Numerical analysis Books

Book SynopsisThis book investigates in detail the emerging deep learning (DL) technique in computational physics, assessing its promising potential to substitute conventional numerical solvers for calculating the fields in real-time. After good training, the proposed architecture can resolve both the forward computing and the inverse retrieve problems.Pursuing a holistic perspective, the book includes the following areas. The first chapter discusses the basic DL frameworks. Then, the steady heat conduction problem is solved by the classical U-net in Chapter 2, involving both the passive and active cases. Afterwards, the sophisticated heat flux on a curved surface is reconstructed by the presented Conv-LSTM, exhibiting high accuracy and efficiency. Additionally, a physics-informed DL structure along with a nonlinear mapping module are employed to obtain the space/temperature/time-related thermal conductivity via the transient temperature in Chapter 4. Finally, in Chapter 5, a series of thTable of Contents1. Deep Learning Framework and Paradigm in Computational Physics 2. Application of U-net in 3D Steady Heat Conduction Solver 3. Inversion of complex surface heat flux based on ConvLSTM 4. Time-domain electromagnetic inverse scattering based on deep learning 5. Reconstruction of thermophysical parameters based on deep learning 6. Advanced Deep Learning Techniques in Computational Physics

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Book SynopsisThis book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing.The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.Table of ContentsSpace-time approximations for linear acoustic, elastic, and electro-magnetic wave equations.- Local wellposedness and long-time behavior of quasilinear Maxwell equations.- Error analysis of second-order time integration methods for discontinuous Galerkin discretizations of Friedrichs’ systems.- An abstract framework for inverse wave problems with applications.

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Book SynopsisThis book is a guide to numerical methods for solving fluid dynamics problems. The most widely used discretization and solution methods, which are also found in most commercial CFD-programs, are described in detail. Some advanced topics, like moving grids, simulation of turbulence, computation of free-surface flows, multigrid methods and parallel computing, are also covered. Since CFD is a very broad field, we provide fundamental methods and ideas, with some illustrative examples, upon which more advanced techniques are built. Numerical accuracy and estimation of errors are important aspects and are discussed in many examples. Computer codes that include many of the methods described in the book can be obtained online. This 4th edition includes major revision of all chapters; some new methods are described and references to more recent publications with new approaches are included. Former Chapter 7 on solution of the Navier-Stokes equations has been split into two Chapters to allow for a more detailed description of several variants of the Fractional Step Method and a comparison with SIMPLE-like approaches. In Chapters 7 to 13, most examples have been replaced or recomputed, and hints regarding practical applications are made. Several new sections have been added, to cover, e.g., immersed-boundary methods, overset grids methods, fluid-structure interaction and conjugate heat transfer.Table of ContentsBasic Concepts of Fluid Flow.- Introduction to Numerical Methods.- Finite Difference Methods.- Finite Volume Methods.- Solution of Linear Equation Systems.-Methods for Unsteady Problems.- Solution of the Navier-Stokes Equations.- Complex Geometries.- Turbulent Flows.- Compressible Flows.- Efficiency, Accuracy and Grid Quality.- Special Topics.

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Book SynopsisWhat sets Numerical Methods and Analysis with Mathematical Modelling apart are the modelling aspects utilizing numerical analysis (methods) to obtain solutions. The authors cover first the basic numerical analysis methods with simple examples to illustrate the techniques and discuss possible errors. The modelling prospective reveals the practical relevance of the numerical methods in context to real-world problems.At the core of this text are the real-world modelling projects. Chapters are introduced and techniques are discussed with common examples. A modelling scenario is introduced that will be solved with these techniques later in the chapter. Often, the modelling problems require more than one previously covered technique presented in the book.Fundamental exercises to practice the techniques are included. Multiple modelling scenarios per numerical methods illustrate the applications of the techniques introduced. Each chapter has several modelling

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Book SynopsisEste livro é uma introdução ao Cálculo Científico. O seu objectivo consiste em apresentar vários métodos numéricos para resolver no computador certos problemas matemáticos que não podem ser tratados de maneira mais simples. São abordadas questões clássicas como o cálculo de zeros ou de integrais de funções contínuas, a resolução de sistemas lineares, a aproximação de funções por polinómios e a construção de aproximações precisas de soluções de equações diferenciais. Todos os algoritmos são apresentados nas linguagens de programação MATLAB e Octave, cujos comandos e instruções principais se introduzem de forma gradual, visando em particular a sua compatibilidade nas duas linguagens. O leitor pode assim verificar experimentalmente propriedades teóricas como a estabilidade, a precisão e a complexidade. O livro inclui ainda a resolução de problemas através de numerosos exercícios e exemplos, frequentemente ligados a aplicações concretas. No fim de cada capítulo encontra-se uma secção específica que apresenta assuntos não abordados e as referências bibliográficas que permitem ao leitor aprofundar os conhecimentos adquiridos.Table of ContentsO que não se pode ignorar.- Equações não lineares.- Aproximação de funções e de dados.- Derivação e integração numéricas.- Sistemas lineares.- Valores próprios e vectores próprios.- Equações diferenciais ordinárias.- Métodos numéricos para problemas de valores iniciais e na fronteira.- Soluções dos exercícios.

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Book SynopsisThis book’s aim is to study the mathematical and computational models to analyze the progress, prognosis, prevention, and panacea of breast cancer. The book discusses application of Markov chains and transient mappings, Charlie–Simpson numerical algorithm, models represented by nonlinear reaction–diffusion-type partial differential equations, and related techniques. The book also attempts to design mathematical model of targeted strategic treatments by using Skilled Killer Drugs (SKD1 and SKD2) to suggest the improvisation of future cancer treatments. Both graduate students and researchers of computational biology and oncologists will benefit by studying this book. Researchers of cancer studies and biological sciences will also find this work helpful.Table of ContentsIntroduction.- Statistics: The Backgrounds & The Basis.- Attacker & Defender Model: The Dynamics of the Immune System.- Mathematical Modeling of Metastatic Cancer.- Mathematical/Computational Modeling of Advanced Immunotherapy.- Mathematical Modeling & Computational Studies On The War Against Breast Cancer.- Gene Therapy.- The Smartest Fighters.- Nutritional Therapy.- The Fateful Code & The Future Course.- Conclusion.

