Maths for computer scientists Books

Book SynopsisThis book gathers papers presented at the Workshop on Computational Diffusion MRI, CDMRI 2020, held under the auspices of the International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), which took place virtually on October 8th, 2020, having originally been planned to take place in Lima, Peru.This book presents the latest developments in the highly active and rapidly growing field of diffusion MRI. While offering new perspectives on the most recent research challenges in the field, the selected articles also provide a valuable starting point for anyone interested in learning computational techniques for diffusion MRI. The book includes rigorous mathematical derivations, a large number of rich, full-colour visualizations, and clinically relevant results. As such, it is of interest to researchers and practitioners in the fields of computer science, MRI physics, and applied mathematics. The reader will find numerous contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation to new computational methods and estimation techniques for the in-vivo recovery of microstructural and connectivity features, as well as diffusion-relaxometry and frontline applications in research and clinical practice.Table of Contents

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Book SynopsisComputation, itself a form of calculation, incorporates steps that include arithmetical and non-arithmetical (logical) steps following a specific set of rules (an algorithm). This uniquely accessible textbook introduces students using a very distinctive approach, quite rapidly leading them into essential topics with sufficient depth, yet in a highly intuitive manner. From core elements like sets, types, Venn diagrams and logic, to patterns of reasoning, calculus, recursion and expression trees, the book spans the breadth of key concepts and methods that will enable students to readily progress with their studies in Computer Science.Trade Review“This book is intended as a textbook for an introductory course in computation for students beginning in informatics. No prerequisites are needed, all concepts, even elementary ones ... . it is also very suited for self-study, even if a reader is interested in Haskell or symbolic logic alone. ... Comprehension is supported by exercises for each chapter ... .” (Dieter Riebesehl, zbMATH 1497.68005, 2022)Table of Contents1 Sets 132 Types 193 Simple Computations 274 Venn Diagrams and Logical Connectives 355 Lists and Comprehensions 456 Features and Predicates 557 Testing Your Programs 638 Patterns of Reasoning 739 More Patterns of Reasoning 8110 Lists and Recursion 9111 More Fun with Recursion 10112 Higher-Order Functions 11113 Higher and Higher 12314 Sequent Calculus 13115 Algebraic Data Types 14316 Expression Trees 15717 Karnaugh Maps 17518 Relations and Quantifiers 18319 Checking Satisfiability 19120 Data Representation 20321 Data Abstraction 22122 Efficient CNF Conversion 23723 Counting Satisfying Valuations 24924 Type Classes 26325 Search in Trees 27526 Combinatorial Algorithms 28527 Finite Automata 29928 Deterministic Finite Automata 31129 Non-Deterministic Finite Automata 32130 Input/Output and Monads 34131 Regular Expressions 35932 Non-Regular Languages 369Index 377

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Book SynopsisThe main focus of this book is on presenting advances in fuzzy statistics, and on proposing a methodology for testing hypotheses in the fuzzy environment based on the estimation of fuzzy confidence intervals, a context in which not only the data but also the hypotheses are considered to be fuzzy. The proposed method for estimating these intervals is based on the likelihood method and employs the bootstrap technique. A new metric generalizing the signed distance measure is also developed. In turn, the book presents two conceptually diverse applications in which defended intervals play a role: one is a novel methodology for evaluating linguistic questionnaires developed at the global and individual levels; the other is an extension of the multi-ways analysis of variance to the space of fuzzy sets. To illustrate these approaches, the book presents several empirical and simulation-based studies with synthetic and real data sets. In closing, it presents a coherent R package called “FuzzySTs” which covers all the previously mentioned concepts with full documentation and selected use cases. Given its scope, the book will be of interest to all researchers whose work involves advanced fuzzy statistical methods.Table of Contents- 1. Introduction. - Part I Theoretical Part. - 2. Fundamental Concepts on Fuzzy Sets. - 3. Fuzzy Rule-Based Systems. - 4. Distances Between Fuzzy Sets. - 5. Fuzzy Random Variables and Fuzzy Distributions. - 6. Fuzzy Statistical Inference. - Conclusion Part I. - Part II Applications. - 7. Evaluation of Linguistic Questionnaire. - 8. Fuzzy Analysis of Variance. - Part III An R Package for Fuzzy Statistical Analysis: A DetailedDescription. - 9. FuzzySTs: Fuzzy Statistical Tools: A Detailed Description. - Conclusion.

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Book SynopsisThis textbook offers an algorithmic introduction to the field of computer algebra. A leading expert in the field, the author guides readers through numerous hands-on tutorials designed to build practical skills and algorithmic thinking. This implementation-oriented approach equips readers with versatile tools that can be used to enhance studies in mathematical theory, applications, or teaching. Presented using Mathematica code, the book is fully supported by downloadable sessions in Mathematica, Maple, and Maxima. Opening with an introduction to computer algebra systems and the basics of programming mathematical algorithms, the book goes on to explore integer arithmetic. A chapter on modular arithmetic completes the number-theoretic foundations, which are then applied to coding theory and cryptography. From here, the focus shifts to polynomial arithmetic and algebraic numbers, with modern algorithms allowing the efficient factorization of polynomials. The final chapters offer extensions into more advanced topics: simplification and normal forms, power series, summation formulas, and integration. Computer Algebra is an indispensable resource for mathematics and computer science students new to the field. Numerous examples illustrate algorithms and their implementation throughout, with online support materials to encourage hands-on exploration. Prerequisites are minimal, with only a knowledge of calculus and linear algebra assumed. In addition to classroom use, the elementary approach and detailed index make this book an ideal reference for algorithms in computer algebra.Trade Review“Strong interplay between the abstract exposition, which includes the relevant theorems as well as their proofs, and the practical utilization of those concepts in Mathematica is certainly a remarkable feature of this textbook. … Overall, the book is very well written and the approach to provide examples as actual Mathematica sessions is commendable.” (Andreas Maletti, zbMATH 1484.68004, 2022)Table of Contents

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Book SynopsisIn the present era dominated by computers, graph theory has come into its own as an area of mathematics, prominent for both its theory and its applications. One of the richest and most studied types of graph structures is that of the line graph, where the focus is more on the edges of a graph than on the vertices. A subject worthy of exploration in itself, line graphs are closely connected to other areas of mathematics and computer science. This book is unique in its extensive coverage of many areas of graph theory applicable to line graphs. The book has three parts. Part I covers line graphs and their properties, while Part II looks at features that apply specifically to directed graphs, and Part III presents generalizations and variations of both line graphs and line digraphs.Line Graphs and Line Digraphs is the first comprehensive monograph on the topic. With minimal prerequisites, the book is accessible to most mathematicians and computer scientists who have had an introduction graph theory, and will be a valuable reference for researchers working in graph theory and related fields.Table of ContentsPart I Line Graphs.- 1 Fundamentals of Line Graphs.- 2 Line Graph Isomorphisms.- 3 Characterization of Line Graphs.- 4 Spectral Properties of Line Graphs.- 5 Planarity of Line Graphs.- 6 Connectivity of Line Graphs.- 7 Tranversability in Line Graphs.- 8 Colorability in Line Graphs.- 9 Distance and Transitivity in Line Graphs.- Part II Line Digraphs.- 10 Fundamentals of Line Digraphs.- 11 Characterizations of Line Digraphs.- 12 Iterated Line Digraphs.- Part III Generalizations.- 13 Total Graphs and Total Digraphs.- 14 Path Graphs and Path Digraphs.- 15 Super Line Graphs and Super Line Digraphs.- 16 Line Graphs of Signed Graphs.- 17 The Krausz Dimension of Graph.- Reference. Index of Names.- Index of Definitions.

