Maths for computer scientists Books
Cambridge University Press An Invitation to Combinatorics
Book SynopsisActive student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author an award-winning teacher writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.Trade Review'I would certainly accept this 'invitation.' The text covers essentially all of the basic combinatorial subjects in a both gentle and intense way. The extensive problems, examples, and 'projects,' especially the collaborative projects, exemplify current pedagogical research on effective teaching methods. I would expect it to remain as a reference on many shelves.' Bruce Rothschild, University of California, Los Angeles'Shahriari's voice as an experienced classroom teacher shines through in this brilliantly crafted student-friendly text. Each mini-project provides a guided exploration of an interesting topic in combinatorics. These, together with the plethora of interesting exercises, help the student to build problem-solving muscle and to experience the joy of mathematical discovery.' Jamie Pommersheim, Reed College'From well-chosen motivating problems in the introduction to deeper material near the book's conclusion, Shahriari invites students encountering combinatorics systematically for the first time to think, to build, and to play. His warm writing style and cross-cultural approach to core topics of the field are sure to engage readers from many backgrounds and levels of preparation.' Joshua Cooper, University of South Carolina'This book is a mathematically rigorous introductory textbook on combinatorics. It contains an excellent range of problems and exercises that will help students practice and learn the material. It also lists open questions in combinatorics so students can see that the field continues to develop. The really special feature of this book is a lovely collection of mini-projects that let students explore a variety of topics and deepen their understanding.' David Auckly, Kansas State University'I highly recommend this text. Among its most interesting, unusual, and valuable features, one finds a long list of collaborative mini-projects for students to work on in groups, together with other problems to work on individually; nice historical asides, including references to the work of non-Western mathematicians; and a very accessible conversational style. It fits well with discovery-style or problem-oriented courses on the subject.' William Monty McGovern, University of Washington'One of the major attractions of this textbook is the writing style - it is designed to be very readable, as though the author were having a conversation with the reader. The result is a text which feels engaging - a quality which is sure to be of great benefit to undergraduate students.' Audie Warren, zbMATHTable of ContentsPreface; Introduction; 1. Induction and Recurrence Relations; 2. The Pigeonhole Principle and Ramsey Theory; 3. Counting, Probability, Balls and Boxes; 4. Permutations and Combinations; 5. Binomial and Multinomial Coefficients; 6. Stirling Numbers; 7. Integer Partitions; 8. The Inclusion-Exclusion Principle; 9. Generating Functions; 10. Graph Theory; 11. Posets, Matchings, and Boolean Lattices; Appendices; Bibliography; Index.
£37.04
O'Reilly Media Essential Math for Data Science
Book SynopsisTo succeed in data science you need some math proficiency. But not just any math. This common-sense guide provides a clear, plain English survey of the math you'll need in data science, including probability, statistics, hypothesis testing, linear algebra, machine learning, and calculus.
£39.74
Oxford University Press Modern Fortran Explained
Book SynopsisThis new edition of Modern Fortran Explained provides a clear and thorough description of the latest version of Fortran, written by experts in the field with the intention that it remain the main reference work in the field.Table of Contents1: Whence Fortran? 2: Language elements 3: Expressions and assignments 4: Control constructs 5: Program units and procedures 6: Allocation of data 7: Array features 8: Specification statements 9: Intrinsic procedures and modules 10: Data transfer 11: Edit descriptors 12: Operations on external files 13: Further type parameter featur 14: Abstract interfaces and procedure pointers 15: Object-oriented programming 16: Submodules 17: Coarrays 18: Coarray teams 19: Floating-point exception handling 20: Basic interoperability with C 21: Interoperating with C using descriptors 22: Generic programming 23: Other Fortran 2023 enhancements A: Deprecated features B: Obsolescent and deleted features C: Significant examples D: Solutions to exercises
£42.75
Manning Publications Math and Architectures of Deep Learning
Book SynopsisThe mathematical paradigms that underlie deep learning typically start out as hard-to-read academic papers, often leaving engineers in the dark about how their models actually function. Math and Architectures of Deep Learning bridges the gap between theory and practice, laying out the math of deep learning side by side with practical implementations in Python and PyTorch. Written by deep learning expert Krishnendu Chaudhury, you'll peer inside the “black box” to understand how your code is working, and learn to comprehend cutting-edge research you can turn into practical applications. about the technology It's important to understand how your deep learning models work, both so that you can maintain them efficiently and explain them to other stakeholders. Learning mathematical foundations and neural network architecture can be challenging, but the payoff is big. You'll be free from blind reliance on pre-packaged DL models and able to build, customize, and re-architect for your specific needs. And when things go wrong, you'll be glad you can quickly identify and fix problems. about the book Math and Architectures of Deep Learning sets out the foundations of DL in a way that's both useful and accessible to working practitioners. Each chapter explores a new fundamental DL concept or architectural pattern, explaining the underpinning mathematics and demonstrating how they work in practice with well-annotated Python code. You'll start with a primer of basic algebra, calculus, and statistics, working your way up to state-of-the-art DL paradigms taken from the latest research. By the time you're done, you'll have a combined theoretical insight and practical skills to identify and implement DL architecture for almost any real-world challenge. Trade Review'This is a book that will reward your patience and perseverance with a clear and detailed knowledge of deep learning mathematics and associated techniques.' Tony Holdroyd 'Most online machine learning courses teach you how to get stuff done, but they don't give you the underlying math. If you want to know, this is the book for you!' Wiebe de Jong 'A really interesting book for people that want to understand the underlying mathematical mechanism of deep learning.' Julien Pohie 'Gives a unique perspective about machine learning and mathematical approaches.' Krzysztof Kamyczek 'An awesome book to get the grasp of the important mathematical skills to understand the very basics of deep learning.' Nicole KoenigsteinTable of Contentstable of contents READ IN LIVEBOOK 1AN OVERVIEW OF MACHINE LEARNING AND DEEP LEARNING READ IN LIVEBOOK 2INTRODUCTION TO VECTORS, MATRICES AND TENSORS FROM MACHINE LEARNING AND DATA SCIENCE POINT OF VIEW READ IN LIVEBOOK 3INTRODUCTION TO VECTOR CALCULUS FROM MACHINE LEARNING POINT OF VIEW READ IN LIVEBOOK 4LINEAR ALGEBRAIC TOOLS IN MACHINE LEARNING AND DATA SCIENCE READ IN LIVEBOOK 5PROBABILITY DISTRIBUTIONS FOR MACHINE LEARNING AND DATA SCIENCE READ IN LIVEBOOK 6BAYESIAN TOOLS FOR MACHINE LEARNING AND DATA SCIENCE READ IN LIVEBOOK 7FUNCTION APPROXIMATION: HOW NEURAL NETWORKS MODEL THE WORLD READ IN LIVEBOOK 8TRAINING NEURAL NETWORKS: FORWARD AND BACKPROPAGATION READ IN LIVEBOOK 9LOSS, OPTIMIZATION AND REGULARIZATION READ IN LIVEBOOK 10ONE, TWO AND THREE DIMENSIONAL CONVOLUTION AND TRANSPOSED CONVOLUTION IN NEURAL NETWORKS 11 IMAGE ANALYSIS: 2D CONVOLUTION BASED NEURAL NETWORK ARCHITECTURES FOR OBJECT RECOGNITION AND DETECTION 12 VIDEO ANALYSIS: 3D CONVOLUTION BASED SPATIO TEMPORAL NEURAL NETWORK ARCHITECTURES READ IN LIVEBOOK APPENDIX A: APPENDIX A.1Dot Product and cosine of the angle between two vectors A.2Computing variance of Gaussian Distribution A.3Two Theorems in Statistic
£37.99
Association of Computing Machinery,U.S. Logic, Automata, and Computational Complexity:
Book SynopsisProfessor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for "his advancement of our understanding of the complexity of computation in a significant and profound way." This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook's synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook's ideas and their enduring impact on the research community. The book also contains biographical material, Cook's Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.
£42.46
Springer-Verlag New York Inc. All of Statistics
Book SynopsisTaken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.Trade ReviewWinner of the 2005 DeGroot Prize.From the reviews:"Presuming no previous background in statistics and described by the author as "demanding" yet "understandable because the material is as intuitive as possible" (p. viii), this certainly would be my choice of textbook if I was required to learn mathematical statistics again for a couple of semesters." Technometrics, August 2004"This book should be seriously considered as a text for a theoretical statsitics course for non-majors, and perhaps even for majors...The coverage of emerging and important topics is timely and welcomed...you should have this book on your desk as a reference to nothing less than 'All of Statistics.'" Biometrics, December 2004"Although All of Statistics is an ambitious title, this book is a concise guide, as the subtitle suggests....I recommend it to anyone who has an interest in learning something new about statistical inference. There is something here for everyone." The American Statistician, May 2005"As the title of the book suggests, ‘All of Statistics’ covers a wide range of statistical topics. … The number of topics covered in this book is vast … . The greatest strength of this book is as a first point of reference for a wide range of statistical methods. … I would recommend this book as a useful and interesting introduction to a large number of statistical topics for non-statisticians and also as a useful reference book for practicing statisticians." (Matthew J. Langdon, Journal of Applied Statistics, Vol. 32 (1), January, 2005)"This book was written specifically to give students a quick but sound understanding of modern statistics, and its coverage is very wide. … The book is extremely well done … ." (N. R. Draper, Short Book Reviews, Vol. 24 (2), 2004)"This is most definitely a book about mathematical statistics. It is full of theorems and proofs … . Presuming no previous background in statistics … this certainly would be my choice of textbook if I was required to learn mathematical statistics again for a couple of semesters." (Eric R. Ziegel, Technometrics, Vol. 46 (3), August, 2004)"The author points out that this book is for those who wish to learn probability and statistics quickly … . this book will serve as a guideline for instructors as to what should constitute a basic education in modern statistics. It introduces many modern topics … . Adequate references are provided at the end of each chapter which the instructor will be able to use profitably … ." (Arup Bose, Sankhya, Vol. 66 (3), 2004)"The amount of material that is covered in this book is impressive. … the explanations are generally clear and the wide range of techniques that are discussed makes it possible to include a diverse set of examples … . The worked examples are complemented with numerous theoretical and practical exercises … . is a very useful overview of many areas of modern statistics and as such will be very useful to readers who require such a survey. Library copies would also see plenty of use." (Stuart Barber, Journal of the Royal Statistical Society, Series A – Statistics in Society, Vol. 168 (1), 2005)Table of ContentsProbability.- Random Variables.- Expectation.- Inequalities.- Convergence of Random Variables.- Models, Statistical Inference and Learning.- Estimating the CDF and Statistical Functionals.- The Bootstrap.- Parametric Inference.- Hypothesis Testing and p-values.- Bayesian Inference.- Statistical Decision Theory.- Linear and Logistic Regression.- Multivariate Models.- Inference about Independence.- Causal Inference.- Directed Graphs and Conditional Independence.- Undirected Graphs.- Loglinear Models.- Nonparametric Curve Estimation.- Smoothing Using Orthogonal Functions.- Classification.- Probability Redux: Stochastic Processes.- Simulation Methods.
£53.99
Springer New York Combinatorial Computational Biology of RNA Pseudoknots and Neutral Networks
Book SynopsisIn this monograph, new combinatorial and computational approaches in the study of RNA structures are presented which enhance both mathematics and computational biology.Trade ReviewFrom the reviews:“This book is devoted to the study of the structure of combinatorial models of the ribonucleic acid (RNA). … This book can serve as an introduction to the study of combinatorial computational biology as well as a reference of known results and state of the art in this topic.” (Ludovit Niepel, Zentralblatt MATH, Vol. 1207, 2011)Table of ContentsIntroduction.- Secondary Structures, Pseudoknot RNA and Beyond.- Folding Sequences into Structures.- Evolution of RNA Sequences.- Methods.- References.- Index.
£49.49
Springer New York Modern Graph Theory
Book SynopsisPresents an account of graph theory. Written with students of mathematics and computer science in mind, this book reflects the state of the subject and emphasizes connections with other branches of pure mathematics. It presents a survey of fresh topics and includes more than 600 exercises.Trade Review"...This book is likely to become a classic, and it deserves to be on the shelf of everyone working in graph theory or even remotely related areas, from graduate student to active researcher."--MATHEMATICAL REVIEWSTable of Contents1: Fundamentals. 2: Electrical Networks. 3: Flows, Connectivity and Matching. 4: Extremal Problems. 5: Colouring. 6: Ramsey Theory. 7: Random Graphs. 8: Graphs, Groups and Matrices. 9: Random Walks on Graphs. 10: The Tutte Polynomial.