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Book SynopsisThis concise introduction covers inverse problems and data assimilation, before exploring their inter-relations. Suitable for both classroom teaching and self-guided study, it is aimed at advanced undergraduates and beginning graduate students in mathematical sciences, together with researchers in science and engineering.Table of ContentsIntroduction; Part I. Inverse Problems: 1. Bayesian inverse problems and well-posedness; 2. The linear-Gaussian setting; 3. Optimization perspective; 4. Gaussian approximation; 5. Monte Carlo sampling and importance sampling; 6. Markov chain Monte Carlo; Exercises for Part I; Part II. Data Assimilation: 7. Filtering and smoothing problems and well-posedness; 8. The Kalman filter and smoother; 9. Optimization for filtering and smoothing: 3DVAR and 4DVAR; 10. The extended and ensemble Kalman filters; 11. Particle filter; 12. Optimal particle filter; Exercises for Part II; Part III. Kalman Inversion: 13. Blending inverse problems and data assimilation; References; Index.

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Book SynopsisThis outrageous graphic novel investigates key concepts in mathematics by taking readers on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics within a thrilling murder mystery.Trade Review"Prime Suspects will appeal to a variety of readers in a variety of venues . . . . For the mathematician who eats, sleeps, and drinks numbers, start on page one and just enjoy the story . . . the book is fun, and interesting, and a challenge on many levels."---Judith Reveal, New York Journal of Books"Prime Suspects blends together the worlds of mathematics and forensic science to give readers both an interesting mystery and an education in numbers."---Anelise Farris, Rogues Portal"A total one-off."---Matthew Reisz, Times Educational Supplement"This is really a great book with so many references to mathematical ideas, that you can read and reread and find every time new details hidden in the graphics."---Adhemar Bultheel, European Mathematical Society"What a spectacular book! I am rather blown away by it."---Jonathan Shock, MathemAfrica"Granville and Granville have performed something of a feat. They've written a graphic detective novel that is both interesting to read and yet simultaneously teaches its readers some deep mathematics . . . . It's very difficult to write a book on an advanced topic in mathematics that's accessible to math students and enthusiasts yet touches on contemporary research that is of interest to a broad swath of practicing mathematicians. Prime Suspects is such a book. And it's entertaining to boot. I recommend it in the strongest terms."---Benjamin Linowitz, MAA Reviews"Bringing in elements from film noir, TV police shows and famous movies, coupled with some amazing art work, subtlemathematical humour and corny science jokes, and what you have is a one-of-a-kind creation – indeed, Prime Suspects has it all from minus to plus infinity."---David Appell, Physics World"Renowned number-theorist Andrew Granville here explores the graphic novel as a format to popularize mathematical discoveries. This absolutely brilliantly illustrated book arose from an earlier play and an accompanying commissioned musical piece. The mathematics too is astonishing—but explained understandably." * Mathematics Magazine *"If you are a mathematician, I definitely recommend reading (and listening to) Prime Suspects. If you are not a mathematician, you might miss a number of references, and some passages might be too mysterious or technical, but still it makes for interesting reading; it might be good for you, too."---Marco Abate, The Mathematical Intelligencer"The artwork and presentation are both well up to the standard of a mainstream graphic novel."---Andrew Ruddle, Mathematics Today"Prime Suspects is a work of art which anyone with a passion for maths will appreciate and enjoy."---Lennie Wells, Mathematical Gazette"I definitely recommend."---Marco Abate, Mathematical Intelligencer

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Book SynopsisLearning Data Science is the first book to cover foundational skills in both programming and statistics that encompass the entire data science lifecycle: the process of collecting, wrangling, analyzing, and drawing conclusions from data.

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Book SynopsisThis book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author’s lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter “Notch Signaling in Embryology and Cancer”, published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.Table of Contents1. Preparation.- 2. Introduction to MATLAB programming .- 3. Simulating time variations in life phenomena.- 4. Simulating temporal and spatial changes in biological phenomena.

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Book SynopsisThis is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties. They were introduced by the authors in 1996 and have been used in many diverse applications. The regression basis makes it straightforward to handle non-normal data, like in generalized linear models. The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R. Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data. Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints. Combining penalties with tensor products of B-splines extends theseTrade Review'The title says it all. This is a practical book which shows how P-splines are used in an astonishingly wide range of settings. If you use P-splines already the book is indispensable; if you don't, then reading it will convince you it's time to start. Every example comes with an R-program available on the book's web-site, an important feature for the experienced user and novice alike.' Iain Currie, Heriot-Watt University'This book is an enlightening and at the same time extremely enjoyable read. It will serve the applied statistician who is looking for practical solutions but also the connoisseur in search of elegant concepts. The accompanying website offers reproducible code and invites to promptly enter the fascinating universe of P-splines.' Jutta Gampe, Max Planck Institute for Demographic Research'Everything you always wanted to know about P-splines, from the inventors themselves. Paul H.C. Eilers and Brian D. Marx make a compelling case for their claim that P-splines are the best practical smoother out there, providing intuition, methodology, applications, and R code that clearly demonstrate the power, flexibility, and wide applicability of this approach to smoothing.' Jeffrey Simonoff, New York University'This is the book that everyone working on smoothing models should keep handy. At last we have a manuscript that shows the real power of P-splines, their versatility, and the different perspectives you can take to use them. Chapters 1 to 3 will certainly appeal to those who want to start working in this field, and to researchers that need to deepen their knowledge of this technique. Scientists and practitioners from other areas will find chapters 4 to 8 very useful for the wide range of examples and applications. The companion package and the fact that all results (even figures) are reproducible is a real bonus. Thank you Paul and Brian for being truthful to your motto: 'show, don't tell'.' Maria Durbán, University Carlos III de MadridTable of Contents1. Introduction; 2. Bases, penalties, and likelihoods; 3. Optimal smoothing in action; 4. Multidimensional smoothing; 5. Smoothing of scale and shape; 6. Complex counts and composite links; 7. Signal regression; 8. Special subjects; A. P-splines for the impatient; B. P-splines and competitors; C. Computational details; D. Array algorithms; E. Mixed model equations; F. Standard errors in detail; G. The website.