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This textbook discusses the design and implementation of basic algebraic graph algorithms, and algebraic graph algorithms for complex networks, employing matroids whenever possible. The text describes the design of a simple parallel matrix algorithm kernel that can be used for parallel processing of algebraic graph algorithms. Example code is presented in pseudocode, together with case studies in Python and MPI. The text assumes readers have a background in graph theory and/or graph algorithms.

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Book SynopsisThis SpringerBrief provides the first systematic review of the existing works of cohesive subgraph search (CSS) over large heterogeneous information networks (HINs). It also covers the research breakthroughs of this area, including models, algorithms and comparison studies in recent years. This SpringerBrief offers a list of promising future research directions of performing CSS over large HINs.The authors first classify the existing works of CSS over HINs according to the classic cohesiveness metrics such as core, truss, clique, connectivity, density, etc., and then extensively review the specific models and their corresponding search solutions in each group. Note that since the bipartite network is a special case of HINs, all the models developed for general HINs can be directly applied to bipartite networks, but the models customized for bipartite networks may not be easily extended for other general HINs due to their restricted settings. The authors also analyze and compare these cohesive subgraph models (CSMs) and solutions systematically. Specifically, the authors compare different groups of CSMs and analyze both their similarities and differences, from multiple perspectives such as cohesiveness constraints, shared properties, and computational efficiency. Then, for the CSMs in each group, the authors further analyze and compare their model properties and high-level algorithm ideas.This SpringerBrief targets researchers, professors, engineers and graduate students, who are working in the areas of graph data management and graph mining. Undergraduate students who are majoring in computer science, databases, data and knowledge engineering, and data science will also want to read this SpringerBrief.Table of Contents1. Introduction2. Preliminaries3. CSS on Bipartite Networks4. CSS on Other General HINs5. Comparison Analysis6. Related Work on CSMs and solutions7. Future Work and Conclusion

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Book SynopsisThis book constitutes the refereed proceedings of the 15th International Conference on Graph Transformation, ICGT 2022, which took place Nantes, France in July 2022.The 10 full papers and 1 tool paper presented in this book were carefully reviewed and selected from 19 submissions. The conference focuses on describing new unpublished contributions in the theory and applications of graph transformation as well as tool presentation papers that demonstrate main new features and functionalities of graph-based tools.Table of ContentsTheoretical Advances.- Application Domains.- Tool Presentation.

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Book SynopsisThis book constitutes the proceedings of the 16th International Conference on Algorithmic Aspects in Information and Management, AAIM 2022, which was held online during August 13-14, 2022. The conference was originally planned to take place in Guangzhou, China, but changed to a virtual event due to the COVID-19 pandemic.The 41 regular papers included in this book were carefully reviewed and selected from 59 submissions. Table of ContentsAn improvement of the bound on the odd chromatic number of 1-planar graphs.- AoI Minimizing of Wireless Rechargeable Sensor Network based on Trajectory Optimization of Laser-Charged UAV.- Monotone k-Submodular Knapsack Maximization: An Analysis of the Greedy+Singleton Algorithm.- The constrained parallel-machine scheduling problem with divisible processing times and penalties.- Energy-constrained Geometric Covering Problem.- Fast searching on $k$-combinable graphs.- Three Algorithms for Converting Control Flow Statements from Python to XD-M.- Class Ramsey numbers involving induced graphs.- An Approximation Algorithm for the Clustered Path Travelling Salesman Problem.- Hyperspectral Image Reconstruction for SD-CASSI systems based on Residual Attention Network.- Improved Approximation Algorithm for the Asymmetric Prize-Collecting TSP.- Injective edge coloring of power graphs and necklaces.- Guarantees for Maximization of $k$-Submodular Functions with a Knapsack and a Matroid Constraint.- Incremental SDN Deployment to Achieve Load Balance in ISP Networks.- Approximation scheme for single-machine rescheduling with job delay and rejection.- Defense of Scapegoating Attack in Network Tomography.- A Binary Search Double Greedy Algorithm for Non-monotone DR-submodular Maximization.- Streaming Adaptive Submodular Maximization.- Constrained Stochastic Submodular Maximization with State-Dependent Costs.- Online early work maximization problem on two hierarchical machines with buffer or rearrangements.- Polynomial time algorithm for k-vertex-edge dominating problem in interval graphs.- Adaptive Competition-based Diversified-profit Maximization with Online Seed Allocation.- Collaborative Service Caching in Mobile Edge Nodes.- A Decentralized Auction Framework with Privacy Protection in Mobile Crowdsourcing.- On-line single machine scheduling with release dates and submodular rejection penalties.- Obnoxious Facility Location Games with Candidate Locations.- Profit Maximization for Multiple Products in Community-based Social Networks.- MCM: A Robust Map Matching Method by Tracking Multiple Road Candidates.- Security on Ethereum: Ponzi Scheme Detection in Smart Contract.- Cyclically orderable generalized Petersen graphs.- The r-dynamic chromatic number of planar graphs without special short cycles.- Distance Labeling of the Halved Folded $n$-Cube.- Signed network embedding based on muti-attention mechanism.- Balanced Graph Partitioning based on Mixed 0-1 Linear Programming and Iteration Vertex Relocation Algorithm.- Partial inverse min-max spanning tree problem under the weighted bottleneck Hamming distance.- Mixed Metric Dimension of Some Plane Graphs.- The Optimal Dynamic Rationing Policy in the Stock-Rationing Queue.- Pilot Pattern Design with Branch and Bound in PSA-OFDM System.- Bicriteria Algorithms for Maximizing the Difference Between Submodular Function and Linear Function under Noise.- On the Transversal Number of k-Uniform Connected Hypergraphs.- Total coloring of planar graphs without some adjacent cycles.

