Mathematics Books

Book SynopsisThe chapters in this contributed volume showcase current theoretical approaches in the modeling of ocular fluid dynamics in health and disease. By including chapters written by experts from a variety of fields, this volume will help foster a genuinely collaborative spirit between clinical and research scientists. It vividly illustrates the advantages of clinical and experimental methods, data-driven modeling, and physically-based modeling, while also detailing the limitations of each approach. Blood, aqueous humor, vitreous humor, tear film, and cerebrospinal fluid each have a section dedicated to their anatomy and physiology, pathological conditions, imaging techniques, and mathematical modeling. Because each fluid receives a thorough analysis from experts in their respective fields, this volume stands out among the existing ophthalmology literature.Ocular Fluid Dynamics is ideal for current and future graduate students in applied mathematics and ophthalmology who wish to explore the field by investigating open questions, experimental technologies, and mathematical models. It will also be a valuable resource for researchers in mathematics, engineering, physics, computer science, chemistry, ophthalmology, and more.Table of ContentsPart I. Introduction.- Mathematical and physical modeling principles of complex biological systems.- Part II. Blood.- Vascular Anatomy and Physiology of the Eye.- Pathological Consequences of Vascular Hemodynamic Alterations in the Eye.- Measurement of geometrical and functional parameters related to ocular blood flow.- Mathematical modeling of blood flow in the eye.- Part III. Aqueous Humor.- Changes in Parameters of Aqueous Humor Dynamics Throughout Life.- Aqueous Humor Dynamics and its Influence on Glaucoma.- Approaches to Aqueous Humor Outflow Imaging.

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Book SynopsisThis monograph could be used for a graduate course on symplectic geometry as well as for independent study.The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.Trade Review“The target audience is graduate students; ... this monograph could easily be used by researchers interested in learning the subject at a fast pace. It is a perfect text for a seminar course. ... the book's material is presented in a crisp and abridged manner. ... This makes the presentation short and highly valuable.” (Eduardo A. Gonzalez, Mathematical Reviews, December, 2020)Table of ContentsSymplectic vector spaces.- Hamiltonian group actions.- The Darboux-Weinstein Theorem.- Elementary properties of moment maps.- The symplectic structure on coadjoint orbits.- Symplectic Reduction.- Convexity.- Toric Manifolds.- Equivariant Cohomology.- The Duistermaat-Heckman Theorem.- Geometric Quantization.- Flat connections on 2-manifolds.

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Book SynopsisThis book provides an essential introduction to Stochastic Programming, especially intended for graduate students. The book begins by exploring a linear programming problem with random parameters, representing a decision problem under uncertainty. Several models for this problem are presented, including the main ones used in Stochastic Programming: recourse models and chance constraint models. The book not only discusses the theoretical properties of these models and algorithms for solving them, but also explains the intrinsic differences between the models. In the book’s closing section, several case studies are presented, helping students apply the theory covered to practical problems. The book is based on lecture notes developed for an Econometrics and Operations Research course for master students at the University of Groningen, the Netherlands - the longest-standing Stochastic Programming course worldwide. Trade Review“The book is well written. The book will be of interest to mathematicians, engineers, economics and especially graduate students.” (I. M. Stancu-Minasian, zbMATH 1446.90118, 2020)Table of ContentsIntroduction.- Random Objective Functions.- Recourse Models.- Stochastic Mixed-integer Programming.- Chance Constraints.- Integrated Chance Constraints.- Assignments.- Case Studies.

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Book SynopsisThis book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions.The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes’s theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics.The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis. Trade Review“The book is carefully prepared and well presented, and I recommend the book … for students who have just mastered vector calculus and Maxwellian electromagnetism.” (Hirokazu Nishimura, zbMATH 1433.58001, 2020)Table of ContentsPrelude: Linear algebra.- Exterior algebra.- Clifford algebra.- Mappings of inner product spaces.- Spinors in inner product spaces.- Interlude: Analysis.- Exterior calculus.- Hodge decompositions.- Hypercomplex analysis.- Dirac equations.- Multivector calculus on manifolds.- Two index theorems.

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Book SynopsisThis book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided. We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications. After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc. The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics. Table of ContentsHolomorphic functions.- Meromorphic functions.- Riemann's theorem.- Harmonic functions.- Riemann surfaces and their modules.- Compact Riemann surfaces and algebraic curves.- Riemann-Roch theorem and theta functions.- Integrable Systems.- The formula for the conformal mapping of an arbitrary domain into the unit disk.

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Book SynopsisThe new edition of this book provides an easily accessible introduction to the statistical analysis of network data using R. It has been fully revised and can be used as a stand-alone resource in which multiple R packages are used to illustrate how to conduct a wide range of network analyses, from basic manipulation and visualization, to summary and characterization, to modeling of network data. The central package is igraph, which provides extensive capabilities for studying network graphs in R. The new edition of this book includes an overhaul to recent changes in igraph. The material in this book is organized to flow from descriptive statistical methods to topics centered on modeling and inference with networks, with the latter separated into two sub-areas, corresponding first to the modeling and inference of networks themselves, and then, to processes on networks. The book begins by covering tools for the manipulation of network data. Next, it addresses visualization and characterization of networks. The book then examines mathematical and statistical network modeling. This is followed by a special case of network modeling wherein the network topology must be inferred. Network processes, both static and dynamic are addressed in the subsequent chapters. The book concludes by featuring chapters on network flows, dynamic networks, and networked experiments. Statistical Analysis of Network Data with R, 2nd Ed. has been written at a level aimed at graduate students and researchers in quantitative disciplines engaged in the statistical analysis of network data, although advanced undergraduates already comfortable with R should find the book fairly accessible as well.Table of Contents1 Introduction.- 2 Manipulating Network Data.- 3 Visualizing Network Data.- 4 Descriptive Analysis of Network Graph Characteristics.- 5 Mathematical Models for Network Graphs.- 6 Statistical Models for Network Graphs.- 7 Network Topology Inference.- 8 Modeling and Prediction for Processes on Network Graphs.- 9 Analysis of Network Flow Data.- 10 Networked Experiments.- 11 Dynamic Networks.- Index.