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Book SynopsisHaskell is a purely functional language that allows programmers to rapidly develop clear, concise, and correct software. The language has grown in popularity in recent years, both in teaching and in industry. This book is based on the author''s experience of teaching Haskell for more than twenty years. All concepts are explained from first principles and no programming experience is required, making this book accessible to a broad spectrum of readers. While Part I focuses on basic concepts, Part II introduces the reader to more advanced topics. This new edition has been extensively updated and expanded to include recent and more advanced features of Haskell, new examples and exercises, selected solutions, and freely downloadable lecture slides and example code. The presentation is clean and simple, while also being fully compliant with the latest version of the language, including recent changes concerning applicative, monadic, foldable, and traversable types.Trade Review'The skills you acquire by studying this book will make you a much better programmer no matter what language you use to actually program in.' Erik Meijer, Facebook, from the ForewordReview of previous edition: 'The best introduction to Haskell available. There are many paths towards becoming comfortable and competent with the language but I think studying this book is the quickest path. I urge readers of this magazine to recommend Programming in Haskell to anyone who has been thinking about learning the language.' Duncan Coutts, The Monad.ReaderReview of previous edition: 'Where this book excels is in the order and style of its exposition … With its ripe selection of examples and its careful clarity of exposition, the book is a welcome addition to the introductory functional programming literature.' Journal of Functional ProgrammingTable of ContentsForeword; Preface; Part I. Basic Concepts: 1. Introduction; 2. First steps; 3. Types and classes; 4. Defining functions; 5. List comprehensions; 6. Recursive functions; 7. Higher-order functions; 8. Declaring types and classes; 9. The countdown problem; Part II. Going Further: 10. Interactive programming; 11. Unbeatable tic-tac-toe; 12. Monads and more; 13. Monadic parsing; 14. Foldables and friends; 15. Lazy evaluation; 16. Reasoning about programs; 17. Calculating compilers; Appendix A. Selected solutions; Appendix B. Standard prelude; Bibliography; Index.

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Book SynopsisProvides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.Table of ContentsMetric Spaces.Normed Spaces;Banach Spaces.Inner Product Spaces;Hilbert Spaces.Fundamental Theorems for Normed and Banach Spaces.Further Applications: Banach Fixed Point Theorem.Spectral Theory of Linear Operators in Normed Spaces.Compact Linear Operators on Normed Spaces and Their Spectrum.Spectral Theory of Bounded Self-Adjoint Linear Operators.Unbounded Linear Operators in Hilbert Space.Unbounded Linear Operators in Quantum Mechanics.Appendices.References.Index.

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Book SynopsisThis book addresses the state of the art of reduced order methods for modelling and computational reduction of complex parametrised systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in various fields.Consisting of four contributions presented at the CIME summer school, the book presents several points of view and techniques to solve demanding problems of increasing complexity. The focus is on theoretical investigation and applicative algorithm development for reduction in the complexity – the dimension, the degrees of freedom, the data – arising in these models.The book is addressed to graduate students, young researchers and people interested in the field. It is a good companion for graduate/doctoral classes.Table of Contents- 1. The Reduced Basis Method in Space and Time: Challenges, Limits and Perspectives. - 2. Inverse Problems: A Deterministic Approach Using Physics-Based Reduced Models. - 3. Model Order Reduction for Optimal Control Problems. - 4. Machine Learning Methods for Reduced Order Modeling.

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Book SynopsisCombining scientific computing methods and algorithms with modern data analysis techniques, including basic applications of compressive sensing and machine learning, this book develops techniques that allow for the integration of the dynamics of complex systems and big data. MATLAB is used throughout for mathematical solution strategies.Trade ReviewThe book allows methods for dealing with large data to be explained in a logical process suitable for both undergraduate and post-graduate students ... With sport performance analysis evolving into deal with big data, the book forms a key bridge between mathematics and sport science * John Francis, University of Worcester *Table of ContentsI BASIC COMPUTATIONS AND VISUALIZATION; II DIFFERENTIAL AND PARTIAL DIFFERENTIAL EQUATIONS; III COMPUTATIONAL METHODS FOR DATA ANALYSIS; IV SCIENTIFIC APPLICATIONS

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Book SynopsisDeveloped from the authorâs course on advanced mechanics of composite materials, Finite Element Analysis of Composite Materials with Abaqus shows how powerful finite element tools tackle practical problems in the structural analysis of composites. This Second Edition includes two new chapters on Fatigue and Abaqus Programmable Features as well as a major update of chapter 10 Delaminations and significant updates throughout the remaining chapters. Furthermore, it updates all examples, sample code, and problems to Abaqus 2020. Unlike other texts, this one takes theory to a hands-on level by actually solving problems. It explains the concepts involved in the detailed analysis of composites, the mechanics needed to translate those concepts into a mathematical representation of the physical reality, and the solution of the resulting boundary value problems using Abaqus. The reader can follow a process to recreate every example using Abaqus graphical user interfacTable of Contents1. Mechanics of Orthotropic Materials. 2. Introduction to Finite Element Analysis. 3. Elasticity and Strength of Laminates. 4. Buckling. 5. Free Edge Stresses. 6. Computational Micromechanics. 7. Viscoelasticity. 8. Continuum Damage Mechanics. 9. Discrete Damage Mechanics. 10. Delaminations. 11. Fatigue. 12. Abaqus Programmable Features.