£41.79
John Wiley & Sons Inc Probability and Statistics for Computer Science
Book SynopsisThis title develops introductory topics in probability and statistics with particular emphasis on concepts that arise in computer science. It starts with the basic definitions of probability distributions and random variables and elaborates their properties and applications.Trade Review"Undoubtedly, this is an excellent and well-organized book." (Computing Reviews, August 27, 2008)Table of ContentsPreface. 1. Combinatorics and Probability. 1.1 Combinatorics. 1.2 Summations. 1.3 Probability spaces and random variables. 1.4 Conditional probability. 1.5 Joint distributions. 1.6 Summary. 2. Discrete Distributions. 2.1 The Bernoulli and binomial distributions. 2.2 Power series. 2.3 Geometric and negative binomial forms. 2.4 The Poisson distribution. 2.5 The hypergeometric distribution. 2.6 Summary. 3. Simulation. 3.1 Random number generation. 3.2 Inverse transforms and rejection filters. 3.3 Client-server systems. 3.4 Markov chains. 3.5 Summary. 4. Discrete Decision Theory. 4.1 Decision methods without samples. 4.2 Statistics and their properties. 4.3 Sufficient statistics. 4.4 Hypothesis testing. 4.5 Summary. 5. Real Line-Probability. 5.1 One-dimensional real distributions. 5.2 Joint random variables. 5.3 Differentiable distributions. 5.4 Summary. 6. Continuous Distributions. 6.1 The normal distributions. 6.2 Limit theorems. 6.3 Gamma and beta distributions. 6.4 The X2 and related distributions. 6.5 Computer simulations. 6.6 Summary. 7. Parameter Estimation. 7.1 Bias, consistency, and efficiency. 7.2 Normal inference. 7.3 Sums of squares. 7.4 Analysis of variance. 7.5 Linear regression. 7.6 Summary. A. Analytical Tools. B. Statistical Tables. Bibliography. Index.
£109.76
John Wiley & Sons Inc Pattern Classification
Book SynopsisPattern recognition is the construction of algorithms to decode and recognize images or data patterns in so-called random data. It is a vital and growing field with applications in artifical intelligence, machine learing, data mining, speech recognition, bioinformatics, and computer vision.Trade Review"...it provides a good introduction to the subject of Pattern Classification." (Journal of Classification, September 2007) "...a fantastic book! The presentation...could not be better, and I recommend that future authors consider...this book as a role model." (Journal of Statistical Computation and Simulation, March 2006) "...strongly recommended both as a professional reference and as a text for students..." (Technometrics, February 2002) "...provides information needed to choose the most appropriate of the many available technique for a given class of problems." (SciTech Book News, Vol. 25, No. 2, June 2001) "I do not believe anybody wishing to teach or do serious work on Pattern Recognition can ignore this book, as it is the sort of book one wishes to find the time to read from cover to cover!" (Pattern Analysis & Applications Journal, 2001) "This book is the unique text/professional reference for any serious student or worker in the field of pattern recognition." (Mathematical Reviews, Issue 2001k) "...gives a systematic overview about the major topics in pattern recognition, based whenever possible on fundamental principles." (Zentralblatt MATH, Vol. 968, 2001/18) "attractively presented and readable" (Journal of Classification, Vol.18, No.2 2001)Table of ContentsBayesian Decision Theory. Maximum-Likelihood and Bayesian Parameter Estimation. Nonparametric Techniques. Linear Discriminant Functions. Multilayer Neural Networks. Stochastic Methods. Nonmetric Methods. Algorithm-Independent Machine Learning. Unsupervised Learning and Clustering. Appendix. Index.
£136.76
John Wiley & Sons Inc ComputerAided Analysis of Difference Schemes for
Book SynopsisAdvances in computer technology have conveniently coincided withtrends in numerical analysis toward increased complexity ofcomputational algorithms based on finite difference methods. It isno longer feasible to perform stability investigation of thesemethods manually--and no longer necessary. As this book shows,modern computer algebra tools can be combined with methods fromnumerical analysis to generate programs that will do the jobautomatically. Comprehensive, timely, and accessible--this is the definitivereference on the application of computerized symbolic manipulationsfor analyzing the stability of a wide range of difference schemes.In particular, it deals with those schemes that are used to solvecomplex physical problems in areas such as gas dynamics, heat andmass transfer, catastrophe theory, elasticity, shallow watertheory, and more. Introducing many new applications, methods, and concepts,Computer-Aided Analysis of Difference Schemes for PartialDifferential EqTable of ContentsThe Necessary Basics from the Stability Theory of DifferenceSchemes and Polynomials. Symbolic-Numerical Method for the Stability Investigation ofDifference Schemes on a Computer. Application of Optimization Methods to the Stability Analysis ofDifference Schemes. Stability Analysis of Difference Schemes by Catastrophe TheoryMethods. Construction of Multiply Connected Stability Regions of DifferenceSchemes by Computer Algebra and Pattern Recognition. Maximally Stable Difference Schemes. Stability Analysis of Nonlinear Difference Schemes. Symbolic Computation of Differential Approximations. Appendices. Index.
£179.06
John Wiley & Sons Inc Probability and Statistics for Computer Science
Book SynopsisThis title develops introductory topics in probability and statistics with particular emphasis on concepts that arise in computer science. It starts with the basic definitions of probability distributions and random variables and elaborates their properties and applications.Trade Review"This text will fill a gap in the education of a sophisticated computer science student who has a firm base in mathematics and statistics." (Computing Reviews, May 7, 2009) "…this textbook would be ideal." (The American Statistician, February 2006) "This is really a statistics textbook written explicitly for undergraduate computer science majors…I found the numerous examples of the use of statistics within the field of computer science extremely informative." (Technometrics, November 2004) "Thorough, in-depth, relatively complete and rigorous introduction to the statistics a CS professional should know." (American Mathematical Monthly, August 2004) "This is a rigorous introductory text in probability and statistics, which also develops in a rigorous fashion all the necessary supporting mathematics beyond calculus and algebra." (Mathematical Reviews, issue 2004i) "...one-of-a-kind resource...proves an ideal resource for computer science students and practitioners interested in a probability study..." (Zentralblatt Math, Vol. 1027, 2004) “...presents introductory topics in probability and statistics with particular emphasis on concepts that arise in computer science...disguised also by the feature that it develops all necessary supporting mathematics in a thorough and rigorous fashion.” (Quarterly of Applied Mathematics, Vol. LXI, No. 4, December 2003)Table of ContentsPreface. 1. Combinatorics and Probability. 2. Discrete Distributions. 3. Simulation. 4. Discrete Decision Theory. 5. Real Line-Probability. 6. Continuous Distributions. 7. Parameter Estimation. Appendix A. Analytical Tools. Appendix B. Statistical Tables. Bibliography. Index.
£209.66
John Wiley & Sons Inc Computational Methods in Physics Chemistry and
Book SynopsisProviding an accessible introduction to a range of modern computational techniques, this volume is perfect for anyone with only a limited knowledge of physics.Trade Review"? Dieses Buch mit seinem klar eingegrenzten Themenspektrum ist ausgezeichnet - gut lesbar und informativ zugleich!" Chemistry in Britain Table of ContentsPreface. Acknowledgments. About the Author. About the Book. Introduction. Numerical Solutions to Schrödinger's Equation. Approximate Methods. Matrix Methods. Deterministic Simulations. Stochastic Simulations. Percolation Theory. Evolutionary Methods. Molecular Dynamics. Appendix A: FORTRAN Implementation of the Shooting Method. Appendix B: ² in Spherical Polar Coordinates. Appendix C: A Comment on the Computer Sourcecodes. Appendix D: Note for Tutors. References. Index.
£178.16
John Wiley & Sons Inc Computational Methods in Physics Chemistry and
Book SynopsisProviding an accessible introduction to a range of modern computational techniques, this book is perfect for anyone with only a limited knowledge of physics. It leads readers through a series of examples, problems, and practical--based tasks covering the basics to more complex ideas and techniques.Trade Review"within its tightly defined scope, the book is excellent, being both readable and informative" (Chemistry in Britain, January 2002) "...The book is fresh in its spirit..." (Zentralblatt Math, Vol.987, No. 12, 2002) "...an excellent book for undergraduate courses..." (Physical Sciences Educational Reviews, November 2002)"? Dieses Buch mit seinem klar eingegrenzten Themenspektrum ist ausgezeichnet - gut lesbar und informativ zugleich!" Chemistry in BritainTable of ContentsPreface Introduction Numerical Solutions to Schrö dinger's Equation Approximate Methods Matrix Methods Deterministic Simulations Stochastic Simulations Percolation Theory Evolutionary Methods Molecular Dynamics Appendices References Index
£65.66
John Wiley & Sons Inc Computational Molecular Biology An Introduction
Book SynopsisThis introductory level text is suitable for use by advanced undergraduate and graduate students of computational biology. Written by experienced authors, it provides detailed coverage of many algorithms, including applications and possible modifications.Trade Review"...much-needed introductory level text..." - La Doc Sti, July 2000Table of ContentsMolecular Biology. Math Primer. Sequence Alignment. All About Eve. Hidden Markov Models. Structure Prediction. Appendices. References. Index.
£231.26
John Wiley & Sons Inc Computational Molecular Biology
Book SynopsisRecently molecular biology has undergone unprecedented development generating vast quantities of data needing sophisticated computational methods for analysis, processing and archiving. This requirement has given birth to the truly interdisciplinary field of computational biology, or bioinformatics, a subject reliant on both theoretical and practical contributions from statistics, mathematics, computer science and biology. * Provides the background mathematics required to understand why certain algorithms work * Guides the reader through probability theory, entropy and combinatorial optimization * In-depth coverage of molecular biology and protein structure prediction * Includes several less familiar algorithms such as DNA segmentation, quartet puzzling and DNA strand separation prediction * Includes class tested exercises useful for self-study * Source code of programs available on a Web site Primarily aimed at advanced undergradTrade Review"...much needed introductory level text on the subject..." (La Doc STI, July 2000) "...very concise and compact..." (Mathematical Reviews, 2002h)Table of ContentsMolecular Biology. Math Primer. Sequence Alignment. All About Eve. Hidden Markov Models. Structure Prediction. Appendices. References. Index.
£77.36
Institute of Physics Publishing Innovative Quantum Computing
Book Synopsis
£108.00
John Wiley & Sons Inc Planning Telecommunication Networks
Book SynopsisThe ever--growing number of new telecommunications technologies, along with the rapid growth of data networks and cable television systems has created a demand for sound network planning.Table of ContentsPreface. Acknowledgments. The Network Planning Problem. Mathematical Programming for Planning. Network Algorithms For Planning. Reliability Theory For Planning. Software and Optimization For Planning. Data Analysis For Planning. Bibliography. Index. About the Author.
£145.76
Springer Us NonFunctional Requirements in Software Engineering 5 International Series in Software Engineering
Book SynopsisDetailed treatments of particular NFRs - accuracy, security and performance requirements - along with treatments of NFRs for information systems are presented as specializations of the NFR Framework.Table of ContentsList of Figures. List of Tables. Legend for Figures. Preface. 1. Introduction. Part I: The NFR Framework. 2. The NFR Framework in Action. 3. Softgoal Interdependency Graphs. 4. Cataloguing Refinement Methods and Correlations. Part II: Types of Non-Functional Requirements. 5. Types of NFRs. 6. Accuracy Requirements. 7. Security Requirements. 8. Performance Requirements. 9. Performance Requirements for Information Systems. Part III. Case Studies and Applications. 10. Introduction to the Studies and Applications. 11. A Credit Card System. 12. An Administrative System. 13. Application to Software Architecture. 14. Enterprise Modelling and Business Process Redesign. 15. Assessment of Studies. Postscript. Bibliography.