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Book SynopsisThis book provides an extensive overview of the principles and methods of sample size calculation and recalculation in clinical trials. Appropriate calculation of the required sample size is crucial for the success of clinical trials. At the same time, a sample size that is too small or too large is problematic due to ethical, scientific, and economic reasons. Therefore, state-of-the art methods are required when planning clinical trials. Part I describes a general framework for deriving sample size calculation procedures. This enables an understanding of the common principles underlying the numerous methods presented in the following chapters. Part II addresses the fixed sample size design, where the required sample size is determined in the planning stage and is not changed afterwards. It covers sample size calculation methods for superiority, non-inferiority, and equivalence trials, as well as comparisons between two and more than two groups. A wide range of further topics is discussed, including sample size calculation for multiple comparisons, safety assessment, and multi-regional trials. There is often some uncertainty about the assumptions to be made when calculating the sample size upfront. Part III presents methods that allow to modify the initially specified sample size based on new information that becomes available during the ongoing trial. Blinded sample size recalculation procedures for internal pilot study designs are considered, as well as methods for sample size reassessment in adaptive designs that use unblinded data from interim analyses. The application is illustrated using numerous clinical trial examples, and software code implementing the methods is provided. The book offers theoretical background and practical advice for biostatisticians and clinicians from the pharmaceutical industry and academia who are involved in clinical trials. Covering basic as well as more advanced and recently developed methods, it is suitable for beginners, experienced applied statisticians, and practitioners. To gain maximum benefit, readers should be familiar with introductory statistics. The content of this book has been successfully used for courses on the topic.Trade Review“The R source code is shown by chapter, well-documented, and easy to find and follow as brief descriptions and necessary specifications for the function calls are given by means of comments. … a wide area of application fields is covered and exhaustive literature references for further reading are given. … The presentation of the material is very reader-friendly, easily accessible and pedagogical … . It is likewise highly recommended … . This is an effective and nicely written reference textbook.” (Oke Gerke, ISCB News, iscb.info, Vol. 72, December, 2021)Table of ContentsPart I Basics 1 Introduction 1.1 Background and outline 1.2 Examples 1.2.1 The ChroPac trial 1.2.2 The Parkinson trial 1.3 General considerations when calculating sample sizes 2 Statistical test and sample size calculation 2.1 The main principle of statistical testing 2.2 The main principle of sample size calculation Part II Sample size calculation 3 Comparison of two groups for normally distributed outcomes and test for difference or superiority 3.1 Background and notation 3.2 z-test 3.3 t-test 3.4 Analysis of covariance 3.5 Bayesian approach 3.5.1 Background 3.5.2 Methods 4 Comparison of two groups for continuous and ordered categorical outcomes and test for difference or superiority 4.1 Background and notation 4.2 Continuous outcomes 4.3 Ordered categorical outcomes 4.3.1 Assumption-free approach 4.3.2 Assuming proportional odds 5 Comparison of two groups for binary outcomes and test for difference and superiority 5.1 Background and notation 5.2 Asymptotic tests 5.2.1 Difference of rates as effect measure 5.2.2 Risk ratio as effect measure 5.2.3 Odds ratio as effect measure 5.2.4 Logistic regression 5.3 Exact unconditional tests 5.3.1 Background 5.3.2 Fisher-Boschloo test 6 Comparison of two groups for time-to-event outcomes and test for differences or superiority 6.1 Background and notation 6.1.1 Time-to-event data 6.1.2 Sample size calculation for time-to-event data 6.2 Exponentially distributed time-to-event data 6.3 Time-to-event data with proportional hazards 6.3.1 Approach of Schoenfeld 6.3.2 Approach of Freedman 7 Comparison of more than two groups and test for difference 7.1 Background and notation 7.2 Normally distributed outcomes 7.3 Continuous outcomes 7.4 Binary outcomes 7.4.1 Analysis with chi-square test 7.4.2 Analysis with Cochran-Armitage test 7.5 Time-to-event outcomes 8 Comparison of two groups and test for non-inferiority 8.1 Background and notation 8.2 Normally distributed outcomes 8.2.1 Difference of means 8.2.2 Ratio of means 8.3 Continuous and ordered categorical outcomes 8.4 Binary outcomes 8.4.1 Analysis with asymptotic tests 8.4.1.1 Difference of rates as effect measure 8.4.1.2 Risk ratio as effect measure 8.4.1.3 Odds ratio as effect measure 8.4.2 Exact unconditional tests 8.4.2.1 Background 8.4.2.2 Difference of rates as effect measure 8.4.2.3 Risk ratio as effect measure 8.4.2.4 Odds ratio as effect measure 8.5 Time-to-event outcomes 9 Comparison of three groups in the gold standard non-inferiority design 9.1 Background and notation 9.2 Net effect approach 9.3 Fraction effect approach 10 Comparison of two groups for normally distributed outcomes and test for equivalence 10.1 Background and notation 10.2 Difference of means 10.3 Ratio of means 11 Multiple comparisons 11.1 Background and notation 11.2 Generally applicable sample size calculation methods and applications 11.2.1 Methods 11.2.2 Applications 11.3 Multiple endpoints 11.3.1 Background and notation 11.3.2 Methods 11.4 More than two groups 11.4.1 Background and notation 11.4.2 Dunnett test 12 Assessment of safety 12.1 Background and notation 12.2 Testing hypotheses on the event probability 12.3 Estimating the occurrence probability of an event with specified precision 12.4 Observing at least one event 13 Cluster-randomized trials 13.1 Background and notation 13.2 Normally distributed outcomes 13.2.1 Cluster-level analysis 13.2.2 Individual-level analysis 13.2.3 Dealing with unequal cluster size 13.3 Other scale levels of the outcome 14 Multi-regional trials 14.1 Background and notation 14.2 Sample size calculation for demonstrating consistency of global results and results for a specified region 14.3 Sample size calculation for demonstrating a consistent trend across all regions 15 Integrated planning of phase II/III drug development programs 15.1 Background and notation 15.2 Optimizing phase II/III programs 16 Simulation-based sample size calculation Part III Sample size recalculation 17 Background Part IIIA Blinded sample size recalculation in internal pilot study designs 18 Background and notation 19 A general approach for controlling the type I error rate for blinded sample size recalculation 20 Comparison of two groups for normally distributed outcomes and test for difference or superiority 20.1 t-Test 20.1.1 Background and notation 20.1.2 Blinded variance estimation 20.1.3 Type I error rate 20.1.4 Power and sample size 20.2 Analysis of covariance 20.2.1 Background and notation 20.2.2 Blinded variance estimation 20.2.3 Type I error rate 20.2.4 Power and sample size 21 Comparison of two groups for binary outcomes and test for difference or superiority 21.1 Background and notation 21.2 Asymptotic tests 21.2.1 Difference of rates as effect measure 21.2.2 Risk ratio and odds ratio as effect measure 21.3 Fisher-Boschloo test 22 Comparison of two groups for normally distributed outcomes and test for non-inferiority 22.1 t-Test 22.1.1 Background and notation 22.1.2 Blinded variance estimation 22.1.3 Type I error rate 22.1.4 Power and sample size 22.2 Analysis of covariance 23 Comparison of two groups for binary outcomes and test for non-inferiority 23.1 Background and notation 23.2 Difference of rates as effect measure 23.3 Risk ratio and odds ratio as effect measure 24 Comparison of two groups for normally distributed outcomes and test for equivalence 25 Regulatory and operational aspects 26 Concluding remarks Part IIIB Unblinded sample size recalculation in adaptive designs 27 Background and notation 27.1 Group-sequential designs 27.2 Adaptive designs 27.2.1 Combination function approach 27.2.2 Conditional error function approach 28 Sample size recalculation based on conditional power 28.1 Background and notation 28.2 Using the interim estimate of the effect 28.3 Using the initially specified effect 28.4 Using prior information as well as the interim effect estimate 29 Sample size recalculation by optimization 30 Regulatory and operational aspects 31 Concluding remarks Appendix: Selected R software code References