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Book Synopsis* Novel approach to the mathematics of problem solving, in particular how to do logical calculations. * Many of the problems are well-known from (mathematical) puzzle books. * The solution method in the book is new and more relevant to the true nature of problem solving in the modern IT-dominated world.Table of ContentsPreface xi PART I Algorithmic Problem Solving 1 CHAPTER 1 – Introduction 3 1.1 Algorithms 3 1.2 Algorithmic Problem Solving 4 1.3 Overview 5 1.4 Bibliographic Remarks 6 CHAPTER 2 – Invariants 7 2.1 Chocolate Bars 10 2.1.1 The Solution 10 2.1.2 The Mathematical Solution 11 2.2 Empty Boxes 16 2.2.1 Review 19 2.3 The Tumbler Problem 22 2.3.1 Non-deterministic Choice 23 2.4 Tetrominoes 24 2.5 Summary 30 2.6 Bibliographic Remarks 34 CHAPTER 3 – Crossing a River 35 3.1 Problems 36 3.2 Brute Force 37 3.2.1 Goat, Cabbage and Wolf 37 3.2.2 State-Space Explosion 39 3.2.3 Abstraction 41 3.3 Nervous Couples 42 3.3.1 What Is the Problem? 42 3.3.2 Problem Structure 43 3.3.3 Denoting States and Transitions 44 3.3.4 Problem Decomposition 45 3.3.5 A Review 48 3.4 Rule of Sequential Composition 50 3.5 The Bridge Problem 54 3.6 Conditional Statements 63 3.7 Summary 65 3.8 Bibliographic Remarks 65 CHAPTER 4 – Games 67 4.1 Matchstick Games 67 4.2 Winning Strategies 69 4.2.1 Assumptions 69 4.2.2 Labelling Positions 70 4.2.3 Formulating Requirements 72 4.3 Subtraction-Set Games 74 4.4 Sums of Games 78 4.4.1 A Simple Sum Game 79 4.4.2 Maintain Symmetry! 81 4.4.3 More Simple Sums 82 4.4.4 Evaluating Positions 83 4.4.5 Using the Mex Function 87 4.5 Summary 91 4.6 Bibliographic Remarks 92 CHAPTER 5 – Knights and Knaves 95 5.1 Logic Puzzles 95 5.2 Calculational Logic 96 5.2.1 Propositions 96 5.2.2 Knights and Knaves 97 5.2.3 Boolean Equality 98 5.2.4 Hidden Treasures 100 5.2.5 Equals for Equals 101 5.3 Equivalence and Continued Equalities 102 5.3.1 Examples of the Associativity of Equivalence 104 5.3.2 On Natural Language 105 5.4 Negation 106 5.4.1 Contraposition 109 5.4.2 Handshake Problems 112 5.4.3 Inequivalence 113 5.5 Summary 117 5.6 Bibliographic Remarks 117 CHAPTER 6 – Induction 119 6.1 Example Problems 120 6.2 Cutting the Plane 123 6.3 Triominoes 126 6.4 Looking for Patterns 128 6.5 The Need for Proof 129 6.6 From Verification to Construction 130 6.7 Summary 134 6.8 Bibliographic Remarks 134 CHAPTER 7 – Fake-Coin Detection 137 7.1 Problem Formulation 137 7.2 Problem Solution 139 7.2.1 The Basis 139 7.2.2 Induction Step 139 7.2.3 The Marked-Coin Problem 140 7.2.4 The Complete Solution 141 7.3 Summary 146 7.4 Bibliographic Remarks 146 CHAPTER 8 – The Tower of Hanoi 147 8.1 Specification and Solution 147 8.1.1 The End of the World! 147 8.1.2 Iterative Solution 148 8.1.3 Why? 149 8.2 Inductive Solution 149 8.3 The Iterative Solution 153 8.4 Summary 156 8.5 Bibliographic Remarks 156 CHAPTER 9 – Principles of Algorithm Design 157 9.1 Iteration, Invariants and Making Progress 158 9.2 A Simple Sorting Problem 160 9.3 Binary Search 163 9.4 Sam Loyd’s Chicken-Chasing Problem 166 9.4.1 Cornering the Prey 170 9.4.2 Catching the Prey 174 9.4.3 Optimality 176 9.5 Projects 177 9.6 Summary 178 9.7 Bibliographic Remarks 180 CHAPTER 10 – The Bridge Problem 183 10.1 Lower and Upper Bounds 183 10.2 Outline Strategy 185 10.3 Regular Sequences 187 10.4 Sequencing Forward Trips 189 10.5 Choosing Settlers and Nomads 193 10.6 The Algorithm 196 10.7 Summary 199 10.8 Bibliographic Remarks 200 CHAPTER 11 – Knight’s Circuit 201 11.1 Straight-Move Circuits 202 11.2 Supersquares 206 11.3 Partitioning the Board 209 11.4 Summary 216 11.5 Bibliographic Remarks 218 PART II Mathematical Techniques 219 CHAPTER 12 – The Language of Mathematics 221 12.1 Variables, Expressions and Laws 222 12.2 Sets 224 12.2.1 The Membership Relation 224 12.2.2 The Empty Set 224 12.2.3 Types/Universes 224 12.2.4 Union and Intersection 225 12.2.5 Set Comprehension 225 12.2.6 Bags 227 12.3 Functions 227 12.3.1 Function Application 228 12.3.2 Binary Operators 230 12.3.3 Operator Precedence 230 12.4 Types and Type Checking 232 12.4.1 Cartesian Product and Disjoint Sum 233 12.4.2 Function Types 235 12.5 Algebraic Properties 236 12.5.1 Symmetry 237 12.5.2 Zero and Unit 238 12.5.3 Idempotence 239 12.5.4 Associativity 240 12.5.5 Distributivity/Factorisation 241 12.5.6 Algebras 243 12.6 Boolean Operators 244 12.7 Binary Relations 246 12.7.1 Reflexivity 247 12.7.2 Symmetry 248 12.7.3 Converse 249 12.7.4 Transitivity 249 12.7.5 Anti-symmetry 251 12.7.6 Orderings 252 12.7.7 Equality 255 12.7.8 Equivalence Relations 256 12.8 Calculations 257 12.8.1 Steps in a Calculation 259 12.8.2 Relations between Steps 260 12.8.3 ‘‘If’’ and ‘‘Only If’’ 262 12.9 Exercises 264 CHAPTER 13 – Boolean Algebra 267 13.1 Boolean Equality 267 13.2 Negation 269 13.3 Disjunction 270 13.4 Conjunction 271 13.5 Implication 274 13.5.1 Definitions and Basic Properties 275 13.5.2 Replacement Rules 276 13.6 Set Calculus 279 13.7 Exercises 281 CHAPTER 14 – Quantifiers 285 14.1 DotDotDot and Sigmas 285 14.2 Introducing Quantifier Notation 286 14.2.1 Summation 287 14.2.2 Free and Bound Variables 289 14.2.3 Properties of Summation 291 14.2.4 Warning 297 14.3 Universal and Existential Quantification 297 14.3.1 Universal Quantification 298 14.3.2 Existential Quantification 300 14.4 Quantifier Rules 301 14.4.1 The Notation 302 14.4.2 Free and Bound Variables 303 14.4.3 Dummies 303 14.4.4 Range Part 303 14.4.5 Trading 304 14.4.6 Term Part 304 14.4.7 Distributivity Properties 304 14.5 Exercises 306 CHAPTER 15 – Elements of Number Theory 309 15.1 Inequalities 309 15.2 Minimum and Maximum 312 15.3 The Divides Relation 315 15.4 Modular Arithmetic 316 15.4.1 Integer Division 316 15.4.2 Remainders and Modulo Arithmetic 320 15.5 Exercises 322 CHAPTER 16 – Relations, Graphs and Path Algebras 325 16.1 Paths in a Directed Graph 325 16.2 Graphs and Relations 328 16.2.1 Relation Composition 330 16.2.2 Union of Relations 332 16.2.3 Transitive Closure 334 16.2.4 Reflexive Transitive Closure 338 16.3 Functional and Total Relations 339 16.4 Path-Finding Problems 341 16.4.1 Counting Paths 341 16.4.2 Frequencies 343 16.4.3 Shortest Distances 344 16.4.4 All Paths 345 16.4.5 Semirings and Operations on Graphs 347 16.5 Matrices 351 16.6 Closure Operators 353 16.7 Acyclic Graphs 354 16.7.1 Topological Ordering 355 16.8 Combinatorics 357 16.8.1 Basic Laws 358 16.8.2 Counting Choices 359 16.8.3 Counting Paths 361 16.9 Exercises 366 Solutions to Exercises 369 References 405 Index 407