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Book SynopsisThis textbook aims to point out the most important principles of data analysis from the mathematical point of view. Specifically, it selected these questions for exploring: Which are the principles necessary to understand the implications of an application, and which are necessary to understand the conditions for the success of methods used? Theory is presented only to the degree necessary to apply it properly, striving for the balance between excessive complexity and oversimplification. Its primary focus is on principles crucial for application success. Topics and features: Focuses on approaches supported by mathematical arguments, rather than sole computing experiences Investigates conditions under which numerical algorithms used in data science operate, and what performance can be expected from them Considers key data science problems: problem formulation including optimality measure; learning and generalization in relationships to training set size and number of free parameters; and convergence of numerical algorithms Examines original mathematical disciplines (statistics, numerical mathematics, system theory) as they are specifically relevant to a given problem Addresses the trade-off between model size and volume of data available for its identification and its consequences for model parametrization Investigates the mathematical principles involves with natural language processing and computer vision Keeps subject coverage intentionally compact, focusing on key issues of each topic to encourage full comprehension of the entire book Although this core textbook aims directly at students of computer science and/or data science, it will be of real appeal, too, to researchers in the field who want to gain a proper understanding of the mathematical foundations “beyond” the sole computing experience.Table of Contents1. Data Science and its Tasks.- 2. Application Specific Mappings and Measuring the Fit to Data.- 3. Data Processing by Neural Networks.- 4. Learning and Generalization.- 5. Numerical Algorithms for Network Learning.- 6. Specific Problems of Natural Language Processing.- 7. Specific Problems of Computer Vision.

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Book SynopsisThis book constitutes the refereed proceedings of the 16th International Conference on Learning and Intelligent Optimization, LION 16, which took place in Milos Island, Greece, in June 2022.The 36 full papers and 3 short papers presented in this volume were carefully reviewed and selected from 60 submissions. LION deals with automatic solver configuration, parallel methods, intelligent optimization, nature-inspired algorithms, hard combinatorial optimization problems, DC learning, computational intelligence, and others. The contributions were organized in topical sections as follows: Invited Papers; Contributed Papers.Table of Contents​Invited Papers.- Optimal Scheduling of the Leaves of a Tree and the SVO Frequencies of Languages.- From Design of Experiments to Combinatorics of Disasters: A Conceptual Framework for Disaster Exercises.- Separating two polyhedra utilizing alternative theorems and penalty function.- Contributed Papers. -A Composite Index Method for Optimization Benchmarking.- Optimal Energy Management of Microgrid Using Multi-objective Optimisation Approach.- A Stochastic Alternating Balance k-Means Algorithm for Fair Clustering.- Binary Black Widow Optimization Algorithm for Feature Selection Problems.- Learning to Solve a Stochastic Orienteering Problem with Time Windows.- ML-based approach for accelerating global search algorithm for solving multicriteria problems .- The Skewed Kruskal algorithm.- Bounds for sparse solutions of K-SVCR multi-class classification model.- Integer Linear Programming in Solving an Optimization Problem at the Mixing Department of the Metallurgical Production.- Realtime Gray-Box Algorithm Configuration.- Dynamic urban solid waste management system for smart cities.- Single MCMC Chain Parallelisation on Decision Trees.- Single MCMC Chain Parallelisation on Decision Trees.- Competitive supply allocation in a distribution network under overproduction.- Safe-exploration of control policies from safe-experience via Gaussian Processes.- Bayesian Optimization in Wasserstein Spaces.- Network Vulnerability Analysis in Wasserstein Spaces.- BERT Self-Learning Approach with Limited Labels for Document Classification.- Autonomous Learning Optimization for Deep Learning.- Optimizing Data Augmentation Policy through Random Unidimensional Search.- Evaluating Student Behaviour on the MathE Platform - Clustering Algorithms Approaches.- Unsupervised Training for Neural TSP Solver.- Comparing surrogate models for tuning optimization algorithms.- Search and Score-based Waterfall Auction Optimization.- Survey on KNN Methods in Data Science.- Constrained Shortest Path and Hierarchical Structures.- Investigation of Graph Neural Networks for Instance Segmentation of Industrial Point Cloud Data.- Fitness landscape ruggedness impact on PSO in dealing with three variants of the travelling salesman problem.- A Multi-UAVs’ Provider Model for the provision of 5G Service Chains: a game theoretic approach.- Metabolic Syndrome Risk Forecasting on Elderly with ML Techniques.- Airport Digital Twins for Resilient Disaster Management Response.- Strategies for Surviving Aggressive Multiparty Repeated Standoffs.- A Hybridization of GRASP and UTASTAR for Solving the Vehicle Routing Problem with Pickups and Deliveries and 3D Loading Constraints.- Packing hypertrees and the k-cut problem in Hypergraphs.- Maximizing the Eigenvalue-Gap and Promoting Sparsity of Doubly Stochastic Matrices with PSO.- Value of Information in the Mean-Square Case and its Application to the Analysis of Financial Time-Series Forecast.