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Book SynopsisThis book contains 296 exercises and solutions covering a wide variety of topics in linear model theory, including generalized inverses, estimability, best linear unbiased estimation and prediction, ANOVA, confidence intervals, simultaneous confidence intervals, hypothesis testing, and variance component estimation. The models covered include the Gauss-Markov and Aitken models, mixed and random effects models, and the general mixed linear model. Given its content, the book will be useful for students and instructors alike. Readers can also consult the companion textbook Linear Model Theory - With Examples and Exercises by the same author for the theory behind the exercises.Trade Review“This volume contains solutions to the book's exercises … Many of those exercises stand as useful applications of results stated in the theory volume. Some of them go one step beyond and extend the theoretical results. I found this to be a very interesting and unique feature of the book on linear models, making the whole set particularly useful for both graduate students and instructors.” (Vassilis G. S. Vasdekis, Mathematical Reviews, August 2022)Table of Contents1 A Brief Introduction.- 2 Selected Matrix Algebra Topics and Results.- 3 Generalized Inverses and Solutions to Sytems of Linear Equations.- 4 Moments of a Random Vector and of Linear and Quadratic Forms in a Random Vector.- 5 Types of Linear Models.- 6 Estimability.- 7 Least Squares Estimation for the Gauss-Markov Model.- 8 Least Squares Geometry and the Overall ANOVA.- 9 Least Squares Estimation and ANOVA for Partitioned Models.- 10 Constrained Least Squares Estimation and ANOVA.- 11 Best Linear Unbiased Estimation for the Aitken Model.- 12 Model Misspecification.- 13 Best Linear Unbiased Prediction.- 14 Distribution Theory.- 15 Inference for Estimable and Predictable Functions.- 16 Inference for Variance-Covariance Parameters.- 17 Empirical BLUE and BLUP.

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

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Book SynopsisThis popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory.Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as: limit theorems for sums of random variables martingales percolation Markov chains and electrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integrals and stochastic differential equations. The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts.This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.Table of Contents1 Basic Measure Theory.- 2 Independence.- 3 Generating Functions.- 4 The Integral.- 5 Moments and Laws of Large Numbers.- 6 Convergence Theorems.- 7 Lp-Spaces and the Radon–Nikodym Theorem.- 8 Conditional Expectations.- 9 Martingales.- 10 Optional Sampling Theorems.- 11 Martingale Convergence Theorems and Their Applications.- 12 Backwards Martingales and Exchangeability.- 13 Convergence of Measures.- 14 Probability Measures on Product Spaces.- 15 Characteristic Functions and the Central Limit Theorem.- 16 Infinitely Divisible Distributions.- 17 Markov Chains.- 18 Convergence of Markov Chains.- 19 Markov Chains and Electrical Networks.- 20 Ergodic Theory.- 21 Brownian Motion.- 22 Law of the Iterated Logarithm.- 23 Large Deviations.- 24 The Poisson Point Process.- 25 The Itô Integral.- 26 Stochastic Differential Equations.- References.- Notation Index.- Name Index.- Subject Index.

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Book SynopsisThis textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results. The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained. Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation. Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus.After a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications. The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics.Sequents and Trees is suitable for graduate and advanced undergraduate students in logic taking courses on proof theory and its application to non-classical logics. It will also be of interest to researchers in computer science and philosophers.Trade Review“Each chapter of the book is structured in a similar way and contains the basic definitions, facts and necessary discussion regarding the key notions, accompanied with new ideas and a wide reference list, followed by the author's clear and approachable style. This book is self-contained, presenting an extensive survey of the applications and usefulness of cut elimination, and seems to be an extremely interesting source not only for logicians and philosophers, but also for researchers in computer science.” (Branislav Boričić, Mathematical Reviews, May, 2022)Table of ContentsIntroduction.- Analytic Sequent Calculus for CPL.- Gentzen's Sequent Calculus LK.- Purely Logical Sequent Calculus.- Sequent Calculi for Modal Logics.- Alternatives to CPL.- Appendix.

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Book SynopsisThis book presents, in a clear and structured way, the set function \mathcal{T} and how it evolved since its inception by Professor F. Burton Jones in the 1940s. It starts with a very solid introductory chapter, with all the prerequisite material for navigating through the rest of the book. It then gradually advances towards the main properties, Decomposition theorems, \mathcal{T}-closed sets, continuity and images, to modern applications.The set function \mathcal{T} has been used by many mathematicians as a tool to prove results about the semigroup structure of the continua, and about the existence of a metric continuum that cannot be mapped onto its cone or to characterize spheres. Nowadays, it has been used by topologists worldwide to investigate open problems in continuum theory.This book can be of interest to both advanced undergraduate and graduate students, and to experienced researchers as well. Its well-defined structure make this book suitable not only for self-study but also as support material to seminars on the subject. Its many open problems can potentially encourage mathematicians to contribute with further advancements in the field.Table of ContentsPreliminaries.- The Set Function T.- Decomposition Theorems.- T-Closed Sets.- Continuity of T.- Images of T.- Applications.- Questions.- References.- Index.