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Book SynopsisThis book provides an extensive introduction to the numerical solution of a large class of integral equations. The initial chapters provide a general framework for the numerical analysis of Fredholm integral equations of the second kind, covering degenerate kernel, projection and Nystrom methods. Additional discussions of multivariable integral equations and iteration methods update the reader on the present state of the art in this area. The final chapters focus on the numerical solution of boundary integral equation (BIE) reformulations of Laplace's equation, in both two and three dimensions. Two chapters are devoted to planar BIE problems, which include both existing methods and remaining questions. Practical problems for BIE such as the set up and solution of the discretised BIE are also discussed. Each chapter concludes with a discussion of the literature and a large bibliography serves as an extended resource for students and researchers needing more information on solving particTrade Review' This outstanding monograph ... represents a major milestone in the list of books on the numerical solution of integral equations ... deserves to be on the shelf of any researcher and graduate student interested in the numerical solution of elliptic boundary-value problems.' H. Brunner, Mathematics Abstracts 'It will become the standard reference in the area.' Zietschrift fur Angwandte Mathematik und PhysikTable of ContentsPreface; 1. A brief discussion of integral equations; 2. Degenerate kernel methods; 3. Projection methods; 4. The Nystrom method; 5. Solving multivariable integral equations; 6. Iteration methods; 7. Boundary integral equations on a smooth planar boundary; 8. Boundary integral equations on a piecewise smooth planar boundary; 9. Boundary integral equations in three dimensions; Discussion of the literature; Appendix; Bibliography; Index.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThe book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The motivation for these topics is the difficulty, both conceptually and in the technical execution, of combining elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains breakthrough solutions to meshing that fit into this category. This book emphasizes topics that are elementary, attractive, useful, interesting, and lend themselves to teaching, making it an ideal graduate text for courses on mesh generation.Trade Review'… a very readable exposition …'. Monatshefte für Mathematik'… well organised … We recommend the book to graduate students and researchers in computational geometry.' János Kincses, Acta Sci. Math.Table of Contents1. Delaunay triangulations; 2. Triangle meshes; 3. Combinatorial topology; 4. Surface simplification; 5. Delaunay tetrahedrizations; 6. Tetrahedron meshes; 7. Open problems.

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Book SynopsisWritten in easy to understand language, this self-explanatory guide introduces the fundamentals of finite element methods and its application to differential equations. Beginning with a brief introduction to Sobolev spaces and elliptic scalar problems, the text progresses through an explanation of finite element spaces and estimates for the interpolation error. The concepts of finite element methods for parabolic scalar parabolic problems, object-oriented finite element algorithms, efficient implementation techniques, and high dimensional parabolic problems are presented in different chapters. Recent advances in finite element methods, including non-conforming finite elements for boundary value problems of higher order and approaches for solving differential equations in high dimensional domains are explained for the benefit of the reader. Numerous solved examples and mathematical theorems are interspersed throughout the text for enhanced learning.Trade Review'The book is written in a very traditional and straightforward style of theory and proof. The organization of the material makes it accessible for the reader to gain a foundational understanding of the topics … This book provides a readable, concise introduction to finite elements. Summing Up: Recommended.' S. L. Sullivan, CHOICETable of ContentsPreface; 1. Sobolev spaces; 1.1. Banach and Hilbert spaces; 1.2. Weak derivatives; 1.3. Sobolev spaces; 2. Elliptic scalar problems; 2.1. A general elliptic problem of second order; 2.2. Weak solution; 2.3. Standard Galerkin method; 2.4. Abstract error estimate; 3. Finite element spaces; 3.1. Simplices and barycentric coordinates; 3.2. Simplicial finite elements and local spaces; 3.3. Construction of finite elements spaces; 3.4. The concept of mapped finite elements: affine mappings; 3.5. Finite elements on rectangular and brick meshes; 3.6. Mapped finite elements: general bijective mappings; 3.7. Mapped Qk finite elements; 3.8. Isoparametric finite elements; 3.9. Further examples of finite elements in C0 and C1; 4. Interpolation and discretization error; 4.1. Transformation formulas; 4.2. Affine equivalent finite elements; 4.3. Canonical interpolation; 4.4. Local and global interpolation error; 4.5. Improved L2 error estimates by duality; 4.6. Interpolation of less smooth functions; 5. Biharmonic equation; 5.1. Deflection of a thin clamped plate; 5.2. Weak formulation of the biharmonic equation; 5.3. Conforming finite element methods; 5.4. Nonconforming finite element methods; 6. Parabolic problems; 6.1. Conservation of energy; 6.2. A general parabolic problem of initial boundary value problems; 6.3. Weak formulation of initial boundary value problems; 6.4. Semidiscretization by finite elements; 6.5. Time discretization; 6.6. Finite elements for high-dimensional parabolic problems; 7. Systems in solid mechanics; 7.1. Linear elasticity; 7.2. Mindlin–Reissner plate; 8. Systems in fluid mechanics; 8.1. Conservation of mass and momentum; 8.2. Weak formulation of the Stokes problem; 8.3. Conforming discretizations of the Stokes problem; 8.4. Nonconforming discretizations of the Stokes problem; 8.5. The nonconforming Crouzeix–Raviart element; 8.6. Further inf–sup stable finite element pairs; 8.7. Equal order stabilized finite elements; 8.8. Navier–Stokes problem with mixed boundary conditions; 8.9. Time discretization and linearization of the Navier–Stokes problem; 9. Implementation of the finite element method; 9.1. Mesh handling and data structure; 9.2. Numerical integration; 9.3. Sparse matrix storage; 9.4. Assembling of system matrices and load vectors; 9.5. Inclusion of boundary conditions; 9.6. Solution of the algebraic systems; 9.7. Object-oriented C++ programming; Bibliography; Index.