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Book SynopsisThis book constitutes the refereed proceedings of the 12th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2022 held in Leiden, The Netherlands, during March 20-24, 2023. The 44 regular papers presented in this book were carefully reviewed and selected from 65 submissions. The papers are divided into the following topical sections: Algorithm Design and Engineering; Machine Learning and Multi-criterion Optimization; Benchmarking and Performance Assessment; Indicator Design and Complexity Analysis; Applications in Real World Domains; and Multi-Criteria Decision Making and Interactive Algorithms..Table of Contents​Algorithm Design and Engineering.- Visual Exploration of the Effect of Constraint Handling in Multiobjective Optimization.- A Two-stage Algorithm for Integer Multiobjective Simulation Optimization.- RegEMO: Sacrificing Pareto-Optimality for Regularity in Multi-objective Problem-Solving.- Cooperative coevolutionary NSGA-II with Linkage Measurement Minimization for Large-scale Multi-objective Optimization.- Data-Driven Evolutionary Multi-Objective Optimization Based on Multiple-Gradient Descent for Disconnected Pareto Fronts.- Eliminating Non-dominated Sorting from NSGA-III.- Scalability of Multi-Objective Evolutionary Algorithms for Solving Real-World Complex Optimization Problems.- Machine Learning and Multi-criterion Optimization.- Multi-Objective Learning using HV Maximization.- Sparse Adversarial Attack via Bi-Objective Optimization.- Investigating Innovized Progress Operators with Different Machine Learning Methods.- End-to-End Pareto Set Prediction with Graph Neural Networks for Multi-objective Facility Location.- Online Learning Hyper-Heuristics in Multi-Objective Evolutionary Algorithms.- Surrogate-assisted Multi-objective Optimization via Genetic Programming based Symbolic Regression.- Learning to Predict Pareto-optimal Solutions From Pseudo-weights.- A Relation Surrogate Model for Expensive Multiobjective Continuous and Combinatorial Optimization.- Pareto Front Upconvert by Iterative Estimation Modeling and Solution Sampling.- Pareto Front Upconvert by Iterative Estimation Modeling and Solution Sampling.- Approximation of a Pareto Set Segment Using a Linear Model with Sharing Variables.- Feature-based Benchmarking of Distance-based Multi/Many-objective Optimisation Problems: A Machine Learning Perspective.- Benchmarking and Performance Assessment.- Partially Degenerate Multi-Objective Test Problems.- Peak-A-Boo! Generating Multi-Objective Multiple Peaks Benchmark Problems with Precise Pareto Sets.- MACO: A Real-world inspired Benchmark for Multi-objective Evolutionary Algorithms.- A scalable test suite for bi-objective multidisciplinary optimisation.- Performance Evaluation of Multi-Objective Evolutionary Algorithms using Artificial and Real-World Problems.- A Novel Performance Indicator based on the Linear Assignment Problem.- A Test Suite for Multi-objective Multi-fidelity Optimization.- Indicator Design and Complexity Analysis.- Diversity enhancement via magnitude.- Two-Stage Greedy Approximated Hypervolume Subset Selection for Large-Scale Problems.- Two-Stage Greedy Approximated Hypervolume Subset Selection for Large-Scale Problems.- On the Computational Complexity of Efficient Non-Dominated Sort using Binary Search.- Applications in Real World Domains.- Evolutionary Algorithms with Machine Learning Models for Multiobjective Optimization in Epidemics Control.- Joint Price Optimization across a Portfolio of Fashion E-commerce Products.- Improving MOEA/D with Knowledge Discovery. Application to a Bi-Objective Routing Problem.- The Prism-Net Search Space Representation for Multi-Objective Building Spatial Design.- Selection Strategies for a Balanced Multi- or Many-Objective Molecular Optimization and Genetic Diversity: a Comparative Study.- A Multi-objective Evolutionary Framework for Identifying Dengue Stage-Specific Differentially Co-expressed and Functionally Enriched Gene Modules.- A Multi-objective Evolutionary Framework for Identifying Dengue Stage-Specific Differentially Co-expressed and Functionally Enriched Gene Modules. -Multiobjective Optimization of Evolutionary Neural Networks for Animal Trade Movements Prediction.- Transfer of Multi-Objectively Tuned CMA-ES Parameters to a Vehicle Dynamics Problem.- Multi-Criteria Decision Making and Interactive Algorithms.- Preference-Based Nonlinear Normalization for Multiobjective Optimization.- Incorporating preference information interactively in NSGA-III by the adaptation of reference vectors.- A Systematic Way of Structuring Real-World Multiobjective Optimization Problems.- IK-EMOViz: An Interactive Knowledge-based Evolutionary Multi-objective Optimization Framework.- An Interactive Decision Tree-Based Evolutionary Multi-Objective Algorithm.

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Book SynopsisThis book constitutes the proceedings of the 20th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2023, which took place in Augsburg, Germany, during April 3–6, 2023. The 17 papers presented in this book were carefully reviewed and selected from 26 submissions. They deal with the development and dissemination of relation algebras, Kleene algebras, and similar algebraic formalisms. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond. Apart from the submitted articles, this volume features the abstracts of the presentations of the three invited speakers. Table of ContentsAmalgamation Property for Some Varieties of BL-algebras Generated by one Finite Set of BL-chains with Finitely-many Components.- Comer Schemes, Relation Algebras, and the Flexible Atom Conjecture.- A General Method for Representing Sets of Relations by Vectors.- Contextuality in Distributed Systems.- The Structure of Locally Integral Involutive Po-monoids and Semirings.- Compatibility of Refining and Controlling Plant Automata with Bisimulation Quotients.- Dependences Between Domain Constructions in Heterogeneous Relation Algebras.- Normal Forms for Elements of the *-Continuous Kleene Algebras K (x) C2’.- Representable and Diagonally rRpresentable Weakening Relation Algebras.- Completeness and the Finite Model Property for Kleene Algebra, Reconsidered.- What Else is Undecidable About Loops.- Implication Algebras and Implication Semigroups of Binary Relations.- On the Complexity of Kleene Algebra with Domain.- Enumerating, Cataloguing and Classifying all Quantales on up to Nine Elements.- Duoidally Enriched Freyd Categories.- Towards a Theory of Conversion Relations for Prefixed Units of Measure.- Relational Algebraic Approach to the Real Numbers - The Additive Group.

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Book SynopsisThis book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. “Safe” – that is, paradox-free – informal set theory is introduced following on the heels of Russell’s Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor’s diagonalisation technique. Predicate logic “for the user” is introduced along with axioms and rules and extensive examples. Partial orders and the minimal condition are studied in detail with the latter shown to be equivalent to the induction principle. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of functions and sets. Techniques for solving recurrence relations including generating functions, the O- and o-notations, and trees are provided. Over 200 end of chapter exercises are included to further aid in the understanding and applications of discrete mathematics. Table of ContentsElementary Informal Set Theory.- Safe Set Theory.- Relations and Functions.- A Tiny Bit of Informal Logic.- Inductively Defined Sets and Structural Induction.- Recurrence Equations.- Trees and Graphs.

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Book SynopsisThis book constitutes the refereed proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2023, held in Madison, WI, USA, during June 21–23, 2023. The 33 full papers presented were carefully reviewed and selected from 119 submissions. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.

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Book SynopsisThis volume constitutes the proceedings of the 9th International Conference on Variable Neighborhood Search, ICVNS 2023, held in Abu Dhabi, United Arab Emirates, in October 2022.The 11 full papers presented in this volume were carefully reviewed and selected from 29 submissions. The papers describe recent advances in methods and applications of variable neighborhood search.Table of ContentsA metaheuristic approach for solving Monitor Placement Problem.- A VNS-based heuristic for the minimum number of resources under a perfect schedule.- BVNS for Overlapping Community Detection.- A Simulation-Based Variable Neighborhood Search Approach for Optimizing Cross-Training Policies.- Multi-Objective Variable Neighborhood Search for improving software modularity.- An Effective VNS for Delivery Districting.- BVNS for the Minimum Sitting Arrangement problem in a cycle.- Assigning Multi-Skill Confgurations to Multiple Servers with a Reduced VNS.- Multi-Round Infuence Maximization: A Variable Neighborhood Search Approach.- A VNS based heuristic for a 2D Open Dimension Problem.- BVNS for the bi-objective multi row equal facility layout problem.

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Book SynopsisThis book constitutes the proceedings of the 6th International Conference on Geometric Science of Information, GSI 2023, held in St. Malo, France, during August 30-September 1, 2023. The 125 full papers presented in this volume were carefully reviewed and selected from 161 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: geometry and machine learning; divergences and computational information geometry; statistics, topology and shape spaces; geometry and mechanics; geometry, learning dynamics and thermodynamics; quantum information geometry; geometry and biological structures; geometry and applications.Table of ContentsGeometry and machine learning.- Divergences and computational information geometry.- Statistics, topology and shape spaces.- Geometry and mechanics.- Geometry, learning dynamics and thermodynamics.- Quantum information geometry.- Geometry and biological structures.- Geometry and applications.