£474.99
Cambridge University Press Connecting Discrete Mathematics and Computer
Book SynopsisThis textbook is designed for undergraduate students taking a course on the mathematical foundations of computer science. It is written from an exclusively CS perspective rather than for a mixed-discipline audience, helping CS students see the ways that foundational mathematical material is central to the discipline of computer science.Trade Review'Finally! I've spent years struggling to find a textbook that makes the topic of Discrete Structures relevant to Computer Science students, David Liben-Nowell has put forth a book that will make CS students invested in the material. He not only connects every topic to Computer Science but does so in a clear and entertaining way.' Dan Arena, Vanderbilt University'Unlike most discrete math texts, here the computer science content and connections are woven extensively throughout, with “forward pointers” that can excite students about numerous computer science areas they will encounter in their future studies. In addition, the book is written TO students, not FOR faculty. It will be a joy to teach with!' Valerie Barr, Mount Holyoke College'By foregrounding the connections between the fields, this outstanding textbook makes a compelling case for why computer science students should embrace the study of discrete mathematics. This is an approachable yet rigorous book, written with wit and verve, that I look forward to teaching from!' Raghuram Ramanujan, Davidson College'David Liben-Nowell's Connecting Discrete Mathematics and Computer Science provides students with a beautifully motivated, clearly written, and accessible exploration of the mathematical foundations of computer science. The “Computer Science Connections” sections provide compelling applications of the mathematical content and the frequent “Taking in further” notes provide extra richness that add to the joy of the experience. This is a discrete math book that truly keeps the reader engaged!' Ran Libeskind-Hadas, Founding Chair of Integrated Sciences, Claremont McKenna College'An inspired approach to the introductory discrete math course, illuminating the aesthetic appeal of the subject together with the profound and inextricable links that connect it to the core ideas of computing.' Jon Kleinberg, Cornell UniversityTable of Contents1. On the point of this book; 2. Basic data types; 3. Logic; 4. Proofs; 5. Mathematical induction; 6. Analysis of algorithms; 7. Number theory; 8. Relations; 9. Counting; 10. Probability; 11. Graphs and trees; 12. Looking forward.
£55.09
Cambridge University Press Proven Impossible
Book SynopsisWritten for any motivated reader with a high-school knowledge of mathematics, and the discipline to follow logical arguments, this book presents the proofs for revolutionary impossibility theorems in an accessible way, with less jargon and notation, and more background, intuition, examples, explanations, and exercises.Trade Review'This unique and lovely book takes us on a grand tour of the limitations of science, mathematics, and of reason itself. To appreciate what is possible we must know the impossible, and such limitations define the boundary between the two. Gusfield offers well-explained gems illustrating various limitations, showing why they arise, giving their historical context, and in contrast to other similar books for a broad audience, presenting rigorous proofs requiring limited background.' Michael Sipser, MIT'There are impossible problems in many different fields (e.g., Physics, Mathematics). This book is an excellent exposition of these difference ways a problem can be impossible. Along the way, the reader will pick up the needed background which is interesting in itself.' William Gasarch, University of MarylandTable of ContentsPreface; 1. Yes you can prove a negative!; 2. Bell's impossibility theorem(s); 3. Enjoying Bell magic; 4. Arrow's (and friends') impossibility theorems; 5. Clustering and impossibility; 6. Gödel-ish impossibility; 7. Turing undecidability and incompleteness; 8. Chaitin's theorem: More devastating; 9. Gödel (for real, this time).
£26.59
Cambridge University Press Proven Impossible
Book SynopsisWritten for any motivated reader with a high-school knowledge of mathematics, and the discipline to follow logical arguments, this book presents the proofs for revolutionary impossibility theorems in an accessible way, with less jargon and notation, and more background, intuition, examples, explanations, and exercises.Trade Review'This unique and lovely book takes us on a grand tour of the limitations of science, mathematics, and of reason itself. To appreciate what is possible we must know the impossible, and such limitations define the boundary between the two. Gusfield offers well-explained gems illustrating various limitations, showing why they arise, giving their historical context, and in contrast to other similar books for a broad audience, presenting rigorous proofs requiring limited background.' Michael Sipser, MIT'There are impossible problems in many different fields (e.g., Physics, Mathematics). This book is an excellent exposition of these difference ways a problem can be impossible. Along the way, the reader will pick up the needed background which is interesting in itself.' William Gasarch, University of MarylandTable of ContentsPreface; 1. Yes you can prove a negative!; 2. Bell's impossibility theorem(s); 3. Enjoying Bell magic; 4. Arrow's (and friends') impossibility theorems; 5. Clustering and impossibility; 6. Gödel-ish impossibility; 7. Turing undecidability and incompleteness; 8. Chaitin's theorem: More devastating; 9. Gödel (for real, this time).
£56.99
Cambridge University Press ACTA Numerica 2023 Volume 32
Book SynopsisActa Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques and analysis.Table of Contents1. Low-rank tensor methods for partial differential equations Markus Bachmayr; 2. The virtual element method Lourenço Beirão da Veiga, Franco Brezzi, L. Donatella Marini and Alessandro Russo; 3. Floating-point arithmetic Sylvie Boldo, Claude-Pierre Jeannerod, Guillaume Melquiond and Jean-Michel Muller; 4. Compatible finite element methods for geophysical fluid dynamics Colin J. Cotter; 5. Control of port-Hamiltonian differential-algebraic systems and applications Volker Mehrmann and Benjamin Unger; 6. Overcoming the timescale barrier in molecular dynamics: transfer operators, variational principles and machine learning Christof Schütte, Stefan Klus and Carsten Hartmann; 7. Linear optimization over homogeneous matrix cones Levent Tunçel and Lieven Vandenberghe.
£155.70
Cambridge University Press Mathematics of Public Key Cryptography
Book SynopsisPublic key cryptography is a major interdisciplinary subject with many real-world applications. This book has been carefully written to communicate the major ideas and techniques in this subject to a wide readership. With numerous examples and exercises, it is suitable as a textbook for an advanced course or for self-study.Trade Review'… the book gathers the main mathematical topics related to public key cryptography and provides an excellent source of information for both students and researchers interested in the field.' Juan Tena Ayuso, Zentralblatt MATHTable of ContentsPreface; Acknowledgements; 1. Introduction; Part I. Background: 2. Basic algorithmic number theory; 3. Hash functions and MACs; Part II. Algebraic Groups: 4. Preliminary remarks on algebraic groups; 5. Varieties; 6. Tori, LUC and XTR; 7. Curves and divisor class groups; 8. Rational maps on curves and divisors; 9. Elliptic curves; 10. Hyperelliptic curves; Part III. Exponentiation, Factoring and Discrete Logarithms: 11. Basic algorithms for algebraic groups; 12. Primality testing and integer factorisation using algebraic groups; 13. Basic discrete logarithm algorithms; 14. Factoring and discrete logarithms using pseudorandom walks; 15. Factoring and discrete logarithms in subexponential time; Part IV. Lattices: 16. Lattices; 17. Lattice basis reduction; 18. Algorithms for the closest and shortest vector problems; 19. Coppersmith's method and related applications; Part V. Cryptography Related to Discrete Logarithms: 20. The Diffie–Hellman problem and cryptographic applications; 21. The Diffie–Hellman problem; 22. Digital signatures based on discrete logarithms; 23. Public key encryption based on discrete logarithms; Part VI. Cryptography Related to Integer Factorisation: 24. The RSA and Rabin cryptosystems; Part VII. Advanced Topics in Elliptic and Hyperelliptic Curves: 25. Isogenies of elliptic curves; 26. Pairings on elliptic curves; Appendix A. Background mathematics; References; Author index; Subject index.
£56.99
Cambridge University Press Calendrical Calculations
Book SynopsisThis unique resource now includes coverage of Unix dates, Italian time, the Akan, Icelandic, Saudi Arabian Umm al-Qura, Babylonian, Samaritan, and Nepalese calendars, plus expanded treatments of Islamic and Hebrew calendars. The astronomical functions have been rewritten for more accurate results and include calculations of moonrise and moonset.Trade Review'It retains all the features that made the first edition … such a wonderful resource, while adding much new material … If you are at all interested in time and calendars, this book must find a place on your desk.' Victor J. Katz, Mathematical ReviewsTable of Contents1. Calendar basics; Part I. Arithmetical Calendars: 2. The Gregorian calendar; 3. The Julian calendar; 4. The Coptic and Ethiopic calendars; 5. The ISO calendar; 6. The Icelandic calendar; 7. The Islamic calendar; 8. The Hebrew calendar; 9. The Ecclesiastical calendars; 10. The old Hindu calendars; 11. The Mayan calendars; 12. The Balinese Pawukon calendar; 13. Generic Cyclical calendars; Part II. Astronomical Calendars: 14. Time and astronomy; 15. The Persian calendar; 16. The Bahá'í calendar; 17. The French Revolutionary calendar; 18. Astronomical Lunar calendars; 19. The Chinese calendar; 20. The modern Hindu calendars; 21. The Tibetan calendar; Part III. Appendices: A. Function, parameter, and constant types; B. Cross references; C. Sample data; D. Lisp implementation.
£97.85
John Wiley & Sons Inc Mathematical Structures for Computer Graphics
Book SynopsisA comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics.Trade Review“The book is suitable for undergraduate students of computer science, mathematics, and engineering, as well as an ideal reference for researchers and professionals in computer graphics.” (Zentralblatt MATH, 1 June 2015) Table of ContentsPreface xiii 1 Basics 1 1.1 Graphics Pipeline 2 1.2 Mathematical Descriptions 4 1.3 Position 5 1.4 Distance 8 1.5 Complements and Details 11 1.5.1 Pythagorean Theorem Continued 11 1.5.2 Law of Cosines Continued 12 1.5.3 Law of Sines 13 1.5.4 Numerical Calculations 13 1.6 Exercises 14 1.6.1 Programming Exercises 16 2 Vector Algebra 17 2.1 Basic Vector Characteristics 18 2.1.1 Points Versus Vectors 20 2.1.2 Addition 20 2.1.3 Scalar Multiplication 21 2.1.4 Subtraction 22 2.1.5 Vector Calculations 22 2.1.6 Properties 24 2.1.7 Higher Dimensions 25 2.2 Two Important Products 25 2.2.1 Dot Product 25 2.2.2 Cross Product 29 2.3 Complements and Details 34 2.3.1 Vector History 34 2.3.2 More about Points Versus Vectors 35 2.3.3 Vector Spaces and Affine Spaces 36 2.4 Exercises 38 2.4.1 Programming Exercises 39 3 Vector Geometry 40 3.1 Lines and Planes 40 3.1.1 Vector Description of Lines 40 3.1.2 Vector Description of Planes 44 3.2 Distances 46 3.2.1 Point to a Line 46 3.2.2 Point to a Plane 48 3.2.3 Parallel Planes and Line to a Plane 48 3.2.4 Line to a Line 50 3.3 Angles 52 3.4 Intersections 54 3.4.1 Intersecting Lines 54 3.4.2 Lines Intersecting Planes 56 3.4.3 Intersecting Planes 57 3.5 Additional Key Applications 61 3.5.1 Intersection of Line Segments 61 3.5.2 Intersection of Line and Sphere 65 3.5.3 Areas and Volumes 66 3.5.4 Triangle Geometry 68 3.5.5 Tetrahedron 69 3.6 Homogeneous Coordinates 71 3.6.1 Two Dimensions 72 3.6.2 Three Dimensions 73 3.7 Complements and Details 75 3.7.1 Intersection of Three Planes Continued 75 3.7.2 Homogeneous Coordinates Continued 77 3.8 Exercises 79 3.8.1 Programming Exercises 82 4 Transformations 83 4.1 Types of Transformations 84 4.2 Linear Transformations 85 4.2.1 Rotation in Two Dimensions 88 4.2.2 Reflection in Two dimensions 90 4.2.3 Scaling in Two Dimensions 92 4.2.4 Matrix Properties 93 4.3 Three Dimensions 95 4.3.1 Rotations in Three Dimensions 95 4.3.2 Reflections in Three Dimensions 101 4.3.3 Scaling and Shear in Three Dimensions 102 4.4 Affine Transformations 103 4.4.1 Transforming Homogeneous Coordinates 105 4.4.2 Perspective Transformations 