Algorithm

Language is a system of communication in which grammatical structures function to express meaning in context. While all languages can achieve the same basic communicative ends, they each use different means to achieve them, particularly in the divergent ways that syntax, semantics and pragmatics interact across languages. This book looks in detail at how structure, meaning, and communicative function interact in human languages. Working within the framework of Role and Reference Grammar (RRG), Van Valin proposes a set of rules, called the 'linking algorithm', which relates syntactic and semantic representations to each other, with discourse-pragmatics playing a role in the linking. Using this model, he discusses the full range of grammatical phenomena, including the structures of simple and complex sentences, verb and argument structure, voice, reflexivization and extraction restrictions. Clearly written and comprehensive, this book will be welcomed by all those working on the interfac

Culture is a unique and fascinating aspect of the human species. How did it emerge and how does it develop? Richard Dawkins suggested culture evolves and that memes are cultural replicators, subject to variation and selection in the same way as genes are in the biological world. Thus human culture is the product of a mindless evolutionary algorithm. Does this imply, as some have argued, that we are mere meme machines and that the conscious self is an illusion? This highly readable and accessible book extends Dawkins's theory, presenting for the first time a fully developed concept of cultural DNA. Distin argues that culture's development can be seen as the result of memetic evolution and as the product of human creativity. Memetic evolution is perfectly compatible with the view of humans as conscious and intelligent. This book should find a wide readership amongst philosophers, psychologists, sociologists and non-academic readers.

Culture is a unique and fascinating aspect of the human species. How did it emerge and how does it develop? Richard Dawkins suggested culture evolves and that memes are cultural replicators, subject to variation and selection in the same way as genes are in the biological world. Thus human culture is the product of a mindless evolutionary algorithm. Does this imply, as some have argued, that we are mere meme machines and that the conscious self is an illusion? This highly readable and accessible book extends Dawkins's theory, presenting for the first time a fully developed concept of cultural DNA. Distin argues that culture's development can be seen as the result of memetic evolution and as the product of human creativity. Memetic evolution is perfectly compatible with the view of humans as conscious and intelligent. This book should find a wide readership amongst philosophers, psychologists, sociologists and non-academic readers.

Kernel methods provide a powerful and unified framework for pattern discovery, motivating algorithms that can act on general types of data (e.g. strings, vectors or text) and look for general types of relations (e.g. rankings, classifications, regressions, clusters). The application areas range from neural networks and pattern recognition to machine learning and data mining. This book, developed from lectures and tutorials, fulfils two major roles: firstly it provides practitioners with a large toolkit of algorithms, kernels and solutions ready to use for standard pattern discovery problems in fields such as bioinformatics, text analysis, image analysis. Secondly it provides an easy introduction for students and researchers to the growing field of kernel-based pattern analysis, demonstrating with examples how to handcraft an algorithm or a kernel for a new specific application, and covering all the necessary conceptual and mathematical tools to do so.

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

This book discusses recent research in the theoretical foundations of several subjects of importance for the design of hardware, and for computer science in general. The physical technologies of very large scale integration (VLSI) are having major effects on the electronic industry. The potential diversity and complexity of digital systems have begun a revolution in the technologies of digital design, involving the application of concepts and methods to do with algorithms and programming. In return, the problems of VLSI design have led to new subjects becoming of importance in computer science. Topics covered in this volume include: models of VLSI complexity; complexity theory; systolic algorithm design; specification theory; verification theory; design by stepwise refinement and transformations. A thorough literature survey with an exhaustive bibliography is also included. The book has grown from a workshop held at the Centre for Theoretical Computer Science at Leeds University and or

This book describes the use of qualified types to provide a general framework for the combination of polymorphism and overloading. For example, qualified types can be viewed as a generalization of type classes in the functional language Haskell and the theorem prover Isabelle. These in turn are extensions of equality types in Standard ML. Other applications of qualified types include extensible records and subtyping. Using a general formulation of qualified types, the author extends the Damas/Milner type inference algorithm to support qualified types, which in turn specifies the set of all possible types for any term. In addition, he describes a new technique for establishing suitable coherence conditions that guarantee the same semantics for all possible translations of a given term. Practical issues that arise in concrete implementations are also discussed, concentrating in particular on the implementation of overloading in Haskell and Gofer, a small functional programming system dev