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Book SynopsisThis book constitutes the proceedings of the 6th International Conference on Geometric Science of Information, GSI 2023, held in St. Malo, France, during August 30-September 1, 2023. The 125 full papers presented in this volume were carefully reviewed and selected from 161 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: geometry and machine learning; divergences and computational information geometry; statistics, topology and shape spaces; geometry and mechanics; geometry, learning dynamics and thermodynamics; quantum information geometry; geometry and biological structures; geometry and applications.Table of ContentsGeometry and machine learning.- Divergences and computational information geometry.- Statistics, topology and shape spaces.- Geometry and mechanics.- Geometry, learning dynamics and thermodynamics.- Quantum information geometry.- Geometry and biological structures.- Geometry and applications.

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Book SynopsisThis book constitutes the refereed proceedings of the 17th International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom (IJTCS-FAW 2023), consisting of the 17th International Conference on Frontier of Algorithmic Wisdom (FAW) and the 4th International Joint Conference on Theoretical Computer Science (IJTCS), held in Macau, China, during August 14–18, 2023.FAW started as the Frontiers of Algorithmic Workshop in 2007 at Lanzhou, China, and was held annually from 2007 to 2021 and published archival proceedings. IJTCS, the International joint theoretical Computer Science Conference, started in 2020, aimed to bring in presentations covering active topics in selected tracks in theoretical computer science. To accommodate the diversified new research directions in theoretical computer science, FAW and IJTCS joined their forces together to organize an event for information exchange of new findings and work of enduring value in the field. The 21 full papers included in this book were carefully reviewed and selected from 34 submissions. They were organized in topical sections as follows: algorithmic game theory; algorithms and data structures; combinatorial optimization; and computational economics.Table of ContentsUnderstanding the Relationship Between Core Constraints and Core-Selecting Payment Rules in Combinatorial Auctions.- An Improved Analysis of the Greedy+Singleton Algorithm for k-Submodular Knapsack Maximization.- Generalized Sorting with Predictions Revisited.- Eliciting Truthful Reports with Partial Signals in Repeated Games.- On the NP-hardness of two scheduling problems under linear constraints.- On the Matching Number of k-Uniform Connected Hypergraphs with Maximum Degree.- Max-Min Greedy Matching Problem: Hardness for the Adversary and Fractional Variant.- Approximate Core Allocations for Edge Cover Games.- Random Approximation Algorithms for Monotone k-Submodular Function Maximization with Size Constraints.- Additive Approximation Algorithms for Sliding Puzzle.- Differential Game Analysis for Cooperation Models in Automotive Supply Chain under Low-Carbon Emission Reduction Policies.- Adaptivity Gap for Influence Maximization with Linear Threshold Model on Trees.- Physically Verifying the First Nonzero Term in a Sequence: Physical ZKPs for ABC End View and Goishi Hiroi.- Mechanism Design in Fair Sequencing.- Red-Blue Rectangular Annulus Cover Problem.- Applying Johnson's Rule in Scheduling Multiple Parallel Two-Stage Flowshops.- The Fair k-Center with Outliers Problem: FPT and Polynomial Approximations.- Constrained Graph Searching on Trees.- EFX Allocations Exist for Binary Valuations.- Maximize Egalitarian Welfare for Cake Cutting.- Stackelberg Strategies on Epidemic Containment Games.

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Book SynopsisThis volume constitutes the thoroughly refereed proceedings of the 49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023. The 33 full papers presented in this volume were carefully reviewed and selected from a total of 116 submissions. The WG 2022 workshop aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science, or by extracting new graph theoretic problems from applications.Table of ContentsProportionally Fair Matching with Multiple Groups.- Reconstructing Graphs from Connected Triples.- Parameterized Complexity of Vertex Splitting to Pathwidth at most 1.- Odd Chromatic Number of Graph Classes.- Deciding the Erdos-P osa property in 3-connected digraphs.- New Width Parameters for Independent Set: One-sided-mim-width and Neighbor-depth.- Computational Complexity of Covering Colored Mixed Multigraphswith Degree Partition Equivalence Classes of Size at Most Two.- Cutting Barnette graphs perfectly is hard.- Metric dimension parameterized by treewidth in chordal graphs.- Efficient Constructions for the Gyori-Lovasz Theorem on Almost Chordal Graphs.- Generating faster algorithms for d-Path Vertex Cover.- A new width parameter of graphs based on edge cuts: -edge-crossing width.- Snakes and Ladders: a Treewidth Story.- Parameterized Results on Acyclic Matchings with Implications for Related Problems.- P-matchings Parameterized by Treewidth.- Algorithms and hardness for Metric Dimension on digraphs.- Degreewidth : a New Parameter for Solving Problems on Tournaments.- Approximating Bin Packing with Con ict Graphs via Maximization Techniques.- i-Metric Graphs: Radius, Diameter and all Eccentricities.- Maximum edge colouring problem on graphs that exclude a xed minor.- Bounds on Functionality and Symmetric Di erence { Two Intriguing Graph Parameters.- Cops and Robbers on Multi-layer Graphs.- Parameterized Complexity of Broadcasting in Graphs.- Turan's Theorem Through Algorithmic Lens.- On the Frank number and nowhere-zero ows on graphs.- On the minimum number of arcs in 4-dicritical oriented graphs.- Tight Algorithms for Connectivity Problems Parameterized byModular-Treewidth.

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Book SynopsisThis book constitutes the refereed proceedings of the 11th International Conference on Code-Based Cryptography, CBCrypto 2023, held in Lyon, France, during April 22–23, 2023. The 8 full papers included in this book were carefully reviewed and selected from 28 submissions. The conference offers a wide range of many important aspects of code-based cryptography such as cryptanalysis of existing schemes, the proposal of new cryptographic systems and protocols as well as improved decoding algorithms.

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Book SynopsisThese two volumes constitute the proceedings of the 10th International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making, IUKM 2023, held in Kanazawa, Japan, during November 2-4, 2023. The 58 full papers presented were carefully reviewed and selected from 107 submissions. The papers deal with all aspects of research results, ideas, and experiences of application among researchers and practitioners involved with all aspects of uncertainty modelling and management.Table of ContentsUncertainty Management and Decision Making.- Optimization and Statistical Methods.- Economic Application