107 4.4.3 Transforming Normals 110 4.4.4 Summary 111 4.5 Complements and Details 112 4.5.1 Vector Approach to Reflection in an Arbitrary Plane 113 4.5.2 Vector Approach to Arbitrary Rotations 115 4.6 Exercises 121 4.6.1 Programming Exercises 123 5 Orientation 124 5.1 Cartesian Coordinate Systems 125 5.2 Cameras 132 5.2.1 Moving the Camera or Objects 134 5.2.2 Euler Angles 137 5.2.3 Quaternions 141 5.2.4 Quaternion Algebra 143 5.2.5 Rotations 145 5.2.6 Interpolation: Slerp 148 5.2.7 From Euler Angles and Quaternions to Rotation Matrices 151 5.3 Other Coordinate Systems 152 5.3.1 Non-orthogonal Axes 152 5.3.2 Polar, Cylindrical, and Spherical Coordinates 154 5.3.3 Barycentric Coordinates 157 5.4 Complements and Details 158 5.4.1 Historical Note: Descartes 158 5.4.2 Historical Note: Hamilton 158 5.4.3 Proof of Quaternion Rotation 159 5.5 Exercises 161 5.5.1 Programming Exercises 163 6 Polygons and Polyhedra 164 6.1 Triangles 164 6.1.1 Barycentric Coordinates 165 6.1.2 Areas and Barycentric Coordinates 166 6.1.3 Interpolation 171 6.1.4 Key Points in a Triangle 172 6.2 Polygons 178 6.2.1 Convexity 179 6.2.2 Angles and Area 180 6.2.3 Inside and Outside 184 6.2.4 Triangulation 187 6.2.5 Delaunay Triangulation 189 6.3 Polyhedra 192 6.3.1 Regular Polyhedra 194 6.3.2 Volume of Polyhedra 196 6.3.3 Euler’s Formula 200 6.3.4 Rotational Symmetries 202 6.4 Complements and Details 205 6.4.1 Generalized Barycentric Coordinates 205 6.4.2 Data Structures 206 6.5 Exercises 208 6.5.1 Programming Exercises 211 7 Curves and Surfaces 212 7.1 Curve Descriptions 213 7.1.1 Lagrange Interpolation 218 7.1.2 Matrix Form for Curves 222 7.2 Bézier Curves 223 7.2.1 Properties for Two-Dimensional Bézier Curves 226 7.2.2 Joining Bézier Curve Segments 228 7.2.3 Three-Dimensional Bézier Curves 229 7.2.4 Rational Bézier Curves 230 7.3 B-Splines 232 7.3.1 Linear Uniform B-Splines 233 7.3.2 Quadratic Uniform B-Splines 235 7.3.3 Cubic Uniform B-Splines 240 7.3.4 B-Spline Properties 242 7.4 Nurbs 246 7.5 Surfaces 250 7.6 Complements and Details 260 7.6.1 Adding Control Points to Bézier Curves 260 7.6.2 Quadratic B-Spline Blending Functions 262 7.7 Exercises 264 7.7.1 Programming Exercises 266 8 Visibility 267 8.1 Viewing 267 8.2 Perspective Transformation 269 8.2.1 Clipping 273 8.2.2 Interpolating the z Coordinate 275 8.3 Hidden Surfaces 278 8.3.1 Back Face Culling 281 8.3.2 Painter’s Algorithm 283 8.3.3 Z-Buffer 286 8.4 Ray Tracing 287 8.4.1 Bounding Volumes 289 8.4.2 Bounding Boxes 289 8.4.3 Bounding Spheres 291 8.5 Complements and Details 293 8.5.1 Frustum Planes 293 8.5.2 Axes for Bounding Volumes 294 8.6 Exercises 297 8.6.1 Programming Exercises 298 9 Lighting 299 9.1 Color Coordinates 299 9.2 Elementary Lighting Models 303 9.2.1 Gouraud and Phong Shading 307 9.2.2 Shadows 311 9.2.3 BRDFs in Lighting Models 315 9.3 Global Illumination 319 9.3.1 Ray Tracing 319 9.3.2 Radiosity 323 9.4 Textures 325 9.4.1 Mapping 325 9.4.2 Resolution 332 9.4.3 Procedural Textures 333 9.5 Complements and Details 335 9.5.1 Conversion between RGB and HSV 335 9.5.2 Shadows on Arbitrary Planes 336 9.5.3 Derivation of the Radiosity Equation 337 9.6 Exercises 339 9.6.1 Programming Exercises 340 10 Other Paradigms 341 10.1 Pixels 342 10.1.1 Bresenham Line Algorithm 342 10.1.2 Anti-Aliasing 345 10.1.3 Compositing 347 10.2 Noise 350 10.2.1 Random Number Generation 350 10.2.2 Distributions 351 10.2.3 Sequences of Random Numbers 353 10.2.4 Uniform and Normal Distributions 354 10.2.5 Terrain Generation 356 10.2.6 Noise Generation 357 10.3 L-Systems 361 10.3.1 Grammars 362 10.3.2 Turtle Interpretation 363 10.3.3 Analysis of Grammars 365 10.3.4 Extending L-Systems 367 10.4 Exercises 368 10.4.1 Programming Exercises 369 Appendix A Geometry and Trigonometry 370 A.1 Triangles 370 A.2 Angles 372 A.3 Trigonometric Functions 373 Appendix B Linear Algebra 376 B.1 Systems of Linear Equations 376 B.1.1 Solving the System 377 B.2 Matrix Properties 379 B.3 Vector Spaces 381 References 383 Index 387
£54.86
John Wiley & Sons Inc Demystifying Deep Learning
Book SynopsisDEMYSTIFYING DEEP LEARNING Discover how to train Deep Learning models by learning how to build real Deep Learning software libraries and verification software! The study of Deep Learning and Artificial Neural Networks (ANN) is a significant subfield of artificial intelligence (AI) that can be found within numerous fields: medicine, law, financial services, and science, for example. Just as the robot revolution threatened blue-collar jobs in the 1970s, so now the AI revolution promises a new era of productivity for white collar jobs. Important tasks have begun being taken over by ANNs, from disease detection and prevention, to reading and supporting legal contracts, to understanding experimental data, model protein folding, and hurricane modeling. AI is everywhereon the news, in think tanks, and occupies government policy makers all over the world and ANNs often provide the backbone for AI. Relying on an informal and succinct approach, Demystifying Deep Learni
£96.30
Springer-Verlag New York Inc. Monte Carlo Statistical Methods
Book SynopsisWe have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments. Trade ReviewFrom the reviews: MATHEMATICAL REVIEWS "Although the book is written as a textbook, with many carefully worked out examples and exercises, it will be very useful for the researcher since the authors discuss their favorite research topics (Monte Carlo optimization and convergence diagnostics) going through many relevant references…This book is a comprehensive treatment of the subject and will be an essential reference for statisticians working with McMC." From the reviews of the second edition: "Only 2 years after its first edition this carefully revised second edition accounts for the rapid development in this field...This book can be highly recommended for students and researchers interested in learning more about MCMC methods and their background." Biometrics, March 2005 "This is a comprehensive book for advanced graduate study by statisticians." Technometrics, May 2005 "This excellent text is highly recommended..." Short Book Reviews of the ISI, April 2005 "This book provides a thorough introduction to Monte Carlo methods in statistics with an emphasis on Markov chain Monte Carlo methods. … Each chapter is concluded by problems and notes. … The book is self-contained and does not assume prior knowledge of simulation or Markov chains. …. on the whole it is a readable book with lots of useful information." (Søren Feodor Nielsen, Journal of Applied Statistics, Vol. 32 (6), August, 2005) "This revision of the influential 1999 text … includes changes to the presentation in the early chapters and much new material related to MCMC and Gibbs sampling. The result is a useful introduction to Monte Carlo methods and a convenient reference for much of current methodology. … The numerous problems include many with analytical components. The result is a very useful resource for anyone wanting to understand Monte Carlo procedures. This excellent text is highly recommended … ." (D.F. Andrews, Short Book Reviews, Vol. 25 (1), 2005) "You have to practice statistics on a desert island not to know that Markov chain Monte Carlo (MCMC) methods are hot. That situation has caused the authors not only to produce a new edition of their landmark book but also to completely revise and considerably expand it. … This is a comprehensive book for advanced graduate study by statisticians." (Technometrics, Vol. 47 (2), May, 2005) "This remarkable book presents a broad and deep coverage of the subject. … This second edition is a considerably enlarged version of the first. Some subjects that have matured more rapidly in the five years following the first edition, like reversible jump processes, sequential MC, two-stage Gibbs sampling and perfect sampling have now chapters of their own. … the book is also very well suited for self-study and is also a valuable reference for any statistician who wants to study and apply these techniques." (Ricardo Maronna, Statistical Papers, Vol. 48, 2006) "This second edition of ‘Monte Carlo Statistical Methods’ has appeared only five years after the first … the new edition aims to incorporate recent developments. … Each chapter includes sections with problems and notes. … The style of the presentation and many carefully designed examples make the book very readable and easily accessible. It represents a comprehensive account of the topic containing valuable material for lecture courses as well as for research in this area." (Evelyn Buckwar, Zentrablatt MATH, Vol. 1096 (22), 2006) "This is a useful and utilitarian book. It provides a catalogue of modern Monte carlo based computational techniques with ultimate emphasis on Markov chain Monte Carlo (MCMC) … . an excellent reference for anyone who is interested in algorithms for various modes of Markov chain (MC) methodology … . a must for any researcher who believes in the importance of understanding what goes on inside of the MCMC ‘black box.’ … I recommend the book to all who wish to learn about statistical simulation." (Wesley O. Johnson, Journal of the American Statistical Association, Vol. 104 (485), March, 2009)Table of ContentsIntroduction * Random Variable Generation * Monte Carlo Integration * Controlling Monte Carlo Variance * Monte Carlo Optimization * Markov Chains * The Metropolis-Hastings Algorithm * The Slice Sampler * The Two-Stage Gibbs Sampler * The Multi-Stage Gibbs Sampler * Variable Dimension Models and Reversible Jump * Diagnosing Convergence * Perfect Sampling * Iterated and Sequential Importance Sampling
£104.49
Springer New York Nonparametric Functional Data Analysis Theory and Practice Springer Series in Statistics
Book SynopsisAt the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.Trade ReviewFrom the reviews: "This is certainly a very valuable book for anyone interested in this new methodology." N.D.C. Veraverbeke for Short Book Reviews of the ISI, December 2006 "The present book does bring something new and, indeed some novel theoretical investigations into the kinds of functional data problems … . I do think the present book is a worthy contribution to the literature. The authors have done a nice job of summarizing some of ongoing research … . Researchers in the growing functional statistics community should be glad to have a copy of the book." (Z. Q. John Lu, Technometrics, Vol. 49 (2), 2007) "This book presents new nonparametric staustical methods for samples of functional data … . The computational aspects of the book are oriented toward practitioners whereas open problems emerging from this new field of statistics will attract Ph. D. students and academic researchers. This book is also accessible to graduate students starting out in the area of functional statistics." (Fazil A. Aliev, Mathematical Reviews, Issue 2007 b) "Nonparametric Functional Data Analysis explores nonparametric methods as that can be applied to functional data, developing new methods and providing theoretical results for the conditional and unconditional mean, median, and mode for independent and dependent functional data. … As a resource for those interested in FDA research and methods, it is highly recommended. … This book should spur new and exciting research in FDA, and it provides new tools that are ready for application to real data sets." (Mark Greenwood, Journal of the American Statistical Association, Vol. 102 (479), 2007) "Example data sets that motivate the development of the models are also provided. … The index provided seems to be fairly complete and is helpful in looking up topics discusses in this monograph. Several chapters end in a section in which the authors provide additional comments, discussions and pose some open problems in this area, which should be appealing for researchers in this field. … This book should be useful for all people interested in the area of functional data analysis." (Anatolij Dvurecenskij, Zentralblatt MATH, Vol. 1119 (21), 2007)Table of ContentsIntroduction to functional nonparametric statistics.- Some functional datasets and associated statistical problematics.- What is a well adapted space for functional data?.- Local weighting of functional variables.- Functional nonparametric prediction methodologies.- Some selected asymptotics.- Computational issues.- Nonparametric supervised classification for functional data.- Nonparametric unsupervised classification for functional data.- Mixing, nonparametric and functional statistics.- Some selected asymptotics.- Application to continuous time processes prediction.- Small ball probabilities, semi-metric spaces and nonparametric statistics.- Conclusion and perspectives.