Numerical simulation of compressible, inviscid time-dependent flow is a major branch of computational fluid dynamics. Its primary goal is to obtain accurate representation of the time evolution of complex flow patterns, involving interactions of shocks, interfaces, and rarefaction waves. The Generalized Riemann Problem (GRP) algorithm, developed by the authors for this purpose, provides a unifying 'shell' which comprises some of the most commonly used numerical schemes of this process. This monograph gives a systematic presentation of the GRP methodology, starting from the underlying mathematical principles, through basic scheme analysis and scheme extensions (such as reacting flow or two-dimensional flows involving moving or stationary boundaries). An array of instructive examples illustrates the range of applications, extending from (simple) scalar equations to computational fluid dynamics. Background material from mathematical analysis and fluid dynamics is provided, making the book

Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of càglàd integrands pathwise. Full proofs are given for all results, and motivation is stressed throughout. A large appendix contains most of the analysis that readers will need as a prerequisite. This will be an invaluable reference for graduate students and researchers in mathematics, physics, electrical en

Mathematics is about proofs, that is the derivation of correct statements; and calculations, that is the production of results according to well-defined sets of rules. The two notions are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. The aim of the author is to explore this relationship. The book itself forms an introduction to simple type theory. Starting from the familiar propositional calculus the author develops the central idea of an applied lambda-calculus. This is illustrated by an account of Gödel's T, a system which codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject, and develop a further understanding. An appendix contains complete solutions of these exercises.

This textbook offers a unified and self-contained introduction to the field of term rewriting. It covers all the basic material (abstract reduction systems, termination, confluence, completion, and combination problems), but also some important and closely connected subjects: universal algebra, unification theory, Gröbner bases and Buchberger's algorithm. The main algorithms are presented both informally and as programs in the functional language Standard ML (an appendix contains a quick and easy introduction to ML). Certain crucial algorithms like unification and congruence closure are covered in more depth and Pascal programs are developed. The book contains many examples and over 170 exercises. This text is also an ideal reference book for professional researchers: results that have been spread over many conference and journal articles are collected together in a unified notation, proofs of almost all theorems are provided, and each chapter closes with a guide to the literature.

This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their

This 1999 book describes the implementation of multilevel methods for the numerical simulation of turbulent flows. The general ideas for the algorithms presented stem from dynamical systems theory and are based on the decomposition of the unknown function into two or more arrays corresponding to different scales in the Fourier space. Before describing in detail the numerical algorithm, survey chapters are included on the mathematical theory of the Navier-Stokes equations and on the physics of the conventional theory of turbulence. The multilevel methods are applied here to the simulation of homogeneous isotropic turbulent flows as well as turbulent channel flows. The implementation issues are discussed in detail and numerical simulations of the flows cited above are presented and analysed. The methods have been applied in the context of the direct numerical simulation and are therefore compared to such simulations.

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

Complex fluid flows are encountered widely in nature, in living beings and in engineering practice. These flows often involve both geometric and dynamic complexity and present problems that are difficult to analyse because of their wide range of length and time scales, as well as their geometric configuration. This book describes some computational techniques and modelling strategies for analysing and predicting complex transport phenomena. It summarizes advances in the context of a pressure-based algorithm. Among methods discussed are discretization schemes for treating convection and pressure, parallel computing, multigrid methods, and composite, multiblock techniques. With respect to physical modelling, the book addresses issues of turbulence closure and multiscale, multiphase transport from an engineering viewpoint. Both fundamental and practical issues are considered, along with the relative merits of competing approaches. Numerous examples are given throughout the text. Mechanica

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 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.

This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.

Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theore

Numerical Mathematics is a unique textbook which presents rudimentary numerical mathematics in conjunction with computational laboratory assignments. No previous knowledge of calculus or linear algebra is presupposed, and thus the book is tailor-made for undergraduate students, as well as prospective mathematics teachers. The material in the book emphasises algorithmic aspects of mathematics, which are made viable through numerical assignments, in which the traditional 'chalk-and-talk' lecturer turns, in part, into a laboratory instructor. The book is not a numerical methods book, containing ready-made computational recipes. Rather, it guides the student to create the algorithm required for any given assignment - expressed in whichever programming language is used - on the basis of the underlying mathematics. The computational assignments cover iterative processes, area approximations, solution of linear systems, acceleration of series summation, interpolative approximations, and const

亞當和弟弟卡倫吵架後，竟意外引發神秘的電腦程式爆炸，兩人被傳送到陌生的平行世界！這裡沒有網路、沒有科技，甚至爸爸都不認識他們。更糟的是，還有邪惡反派想破壞爸爸的重要發明。兩兄弟該如何在這陌生世界中，找到回家的路？The second PHENOMENALLY FUNNY fantasy adventure from YouTube sensation and TV presenter Adam B is perfect for fans of David Baddiel and Ben Miller!Thirteen-year-old Adam has made a lot of mistakes in his life, but this has to be the BIGGEST. Thanks to a MASSIVE fight with his little brother Callum, the mysterious and magical computer algorithm Popularis Incrementum has exploded – and accidentally transported them to a completely different world!No, not just a different world. A different dimension: one where Adam and Callum were never born and the internet doesn't exist, and neither does any of the technology they know and love and rely on to make their epic YouTube videos!Will the brothers survive in this strange Altiverse where everything is THE SAME but DIFFERENT? Can they stop an EVIL VILLAIN from sabotaging their dad's world-changing technology when in this universe their dad

Presents SAR concepts and signal processing techniques unique to spotlight mode and the polar format algorithm, concentrating on practical procedures and advanced analyses in the implementation and ev

A comprehensive introduction to Support Vector Machines and related kernel methods. In the 1990s, a new type of learning algorithm was developed, based on results from statistical learning theory: t

This book presents a new algorithm to calculate fluid flow and heat transfer of laminar mixed convection. It provides step-by-step tutorial help to learn quickly how to set up the theoretical and nume

The gliding nature and dynamic planes of the face present one of the great challenges in aesthetic surgery and volume replenishment is a key component of the treatment algorithm. Facial Volumization:

D3 allows developers to create scalable graphs for any modern browser. They start with a structure, dataset, or algorithm and programmatically generate static, interactive, or animated images that res

A decision procedure is an algorithm that, given a decision problem, terminates with a correct yes/no answer. Here, the authors focus on theories that are expressive enough to model real problems, but

What if there was an algorithm that could predict which novels become mega-bestsellers? Are books like Dan Brown’s The Da Vinci Code and Gillian Flynn’s Gone Girl the Gladwellian outliers of publishi

What is the mathematics behind a twitter trend? Does my food really have an equation? And, is there really an algorithm for Love?Mathematics is inescapable. Wherever you go, whatever you do, however y

Get a hands-on introduction to machine learning with genetic algorithms using Python. Step-by-step tutorials build your skills from Hello World! to optimizing one genetic algorithm with another, and f

This brief provides a detailed introduction, discussion and bibliographic review of the nature1-inspired optimization algorithm called Harmony Search. It uses a large number of simulation results to d

This book addresses the algorithm analysis and VLSI architecture of video encoders, especially for high definition and scalable video coder. The three design challenges and related system issues of?me

From the acclaimed author of A Tour of the Calculus and The Advent of the Algorithm, here is a riveting look at mathematics that reveals a hidden world in some of its most fundamental concepts.?In his

Written by the developers of the first practical boosting algorithm, AdaBoost, this reference covers the background, theory, and advances in the formula. The first part of the book provides a general

In 1994 Peter Shor [65] published a factoring algorithm for a quantum computer that finds the prime factors of a composite integer N more efficiently than is possible with the known algorithms for a c

The Support Vector Machine is a powerful new learning algorithm for solving a variety of learning and function estimation problems, such as pattern recognition, regression estimation, and operator inv

High level linear algebra book that blends both computational and theoretical aspects, using each to enhance the other. Explains the key points of the Gaussian elimination algorithm. Discusses vector