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Book SynopsisDynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks.This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

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Book SynopsisThis book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications. The approach is novel, and the book can be used in undergraduate courses, for example, following a first course in linear algebra, but is also suitable for use in graduate level courses. The book will benefit anyone with a basic background in linear algebra. It defines fundamental concepts in signal processing and wavelet theory, assuming only a familiarity with elementary linear algebra. No background in signal processing is needed. Additionally, the book demonstrates in detail why linear algebra is often the best way to go. Those with only a signal processing background are also introduced to the world of linear algebra, although a full course is recommended. The book comes in two versions: one based on MATLAB, and one on Python, demonstrating the feasibility and applications of both approaches. Most of the MATLAB code is available interactively. The applications mainly involve sound and images. The book also includes a rich set of exercises, many of which are of a computational nature.Trade Review“A beginning student who is unfamiliar with the mathematics behind signal processing will find much here that explains the techniques and the issues associated with their use. Altogether the book presents a beautiful introduction to the uses of linear algebra in signal processing.” (MAA Reviews, July 18, 2020)“This book is a very useful textbook for undergraduate students in applied mathematics and engineering disciplines, but it is also suitable for graduate level courses.” (Manfred Tasche, zbMATH 1420.65001, 2019)Table of Contents1. Sound and Fourier series.- 2. Digital Sound and Discrete Fourier Analysis.- 3. Discrete Time Filters.- 4. Motivation for Wavelets and Some Simple Examples.- 5. The Filter Representation of Wavelets.- 6. Constructing Interesting Wavelets.- 7. The Polyphase Representation of Filter Bank Transforms.- 8. Digital Images.- 9. Using Tensor Products to Apply Wavelets to Images.- A Basic Linear Algebra.

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Book SynopsisThis volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text.Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful. Trade Review“The book can be of special interest to mathematicians, STEM students, and engineers working in multidisciplinary industry settings where the insight provided by differential-algebraic equations can be determinant in decision making.” (Andrzej Sokolowski, MAA Reviews, August 11, 2019)Table of ContentsGeneral Nonlinear Differential Algebraic Equations and Tracking Problems: A Robotics Example.- DAE Aspects in Vehicle Dynamics and Mobile Robotics.- Open-loop Control of Underactuated Mechanical Systems Using Servo-constraints: Analysis and Some Examples.- Systems of Differential Algebraic Equations in Computational Electromagnetics.- Gas Network Benchmark Models.- Topological Index Analysis Applied to Coupled Flow Networks.- Nonsmooth DAEs with Applications in Modeling Phase Changes.- Continuous, Semi-Discrete, and Fully Discretized Navier-Stokes Equations.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis book constitutes the proceedings of the 18th International Conference on Unconventional Computation and Natural Computation, UCNC 2019, held in Tokyo, Japan, in June 2019.The 19 full papers presented were carefully reviewed and selected from 32 submissions. The papers cover topics such as hypercomputation; chaos and dynamical systems based computing; granular, fuzzy and rough computing; mechanical computing; cellular, evolutionary, molecular, neural, and quantum computing; membrane computing; amorphous computing, swarm intelligence; artificial immune systems; physics of computation; chemical computation; evolving hardware; the computational nature of self-assembly, developmental processes, bacterial communication, and brain processes.Table of ContentsInvited Paper.- Co-designing the computational model and the computing substrate.- Contributed Papers.- Generalized Membrane Systems with Dynamical Structure, Petri Nets, and Multiset Approximation Spaces.- Quantum Dual Adversary for Hidden Subgroups and Beyond.- Further Properties of Self-assembly by Hairpin Formation.- The Role of Structure and Complexity on Reservoir Computing Quality.- Lindenmayer Systems and Global Transformations.- Swarm-based multiset rewriting computing models.- DNA Origami Words and Rewriting Systems.- Computational Limitations of Affine Automata.- An Exponentially Growing Nubot System Without State Changes.- Impossibility of Sufficiently Simple Chemical Reaction Network Implementations in DNA Strand Displacement.- Quantum Algorithm for Dynamic Programming Approach for DAGs. Applications for Zhegalkin Polynomial Evaluation and Some Problems on DAGs.- Viewing rate-based neurons as biophysical conductance outputting models.- The Lyapunov Exponents of Reversible Cellular Automata Are Uncomputable.- Geometric Tiles and Powers and Limitations of Geometric Hindrance in Self-Assembly.- DNA Computing Units Based on Fractional Coding.- The role of the representational entity in physical computing.- OIM: Oscillator-based Ising Machines for Solving Combinatorial Optimisation Problems.- Relativizations of Nonuniform Quantum Finite Automata Families.- Self-stabilizing Gellular Automata.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2019. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance.The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.Table of ContentsPart 1, Physics.- Part 2, Solid State Physics.- Part 3, Chemistry.- Part 4, Material Science.- Part 5, Reactive Flows.- Part 6, Computational Fluid Dynamics.- Part 7, Transport and Climate.- Part 8, Computer Science.- Part 9, Miscellaneous Topics.

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Book SynopsisThis book presents the state of the art in High Performance Computing on modern supercomputer architectures. It addresses trends in hardware and software development in general. The contributions cover a broad range of topics, from performance evaluations in context with power efficiency to Computational Fluid Dynamics and High Performance Data Analytics. In addition, they explore new topics like the use of High Performance Computers in the field of Artificial Intelligence and Machine Learning. All contributions are based on selected papers presented at the 30th Workshop on Sustained Simulation Performance (WSSP) held at the High Performance Computing Center, University of Stuttgart, Germany in October 2019 and on the papers for the planned Workshop on Sustained Simulation Performance in March 2020, which could not take place due to the Covid-19 pandemic.Table of ContentsPerformance and Power.- Numeric and Optimization.- Data Handling and New Concepts.- Trends in HPC and AI.

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Book SynopsisThis graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number of exercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization. Table of ContentsIntroduction.- Matrix analysis and differentiation.- Matrix manifolds in MDA.- Principal component analysis (PCA).- Factor analysis (FA).- Procrustes analysis (PA).- Linear discriminant analysis (LDA).- Canonical correlation analysis (CCA).- Common principal components (CPC).- Metric multidimensional scaling (MDS) and related methods.- Data analysis on simplexes.