£104.99
Springer-Verlag New York Inc. R for SAS and SPSS Users
Book SynopsisR is a powerful and free software system for data analysis and graphics, with over 5,000 add-on packages available. This book introduces R using SAS and SPSS terms with which you are already familiar. It demonstrates which of the add-on packages are most like SAS and SPSS and compares them to R''s built-in functions. It steps through over 30 programs written in all three packages, comparing and contrasting the packages'' differing approaches. The programs and practice datasets are available for download.The glossary defines over 50 R terms using SAS/SPSS jargon and again using R jargon. The table of contents and the index allow you to find equivalent R functions by looking up both SAS statements and SPSS commands. When finished, you will be able to import data, manage and transform it, create publication quality graphics, and perform basic statistical analyses.This new edition has updated programming, an expanded index, and even more statistical methods covered in overTrade ReviewFrom the reviews of the second edition:“This is a greatly expanded second edition of a text that has already proved widely popular. The explanation is careful and detailed. It uses SAS and SPSS terminology, matching it with R terminology … . A glossary translates R terminology into terminology that is likely to be more familiar to SAS and SPSS users. … a wide-ranging and carefully compiled source of information on R. It is a strongly recommended addition to the library of anyone who comes to R from SAS or SPSS.” (John H. Maindonald, International Statistical Review, Vol. 80 (1), 2012)Table of ContentsIntroduction.- Installing and Updating R.- Running R.- Help and Documentation.- Programming Language Basics.- Data Acquisition.- Selecting Variables.- Selecting Observations.- Selecting Variables and Observations.- Data Management.- Enhancing Your Output.- Generating Data.- Managing Your Files and Workspace.- Graphics Overview.- Traditional Graphics- Graphics with ggplot2.- Statistics.- Conclusion.
£112.49
Springer New York Bayesian Networks and Influence Diagrams A Guide to Construction and Analysis 22 Information Science and Statistics
Book SynopsisThe techniques and methods presented for knowledge elicitation, model construction and verification, modeling techniques and tricks, learning models from data, and analyses of models have all been developed and refined on the basis of numerous courses that the authors have held for practitioners worldwide.Trade ReviewFrom the book reviews:“The monograph concentrates on intelligent systems for decision support based on probabilistic models, including Bayesian networks and influence diagrams. … This monograph provides a review of recent state affairs of probabilistic networks that can be useful for professionals, practitioners, and researchers from diverse fields of statistics and related disciplines. I think it can be used as a textbook in its own right for an upper level undergraduate course, especially for a reading course.” (Technometrics, Vol. 55 (2), May, 2013)Table of ContentsIntroduction.- Networks.- Probabilities.- Probabilistic Networks.- Solving Probabilistic Networks.- Eliciting the Model.- Modeling Techniques.- Data-Driven Modeling.- Conflict Analysis.- Sensitivity Analysis.- Value of Information Analysis.- Quick Reference to Model Construction.- List of Examples.- List of Figures.- List of Tables.- List of Symbols.- References.- Index.
£82.49
American Mathematical Society The Mathematics of Data
Book SynopsisData science is a highly interdisciplinary field, incorporating ideas from applied mathematics, statistics, probability, and computer science, as well as many other areas. This book provides an introduction to the mathematical methods that form the foundations of machine learning and data science.Table of Contents P. Drineas and M. W. Mahoney, Lectures on randomized numerical linear algebra S. J. Wright, Optimization algorithms for data analysis J. C. Duchi, Introductory lectures on stochastic optimization P.-G. Martinsson, Randomized methods for matrix computations R. Vershynin, Four lectures on probabilistic methods for data science R. Ghrist, Homological algebra and data.
£98.10
APress Beginning R 4
Book SynopsisLearn how to use R 4, write and save R scripts, read in and write out data files, use built-in functions, and understand common statistical methods. This in-depth tutorial includes key R 4 features including a new color palette for charts, an enhanced reference counting system (useful for big data), and new data import settings for text (as well as the statistical methods to model text-based, categorical data). Each chapter starts with a list of learning outcomes and concludes with a summary of any R functions introduced in that chapter, along with exercises to test your new knowledge. The text opens with a hands-on installation of R and CRAN packages for both Windows and macOS. The bulk of the book is an introduction to statistical methods (non-proof-based, applied statistics) that relies heavily on R (and R visualizations) to understand, motivate, and conduct statistical tests and modeling.Beginning R 4 shows the use of R in specific cases such as ANOTable of Contents1: Installing R2: Installing Packages and Using Libraries3: Data Input and Output4: Working with Data5: Data and Samples6: Descriptive Statistics7: Understanding Probability and Distribution8: Correlation and Regression9: Confidence Intervals10: Hypothesis Testing11: Multiple Regression12: Moderated Regression13: Analysts of VarianceBibliography
£41.24
APress Beginning MATLAB and Simulink
Book SynopsisEmploy essential tools and functions of the MATLAB and Simulink packages, which are explained and demonstrated via interactive examples and case studies. This revised edition covers features from the latest MATLAB 2022b release, as well as other features that have been released since the first edition published. This book contains dozens of simulation models and solved problems via m-files/scripts and Simulink models which will help you to learn programming and modelling essentials. You''ll become efficient with many of the built-in tools and functions of MATLAB/Simulink while solving engineering and scientific computing problems. Beginning MATLAB and Simulink, Second Edition explains various practical issues of programming and modelling in parallel by comparing MATLAB and Simulink. After studying and using this book, you''ll be proficient at using MATLAB and Simulink and applying the source code and models from the book''s examples as templTable of Contents1. Introduction to MATLAB.- 2. Programming Essentials.- 3. Graphical User Interface Model Development.- 4. MEX files, C/C++ and Standalone Applications.- 5. Simulink Modeling Essentials.- 6. Plots.- 7. Matrix Algebra.- 8. Ordinary Differential Equations.
£49.49
Springer New York Bayesian Networks and Influence Diagrams A Guide to Construction and Analysis
Book SynopsisThe techniques and methods presented for knowledge elicitation, model construction and verification, modeling techniques and tricks, learning models from data, and analyses of models have all been developed and refined on the basis of numerous courses that the authors have held for practitioners worldwide.Trade ReviewFrom the book reviews:“The monograph concentrates on intelligent systems for decision support based on probabilistic models, including Bayesian networks and influence diagrams. … This monograph provides a review of recent state affairs of probabilistic networks that can be useful for professionals, practitioners, and researchers from diverse fields of statistics and related disciplines. I think it can be used as a textbook in its own right for an upper level undergraduate course, especially for a reading course.” (Technometrics, Vol. 55 (2), May, 2013)Table of ContentsIntroduction.- Networks.- Probabilities.- Probabilistic Networks.- Solving Probabilistic Networks.- Eliciting the Model.- Modeling Techniques.- Data-Driven Modeling.- Conflict Analysis.- Sensitivity Analysis.- Value of Information Analysis.- Quick Reference to Model Construction.- List of Examples.- List of Figures.- List of Tables.- List of Symbols.- References.- Index.
£59.99
Springer-Verlag New York Inc. A Course in Mathematical Statistics and Large
Book SynopsisThis graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics.Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.Trade Review“It deals with advanced statistical theory with a special focus on statistical inference and large sample theory, aiming to cover the material for a modern two-semester graduate course in mathematical statistics. … Overall, the book is very advanced and is recommended to graduate students with sound statistical backgrounds, as well as to teachers, researchers, and practitioners who wish to acquire more knowledge on mathematical statistics and large sample theory.” (Lefteris Angelis, Computing Reviews, March, 2017)“This is a very nice book suitable for a theoretical statistics course after having worked through something at the level of Casella & Berger, as well as some measure theory. … In addition to the exercises, which range from doable to interesting, there are several projects scattered throughout the text. The explanations are clear and crisp, and the presentation is interesting. … the book would be a worthy addition to your statistics library.” (Peter Rabinovitch, MAA Reviews, maa.org, March, 2017)Table of Contents1 Introduction.- 2 Decision Theory.- 3 Introduction to General Methods of Estimation.- 4 Sufficient Statistics, Exponential Families, and Estimation.- 5 Testing Hypotheses.- 6 Consistency and Asymptotic Distributions and Statistics.- 7 Large Sample Theory of Estimation in Parametric Models.- 8 Tests in Parametric and Nonparametric Models.- 9 The Nonparametric Bootstrap.- 10 Nonparametric Curve Estimation.- 11 Edgeworth Expansions and the Bootstrap.- 12 Frechet Means and Nonparametric Inference on Non-Euclidean Geometric Spaces.- 13 Multiple Testing and the False Discovery Rate.- 14 Markov Chain Monte Carlo (MCMC) Simulation and Bayes Theory.- 15 Miscellaneous Topics.- Appendices.- Solutions of Selected Exercises in Part 1.
£98.99
Society for Industrial & Applied Mathematics,U.S. Introduction to Numerical Linear Algebra
Book SynopsisFit for students just starting to build a background in mathematics, this textbook provides an introduction to numerical methods for linear algebra problems.Introduction to Numerical Linear Algebra is ideal for a flipped classroom, as it provides detailed explanations that allow students to read on their own and instructors to go beyond lecturing, assumes that the reader has taken a course on linear algebra, but reviews background as needed, and covers several topics not commonly addressed in related introductory books, including diffusion, a toy model of computed tomography, global positioning systems, the use of eigenvalues in analyzing stability of equilibria, a detailed derivation and careful motivation of the QR method for eigenvalues starting from power iteration, a discussion of the use of the SVD for assigning grades, and multigrid methods. This textbook is appropriate for undergraduate and beginning graduate students in mathematics and related fields. It can be used in the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory
£67.15
Society for Industrial & Applied Mathematics,U.S. Rounding Errors in Algebraic Processes
Book SynopsisRounding Errors in Algebraic Processes was the first book to give systematic analyses of the effects of rounding errors on a variety of key computations involving polynomials and matrices.A detailed analysis is given of the rounding errors made in the elementary arithmetic operations and inner products, for both floating-point arithmetic and fixed-point arithmetic. The results are then applied in the error analyses of a variety of computations involving polynomials as well as the solution of linear systems, matrix inversion, and eigenvalue computations.The conditioning of these problems is investigated. The aim was to provide a unified method of treatment, and emphasis is placed on the underlying concepts.This book is intended for mathematicians, computer scientists, those interested in the historical development of numerical analysis, and students in numerical analysis and numerical linear algebra.Trade Review[This book] combines a rigorous mathematical analysis with a practicality that stems from an obvious first-hand contact with the actual numerical computation. The well-chosen examples alone show vividly both the importance of the study of rounding errors and the perils of its neglect. A. A. Grau, SIAM Review (1966)
£56.95
Manning Publications Graph Algorithms for Data Science