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Book SynopsisThis textbook is a step-by-step guide for high school, community college, and undergraduate students who are taking a course in applied statistics and wish to learn how to use Excel to solve statistical problems. All of the statistics problems in this book come from the following fields of study: business, education, psychology, marketing, engineering and advertising. Students will learn how to perform key statistical tests in Excel without being overwhelmed by statistical theory. Each chapter briefly explains a topic and then demonstrates how to use Excel commands and formulas to solve specific statistics problems. The book offers guidance in using Excel in two different ways: (1) writing formulas (e.g., confidence interval about the mean, one-group t-test, two-group t-test, correlation) and (2) using Excel’s drop-down formula menus (e.g., simple linear regression, multiple correlations and multiple regression, and one-way ANOVA). Three practice problems are provided at the end of each chapter, along with their solutions in an appendix. An additional practice test allows readers to test their understanding of each chapter by attempting to solve a specific statistics problem using Excel; the solution to each of these problems is also given in an appendix. This book is a tool that can be used either by itself or along with any good statistics book.​Table of ContentsPreface.- Acknowledgements.- 1 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean.- 2 Random Number Generator.- 3 Confidence Interval About the Mean Using the TINV Function and Hypothesis Testing.- 4 One-Group t-Test for the Mean.- 5 Two-Group t-Test of the Difference of the Means for Independent Groups.- 6 Correlation and Simple Linear Regression.- 7 Multiple Correlation and Multiple Regression.- 8 One-Way Analysis of Variance (ANOVA).- Appendix A: Answers to End-of-Chapter Practice Problems.- Appendix B: Practice Test.- Appendix C: Answers to Practice Test.- Appendix D: Statistical Formulas.- Appendix E: t-table.- Index.

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

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

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Book SynopsisThis book presents a history of differential equations, both ordinary and partial, as well as the calculus of variations, from the origins of the subjects to around 1900. Topics treated include the wave equation in the hands of d’Alembert and Euler; Fourier’s solutions to the heat equation and the contribution of Kovalevskaya; the work of Euler, Gauss, Kummer, Riemann, and Poincaré on the hypergeometric equation; Green’s functions, the Dirichlet principle, and Schwarz’s solution of the Dirichlet problem; minimal surfaces; the telegraphists’ equation and Thomson’s successful design of the trans-Atlantic cable; Riemann’s paper on shock waves; the geometrical interpretation of mechanics; and aspects of the study of the calculus of variations from the problems of the catenary and the brachistochrone to attempts at a rigorous theory by Weierstrass, Kneser, and Hilbert. Three final chapters look at how the theory of partial differential equations stood around 1900, as they were treated by Picard and Hadamard. There are also extensive, new translations of original papers by Cauchy, Riemann, Schwarz, Darboux, and Picard. The first book to cover the history of differential equations and the calculus of variations in such breadth and detail, it will appeal to anyone with an interest in the field. Beyond secondary school mathematics and physics, a course in mathematical analysis is the only prerequisite to fully appreciate its contents. Based on a course for third-year university students, the book contains numerous historical and mathematical exercises, offers extensive advice to the student on how to write essays, and can easily be used in whole or in part as a course in the history of mathematics. Several appendices help make the book self-contained and suitable for self-study.Trade Review“This book is a very good example of a text for a course in the history of mathematics. … the author provides for students and readers a historical overview of how mathematics, physics, celestial mechanics and difficult problems to tackle from differential equations as well as applications were intertwined, and the resulting dialogues between mathematicians, physicists and astronomers. This book is a successful attempt to fill in some of the gaps on the history of differential equations.” (‪Clara Silvia Roero, Mathematical Reviews, September, 2022)Table of Contents1 The First Ordinary Differential Equations.- 2 Variational Problems and the Calculus.- 3 The Partial Differential Calculus.- 4 Rational Mechanics.- 5 Partial Differential Equations.- 6 Lagrange's General Theory.- 7 The Calculus of Variations.- 8 Monge and Solutions to Partial Differential Equations.- 9 Revision.- 10 The Heat Equation.- 11 Gauss and the Hypergeometric Equation.- 12 Existence Theorem.- 13 Riemann and Complex Function Theory.- 14 Riemann and the Hypergeometric Equation.- 15 Schwarz and the Complex Hypergeometric Equation.- 16 Complex Ordinary Differential Equations: Poincaré.- 17 More General Partial Differential Equations.- 18 Green's Functions and Dirichlet's Principle.- 19 Attempts on Laplace's Equation.- 20 Applied Wave Equations.- 21 Revision.- 22 Riemann's Shock Wave Paper.- 23 The Example of Minimal Surfaces.- 24 Partial Differential Equations and Mechanics.- 25 Geometrical Interpretations of Mechanics.- 26 The Calculus of Variations in the 19th Century.- 27 Poincaré and Mathematical Physics.- 28 Elliptic Equations and Regular Variational Problems.- 29 Hyperbolic Equations.- 30 Revision.- 32 Translations.- A Newton's Principia Mathematica.- B Characteristics.- C First-order Non-linear Equations.- D Green's Theorem and Heat Conduction.- E Complex Analysis.- F Möbius Transformations.- G Lipschitz and Picard.- H The Assessment.- Bibliography.- Index.

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Book SynopsisThis introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.Trade Review“This newest edition has been reclassified, fittingly, as a graduate text, and it is admirably suited to that role. … Those who are already well-versed in logic will find this text to be a valuable reference and a strong resource for teaching at the graduate level, while those who are new to the field will come to know not only how mathematical logic is studied but also, perhaps more importantly, why.” (Stephen Walk, MAA Reviews, January 6, 2023)Table of ContentsA.- I Introduction.- II Syntax of First-Order Languages.- III Semantics of First-Order Languages.- IV A Sequent Calculus.- V The Completeness Theorem.- VI The Löwenheim–Skolem and the Compactness Theorem.- VII The Scope of First-Order Logic.- VIII Syntactic Interpretations and Normal Forms.- B.- IX Extensions of First-Order Logic.- X Computability and Its Limitations.- XI Free Models and Logic Programming.- XII An Algebraic Characterization of Elementary Equivalence.- XIII Lindström’s Theorems.- References.- List of Symbols.- Subject Index.