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Book SynopsisThis book constitutes the proceedings of the 4th Iberoamerican Conference and third Indo-American Conference on Knowledge Graphs and Semantic Web, KGSWC 2022, which took place in Madrid, Spain, in November 2022.The 22 full and 3 short research papers presented in this volume were carefully reviewed and selected from 63 submissions. The papers cover topics related to software and its engineering, software creation and management, Emerging technologies, Analysis and design of emerging devices and systems, Emerging tools and methodologies and others.Table of ContentsDBkWik++ - Multi Source Matching of Knowledge Graphs.- A Survey on Knowledge Graph-based Methods for Automated Driving.- Physicians’ Brain Digital Twin: Holistic Clinical & Biomedical Knowledge Graphs for Patient Safety and Value-Based Care to Prevent The Post-pandemic Healthcare Ecosystem Crisis.- Combining Ontology and Natural Language Processing methods for Prevention of Falls from Height.- Learning to Automatically Generating Genre-Specific Song Lyrics: A Comparative Study.- DLIME-Graphs: A DLIME Extension based on Triple Embedding for Graphs.- Edge-labelled graphs and property graphs - to the user, more similar than different.- Knowledge Graph supported machine parameterization for the injection moulding industry.- IPR: Integrative Policy Recommendation Framework based on Hybrid Semantics.- Convolutional Neural Networks applied to emotion analysis in texts: Experimentation from the Mexican context.- Proficient Annotation Recommendation in a Biomedical Content Authoring Environment.- DKMI: Diversification of Web Image Search using Knowledge Centric Machine Intelligence.- Does Wikidata Support Analogical Reasoning?.- Flexible Queries over Knowledge Graphs.- Knowledge Graphs for Community Detection in Textual Data.- Framework for Author Name Disambiguation in Scientific Papers Using an Ontological Approach and Deep Learning.- On contrasting and completing YAGO with GPT language models: an experiment for person-related attributes.- Easy and complex: new perspectives for metadata modeling using RDF-star and Named Graphs.- Multi-Aspect Sentiment Analysis using Domain Ontologies.- Popularity Driven Data Integration.- Methodology for Creating a Community Corpus using a Wikibase Knowledge Graph.- Understanding Human Activity Patterns in Smart Homes with Process Mining.- String Matching based Framework for Online Hindi Question Answering System.- Towards an ontological approach to business continuity assessment.- From Ontology to Knowledge Graph Trend: Ontology As Foundation Layer For Knowledge Graph.

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Book SynopsisThis book constitutes the refereed proceedings of the 5th International Conference on Optimization and Learning, OLA 2022, which took place in Syracuse, Sicilia, Italy, in July 2022. The 19 full papers presented in this volume were carefully reviewed and selected from 52 submissions. The papers are organized in the following topical sections: Optimization and Learning; Novel Optimization Techniques; Logistics; and Applications.Table of ContentsOptimization and Learning.- Evolutionary-Based Co-Optimization of DNN and Hardware Configurations on Edge GPU.- Maximum Information Coverage and Monitoring Path Planning With Unmanned Surface Vehicles Using Deep Reinforcement Learning.- Tuning ForestDisc hyperparameters: A sensitivity analysis.- Multi-objective hyperparameter optimization with performance uncertainty.- Novel Optimization Techniques.- A new algorithm for bi-objective problems based on gradient information.- Adaptive Continuous Multi-Objective Optimization using Cooperative Agents.- Integer Linear Programming reformulations for the linear ordering problem.- SHAMan: a versatile auto-tuning framework for costly and noisy HPC systems.- Cooperation-based search of global optima.- Date-driven Simulation-Optimization (DSO): An Efficient Approach to Optimize Simulation Models with Databases.- Logistics.- Sweep Algorithms for the Vehicle Routing Problem with TimeWindows.- Improving the accuracy of vehicle routing problem approximation using the formula for the average distance between a point and a rectangular area.- Optimal Delivery Area Assignment for the Capital Vehicle Routing Problem Based on a Maximum Likelihood Approach.- Neural Order-First Split-Second Algorithm for the Capacitated Vehicle Routing Problem.- Applications.- GRASP-based hybrid search to solve the multi-objective requirements selection problem.- Comparing Parallel Surrogate-based and Surrogate-free Multi-Objective Optimization of COVID-19 vaccines allocation.- Decentralizing and Optimizing Nation-Wide Employee Allocation while Simultaneously Maximizing Employee Satisfaction.- Categorical-Continuous Bayesian optimization applied to chemical reactions.- Assessing Similarity-Based Grammar-Guided Genetic Programming Approaches for Program Synthesis.

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Book SynopsisThis book constitutes the conference proceedings of the 48th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2023, held in Nový Smokovec, Slovakia, during January 15–18, 2023.The 22 full papers presented together with 2 best papers and 2 best students papers in this book were carefully reviewed and selected from 43 submissions.This workshop focuses on graphs problems and optimization; graph drawing and visualization; NP-hardness and fixed parameter tractability; communication and temporal graphs; complexity and learning; and robots and strings. Table of ContentsThe Complexity of Finding Tangles.- A spectral algorithm for finding maximum cliques in dense random intersection graphs.- Solving Cut-Problems in Quadratic Time for Graphs With Bounded Treewidth.- More Effort Towards Multiagent Knapsack.- Dominance Drawings for DAGs with Bounded Modular Width.- Morphing Planar Graph Drawings Through 3D.- Visualizing Multispecies Coalescent Trees: Drawing Gene Trees Inside Species Trees.- Parameterized Approaches to Orthogonal Compaction.- Hardness of bounding influence via graph modification.- On the Parameterized Complexity of $s$-club Cluster Deletion Problems.- Balanced Substructures in Bicolored Graphs.- On the Complexity of Scheduling Problems With a Fixed Number of Parallel Identical Machines.- On the 2-Layer Window Width Minimization Problem.- Sequentially Swapping Tokens: Further on Graph Classes.- On the Preservation of Properties when Changing Communication Models.- Introduction to Routing Problems with Mandatory Transitions .- Multi-Parameter Analysis of Finding Minors and Subgraphs in Edge-Periodic Temporal Graphs.- Lower Bounds for Monotone $q$-Multilinear Boolean Circuits.- A faster algorithm for determining the linear feasibility of systems of BTVPI constraints.- Quantum complexity for vector domination problem.- Learning through Imitation by using Formal Verification.- Delivery to Safety with Two Cooperating Robots.- Space-Efficient STR-IC-LCS Computation.- The k-center Problem for Classes of Cyclic Words.