Book SynopsisGraphs are the natural way to understand connected data. This book explores the most important algorithms and techniques for graphs in data science, with practical examples and concrete advice on implementation and deployment. In Graph Algorithms for Data Science you will learn: Labeled-property graph modeling Constructing a graph from structured data such as CSV or SQL NLP techniques to construct a graph from unstructured data Cypher query language syntax to manipulate data and extract insights Social network analysis algorithms like PageRank and community detection How to translate graph structure to a ML model input with node embedding models Using graph features in node classification and link prediction workflows Graph Algorithms for Data Science is a hands-on guide to working with graph-based data in applications like machine learning, fraud detection, and business data analysis. It's filled with fascinating and fun projects, demonstrating the ins-and-outs of graphs. You'll gain practical skills by analyzing Twitter, building graphs with NLP techniques, and much more. You don't need any graph experience to start benefiting from this insightful guide. These powerful graph algorithms are explained in clear, jargon-free text and illustrations that makes them easy to apply to your own projects. about the technology Graphs reveal the relationships in your data. Tracking these interlinking connections reveals new insights and influences and lets you analyze each data point as part of a larger whole. This interconnected data is perfect for machine learning, as well as analyzing social networks, communities, and even product recommendations. about the book Graph Algorithms for Data Science teaches you how to construct graphs from both structured and unstructured data. You'll learn how the flexible Cypher query language can be used to easily manipulate graph structures, and extract amazing insights. The book explores common and useful graph algorithms like PageRank and community detection/clustering algorithms. Each new algorithm you learn is instantly put into action to complete a hands-on data project, including modeling a social network! Finally, you'll learn how to utilize graphs to upgrade your machine learning, including utilizing node embedding models and graph neural networks.Trade Review'The book covers topics in-depth but is easy to understand. Though delving into theory, it doesn't lose its focus of being a more practical guide. ' Carl Yu 'A good starting point to getting started with network analysis and how to extract the essential information you need easily.' Andrea Paciolla 'A great introduction to how to use graphs and data they can provide.' Marcin SękTable of Contentstable of contents detailed TOC READ IN LIVEBOOK 1GRAPHS AND NETWORK SCIENCE: AN INTRODUCTION READ IN LIVEBOOK 2REPRESENTING NETWORK STRUCTURE - DESIGN YOUR FIRST GRAPH MODEL READ IN LIVEBOOK 3YOUR FIRST STEPS WITH THE CYPHER QUERY LANGUAGE READ IN LIVEBOOK 4CYPHER AGGREGATIONS AND SOCIAL NETWORK ANALYSIS 5 INFERRING NETWORKS AND MONOPARTITE PROJECTIONS 6 CONSTRUCT A GRAPH USING NLP TECHNIQUES 7 NODE EMBEDDINGS AND CLASSIFICATION 8 IMPROVE DOCUMENT CLASSIFICATION WITH GRAPH NEURAL NETWORKS 9 PREDICT NEW CONNECTIONS 10 KNOWLEDGE GRAPH COMPLETION READ IN LIVEBOOK APPENDIX A: ADJACENCY MATRIX
£39.09
No Starch Press,US Math For Security: From Graphs and Geometry to
Book SynopsisApplied Math for Security is one of the first math-based guides specifically geared for information security practitioners. Readers will learn how to use concepts from various fields of mathematics - like graph theory, computational geometry, and statistics - to create and implement ready-to-use security tools. The book is written in a lively, conversational style that engages readers from the get-go. Chapters are enriched with code examples written in Python, and feature hands-on 'proof of concept' projects that involve developing math-based applications to solve real-world problems. Readers are also able to apply the mathematical constructs that they learn to a variety of challenging scenarios, like determining the ideal location for fire stations, disrupting information flow in a social network, building facial recognition software, and designing custom tools for modern security work.Trade Review"A very practical book for security. . . . a real eye-opener."—William Gasarch, Professor, University of Maryland-Dept of Computer Science"A really nice introduction to graph theory and computational geometry for people who know a bit of Python and without a mathematical background."—Julien Voisin, Artificial Truth"The book was very easy to follow, I'd expect anyone with a technical or stats background to be able to dive right in given the step-by-step instructions and explanations provided by Daniel."—@WithSandra, tech YouTuber and security analyst"Whether you're an aspiring security professional, a social network analyst, or an innovator seeking to create cutting-edge security solutions, Math for Security will empower you to solve complex problems with precision and confidence. "—Midwest Book ReviewTable of ContentsAcknowledgments IntroductionPART I: ENVIRONMENT AND CONVENTIONSChapter 1: Setting up the EnvironmentChapter 2: Programming and Math ConventionsPART II: GRAPH THEORY AND COMPUTATIONAL GEOMETRYChapter 3: Securing Networks with Graph TheoryChapter 4: Building a Network Traffic Analysis Tool Chapter 5: Identifying Threats with Social Network AnalysisChapter 6: Analyzing Social Networks to Prevent Security IncidentsChapter 7: Using Geometry to Improve Security PracticesChapter 8: Tracking People in Physical Space with Digital InformationChapter 9: Computational Geometry for Safety Resource DistributionChapter 10: Computational Geometry for Facial RecognitionPART III: THE ART GALLERY PROBLEMChapter 11: Distributing Security Resources to Guard a SpaceChapter 12: The Minimum Viable Product Approach to Security Software DevelopmentChapter 13: Delivering Python ApplicationsNotesIndex
£35.99
Springer London Ltd Graph Theory
Book SynopsisThe primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. The book also serves as an introduction to research in graph theory.Trade Reviewdeveloped by Paul Seymour and Neil Robertson and followers), which certainly now deserves a monographic treatment of its own. Summing up: Recommended. Lower-division undergraduate through professional collections. CHOICE This book is a follow-on to the authors' 1976 text, Graphs with Applications. What began as a revision has evolved into a modern, first-class, graduate-level textbook reflecting changes in the discipline over the past thirty years... This text hits the mark by appearing in Springer’s Graduate Texts in Mathematics series, as it is a very rigorous treatment, compactly presented, with an assumption of a very complete undergraduate preparation in all of the standard topics. While the book could ably serve as a reference for many of the most important topics in graph theory, it fulfills the promise of being an effective textbook. The plentiful exercises in each subsection are divided into two groups, with the second group deemed "more challenging". Any exercises necessary for a complete understanding of the text have also been marked as such. There is plenty here to keep a graduate student busy, and any student would learn much in tackling a selection of the exercises... Not only is the content of this book exceptional, so too is its production. The high quality of its manufacture, the crisp and detailed illustrations, and the uncluttered design complement the attention to the typography and layout. Even in simple black and white with line art, it is a beautiful book. SIAM Book Reviews "A text which is designed to be usable both for a basic graph theory course … but also to be usable as an introduction to research in graph theory, by including more advanced topics in each chapter. There are a large number of exercises in the book … . The text contains drawings of many standard interesting graphs, which are listed at the end." (David B. Penman, Zentralblatt MATH, Vol. 1134 (12), 2008) MathSciNet Reviews "The present volume is intended to serve as a text for "advanced undergraduate and beginning graduate students in mathematics and computer science" (p. viii). It is well suited for this purpose. The writing is fully accessible to the stated groups of students, and indeed is not merely readable but is engaging… Even a complete listing of the chapters does not fully convey the breadth of this book… For researchers in graph theory, this book offers features which parallel the first Bondy and Murty book: it provides well-chosen terminology and notation, a multitude of especially interesting graphs, and a substantial unsolved problems section…One-hundred unsolved problems are listed in Appendix A, a treasure trove of problems worthy of study… (In short) this rewrite of a classic in graph theory stands a good chance of becoming a classic itself." "The present volume is intended to serve as a text for ‘advanced undergraduate and beginning graduate students in mathematics and computer science’ … . The writing is fully accessible to the stated groups of students, and indeed is not merely readable but is engaging. The book has many exercise sets, each containing problems … ." (Arthur M. Hobbs, Mathematical Reviews, Issue 2009 C) "A couple of fantastic features: Proof techniques: I love these nutshelled essences highlighted in bordered frames. They look like pictures on the wall and grab the view of the reader. Exercises: Their style, depth and logic remind me of Lovász’ classical exercise book. Also the fact that the name of the author is bracketed after the exercise…Figures: Extremely precise and high-tech…The book contains very recent results and ideas. It is clearly an up-to-date collection of fundamental results of graph theory…All-in-all, it is a marvelous book." (János Barát, Acta Scientiarum Mathematicarum, Vol. 75, 2009)Table of ContentsGraphs.- Subgraphs.- Connected Graphs.- Trees.- Nonseparable Graphs.- Tree-Search Algorithms.- Flows in Networks.- Complexity of Algorithms.- Connectivity.- Planar Graphs.- The Four-Colour Problem.- Stable Sets and Cliques.- The Probabilistic Method.- Vertex Colourings.- Colourings of Maps.- Matchings.- Edge Colourings.- Hamilton Cycles.- Coverings and Packings in Directed Graphs.- Electrical Networks.- Integer Flows and Coverings.
£43.70
ISTE Ltd and John Wiley & Sons Inc Bayesian Approach to Inverse Problems
Book SynopsisMany scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.Table of ContentsIntroduction 15 Jérôme IDIER PART I. FUNDAMENTAL PROBLEMS AND TOOLS 23 Chapter 1. Inverse Problems, Ill-posed Problems 25 Guy DEMOMENT, Jérôme IDIER 1.1. Introduction 25 1.2. Basic example 26 1.3. Ill-posed problem 30 1.3.1. Case of discrete data 31 1.3.2. Continuous case 32 1.4. Generalized inversion 34 1.4.1. Pseudo-solutions 35 1.4.2. Generalized solutions 35 1.4.3. Example 35 1.5. Discretization and conditioning 36 1.6. Conclusion 38 1.7. Bibliography 39 Chapter 2. Main Approaches to the Regularization of Ill-posed Problems 41 Guy DEMOMENT, Jérôme IDIER 2.1. Regularization 41 2.1.1. Dimensionality control 42 2.1.2. Minimization of a composite criterion 44 2.2. Criterion descent methods 48 2.2.1.Criterion minimization for inversion 48 2.2.2. The quadratic case 49 2.2.3. The convex case 51 2.2.4. General case 52 2.3. Choice of regularization coefficient 53 2.3.1. Residual error energy control 53 2.3.2. “L-curve” method 53 2.3.3. Cross-validation 54 2.4. Bibliography 56 Chapter 3. Inversion within the Probabilistic Framework 59 Guy DEMOMENT, Yves GOUSSARD 3.1. Inversion and inference 59 3.2. Statistical inference 60 3.2.1. Noise law and direct distribution for data 61 3.2.2. Maximum likelihood estimation 63 3.3. Bayesian approach to inversion 64 3.4. Links with deterministic methods 66 3.5. Choice of hyperparameters 67 3.6. A priori model68 3.7. Choice of criteria 70 3.8. The linear, Gaussian case 71 3.8.1. Statistical properties of the solution 71 3.8.2. Calculation of marginal likelihood 73 3.8.3. Wiener filtering 74 3.9. Bibliography 76 PART II. DECONVOLUTION 79 Chapter 4. Inverse Filtering and Other Linear Methods 81 Guy LE BESNERAIS, Jean-François GIOVANNELLI, Guy DEMOMENT 4.1. Introduction 81 4.2. Continuous-time deconvolution 82 4.2.1. Inverse filtering 82 4.2.2. Wiener filtering 84 4.3. Discretization of the problem 85 4.3.1. Choice of a quadrature method 85 4.3.2. Structure of observation matrix H 87 4.3.3. Usual boundary conditions 89 4.3.4. Problem conditioning 89 4.3.5.Generalized inversion 91 4.4. Batch deconvolution 92 4.4.1. Preliminary choices 92 4.4.2. Matrix form of the estimate 93 4.4.3. Hunt’s method (periodic boundary hypothesis) 94 4.4.4. Exact inversion methods in the stationary case 96 4.4.5. Case of non-stationary signals 98 4.4.6. Results and discussion on examples 98 4.5. Recursive deconvolution 102 4.5.1. Kalman filtering 102 4.5.2. Degenerate state model and recursive least squares 104 4.5.3. Autoregressive state model 105 4.5.4. Fast Kalman filtering 108 4.5.5. Asymptotic techniques in the stationary case 110 4.5.6. ARMA model and non-standard Kalman filtering 111 4.5.7. Case of non-stationary signals 111 4.5.8. On-lineprocessing: 2Dcase 112 4.6. Conclusion 112 4.7. Bibliography 113 Chapter 5. Deconvolution of Spike Trains 117 Frédéric CHAMPAGNAT, Yves GOUSSARD, Stéphane GAUTIER, Jérôme IDIER 5.1. Introduction 117 5.2. Penalization of reflectivities, L2LP/L2Hy deconvolutions 119 5.2.1. Quadratic regularization 121 5.2.2. Non-quadratic regularization 122 5.2.3. L2LPorL2Hy deconvolution 123 5.3. Bernoulli-Gaussian deconvolution 124 5.3.1. Compound BG model 124 5.3.2. Various strategies for estimation 124 5.3.3. General expression for marginal likelihood 125 5.3.4. An iterative method for BG deconvolution 126 5.3.5. Other methods 128 5.4. Examples of processing and discussion 130 5.4.1. Nature of the solutions 130 5.4.2. Setting the parameters 132 5.4.3. Numerical complexity 133 5.5. Extensions 133 5.5.1. Generalization of structures of R and H 134 5.5.2. Estimation of the impulse response . . . 