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Book SynopsisThis richly illustrated book describes statistical extreme value theory for the quantification of natural hazards, such as strong winds, floods and rainfall, and discusses an interdisciplinary approach to allow the theoretical methods to be applied. The approach consists of a number of steps: data selection and correction, non-stationary theory (to account for trends due to climate change), and selecting appropriate estimation techniques based on both decision-theoretic features (e.g., Bayesian theory), empirical robustness and a valid treatment of uncertainties. It also examines and critically reviews alternative approaches based on stochastic and dynamic numerical models, as well as recently emerging data analysis issues and presents large-scale, multidisciplinary, state-of-the-art case studies. Intended for all those with a basic knowledge of statistical methods interested in the quantification of natural hazards, the book is also a valuable resource for engineers conducting risk analyses in collaboration with scientists from other fields (such as hydrologists, meteorologists, climatologists). Table of Contents1 E. Garnier: Extreme Events and History: for a better consideration of natural hazards.- 2 N. Bousquet and P. Bernardara: Introduction.- Part I Standard Extreme Value Theory.- 3 P. Bernardara and N. Bousquet: Probabilistic modeling and statistical quantification of natural hazards.- 4 N. Bousquet: Fundamental concepts of probability and statistics.- 5 M. Andreewsky and N. Bousquet: Collecting and analyzing data.- 6 A. Dutfoy: Univariate extreme value theory: practice and limitations.- Part II Elements of Extensive Statistical Analysis.- 7 J. Weiss and M. Andreewsky: Regional extreme value analysis.- 8 S. Parey, T. Hoang: Extreme values of non-stationary time series.- 9 A. Dutfoy: Multivariate extreme value theory: practice and limits.- 10 S., T. Hoang and N. Bousquet: Stochastic and physics-based simulation of extreme situations.- 11 N. Bousquet: Bayesian extreme value theory.- 12 M. Andreewsky, P. Bernardara, N. Bousquet, A. Dutfoy and S. Parey: Perspectives.- Part III Detailed Case Studies on Natural Hazards.- 13 P. Bernardara: Predicting extreme ocean swells.- 14 M. Andreewsky: Predicting storm surges.- 15 S. Parey: Forecasting extreme winds.- 16 N. Roche and A. Dutfoy: Conjunction of rainfall in neighboring watersheds.- 17 A. Sibler and A. Dutfoy: Conjunction of a flood and a storm.- 18 E. Paquet: SCHADEX: an alternative to extreme value statistics in hydrology.- Appendix A.- Appendix B.- References.- Index.

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Book SynopsisThis richly illustrated book introduces the subject of optimization to a broad audience with a balanced treatment of theory, models and algorithms. Through numerous examples from statistical learning, operations research, engineering, finance and economics, the text explains how to formulate and justify models while accounting for real-world considerations such as data uncertainty. It goes beyond the classical topics of linear, nonlinear and convex programming and deals with nonconvex and nonsmooth problems as well as games, generalized equations and stochastic optimization.The book teaches theoretical aspects in the context of concrete problems, which makes it an accessible onramp to variational analysis, integral functions and approximation theory. More than 100 exercises and 200 fully developed examples illustrate the application of the concepts. Readers should have some foundation in differential calculus and linear algebra. Exposure to real analysis would be helpful but is not prerequisite. Trade Review“In the reviewer's opinion, this is an important book … . a lot of applications are given, so on one hand the readers can benefit from deep insights into the mathematical background of optimization theory … . This book, which as all books reflects the tastes of its authors, is a solid reference, not only for graduate students and postgraduate students, but also for all those researchers interested in recent developments of optimization theory and methods.” (Giorgio Giorgi, Mathematical Reviews, December, 2022)Table of ContentsPrelude.- Convex optimization.- Optimization under uncertainty.- Minimization problems.- Perturbation and duality.- Without convexity or smoothness.- Generalized Equations.- Risk modeling and sample averages.- Games and minsup problems.- Decomposition.

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

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Book SynopsisThis book presents covariance matrix estimation and related aspects of random matrix theory. It focuses on the sample covariance matrix estimator and provides a holistic description of its properties under two asymptotic regimes: the traditional one, and the high-dimensional regime that better fits the big data context. It draws attention to the deficiencies of standard statistical tools when used in the high-dimensional setting, and introduces the basic concepts and major results related to spectral statistics and random matrix theory under high-dimensional asymptotics in an understandable and reader-friendly way. The aim of this book is to inspire applied statisticians, econometricians, and machine learning practitioners who analyze high-dimensional data to apply the recent developments in their work.Table of ContentsForeword.- 1 Introduction.- 2 Traditional Estimators and Standard Asymptotics.- 3 Finite Sample Performance of Traditional Estimators.- 4 Traditional Estimators and High-Dimensional Asymptotics.- 5 Summary and Outlook.- Appendices.

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Book SynopsisThis Fourth Edition updates the "Solutions Manual for Econometrics" to match the Sixth Edition of the Econometrics textbook. It adds problems and solutions using latest software versions of Stata and EViews. Special features include empirical examples replicated using EViews, Stata as well as SAS. The book offers rigorous proofs and treatment of difficult econometrics concepts in a simple and clear way, and provides the reader with both applied and theoretical econometrics problems along with their solutions. These should prove useful to students and instructors using this book.Table of ContentsWhat Is Econometrics?.- A Review of Some Basic Statistical Concepts.- Simple Linear Regression.- Multiple Regression Analysis.- Violations of the Classical Assumptions.- Distributed Lags and Dynamic Models.- The General Linear Model: The Basics.- Regression Diagnostics and Specification Tests.- Generalized Least Squares.- Seemingly Unrelated Regressions.- Simultaneous Equations Model.- Pooling Time-Series of Cross-Section Data.- Limited Dependent Variables.- Time-Series Analysis.

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Book SynopsisGraph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, such as approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. This book introduces graph algorithms on an intuitive basis followed by a detailed exposition in a literate programming style, with correctness proofs as well as worst-case analyses. Furthermore, full C++ implementations of all algorithms presented are given using the LEDA library of efficient data structures and algorithms.Table of Contents1. Introduction.- 2. Algorithmic Techniques.- 3. Tree Traversal.- 4. Tree Isomorphism.- 5. Graph Traversal.- 6. Clique, Independent Set, and Vertex Cover.- 7. Graph Isomorphism.

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Book SynopsisThis book discusses a link between statistical theory and quantum theory based on the concept of epistemic processes. The latter are processes, such as statistical investigations or quantum mechanical measurements, that can be used to obtain knowledge about something. Various topics in quantum theory are addressed, including the construction of a Hilbert space from reasonable assumptions and an interpretation of quantum states. Separate derivations of the Born formula and the one-dimensional Schrödinger equation are given. In concrete terms, a Hilbert space can be constructed under some technical assumptions associated with situations where there are two conceptual variables that can be seen as maximally accessible. Then to every accessible conceptual variable there corresponds an operator on this Hilbert space, and if the variables take a finite number of values, the eigenspaces/eigenvectors of these operators correspond to specific questions in nature together with sharp answers to these questions. This paves a new way to the foundations of quantum theory. The resulting interpretation of quantum mechanics is related to Hervé Zwirn's recent Convivial Solipsism, but it also has some relations to Quantum Bayesianism and to Rovelli's relational quantum mechanics. Niels Bohr's concept of complementarity plays an important role. Philosophical implications of this approach to quantum theory are discussed, including consequences for macroscopic settings.The book will benefit a broad readership, including physicists and statisticians interested in the foundations of their disciplines, philosophers of science and graduate students, and anyone with a reasonably good background in mathematics and an open mind.Table of Contents1. The epistemic view upon science.- 2. Statistical inference.- 3. Inference in an epistemic process.- 4. Towards quantum theory.- 5. Aspects of quantum theory.- 6. Macroscopic consequences.

