophysics, plasma physics, nuclear and particle physics, condensed matter physics and materials science.

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

Finite fields are algebraic structures in which there is much research interest and they have been shown to have a wide range of applications. These proceedings give a state-of-the-art account of the area of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. These also demonstrate inter-connections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable resource for any researcher in finite fields or related areas.

In this volume, which was originally published in 1996, noisy information is studied in the context of computational complexity; in other words the text deals with the computational complexity of mathematical problems for which information is partial, noisy and priced. The author develops a general theory of computational complexity of continuous problems with noisy information and gives a number of applications; deterministic as well as stochastic noise is considered. He presents optimal algorithms, optimal information, and complexity bounds in different settings: worst case, average case, mixed worst-average and average-worst, and asymptotic. The book integrates the work of researchers in such areas as computational complexity, approximation theory and statistics, and includes many fresh results as well. About two hundred exercises are supplied with a view to increasing the reader's understanding of the subject. The text will be of interest to professional computer scientists, statis

This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a 'learning algorithm' of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints. This book will be of value to anyone with an interest in neural networks and cognitive systems.

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.

This book explores the many engineering and architectural aspects of submarine design and how they relate to each other and the operational performance required of the vessel. Concepts of hydrodynamics, structure, powering and dynamics are explained, in addition to architectural considerations which bear on the submarine design process. The interplay between these aspects of design is given particular attention, and a final chapter is devoted to the generation of the concept design for the submarine as a whole. Submarine design makes extensive use of computer aids, and examples of algorithms used in concept design are given. The emphasis in the book is on providing engineering insight as well as an understanding of the intricacies of the submarine design process. It will serve as a text for students and as a reference manual for practising engineers and designers.

This text covers the field of steady-state kinetics from basic principles to the control of the multi-enzyme systems which constitute metabolic pathways. Emphasis is placed on the interpretation of the kinetic behaviour of enzyme-catalyzed reactions in terms of mechanisms. Algorithms are developed which can be implemented in computer programs for the derivation of equations. The treatment of steady-state enzyme kinetics is extended to allosteric enzymes and subunit interactions in polymeric enzymes. Principles are presented which provide for mathematical analysis of the control of multi-enzyme systems. Problems are included at the end of each chapter and their solutions are found at the end of the book. This book will be a useful text for advanced undergraduates and graduate students taking courses in enzyme chemistry and enzyme kinetics.

This text covers the field of steady-state kinetics from basic principles to the control of the multi-enzyme systems which constitute metabolic pathways. Emphasis is placed on the interpretation of the kinetic behaviour of enzyme-catalyzed reactions in terms of mechanisms. Algorithms are developed which can be implemented in computer programs for the derivation of equations. The treatment of steady-state enzyme kinetics is extended to allosteric enzymes and subunit interactions in polymeric enzymes. Principles are presented which provide for mathematical analysis of the control of multi-enzyme systems. Problems are included at the end of each chapter and their solutions are found at the end of the book. This book will be a useful text for advanced undergraduates and graduate students taking courses in enzyme chemistry and enzyme kinetics.

This book describes the structure of simulators suitable for use in the design of digital electronic systems. It includes the compiled code and event driven algorithms for digital electronic system simulators, together with timing verification. Limitations of the structures are also discussed. An introduction to the problems of designing models is included, partly to point to how user models might be constructed for application specific integrated circuits (ASICs) and so on, and partly to expose the limitations of the modelling process. As a guide to the use of simulators the book includes chapters which introduce the subjects of testing and design for testability. A major chapter is devoted to fault simulation. The text has an introduction to hardware accelerators and modellers.

This book describes the structure of simulators suitable for use in the design of digital electronic systems. It includes the compiled code and event driven algorithms for digital electronic system simulators, together with timing verification. Limitations of the structures are also discussed. An introduction to the problems of designing models is included, partly to point to how user models might be constructed for application specific integrated circuits (ASICs) and so on, and partly to expose the limitations of the modelling process. As a guide to the use of simulators the book includes chapters which introduce the subjects of testing and design for testability. A major chapter is devoted to fault simulation. The text has an introduction to hardware accelerators and modellers.

These notes are based on a series of lectures given at the Advanced Research Institute of Discrete Applied Mathematics held at Rutgers University. Their aim is to link together algorithmic problems arising in knot theory, statistical physics and classical combinatorics. Apart from the theory of computational complexity concerned with enumeration problems, introductions are given to several of the topics treated, such as combinatorial knot theory, randomised approximation algorithms, percolation and random cluster models. To researchers in discrete mathematics, computer science and statistical physics, this book will be of great interest, but any non-expert should find it an appealing guide to a very active area of research.

Games Programming has been written for the personal computer owner who is setting out to write fams programs. It charts the territory which lies beyond the simplistic arcade game and which leads to the more intellectually exciting game moderators and learning programs. This is not another book of program listings, nor does it present game algorithms in isolation from the computer methods which make them work. The aim is to equip the reader with an awareness of modern techniques of structured programming, a robust attitude to computer languages, and a source of valuable 'know how'.

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

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.