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Book SynopsisThis book constitutes the refereed proceedings of the 21st International Workshop, IWDW 2022, held in Guilin, China, during November 18-19, 2022. The 14 full papers included in this book were carefully reviewed and selected from 30 submissions. They were organized in topical sections as follows: Steganology, Forensics and Security Analysis, Watermarking.Table of ContentsSteganology.- High-Performance Steganographic Coding Based on Sub-Polarized Channel.- High-Capacity Adaptive Steganography Based on Transform Coefficient for HEVC.- Forensics and Security Analysis.- SE-ResNet56: Robust Network Model for Deepfake Detection.- Voice Conversion Using Learnable Similarity-Guided Masked Autoencoder.- Visual Explanations for Exposing Potential Inconsistency of Deepfakes.- Improving the Transferability of Adversarial Attacks through Both Front and Rear Vector Method.- Manipulated Face Detection and Localization Based on Semantic Segmentation.- Deep Learning Image Age Approximation - What is more Relevant: Image Content or Age Information?.- Watermarking.- Physical Anti-Copying Semi-Robust Random Watermarking for QR Code.- Robust and Imperceptible Watermarking Scheme for GWAS Data Traceability.- Adaptive Robust Watermarking Method Based on Deep Neural Networks.- Adaptive Despread Spectrum-Based Image Watermarking for Fast Product Tracking.- Reversible Data Hiding via Arranging Blocks of Bit-Planes in Encrypted Images.- High Capacity Reversible Data Hiding for Encrypted 3D Mesh Models Based on Topology.

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Book SynopsisThis book constitutes the refereed proceedings of the 14th International Conference on Metaheuristics, MIC 2022, held in Syracuse, Italy, in July 2022.The 48 full papers together with 17 short papers presented were carefully reviewed and selected from 72 submissions. The papers detail metaheuristic techniques.Chapter “Evaluating the Effects of Chaos in Variable Neighbourhood Search” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

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Book SynopsisPresenting topics that have not previously been contained in a single volume, this book offers an up-to-date review of computational methods in electromagnetism, with a focus on recent results in the numerical simulation of real-life electromagnetic problems and on theoretical results that are useful in devising and analyzing approximation algorithms. Based on four courses delivered in Cetraro in June 2014, the material covered includes the spatial discretization of Maxwell’s equations in a bounded domain, the numerical approximation of the eddy current model in harmonic regime, the time domain integral equation method (with an emphasis on the electric-field integral equation) and an overview of qualitative methods for inverse electromagnetic scattering problems.Assuming some knowledge of the variational formulation of PDEs and of finite element/boundary element methods, the book is suitable for PhD students and researchers interested in numerical approximation of partial differential equations and scientific computing.Table of ContentsPreface, Ralf Hiptmair: Maxwell's Equations: Continuous and Discrete Peter Monk: Numerical Methods for Maxwell's Equations, Rodolfo Rodriguez: Numerical Approximation of Low-Frequency Problems; Houssem Haddar: Inverse Electromagnetic Scattering Problems.

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Book SynopsisThis volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems.The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors.Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.Trade Review“The book is written in an engaging and lively style that will appeal to students. … aim of the Springer SUMS series is to take a ‘fresh and modern approach’ to core foundational material through to final year topics. This book delivers on that promise with great success. ... As a first text that is set at the appropriate level … which recognizes and incorporates numerical computation as an essential tool for learning and understanding, it looks hard to beat.” (Mark Blyth, SIAM Review, Vol. 59 (1), March, 2017)“UK mathematicians Griffiths (Univ. of Dundee) and Dold and Silvester (both, Univ. of Manchester) introduce undergraduates to partial differential equations (PDEs) from both the analytical and numerical points of view. … Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners.” (D. P. Turner, Choice, Vol. 53 (11), July, 2016)“This introduction to partial differential equations is designed for upper level undergraduates in mathematics. … The writing is lively, the authors make appealing use of computational examples and visualization, and they are very successful at conveying and integrating physical intuition. … This is probably the best introductory book on PDEs that I have seen in some time. It is well worth a look.” (William J. Satzer, MAA Reviews, maa.org, April, 2016)“This textbook offers a nice introduction to analytical and numerical methods for partial differential equations. … The book is self-contained and the prerequisites is a standard course in calculus and linear algebra. The textbook appeals to undergraduate students in both scientific and engineering programs in which PDEs are of practical importance.” (Marius Ghergu, zbMATH 1330.35001, 2016)Table of ContentsSetting the scene.- Boundary and initial data.- The origin of PDEs.- Classification of PDEs.- Boundary value problems in R1.- Finite difference methods in R1.- Maximum principles and energy methods.- Separation of variables.- The method of characteristics.- Finite difference methods for elliptic PDEs.- Finite difference methods for parabolic PDEs.- Finite difference methods for hyperbolic PDEs.- Projects.

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Book SynopsisFocusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.Table of Contents Preface.-Charles F. Van Loan: Structured Matrix Problems from Tensors.-Dario A. Bini: Matrix Structures in Queuing Models.-. Jonas Ballani and Daniel Kressner: Matrices with Hierarchical Low-Rank Structures.-Michele Benzi: Localization in Matrix Computations: Theory and Applications.-Munthe-Kaas: Groups and Symmetries in Numerical Linear Algebra.

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Book SynopsisThis book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds.Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory.Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups.Table of ContentsPart I Stein Manifolds.- 1 Preliminaries.- 2 Stein Manifolds.- 3 Stein Neighborhoods and Approximation.- 4 Automorphisms of Complex Euclidean Spaces.- Part II Oka Theory.- 5 Oka Manifolds.- 6 Elliptic Complex Geometry and Oka Theory.- 7 Flexibility Properties of Complex Manifolds and Holomorphic Maps.- Part III Applications.- 8 Applications of Oka Theory and its Methods.- 9 Embeddings, Immersions and Submersions.- 10 Topological Methods in Stein Geometry.- References.- Index.

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Book SynopsisThis book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.Table of ContentsFoundations of Spline Theory: B-Splines, Spline Approximation, and Hierarchical Refinement.- Adaptive Multiscale Methods for the Numerical Treatment of Systems of PDEs.- Generalized Locally Toeplitz Sequences: A Spectral Analysis Tool for Discretized Differential Equations.- Isogeometric Analysis: Mathematical and Implementational Aspects, with Applications.

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