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Book SynopsisThis textbook covers all central activities of data warehousing and analytics, including transformation, preparation, aggregation, integration, and analysis. It discusses the full spectrum of the journey of data from operational/transactional databases, to data warehouses and data analytics; as well as the role that data warehousing plays in the data processing lifecycle. It also explains in detail how data warehouses may be used by data engines, such as BI tools and analytics algorithms to produce reports, dashboards, patterns, and other useful information and knowledge.The book is divided into six parts, ranging from the basics of data warehouse design (Part I - Star Schema, Part II - Snowflake and Bridge Tables, Part III - Advanced Dimensions, and Part IV - Multi-Fact and Multi-Input), to more advanced data warehousing concepts (Part V - Data Warehousing and Evolution) and data analytics (Part VI - OLAP, BI, and Analytics).This textbook approaches data warehousing from the case study angle. Each chapter presents one or more case studies to thoroughly explain the concepts and has different levels of difficulty, hence learning is incremental. In addition, every chapter has also a section on further readings which give pointers and references to research papers related to the chapter. All these features make the book ideally suited for either introductory courses on data warehousing and data analytics, or even for self-studies by professionals. The book is accompanied by a web page that includes all the used datasets and codes as well as slides and solutions to exercises.Table of Contents1. Introduction.- Part I: Star Schema.- 2. Simple Star Schemas.- 3. Creating Facts and Dimensions: More Complex Processes.- Part II: Snowflake and Bridge Tables.- 4. Hierarchies.- 5. Bridge Tables.- 6. Temporal Data Warehousing.- Part III: Advanced Dimension.- 7. Determinant Dimensions.- 8. Junk Dimensions.- 9. Dimension Keys.- 10. One-Attribute Dimensions.- Part IV: Multi-Fact and Multi-Input.- 11. Multi-Fact Star Schemas.- 12. Slicing a Fact.- 13. Multi-Input Operational Databases.- Part V: Data Warehousing Granularity and Evolution.- 14. Data Warehousing Granularity and Levels of Aggregation.- 15. Designing Lowest-Level Star Schemas.- 16. Levels of Aggregation: Adding and Removing Dimensions.- 17. Levels of Aggregation and Bridge Tables.- 18. Active Data Warehousing.- Part VI: OLAP, Business Intelligence, and Data Analytics.- 19. Online Analytical Processing (OLAP).- 20. Pre- and Post-Data Warehousing.- 21. Data Analytics for Data Warehousing.

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Book SynopsisThis survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of “mechanical process” using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs. Advanced chapters cover the Ackerman function, Tarski’s theorem on the non-representability of truth, Goedel’s incompleteness and Rosser’s incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church’s thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum’s complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.Trade Review“This textbook is suited for self-study … . As a second reading however a reader interested in rigorous proofs and/or different approaches to known concepts will benefit from this wealth of material.” (Dieter Riebesehl, zbMATH 1507.03002, 2023)Table of ContentsMathematical Background; a Review.- A Theory of Computability.- Primitive Recursive Functions.- Loop Programs.-The Ackermann Function.- (Un)Computability via Church's Thesis.- Semi-Recursiveness.- Yet another number-theoretic characterisation of P.- Godel's Incompleteness Theorem via the Halting Problem.- The Recursion Theorem.- A Universal (non-PR) Function for PR.- Enumerations of Recursive and Semi-Recursive Sets.- Creative and Productive Sets Completeness.- Relativised Computability.- POSSIBILITY: Complexity of P Functions.- Complexity of PR Functions.- Turing Machines and NP-Completeness.

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Book SynopsisThis book gives a brief treatment of the equivariant cohomology of the classical configuration space F(ℝ^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F(ℝ^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main theorem is given, however it is shown that some of the arguments given by him on the way to his result are incorrect, as are some of the intermediate results in his paper.This invalidates a paper by three of the authors, Blagojević, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and ℓ-skew embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence of highly regular embeddings are obtained: Some of them agree with the previously claimed bounds, some are weaker.Assuming only a standard graduate background in algebraic topology, this book carefully guides the reader on the way into the subject. It is aimed at graduate students and researchers interested in the development of algebraic topology in its applications in geometry.Trade Review“The book is well written. … The book will be important for those who study the cohomology rings of configuration spaces.” (Shintarô Kuroki, Mathematical Reviews, November, 2022)Table of Contents​- 1. Snapshots from the History. - Part I Mod 2 Cohomology of Configuration Spaces. - 2. The Ptolemaic Epicycles Embedding. - 3. The Equivariant Cohomology of Pe(Rd, 2m). - 4. Hu’ng’s Injectivity Theorem. - Part II Applications to the (Non-)Existence of Regular and SkewEmbeddings. - 5. On Highly Regular Embeddings: Revised. - 6. More Bounds for Highly Regular Embeddings. - Part III Technical Tools. - 7. Operads. - 8. The Dickson Algebra. - 9. The Stiefel–Whitney Classes of the Wreath Square of a Vector Bundle. - 10. Miscellaneous Calculations.

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Book SynopsisScientific visualization has always been an integral part of discovery, starting first with simplified drawings of the pre-Enlightenment and progressing to present day. Mathematical formalism often supersedes visual methods, but their use is at the core of the mental process. As historical examples, a spatial description of flow led to electromagnetic theory, and without visualization of crystals, structural chemistry would not exist. With the advent of computer graphics technology, visualization has become a driving force in modern computing. A Concise Introduction to Scientific Visualization – Past, Present, and Future serves as a primer to visualization without assuming prior knowledge. It discusses both the history of visualization in scientific endeavour, and how scientific visualization is currently shaping the progress of science as a multi-disciplinary domain. Table of ContentsPreface.- Early Visual Models.- Illustration and Analysis.- Scientific Visualization in the 19th Century.- A Convergence with Computer Science.- Recent Developments.- The Future.- Bibliography

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Book SynopsisThis monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications.Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or “dit” of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory) and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits—so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general—and to Hilbert spaces in particular—for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement.Relatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory, maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to quantum information theory.Table of Contents- Logical entropy.- The relationship between logical entropy and Shannon entropy.- The compound notions for logical and Shannon entropies.- Further developments of logical entropy.- Logical Quantum Information Theory.- Conclusion.- Appendix: Introduction to the logic of partitions.