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Book SynopsisThis book constitutes the refereed proceedings of the 4th Southern African Conference on Artificial Intelligence Research, SACAIR 2023, held in Muildersdrift, South Africa, in December 2023. The 22 full papers presented in these proceedings were carefully reviewed and selected from 66 submissions. The papers are organized in the following topical sections: Responsible and Ethical AI Track; Socio-Technical and Human-Centered AI Track; Algorithmic, and Data Driven and Symbolic AI.Table of ContentsResponsible and Ethical AI track.- Emerging AI Discourses and Policies in the EU: Implications for Evolving AI Governance.- Intergenerational Justice as Driver for Responsible AI.- AI Literacy: A Primary Good.- Exploring the ethical and societal concerns of Generative AI in Internet of Things (IoT) environments.- Warfare in the Age of AI: A Critical Evaluation of ArkinÕs Case for Ethical Autonomy in Unmanned Systems.- Socio-technical and human-centered AI track.- The decision criteria used by large organisations in South Africa for adopting Artificial Intelligence.- Let’s play games: Using no-code AI to reduce human cognitive load during AI solution development.- Algorithmic, Data Driven and Symbolic AI.- Unit-Based Genetic Algorithmic Approach for Optimal Multipurpose Batch Plant Scheduling.- Investigating the extent and usability of webtext available in South Africa’s official languages.- Voice Conversion for Stuttered Speech, Instruments, Unseen Languages and Textually Described Voices.- Extending Defeasible Reasoning Beyond Rational Closure.- Sequence Based Deep Neural Networks for Channel Estimation in Vehicular Communication Systems.- Comparative Study of Image Resolution Techniques in the Detection of Cancer Using Neural Networks.- Investigating Frequent Pattern-based Models for Improving Community Policing in South Africa.- Financial Inclusion in Sub-Saharan Emerging Markets: The Application of Deep Learning to Improve Determinants.- Viability of Convolutional Variational Autoencoders for Lifelong Class Incremental Similarity Learning.- PuoBERTa: Training and evaluation of a curated language model for Setswana.- Hierarchical Text Classification using Language Models with Global Label-wise Attention Mechanisms.- Multimodal Misinformation Detection in a South African Social Media Environment.- Improving Semi-Supervised Learning in Generative Adversarial Networks.- Impacts of Architectural Enhancements on Sequential Recommendation Models.- A comparative study of over-sampling techniques as applied to seismic events.

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Book SynopsisThis book constitutes the proceedings of the 49th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2024, held in Cochem, Germany, in February 2024. The 33 full papers presented in this book were carefully reviewed and selected from 81 submissions. The book also contains one invited talk in full paper length. They focus on original research and challenges in foundations of computer science including algorithms, AI-based methods, computational complexity, and formal models.Table of ContentsThe Information Extraction Framework of Document Spanners - A Very Informal Survey.- Generalized Distance Polymatrix Games.- Relaxed agreement forests.- On the Computational Complexity of Generalized Common Shape Puzzles.- Fractional Bamboo Trimming and Distributed Windows Scheduling.- New support size bounds and proximity bounds for integer linear programming.- On the Parameterized Complexity of Minus Domination.- Exact and Parameterized Algorithms for Choosability.- Parameterized Algorithms for Covering by Arithmetic Progressions.- Row-column combination of Dyck words.- Group Testing in Arbitrary Hypergraphs and Related Combinatorial Structures.- On the parameterized complexity of the Perfect Phylogeny problem.- Data reduction for directed feedback vertex set on graphs without long induced cycles.- Visualization of Bipartite Graphs in Limited Window Size.- Outerplanar and Forest Storyplans.- The Complexity of Cluster Vertex Splitting and Company.- Morphing Graph Drawings in the Presence of Point Obstacles.- Word-Representable Graphs from a Word’s Perspective.- Removable Online Knapsack with Bounded Size Items.- The Complexity of Online Graph Games.- Faster Winner Determination Algorithms for (Colored) Arc Kayles.- Automata Classes Accepting Languages Whose Commutative Closure is Regular.- Shortest Characteristic Factors of a Deterministic Finite Automaton and Computing Its Positive Position Run by Pattern Set Matching.- Query Learning of Minimal Deterministic Symbolic Finite Automata Separating Regular Languages.- Apportionment with Thresholds: Strategic Campaigns Are Easy in the Top-Choice But Hard in the Second-Chance Mode.- Local Certification of Majority Dynamics.- Complexity of Spherical Equations in Finite Groups.- Positive Characteristic Sets for Relational Pattern Languages.- Algorithms and Turing Kernels for Detecting and Counting Small Patterns in Unit Disk Graphs.- The Weighted HOM-Problem over Fields.- Combinatorics of block-parallel automata networks.- On the piecewise complexity of words and periodic words.- Distance Labeling for Families of Cycles.- On the induced problem for fixed-template CSPs.

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Book SynopsisOptimized Scheduling of Medical Appointment Sequences using Constraint Programming.- An integrated optimisation method for aluminium hot rolling.- Determining the Most Promising Selective Backbone Size for Partial Knowledge Compilation.- Leveraging Quantum Computing for Accelerated Classical Algorithms in Power Systems Optimization.- Hybridizing Machine Learning and Optimization for Planning Satellite Observations.- Algorithm Configuration in Sequential Decision-Making.- Self-Supervised Penalty-Based Learning for Robust Constrained Optimization.- Revisiting Pseudo-Boolean Encodings from an Integer Perspective.- Multi-task Representation Learning for Mixed Integer Linear Programming.- Breaking the Symmetries of Indistinguishable Objects.- Tackling Symmetry Breaking as a Symbolic Set Cover.- Modeling and Solving the Generalized Test Laboratory Scheduling Problem.- Parallelising Lazy Clause Generation with Trail Sharing.- Learning Primal Heuristics for 0–1 Knapsack Interdiction Problems.- Bounded-Error Policy Optimization for Mixed Discrete-Continuous MDPs via Constraint Generation in Nonlinear Programming.- Minimising Source-Plate Swaps for Robotised Compound Dispensing in Microplates.

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Book SynopsisThis book analyzes the generation of the arrow-categories of a given category, which is a foundational and distinguishable Category Theory phenomena, in analogy to the foundational role of sets in the traditional set-based Mathematics, for defi nition of natural numbers as well. This inductive transformation of a category into the infinite hierarchy of the arrowcategories is extended to the functors and natural transformations. The author considers invariant categorial properties (the symmetries) under such inductive transformations. The book focuses in particular on Global symmetry (invariance of adjunctions) and Internal symmetries between arrows and objects in a category (in analogy to Field Theories like Quantum Mechanics and General Relativity). The second part of the book is dedicated to more advanced applications of Internal symmetry to Computer Science: for Intuitionistic Logic, Untyped Lambda Calculus with Fixpoint Operators, Labeled Transition Systems in Process Algebras and Modal logics as well as Data Integration Theory.