★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

是一部探討數位生活影響的實用書籍，由倫敦大學學院Dr Kaitlyn Regehr撰寫。書中以平實的方式說明智慧手機、演算法與人工智慧如何改變我們的思考與生活，同時提供具體方法，幫助讀者更健康地使用科技。內容涵蓋身體意象、廣告、錯假資訊等常見議題，也介紹如何辨識風險、調整使用習慣與照顧心理健康。這本書適合關心孩子與自身網路使用方式的讀者閱讀，是理解現代數位環境與學習自我保護的實用指南。A groundbreaking exploration of how smartphones, algorithms and AI are changing the way we think, act and feel, and a clear, empowering toolkit for living a healthier, happier life online, from leading expert and Associate Professor at University College London, Dr Kaitlyn Regehr.The tools and understanding you need to protect yourself, and your family.Smartphone Nation will transform the way you – and your children – understand your devices and how they affect you. In this practical, agenda-setting book, Dr Kaitlyn Regehr – one of the world’s foremost experts on digital literacy – sets out how you can keep the advantages of the internet whilst identifying often hidden dangers and stepping away when you’re over-reliant.Grassroots movements have done an amazing job of alerting many of us to the d

《計算機程序設計藝術》系列被公認為計算機科學領域的傑出之作，深入闡述了程序設計理論，對計算機領域的發展有著極為深遠的影響。本卷為系列的第 2卷，講解了半數值算法，分“隨機數”和“算術”兩章。書中總結了主要算法範例及這些算法的基本理論，廣泛剖析了計算機程序設計與數值分析間的相互聯繫。

Can we rely solely on statistics when we judge what is true and just? This book takes a holistic approach to addressing this question. It takes the legal trial as its paradigmatic case study before considering a wider range of cases, including profiling, the use of algorithms to predict students’ grades, and the authorisation of automated cars. The book suggests that when we make judgements about the truth or about justice, approximations are not good enough. Truth and justice are uncompromising; they must be so, because the value that underlies them both is respect; and respect takes no compromise. Thus, in the search for truth as in the search for justice, a body of evidence that imposes a statistical compromise will not do. Only evidence that in principle allows reaching the truth and doing justice is good evidence. Once such evidence has been traced, the burden is on us to make good use of the evidence and reach truth and justice. We might or might not succeed, but once we have don

How do you remember more and forget less?How can you earn more and become more creative just by moving house? And how do you pack a car boot most efficiently? Mathematics is full of better ways of thinking, and with over 2,000 years of knowledge to draw on, Oxford mathematician Marcus du Sautoy interrogates his passion for shortcuts in this fresh and fascinating guide. After all, shortcuts have enabled so much of human progress, whether in constructing the first cities around the Euphrates 5,000 years ago, using calculus to determine the scale of the universe or in writing today’s algorithms that help us find a new life partner. As well as looking at the most useful shortcuts in history – such as measuring the circumference of the earth in 240 BC to diagrams that illustrate how modern GPS works – Marcus also looks at how you can use shortcuts in investing or how to learn a musical instrument to memory techniques. He talks to, among many, the writer Robert MacFarlane, cel

在疫情防控中，健康碼等科技抗疫手段業已證明：算法比以往任何時候更有可能取代人工決策。2021年，西班牙金融研究學院的Marta Cantero Gamito 和德國洪堡大學法學院Martin Ebers編著《算法治理和治理算法：法律和道德挑戰――數據科學，機器智能和法律》(Algorithmic Governance and Governance of Algorithms: Legal and Ethical Challenges - Data Science, Machine Intelligence, and Law)一書，深入討論了算法治理(基於算法的決策)的潛力以及可能引發的操縱、偏見、監控、社會歧視以及對隱私權和財產權的侵害，並梳理了歐盟對算法開展治理的近期新動態。在人工智能蓬勃發展的中國，不論是“算法治理”還是“治理算法”，都是緊迫而重要的重大問題。

Not Your Average Maths Book presents a fun and accessible look at numbers, filled with great facts and fascinating insights into numbers, their history and the mathematicians who made key breakthroughs in their fields. From how long it would take to count to a billion, to why bubbles are always round, to what the ham sandwich theorem is, this book answers all these questions and many many more!Not Your Average Maths Book looks at how maths is useful in our everyday lives, from how it is useful on the construction site to how algorithms dictate what music we listen to on our smart phones, as well as setting out a short history of maths, starting with the first written numbers, from 43,000 years ago, through all the major mathematical discoveries right up to the present day! Complete with a mathemetician's hall of fame, highlighting some of the brilliant minds who have advanced our understanding of numbers, to awards for the most special numbers as well as explanations of what makes them

本書詳細地介紹了概率技術以及在概率算法與分析發展中使用過的範例。本書分兩部分，第壹部分介紹了隨機抽樣、期望、馬爾可夫不等式、切比雪夫不等式、切爾諾夫界、球和箱子模型、概率技術和馬爾可夫鏈等核心內容。第二部分主要研究連續概率、有限獨立性的應用、熵、馬爾可夫鏈蒙特卡羅方法、耦合、鞅和平衡配置等比較高深的課題。本書適合作為高等院校計算機科學和應用數學專業高年級本科生與低年級研究生的教材，也適合作為數學工

經典《神邏輯》作者全新作品！邏輯無時無刻不在服務於我們的生活，是我們認知世界、做出選擇、看待問題的基礎。然而邏輯到底是什麼，卻並沒有太多的人有很清楚的概念。在這本足以改變你的認識世界的方式的書中，MIT多媒體實驗室老師、蘋果公司資深軟件專家阿裡·阿莫薩維以其簡練而又充滿趣味的筆觸，將晦澀、深奧的邏輯科學以貼近生活、通俗易懂、妙趣橫生的方式展現給讀者。用12個日常案例引出推理過程、邏輯原理和提升建議