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Book SynopsisThis book constitutes the refereed proceedings of the First Workshop on Monte Carlo Search, MCS 2020, organized in conjunction with IJCAI 2020. The event was supposed to take place in Yokohama, Japan, in July 2020, but due to the Covid-19 pandemic was held virtually on January 7, 2021. The 9 full papers of the specialized project were carefully reviewed and selected from 15 submissions. The following topics are covered in the contributions: discrete mathematics in computer science, games, optimization, search algorithms, Monte Carlo methods, neural networks, reinforcement learning, machine learning.Table of ContentsThe αµ Search Algorithm for the Game of Bridge.- Stabilized Nested Rollout Policy Adaptation.- zoNNscan: A Boundary-Entropy Index for Zone Inspection of Neural Models.- Ordinal Monte Carlo Tree Search.- Monte Carlo Game Solver.- Generalized Nested Rollout Policy Adaptation.- Monte Carlo Inverse Folding.- Monte Carlo Graph Coloring.- Enhancing Playout Policy Adaptation for General Game Playing.

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Book SynopsisThis book introduces readers to benchmarking techniques in the stochastic environment, primarily stochastic data envelopment analysis (DEA), and provides stochastic models in DEA for the possibility of variations in inputs and outputs. It focuses on the application of theories and interpretations of the mathematical programs, which are combined with economic and organizational thinking. The book’s main purpose is to shed light on the advantages of the different methods in deterministic and stochastic environments and thoroughly prepare readers to properly use these methods in various cases. Simple examples, along with graphical illustrations and real-world applications in industry, are provided for a better understanding. The models introduced here can be easily used in both theoretical and real-world evaluations. This book is intended for graduate and PhD students, advanced consultants, and practitioners with an interest in quantitative performance evaluation.Table of Contents1. Benchmarking.- 2. An Introduction to Data Envelopment Analysis.- 3. Probability Theory.- 4. Stochastic Data Envelopment Analysis.- 5. Stochastic Network Data Envelopment Analysis.- 6. Stochastic Scale Elasticity.

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Book SynopsisTeaching quantum computation and information is notoriously difficult, because it requires covering subjects from various fields of science, organizing these subjects consistently in a unified way despite their tendency to favor their specific languages, and overcoming the subjects’ abstract and theoretical natures, which offer few examples of actual realizations. In this book, we have organized all the subjects required to understand the principles of quantum computation and information processing in a manner suited to physics, mathematics, and engineering courses as early as undergraduate studies.In addition, we provide a supporting package of quantum simulation software from Wolfram Mathematica, specialists in symbolic calculation software. Throughout the book’s main text, demonstrations are provided that use the software package, allowing the students to deepen their understanding of each subject through self-practice. Readers can change the code so as to experiment with their own ideas and contemplate possible applications. The information in this book reflects many years of experience teaching quantum computation and information. The quantum simulation-based demonstrations and the unified organization of the subjects are both time-tested and have received very positive responses from the students who have experienced them.Trade Review“The book provides an extensive bibliography and index. … this volume is well suited for a advanced graduate or first-year PhD course in quantum mechanics, with ample time available for self-study.” (L.-F. Pau, Computing Reviews, January 30, 2023)Table of Contents1 The Postulates of Quantum Mechanics.- 2 Virtual Realization of Quantum Computers.- 3 Quantum Computation: Overview.- 4 Quantum Algorithms: Introduction.- 5 Quantum Information: Introduction.- 6 Quantum Error Correction Codes: Introduction.- Appendix A Linear Algebra.- Appendix B Mathematica Application Q3.- References.

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Book SynopsisThis compact textbook provides a foundation in mathematics for STEM students entering university. The book helps students from different disciplines and backgrounds make the transition to university. Based on the author’s teaching for many years, the book can be used as a textbook and a resource for lecturers and professors. Its accessibility is such that it is can also be used by students in their final year in school before university and help them continue their mathematical studies at college. The book is designed so that students will return to the book repeatedly as their undergraduate careers progress. Although compact and concise, it loses no rigour. All the topics are carefully explained meaningfully, not just presented as a set of rules or rote-learned procedures. Table of ContentsTrigonometry.- Real and Complex Numbers.- Vector Algebra.- Matrices.- Differentiation.

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Book SynopsisThis compact textbook provides a foundation in mathematics for STEM students entering university. The book helps students from different disciplines and backgrounds make the transition to university. Based on the author’s teaching for many years, the book can be used as a textbook and a resource for lecturers and professors. Its accessibility is such that it is can also be used by students in their final year in school before university and help them continue their mathematical studies at college. The book is designed so that students will return to the book repeatedly as their undergraduate careers progress. Although compact and concise, it loses no rigour. All the topics are carefully explained meaningfully, not just presented as a set of rules or rote-learned procedures. Table of ContentsTrigonometry.- Real and Complex Numbers.- Vector Algebra.- Matrices.- Differentiation.

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Book SynopsisThis book combines the classical and contemporary approaches to differential geometry. An introduction to the Riemannian geometry of manifolds is preceded by a detailed discussion of properties of curves and surfaces.The chapter on the differential geometry of plane curves considers local and global properties of curves, evolutes and involutes, and affine and projective differential geometry. Various approaches to Gaussian curvature for surfaces are discussed. The curvature tensor, conjugate points, and the Laplace-Beltrami operator are first considered in detail for two-dimensional surfaces, which facilitates studying them in the many-dimensional case. A separate chapter is devoted to the differential geometry of Lie groups.Trade Review“All chapters are supplemented with solutions of the problems scattered throughout the text. Designed as a text for a lecturer course on the subject, it is perfect and can be recommended for students interested in this classical field.” (Ivailo. M. Mladenov, zbMATH 1498.53001, 2022)Table of ContentsCurves in the Plane.- Curves in Space.- Surfaces in Space.- Hypersurfaces in Rn+1.- Connections.- Riemannian Manifolds.- Lie Groups.- Comparison Theorems.- Curvature and Topology.- Laplacian.- Appendix.- Bibliography.- Index.

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Book SynopsisConservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks. Table of ContentsIntroduction.- Boundary Control.- Decentralized Control.- Distributed Control.- Lagrangian Control.- Hamilton-Jacobi Equations.- Appendix A: Balance Laws with Boundary.- Conservation Laws on Networks.