134 5.6. Conclusion 136 5.7. Bibliography 137 Chapter 6. Deconvolution of Images 141 Jérôme IDIER, Laure BLANC-FÉRAUD 6.1. Introduction 141 6.2. Regularization in the Tikhonov sense 142 6.2.1. Principle 142 6.2.2. Connection with image processing by linear PDE 144 6.2.3. Limits of Tikhonov’s approach 145 6.3. Detection-estimation 148 6.3.1. Principle 148 6.3.2. Disadvantages 149 6.4. Non-quadratic approach 150 6.4.1. Detection-estimation and non-convex penalization 154 6.4.2. Anisotropic diffusion by PDE 155 6.5. Half-quadratic augmented criteria 156 6.5.1. Duality between non-quadratic criteria and HQ criteria 157 6.5.2. Minimization of HQ criteria 158 6.6. Application in image deconvolution 159 6.6.1. Calculation of the solution 159 6.6.2. Example 161 6.7. Conclusion 164 6.8. Bibliography 165 PART III. ADVANCED PROBLEMS AND TOOLS 169 Chapter 7. Gibbs-Markov Image Models 171 Jérôme IDIER 7.1. Introduction 171 7.2. Bayesian statistical framework 172 7.3. Gibbs-Markov fields 173 7.3.1. Gibbs fields 174 7.3.2. Gibbs-Markov equivalence 177 7.3.3. Posterior law of a GMRF 180 7.3.4. Gibbs-Markov models for images 181 7.4. Statistical tools, stochastic sampling 185 7.4.1. Statistical tools 185 7.4.2. Stochastic sampling 188 7.5. Conclusion 194 7.6. Bibliography 195 Chapter 8. Unsupervised Problems 197 Xavier DESCOMBES, Yves GOUSSARD 8.1. Introduction and statement of problem 197 8.2. Directly observed field 199 8.2.1. Likelihood properties 199 8.2.2. Optimization 200 8.2.3. Approximations 202 8.3. Indirectly observed field 205 8.3.1. Statement of problem 205 8.3.2. EM algorithm 206 8.3.3. Application to estimation of the parameters of a GMRF 207 8.3.4. EM algorithm and gradient 208 8.3.5. Linear GMRF relative to hyperparameters 210 8.3.6. Extensions and approximations 212 8.4. Conclusion 215 8.5. Bibliography 216 PART IV. SOME APPLICATIONS 219 Chapter 9. Deconvolution Applied to Ultrasonic Non-destructive Evaluation 221 Stéphane GAUTIER, Frédéric CHAMPAGNAT, Jérôme IDIER 9.1. Introduction 221 9.2. Example of evaluation and difficulties of interpretation 222 9.2.1. Description of the part to be inspected 222 9.2.2. Evaluation principle 222 9.2.3. Evaluation results and interpretation 223 9.2.4. Help with interpretation by restoration of discontinuities 224 9.3. Definition of direct convolution model 225 9.4. Blind deconvolution 226 9.4.1. Overview of approaches for blind deconvolution 226 9.4.2. DL2Hy/DBGd econvolution 230 9.4.3. Blind DL2Hy/DBG deconvolution 232 9.5. Processing real data 232 9.5.1. Processing by blind deconvolution 233 9.5.2. Deconvolution with a measured wave 234 9.5.3. Comparison between DL2Hy and DBG 237 9.5.4. Summary 240 9.6. Conclusion 240 9.7. Bibliography 241 Chapter 10. Inversion in Optical Imaging through Atmospheric Turbulence 243 Laurent MUGNIER, Guy LE BESNERAIS, Serge MEIMON 10.1. Optical imaging through turbulence 243 10.1.1. Introduction 243 10.1.2. Image formation 244 10.1.4. Imaging techniques 249 10.2. Inversion approach and regularization criteria used 253 10.3. Measurement of aberrations 254 10.3.1. Introduction 254 10.3.2. Hartmann-Shack sensor 255 10.3.3. Phase retrieval and phase diversity 257 10.4. Myopic restoration in imaging 258 10.4.1. Motivation and noise statistic 258 10.4.2. Data processing in deconvolution from wavefront sensing 259 10.4.3. Restoration of images corrected by adaptive optics 263 10.4.4. Conclusion 267 10.5. Image reconstruction in optical interferometry (OI) 268 10.5.1. Observation model 268 10.5.2. Traditional Bayesian approach 271 10.5.3. Myopic modeling 272 10.5.4. Results 274 10.6. Bibliography 277 Chapter 11. Spectral Characterization in Ultrasonic Doppler Velocimetry 285 Jean-François GIOVANNELLI, Alain HERMENT 11.1. Velocity measurement in medical imaging 285 11.1.1. Principle of velocity measurement in ultrasound imaging 286 11.1.2. Information carried by Doppler signals 286 11.1.3.Some characteristics and limitations 288 11.1.4. Data and problems treated 288 11.2. Adaptive spectral analysis 290 11.2.1. Least squares and traditional extensions 290 11.2.2. Long AR models – spectral smoothness – spatial continuity 291 11.2.3. Kalman smoothing 293 11.2.4. Estimation of hyperparameters 294 11.2.5. Processing results and comparisons 296 11.3. Tracking spectral moments 297 11.3.1. Proposed method 298 11.3.2. Likelihood of the hyperparameters 302 11.3.3. Processing results and comparisons 304 11.4. Conclusion 306 11.5. Bibliography 307 Chapter 12. Tomographic Reconstruction from Few Projections 311 Ali MOHAMMAD-DJAFARI, Jean-Marc DINTEN 12.1. Introduction 311 12.2. Projection generation model 312 12.3. 2D analytical methods 313 12.4. 3D analytical methods 317 12.5. Limitations of analytical methods 317 12.6. Discrete approach to reconstruction 319 12.7. Choice of criterion and reconstruction methods 321 12.8. Reconstruction algorithms 323 12.8.1. Optimization algorithms for convex criteria 323 12.8.2. Optimization or integration algorithms 327 12.9. Specific models for binary objects 328 12.10. Illustrations 328 12.10.1.2D reconstruction 328 12.10.2.3Dreconstruction 329 12.11. Conclusions 331 12.12. Bibliography 332 Chapter 13. Diffraction Tomography 335 Hervé CARFANTAN, Ali MOHAMMAD-DJAFARI 13.1. Introduction 335 13.2. Modeling the problem 336 13.2.1. Examples of diffraction tomography applications 336 13.2.2. Modeling the direct problem 338 13.3. Discretization of the direct problem 340 13.3.1. Choice of algebraic framework 340 13.3.2. Method of moments 341 13.3.3. Discretization by the method of moments 342 13.4. Construction of criteria for solving the inverse problem 343 13.4.1. First formulation: estimation of x 344 13.4.2. Second formulation: simultaneous estimation of x and φ 345 13.4.3. Properties of the criteria 347 13.5. Solving the inverse problem 347 13.5.1. Successive linearizations 348 13.5.2. Joint minimization 350 13.5.3. Minimizing MAP criterion 351 13.6. Conclusion 353 13.7. Bibliography 354 Chapter 14. Imaging from Low-intensity Data 357 Ken SAUER, Jean-Baptiste THIBAULT 14.1. Introduction 357 14.2. Statistical properties of common low-intensity image data 359 14.2.1. Likelihood functions and limiting behavior 359 14.2.2. Purely Poisson measurements 360 14.2.3. Inclusion of background counting noise 362 14.2.4. Compound noise models with Poisson information 362 14.3. Quantum-limited measurements in inverse problems 363 14.3.1. Maximum likelihood properties 363 14.3.2. Bayesian estimation 366 14.4. Implementation and calculation of Bayesian estimates 368 14.4.1. Implementation for pure Poisson model 368 14.4.2. Bayesian implementation for a compound data model 370 14.5. Conclusion 372 14.6. Bibliography 372 List of Authors 375 Index 377
£170.95
ISTE Ltd and John Wiley & Sons Inc Mathematical Programming Solver Based on Local
Book SynopsisThis book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search. First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern regarding industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces extra costs in development and maintenance in comparison with the direct use of mixed-integer linear programming solvers. The authors then move on to present the LocalSolver project whose goal is to offer the power of local search through a model-and-run solver for large-scale 0-1 nonlinear programming. They conclude by presenting their ongoing and future work on LocalSolver toward a full mathematical programming solver based on local search.Table of ContentsAcknowledgments vii Preface ix Introduction xi Chapter 1 Local Search: Methodology and Industrial Applications 1 1.1 Our methodology: back to basics 1 1.2 Car sequencing for painting and assembly lines 10 1.3 Vehicle routing with inventory management 17 Chapter 2 Local Search for 0-1 Nonlinear Programming 29 2.1 The LocalSolver project 29 2.2 State-of-the-art 32 2.3 Enriching modeling standards 33 2.4 The core algorithmic ideas 39 2.5 Benchmarks 44 Chapter 3 Toward an Optimization Solver Based on Neighborhood Search 53 3.1 Using neighborhood search as global search strategy 53 3.2 Extension to continuous and mixed optimization 56 3.3 Separating the computation of solutions and bounds 59 3.4 A new-generation, hybrid mathematical programming solver 62 Bibliography 65 Lists of Figures and Tables 79 Index 81
£125.06
ISTE Ltd and John Wiley & Sons Inc Mathematics for Modeling and Scientific Computing
Book SynopsisThis book provides the mathematical basis for investigating numerically equations from physics, life sciences or engineering. Tools for analysis and algorithms are confronted to a large set of relevant examples that show the difficulties and the limitations of the most naïve approaches. These examples not only provide the opportunity to put into practice mathematical statements, but modeling issues are also addressed in detail, through the mathematical perspective.Table of ContentsPreface ix Chapter 1. Ordinary Differential Equations 1 1.1. Introduction to the theory of ordinary differential equations 1 1.1.1. Existence–uniqueness of first-order ordinary differential equations 1 1.1.2. The concept of maximal solution 11 1.1.3. Linear systems with constant coefficients 16 1.1.4. Higher-order differential equations 20 1.1.5. Inverse function theorem and implicit function theorem 21 1.2. Numerical simulation of ordinary differential equations, Euler schemes, notions of convergence, consistence and stability 27 1.2.1. Introduction 27 1.2.2. Fundamental notions for the analysis of numerical ODE methods 29 1.2.3. Analysis of explicit and implicit Euler schemes 33 1.2.4. Higher-order schemes 50 1.2.5. Leslie’s equation (Perron–Frobenius theorem, power method) 51 1.2.6. Modeling red blood cell agglomeration 78 1.2.7. SEI model 87 1.2.8. A chemotaxis problem 93 1.3. Hamiltonian problems 102 1.3.1. The pendulum problem 106 1.3.2. Symplectic matrices; symplectic schemes 112 1.3.3. Kepler problem 125 1.3.4. Numerical results 129 Chapter 2. Numerical Simulation of Stationary Partial Differential Equations: Elliptic Problems 141 2.1. Introduction 141 2.1.1. The 1D model problem; elements of modeling and analysis 144 2.1.2. A radiative transfer problem 155 2.1.3. Analysis elements for multidimensional problems 163 2.2. Finite difference approximations to elliptic equations 166 2.2.1. Finite difference discretization principles 166 2.2.2. Analysis of the discrete problem 173 2.3. Finite volume approximation of elliptic equations 180 2.3.1. Discretization principles for finite volumes 180 2.3.2. Discontinuous coefficients 187 2.3.3. Multidimensional problems 189 2.4. Finite element approximations of elliptic equations 191 2.4.1. P1 approximation in one dimension 191 2.4.2. P2 approximations in one dimension 197 2.4.3. Finite element methods, extension to higher dimensions 200 2.5. Numerical comparison of FD, FV and FE methods 204 2.6. Spectral methods 205 2.7. Poisson–Boltzmann equation; minimization of a convex function, gradient descent algorithm 217 2.8. Neumann conditions: the optimization perspective 224 2.9. Charge distribution on a cord 228 2.10. Stokes problem 235 Chapter 3. Numerical Simulations of Partial Differential Equations: Time-dependent Problems 267 3.1. Diffusion equations 267 3.1.1. L2 stability (von Neumann analysis) and L∞ stability: convergence 269 3.1.2. Implicit schemes 276 3.1.3. Finite element discretization 281 3.1.4. Numerical illustrations 283 3.2. From transport equations towards conservation laws 291 3.2.1. Introduction 291 3.2.2. Transport equation: method of characteristics 295 3.2.3. Upwinding principles: upwind scheme 299 3.2.4. Linear transport at constant speed; analysis of FD and FV schemes 301 3.2.5. Two-dimensional simulations 326 3.2.6. The dynamics of prion proliferation 329 3.3. Wave equation 345 3.4. Nonlinear problems: conservation laws 354 3.4.1. Scalar conservation laws 354 3.4.2. Systems of conservation laws 387 3.4.3. Kinetic schemes 393 Appendices 407 Appendix 1 409 Appendix 2 417 Appendix 3 427 Appendix 4 433 Appendix 5 443 Bibliography 447 Index 455
£125.06
Springer London Ltd A First Course in Discrete Mathematics
Book SynopsisDrawing on many years'experience of teaching discrete mathem atics to students of all levels, Anderson introduces such as pects as enumeration, graph theory and configurations or arr angements. Starting with an introduction to counting and rel ated problems, he moves on to the basic ideas of graph theor y with particular emphasis on trees and planar graphs. He de scribes the inclusion-exclusion principle followed by partit ions of sets which in turn leads to a study of Stirling and Bell numbers. Then follows a treatment of Hamiltonian cycles, Eulerian circuits in graphs, and Latin squares as well as proof of Hall's theorem. He concludes with the constructions of schedules and a brief introduction to block designs. Each chapter is backed by a number of examples, with straightforw ard applications of ideas and more challenging problems.Trade Review"Wie der Titel andeutet, handelt es sich bei diesem Buch um eine elementare Einführung in Denkweisen und Methoden der Diskreten Mathematik. Die fachlichen Voraussetzungen an den Leser sind minimal. Darauf aufbauend wird ein doch recht buntes Bild entwickelt, bestehend vor allem aus den wichtigsten Konzepten aus Kombinatorik und Graphentheorie sowie einigen spezielleren Themen wie Designs und Codes.... Der Vorteil besteht darin, dass auch dem mathematischen Laien auf knapp 200 Seiten ein durchaus einprägsames Bild von einem Zweig der Mathematik vermittelt wird, der in unserer Zeit u.a. durch die Allgegenwart der sogenannten Informationstechnologie extrem an Bedeutung gewonnen hat."Internationale Mathematische Nachrichten, Nr. 187, August 2001Table of Contents1. Counting and Binomial Coefficients.- 2. Recurrence.- 3. Introduction to Graphs.- 4. Travelling Round a Graph.- 5. Partitions and Colourings.- 6. The Inclusion Exclusion Principle.- 7. Latin Squares and Hall’s Theorem.- 8. Schedules and 1-Factorisations.- 9. Introduction to Designs.- Solutions.- Further Reading.