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Book SynopsisNow in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics.Key features in new edition:* 35 new exercises* Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples* New section on regression* Online instructors' manual containing solutions to all exercises<Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications.Review of the first edition: This textbook is a classical and well-written introduction to probability theory and statistics. … the book is written ‘for an audience such as computer science students, whose mathematical background is not very strong and who do not need the detail and mathematical depth of similar books written for mathematics or statistics majors.’ … Each new concept is clearly explained and is followed by many detailed examples. … numerous examples of calculations are given and proofs are well-detailed." (Sophie Lemaire, Mathematical Reviews, Issue 2008 m)Trade Review“Schay (emer., Univ. of Massachusetts) has created a text for a two semester, calculus-based course in mathematical statistics. … The prose reads well. Physical production is good. … Summing Up: Recommended. Upper-division undergraduates and graduate students.” (W. R. Lee, Choice, Vol. 54 (6), February, 2017)“I believe that students concentrating in mathematics and related subjects will find this book readable and interesting. … I think that students learning the probability for the first time will get real value out of working through the examples and exercises of the text. … Introduction to Probability with Statistical Applications is very clearly written and reading the book is enjoyable. I would certainly recommend Schay’s book as a primary textbook for an undergraduate course in calculus-based probability.” (Jason M. Graham, MAA Reviews, September, 2016)Table of ContentsIntroduction.- The Algebra of Events.- Combinatorial Problems.- Probabilities.- Random Variables.- Expectation, Variance, Moments.- Some Special Distributions.- The Elements of Mathematical Statistics.

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Book Synopsis This book presents two new decomposition methods to decompose a time series in intrinsic components of low and high frequencies. The methods are based on Singular Value Decomposition (SVD) of a Hankel matrix (HSVD). The proposed decomposition is used to improve the accuracy of linear and nonlinear auto-regressive models. Linear Auto-regressive models (AR, ARMA and ARIMA) and Auto-regressive Neural Networks (ANNs) have been found insufficient because of the highly complicated nature of some time series. Hybrid models are a recent solution to deal with non-stationary processes which combine pre-processing techniques with conventional forecasters, some pre-processing techniques broadly implemented are Singular Spectrum Analysis (SSA) and Stationary Wavelet Transform (SWT). Although the flexibility of SSA and SWT allows their usage in a wide range of forecast problems, there is a lack of standard methods to select their parameters. The proposed decomposition HSVD and Multilevel SVD are described in detail through time series coming from the transport and fishery sectors. Further, for comparison purposes, it is evaluated the forecast accuracy reached by SSA and SWT, both jointly with AR-based models and ANNs. Table of ContentsPreface 1. Time Series and Forecasting 1.1. Introduction 1.2. Time series 1.3. Linear Autoregressive Models 1.4. Artificial Neural Networks 1.5. Hybrid models 1.5.1. Singular Spectrum Analysis 1.5.2. Wavelet Transform 1.6. Forecasting Accuracy Measures 1.7. Empirical Applications 1.7.1. Traffic Accidents Forecasting based on AR, ANNs and Hybrid models. 1.7.2. Anchovy Stock Forecasting based on AR, ANNs and Hybrid models. 1.7.3. Sardine Stock Forecasting based on AR, ANNs and Hybrid models. 2. Decomposition methods based on Singular Value Decomposition of a Hankel matrix 2.1. Introduction 2.2. Eigenvalues and Eigenvectors 2.3. Theorem of Singular Values Decomposition 2.4. One-level Singular Value Decomposition of a Hankel matrix 2.4.1. Embedding 2.4.2. Decomposition 2.4.3. Unembedding 2.4.4. Window Length Selection 2.5. Multi-level Singular Value Decomposition of a Hankel matrix 2.5.1. Embedding 2.5.2. Decomposition 2.5.3. Unembedding 2.5.4. Singular Spectrum Rate 2.6. Empirical Applications 2.6.1. Extraction of Components from traffic accidents time series based on HSVD and MSVD 2.6.2. Extraction of Components from fishery time series based on HSVD and MSVD 3. Forecasting based on components 3.1. Introduction 3.2. One-step ahead forecasting 3.3. Multi-step ahead forecasting 3.3.1. Direct Strategy 3.3.2. MIMO Strategy 3.4. Empirical Applications 3.4.1. Forecasting of traffic accidents based on HSVD and MSVD 3.4.2. Forecasting of anchovy stock based on HSVD and MSVD 3.4.3. Forecasting of sardine stock based on HSVD and MSVD List of Figures List of Tables List of Acronyms List of Symbols References

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Book SynopsisThis book is a concise, self-contained, up-to-date introduction to extremal combinatorics for nonspecialists. There is a strong emphasis on theorems with particularly elegant and informative proofs, they may be called gems of the theory. The author presents a wide spectrum of the most powerful combinatorial tools together with impressive applications in computer science: methods of extremal set theory, the linear algebra method, the probabilistic method, and fragments of Ramsey theory. No special knowledge in combinatorics or computer science is assumed – the text is self-contained and the proofs can be enjoyed by undergraduate students in mathematics and computer science. Over 300 exercises of varying difficulty, and hints to their solution, complete the text.This second edition has been extended with substantial new material, and has been revised and updated throughout. It offers three new chapters on expander graphs and eigenvalues, the polynomial method and error-correcting codes. Most of the remaining chapters also include new material, such as the Kruskal—Katona theorem on shadows, the Lovász—Stein theorem on coverings, large cliques in dense graphs without induced 4-cycles, a new lower bounds argument for monotone formulas, Dvir's solution of the finite field Kakeya conjecture, Moser's algorithmic version of the Lovász Local Lemma, Schöning's algorithm for 3-SAT, the Szemerédi—Trotter theorem on the number of point-line incidences, surprising applications of expander graphs in extremal number theory, and some other new results.Trade ReviewFrom the reviews of the second edition:“This is an entertaining and impressive book. I say impressive because the author managed to cover a very large part of combinatorics in 27 short chapters, without assuming any graduate-level knowledge of the material. … The collection of topics covered is another big advantage of the book. … The book is ideal as reference material or for a reading course for a dedicated graduate student. One could teach a very enjoyable class from it as well … .” (Miklós Bóna, The Mathematical Association of America, May, 2012)"[R]eaders interested in any branch of combinatorics will find this book compelling. ... This book is very suitable for advanced undergraduate and graduate mathematics and computer science majors. It requires a very solid grounding in intermediate-level combinatorics and an appreciation for several proof methods, but it is well worth the study." (G.M. White, ACM Computing Reviews, May 2012)“This is the second edition of a well-received textbook. It has been extended with new and updated results. Typographical errors in the first edition are corrected. … This textbook is suitable for advanced undergraduate or graduate students as well as researchers working in discrete mathematics or theoretical computer science. The author’s enthusiasm for the subject is evident and his writing is clear and smooth. This is a book deserving recommendation.” (Ko-Wei Lih, Zentralblatt MATH, Vol. 1239, 2012)“This is an introductory book that deals with the subject of extremal combinatorics. … The book is nicely written and the author has included many elegant and beautiful proofs. The book contains many interesting exercises that will stimulate the motivated reader to get a better understanding of this area. … author’s goal of writing a self-contained book that is more or less up to date … and that is accessible to graduate and motivated undergraduate students in mathematics and computer science, has been successfully achieved.” (Sebastian M. Cioabă, Mathematical Reviews, January, 2013)Table of ContentsPreface.- Prolog: What this Book Is About.- Notation.- Counting.- Advanced Counting.- Probabilistic Counting.- The Pigeonhole Principle.- Systems of Distinct Representatives.- Sunflowers.- Intersecting Families.- Chains and Antichains.- Blocking Sets and the Duality.- Density and Universality.- Witness Sets and Isolation.- Designs.- The Basic Method.- Orthogonality and Rank Arguments.- Eigenvalues and Graph Expansion.- The Polynomial Method.- Combinatorics of Codes.- Linearity of Expectation.- The Lovász Sieve.- The Deletion Method.- The Second Moment Method.- The Entropy Function.- Random Walks.- Derandomization.- Ramseyan Theorems for Numbers.- The Hales–Jewett Theorem.- Applications in Communications Complexity.- References.- Index.

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Book SynopsisThis book constitutes the refereed proceedings of the 13th Algorithms and Data Structures Symposium, WADS 2013, held in London, ON, Canada, August 2013. The Algorithms and Data Structures Symposium - WADS (formerly "Workshop on Algorithms and Data Structures") is intended as a forum for researchers in the area of design and analysis of algorithms and data structures. The 44 revised full papers presented in this volume were carefully reviewed and selected from 139 submissions. The papers present original research on algorithms and data structures in all areas, including bioinformatics, combinatorics, computational geometry, databases, graphics, and parallel and distributed computing.Table of ContentsAlgorithms and data structures in bioinformatics.- Algorithms and data structures in combinatorics.- Algorithms and data structures in computational geometry.- Algorithms and data structures in databases.- Algorithms and data structures in graphics.- Parallel and distributed computing.

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Book SynopsisThis textbook contains the mathematics needed to study computer science in application-oriented computer science courses. The content is based on the author's many years of teaching experience.The translation of the original German 7th edition Mathematik für Informatiker by Peter Hartmann was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.Textbook Features You will always find applications to computer science in this book. Not only will you learn mathematical methods, you will gain insights into the ways of mathematical thinking to form a foundation for understanding computer science. Proofs are given when they help you learn something, not for the sake of proving. Mathematics is initially a necessary evil for many students. The author explains in each lesson how students can apply what they have learned by giving many real world examples, and by constantly cross-referencing math and computer science. Students will see how math is not only useful, but can be interesting and sometimes fun.The Content Sets, logic, number theory, algebraic structures, cryptography, vector spaces, matrices, linear equations and mappings, eigenvalues, graph theory. Sequences and series, continuous functions, differential and integral calculus, differential equations, numerics. Probability theory and statistics. The Target AudiencesStudents in all computer science-related coursework, and independent learners.Table of ContentsDISCRETE MATHEMATICS AND LINEAR ALGEBRA.- Sets and mappings.- Logic.- Natural numbers, complete induction, recursion.- Some number theory.- Algebraic structures.- Vector spaces.- Matrices.- Gaussian algorithm and systems of linear equations.- Eigenvalues, eigenvectors and basis transformations.- Scalar product and orthogonal maps.- Graph theory.- ANALYSIS.- The real numbers.- Sequences and series.- Continuous functions.- Differential calculus.- Integral calculus.- Differential equations.- Numerical methods.- PROBABILITY AND STATISTICS.- Probability spaces.- Random variables.- Important distributions and stochastic processes.- Statistical methods.- Appendix.

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Book SynopsisZahlen und Mengen.- Arithmetik.- Folgen, Summen und vollständige Induktion.- Zahlensysteme.- Spezielle Mengen.- Logik.- Abbildungen und Funktionen.- Relationen.- Einführung in die Modulare Artihmetik.- Einführung in die Algorithmen.- Modulare Arithmetik: Teilbarkeit, Division, Potenzen.- Chinesische Restsatz.- Kleine Satz von Fermat, Satz von Euler.- Kryptographie.- Rekursion und Iteration.- Laufzeiten von Algorithmen.- Datenstrukturen und Algorithmen.- Binäre Bäume.- Sortieren.- Suchen in Graphen.- Lineare Algebra.- Kombinatorik und Wahrscheinlichkeitsrechnung.- Natural Language Processing (NLP).

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Book SynopsisNeural Network (NN) Theory, NN-based Control Systems, Neuro-system Integration and Engineering Applications.- Explainable Strategy Generation Based on Neurally Directed Program Search in Adversarial Environment.- An Efficient Mapping Framework for 2D Quantum Architecture.- Improved Soft Actor-Critic Algorithm for Autonomous Helicopter Target Hovering.- Dynamic Weighted Voting Fusion Network for Raman Spectra of Hydroxylated Polycyclic Aromatic Hydrocarbons.- KAN-Driven Graph Networks: Multi-Domain Randomization and Regularization.- Energy Management in Microgrids Using Deep Reinforcement Learning.- Building a Surrogate Model for Diesel Engine Intake-Exhaust Systems Using Neural Ordinary Differential Equations.- Dynamic Path Planning of UAV by Using TD3-Enhanced Adaptive Potential Field.- Exploring Emotion Regulation Mechanisms in Healthy Aging based on EEG Multiband Functional Connectivity.- Structured Pruning for Model Compression in Passionflower Recognition.- Robust Reinforcement Learning for UAV via Contrastive Feature Representations.- The Paradox of Uncertainty: How Tolerance for Uncertainty Modulates Approach Motivation - Evidence from ERPs Experiments.- Design of Triple Notch Ultra-wideband Antenna Based on Multi-strategy Improved Whale Optimization Algorithm.- Indoor Decoration Robot Localization Method Based on Building Information Modeling.- Deep Learning-driven Pattern Recognition, Computer Vision and its Industrial Applications.- Neural Architecture Search for Medical Image Classification via Latent Space and Evolutionary Optimization.- PMF-YOLO: Object Detection in Multimodal Remote Sensing Images Based on Pixel and Multi-scale Fusion.- A Challenge on Gradient Compression of Distributed Training in Image Classification.- Research on Visual Automatic Detection and Tracking Algorithm for Horizontal Transportation Vehicles in Container Terminals.- TOAF-Det: A Remote Sensing Image Detector with Supervised Attention Mechanism.- Edge Feature-enhanced Swin Transformer for Insect Image Classification.- Brain Network Analysis Based on Fine-tuned Self-supervised Model for Brain Disease Diagnosis.- A Machine Vision-Based Method for Pantograph–Catenary Contact Point Position Detection on Electrified Highways.- An Advanced WaveGAN Approach for Data Generation of ECG Images.- Design of Lightweight Fish Classification Model based on Neural Architecture Search.- Deep Learning-Based Cell Type Deconvolution in Spatial Transcriptomics: A Brief Review.- LViT: A Lightweight ViT for Stroke Lesion Segmentation.- Dynamic Threshold Token Subsampling for Vision Transformer in Cloud Computing.- HCEVAE: A Robust Heterogeneous Causal Effects Variational Autoencoder Framework.- EEG and fNIRS-Based Emotion Recognition Using an Improved Graph Isomorphism Network.

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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.

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

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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.

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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.

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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.

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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

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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

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