£29.99
ISTE Ltd and John Wiley & Sons Inc Wavelets and their Applications
Book SynopsisThe last 15 years have seen an explosion of interest in wavelets with applications in fields such as image compression, turbulence, human vision, radar and earthquake prediction. Wavelets represent an area that combines signal in image processing, mathematics, physics and electrical engineering. As such, this title is intended for the wide audience that is interested in mastering the basic techniques in this subject area, such as decomposition and compression.Table of ContentsNotations xiii Introduction xvii Chapter 1. A Guided Tour 1 1.1. Introduction 1 1.2. Wavelets 2 1.2.1. General aspects 2 1.2.2. A wavelet 6 1.2.3. Organization of wavelets 8 1.2.4. The wavelet tree for a signal 10 1.3. An electrical consumption signal analyzed by wavelets 12 1.4. Denoising by wavelets: before and afterwards 14 1.5. A Doppler signal analyzed by wavelets 16 1.6. A Doppler signal denoised by wavelets 17 1.7. An electrical signal denoised by wavelets 19 1.8. An image decomposed by wavelets 21 1.8.1. Decomposition in tree form 21 1.8.2. Decomposition in compact form 22 1.9. An image compressed by wavelets 24 1.10. A signal compressed by wavelets 25 1.11. A fingerprint compressed using wavelet packets 27 Chapter 2. Mathematical Framework 29 2.1. Introduction 29 2.2. From the Fourier transform to the Gabor transform 30 2.2.1. Continuous Fourier transform 30 2.2.2. The Gabor transform 35 2.3. The continuous transform in wavelets 37 2.4. Orthonormal wavelet bases 41 2.4.1. From continuous to discrete transform 41 2.4.2. Multi-resolution analysis and orthonormal wavelet bases 42 2.4.3. The scaling function and the wavelet 46 2.5. Wavelet packets 50 2.5.1. Construction of wavelet packets 50 2.5.2. Atoms of wavelet packets 52 2.5.3. Organization of wavelet packets 53 2.6. Biorthogonal wavelet bases 55 2.6.1. Orthogonality and biorthogonality 55 2.6.2. The duality raises several questions 56 2.6.3. Properties of biorthogonal wavelets 57 2.6.4. Semi-orthogonal wavelets 60 Chapter 3. From Wavelet Bases to the Fast Algorithm 63 3.1. Introduction. 63 3.2. From orthonormal bases to the Mallat algorithm 64 3.3. Four filters 65 3.4. Efficient calculation of the coefficients 67 3.5. Justification: projections and twin scales 68 3.5.1. The decomposition phase 69 3.5.2. The reconstruction phase 72 3.5.3. Decompositions and reconstructions of a higher order 75 3.6. Implementation of the algorithm 75 3.6.1. Initialization of the algorithm 76 3.6.2. Calculation on finite sequences 77 3.6.3. Extra coefficients 77 3.7. Complexity of the algorithm 78 3.8. From 1D to 2D 79 3.9. Translation invariant transform 81 3.9.1. e-decimated DWT 83 3.9.2. Calculation of the SWT 83 3.9.3. Inverse SWT 87 Chapter 4. Wavelet Families 89 4.1. Introduction 89 4.2. What could we want from a wavelet? 90 4.3. Synoptic table of the common families 91 4.4. Some well known families 92 4.4.1. Orthogonal wavelets with compact support 93 4.4.2. Biorthogonal wavelets with compact support: bior 99 4.4.3. Orthogonal wavelets with non-compact support 101 4.4.4. Real wavelets without filters 104 4.4.5. Complex wavelets without filters 106 4.5. Cascade algorithm 109 4.5.1. The algorithm and its justification 110 4.5.2. An application 112 4.5.3. Quality of the approximation 113 Chapter 5. Finding and Designing a Wavelet 115 5.1. Introduction 115 5.2. Construction of wavelets for continuous analysis 116 5.2.1. Construction of a new wavelet 116 5.2.2. Application to pattern detection 124 5.3. Construction of wavelets for discrete analysis 131 5.3.1. Filter banks 132 5.3.2. Lifting 140 5.3.3. Lifting and biorthogonal wavelets 146 5.3.4. Construction examples 149 Chapter 6. A Short 1D Illustrated Handbook 159 6.1. Introduction 159 6.2. Discrete 1D illustrated handbook 160 6.2.1. The analyzed signals 160 6.2.2. Processing carried out 161 6.2.3. Commented examples 162 6.3. The contribution of analysis by wavelet packets 178 6.3.1. Example 1: linear and quadratic chirp 178 6.3.2. Example 2: a sine181 6.3.3. Example 3: a composite signal 182 6.4. “Continuous” 1D illustrated handbook 183 6.4.1. Time resolution 183 6.4.2. Regularity analysis 187 6.4.3. Analysis of a self-similar signal 193 Chapter 7. Signal Denoising and Compression 197 7.1. Introduction 197 7.2. Principle of denoising by wavelets 198 7.2.1. The model 198 7.2.2. Denoising: before and after 198 7.2.3. The algorithm 199 7.2.4. Why does it work? 200 7.3. Wavelets and statistics 200 7.3.1. Kernel estimators and estimators by orthogonal projection 201 7.3.2. Estimators by wavelets 201 7.4. Denoising methods 202 7.4.1. A first estimator 203 7.4.2. From coefficient selection to thresholding coefficients 204 7.4.3. Universal thresholding 206 7.4.4. Estimating the noise standard deviation 206 7.4.5. Minimax risk 207 7.4.6. Further information on thresholding rules 208 7.5. Example of denoising with stationary noise 209 7.6. Example of denoising with non-stationary noise 212 7.6.1. The model with ruptures of variance 213 7.6.2. Thresholding adapted to the noise level change-points 214 7.7. Example of denoising of a real signal 216 7.7.1. Noise unknown but “homogenous” in variance by level 216 7.7.2. Noise unknown and “non-homogenous” in variance by level 217 7.8. Contribution of the translation invariant transform 218 7.9. Density and regression estimation 221 7.9.1. Density estimation 221 7.9.2. Regression estimation 224 7.10. Principle of compression by wavelets 225 7.10.1. The problem 225 7.10.2. The basic algorithm 225 7.10.3. Why does it work? 226 7.11. Compression methods 226 7.11.1. Thresholding of the coefficients 226 7.11.2. Selection of coefficients 228 7.12. Examples of compression 229 7.12.1. Global thresholding 229 7.12.2. A comparison of the two compression strategies 230 7.13. Denoising and compression by wavelet packets 233 7.14. Bibliographical comments 234 Chapter 8. Image Processing with Wavelets 235 8.1. Introduction 235 8.2. Wavelets for the image 236 8.2.1. 2D wavelet decomposition 237 8.2.2. Approximation and detail coefficients 238 8.2.3. Approximations and details 241 8.3. Edge detection and textures 243 8.3.1. A simple geometric example 243 8.3.2. Two real life examples 245 8.4. Fusion of images 247 8.4.1. The problem through a simple example 247 8.4.2. Fusion of fuzzy images 250 8.4.3. Mixing of images 252 8.5. Denoising of images 256 8.5.1. An artificially noisy image 257 8.5.2. A real image 260 8.6. Image compression 262 8.6.1. Principles of compression 262 8.6.2. Compression and wavelets 263 8.6.3. “True” compression 269 Chapter 9. An Overview of Applications 279 9.1. Introduction 279 9.1.1. Why does it work? 279 9.1.2. A classification of the applications 281 9.1.3. Two problems in which the wavelets are competitive 283 9.1.4. Presentation of applications 283 9.2. Wind gusts 285 9.3. Detection of seismic jolts 287 9.4. Bathymetric study of the marine floor 290 9.5. Turbulence analysis 291 9.6. Electrocardiogram (ECG): coding and moment of the maximum 294 9.7. Eating behavior 295 9.8. Fractional wavelets and fMRI 297 9.9. Wavelets and biomedical sciences 298 9.9.1. Analysis of 1D biomedical signals 300 9.9.2. 2D biomedical signal analysis 301 9.10. Statistical process control 302 9.11. Online compression of industrial information 304 9.12. Transitories in underwater signals 306 9.13. Some applications at random 308 9.13.1. Video coding 308 9.13.2. Computer-assisted tomography 309 9.13.3. Producing and analyzing irregular signals or images 309 9.13.4. Forecasting 310 9.13.5. Interpolation by kriging 310 Appendix. The EZW Algorithm 313 A.1. Coding 313 A.1.1. Detailed description of the EZW algorithm (coding phase) 313 A.1.2. Example of application of the EZW algorithm (coding phase) 314 A.2. Decoding 317 A.2.1. Detailed description of the EZW algorithm (decoding phase) 317 A.2.2. Example of application of the EZW algorithm (decoding phase) 318 A.3. Visualization on a real image of the algorithm’s decoding phase 318 Bibliography 321 Index 329
£194.70
Springer Nature Switzerland AG Geometric Multiplication of Vectors: An
Book SynopsisThis book enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra? What if there existed a universal mathematical language that allowed one: to make rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their products, to solve problems of the special theory of relativity in three-dimensional Euclidean space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult problems of electromagnetism, to treat the Kepler problem with the formulas for a harmonic oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of mathematical physics? What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a language provided a clear, geometric interpretation of mathematical objects, even for the imaginary unit in quantum mechanics? Such a mathematical language exists and it is called geometric algebra. High school students have the potential to explore it, and undergraduate students can master it. The universality, the clear geometric interpretation, the power of generalizations to any dimension, the new insights into known theories, and the possibility of computer implementations make geometric algebra a thrilling field to unearth.Table of ContentsBasic Concepts.- Euclidean 3D Geometric Algebra.- Applications.- Geometric Algebra and Matrices.- Appendix.- Solutions for Some Problems.- Problems.- Why Geometric Algebra?.- Formulae.- Literature.- References.
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Springer Nature Switzerland AG Mathematical Foundations of Advanced Informatics: Volume 1: Inductive Approaches
Book SynopsisThe books in this trilogy capture the foundational core of advanced informatics. The authors make the foundations accessible, enabling students to become effective problem solvers.This first volume establishes the inductive approach as a fundamental principle for system and domain analysis. After a brief introduction to the elementary mathematical structures, such as sets, propositional logic, relations, and functions, the authors focus on the separation between syntax (representation) and semantics (meaning), and on the advantages of the consistent and persistent use of inductive definitions. They identify compositionality as a feature that not only acts as a foundation for algebraic proofs but also as a key for more general scalability of modeling and analysis. A core principle throughout is invariance, which the authors consider a key for the mastery of change, whether in the form of extensions, transformations, or abstractions.This textbook is suitable for undergraduate and graduate courses in computer science and for self-study. Most chapters contain exercises and the content has been class-tested over many years in various universities.Table of ContentsIntroduction.- Propositions and Sets.- Relations and Functions.- Inductive Definitions.- Inductive Proofs.- Inductive Approach: Potential, Limitations, and Pragmatics.
£27.99