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Book SynopsisThis book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2022, held in Deerfield Beach, FL, USA, in January 2022. The 23 revised full papers were carefully reviewed and selected from 35 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.Table of ContentsA Non-Hyperarithmetical Gödel Logic.- Shorten Resolution Proofs Non-Elementarily.- The Isomorphism Problem for FST Injection Structures.- Justification Logic and Type Theory as Formalizations of Intuitionistic Propositional Logic.- Hyperarithmetical Worm Battles.- Parametric Church’s Thesis: Synthetic Computability Without Choice.- Constructive and Mechanised Meta-Theory of Intuitionistic Epistemic Logic.- A Parametrized Family of Tversky Metrics Connecting the Jaccard Distance to an Analogue of the Normalized Information Distance.- A Parameterized View on the Complexity of Dependence Logic.- A Logic of Interactive Proofs.- Recursive Rules With Aggregation: A Simple Unified Semantics.- Computational Properties of Partial Non-deterministic Matrices and Their Logics.- Soundness and Completeness Results for LEA and Probability Semantics.- On Inverse Operators in Dynamic Epistemic Logic.- Computability Models Over Categories and Presheaves.- Reducts of Relation Algebras: The Aspects of Axiomatisability and Finite Representability.- Between Turing and Kleene.- Propositional Dynamic Logic With Quantification Over Regular Computation Sequences.- Finite Generation and Presentation Problems for Lambda Calculus and Combinatory Logic.- Exact and Parameterized Algorithms for Read-Once Refutations in Horn Constraint Systems.- Logical Principles.- Small Model Property Reflects in Games and Automata.

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Book SynopsisThis book reviews the theory of 'generalized B*-algebras' (GB*-algebras), a class of complete locally convex *-algebras which includes all C*-algebras and some of their extensions. A functional calculus and a spectral theory for GB*-algebras is presented, together with results such as Ogasawara's commutativity condition, Gelfand–Naimark type theorems, a Vidav–Palmer type theorem, an unbounded representation theory, and miscellaneous applications. Numerous contributions to the subject have been made since its initiation by G.R. Allan in 1967, including the notable early work of his student P.G. Dixon. Providing an exposition of existing research in the field, the book aims to make this growing theory as familiar as possible to postgraduate students interested in functional analysis, (unbounded) operator theory and its relationship to mathematical physics. It also addresses researchers interested in extensions of the celebrated theory of C*-algebras.Trade Review“This book deals with the theory of locally convex algebras, in general, and of generalized B_-algebras (GB_-algebras in short) in particular. It is well written and self-contained.” (Lahbib Oubbi, Mathematical Reviews, November, 2023)“The book has been written by specialists that are actively working in the field. The choice of the presented material has been done with great care. The bibliography contains all classical monographs, all important papers, and most recent ones. The book leads the reader 'smoothly' ... . It will therefore serve as an excellent introduction to this theory for graduate students. It should also provide a valuable reference source for researchers in the field.” (Andrzej Sołtysiak, zbMATH 1498.46001, 2022)Table of Contents1. Introduction.- 2. A Spectral Theory for Locally Convex Algebras.- 3. Generalized B*-Algebras: Functional Representation Theory.- 4. Commutative Generalized B*-Algebras: Functional Calculus and Equivalent Topologies.- 5. Extended C*-Algebras and Extended W*-Algebras.- 6. Generalized B*-Algebras: Unbounded *-Representation Theory.- 7. Applications I: Miscellanea.- 8. Applications II: Tensor Products.

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Book SynopsisThis monograph provides a concise overview of nonlinear internal wave theory. It serves as a self-contained reference for both students of mathematics as well as scientific professionals by presenting the material in two parts, isolating the narrative analysis from the mathematical detail. This unique format allows the text to remain accessible to oceanographers and researchers outside of mathematics by presenting a range of relevant theories on their own terms. Conversely, it enables applied mathematicians to understand how the conversation between mathematics and sciences proceeds in a field that has developed through a combination of the two. In addition, the text is supplemented by hands-on Matlab software, as the book incorporates a collection of working codes that enable readers to reproduce all theoretical figures in the text, with modification potential to fit a range of applications including a number of mini-projects outlined throughout the text.Table of ContentsPreface.- Background and Equation Summaries.- Derivations: Linear, Weakly Nonlinear and Conjugate Flow Theory.- Using Linear and Weakly Nonlinear Theory.- Exact Internal Solitary Waves.- Exact Internal Hydraulics.- Mode-2 Waves.- Concluding Thoughts.

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Book SynopsisSemi-supervised learning is a learning paradigm concerned with the study of how computers and natural systems such as humans learn in the presence of both labeled and unlabeled data. Traditionally, learning has been studied either in the unsupervised paradigm (e.g., clustering, outlier detection) where all the data are unlabeled, or in the supervised paradigm (e.g., classification, regression) where all the data are labeled. The goal of semi-supervised learning is to understand how combining labeled and unlabeled data may change the learning behavior, and design algorithms that take advantage of such a combination. Semi-supervised learning is of great interest in machine learning and data mining because it can use readily available unlabeled data to improve supervised learning tasks when the labeled data are scarce or expensive. Semi-supervised learning also shows potential as a quantitative tool to understand human category learning, where most of the input is self-evidently unlabeled. In this introductory book, we present some popular semi-supervised learning models, including self-training, mixture models, co-training and multiview learning, graph-based methods, and semi-supervised support vector machines. For each model, we discuss its basic mathematical formulation. The success of semi-supervised learning depends critically on some underlying assumptions. We emphasize the assumptions made by each model and give counterexamples when appropriate to demonstrate the limitations of the different models. In addition, we discuss semi-supervised learning for cognitive psychology. Finally, we give a computational learning theoretic perspective on semi-supervised learning, and we conclude the book with a brief discussion of open questions in the field. Table of Contents: Introduction to Statistical Machine Learning / Overview of Semi-Supervised Learning / Mixture Models and EM / Co-Training / Graph-Based Semi-Supervised Learning / Semi-Supervised Support Vector Machines / Human Semi-Supervised Learning / Theory and OutlookTable of ContentsIntroduction to Statistical Machine Learning.- Overview of Semi-Supervised Learning.- Mixture Models and EM.- Co-Training.- Graph-Based Semi-Supervised Learning.- Semi-Supervised Support Vector Machines.- Human Semi-Supervised Learning.- Theory and Outlook.

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Book SynopsisAnswer Set Programming (ASP) is a declarative problem solving approach, initially tailored to modeling problems in the area of Knowledge Representation and Reasoning (KRR). More recently, its attractive combination of a rich yet simple modeling language with high-performance solving capacities has sparked interest in many other areas even beyond KRR. This book presents a practical introduction to ASP, aiming at using ASP languages and systems for solving application problems. Starting from the essential formal foundations, it introduces ASP's solving technology, modeling language and methodology, while illustrating the overall solving process by practical examples. Table of Contents: List of Figures / List of Tables / Motivation / Introduction / Basic modeling / Grounding / Characterizations / Solving / Systems / Advanced modeling / ConclusionsTable of ContentsList of Figures.- List of Tables.- Motivation.- Introduction.- Basic modeling.- Grounding.- Characterizations.- Solving.- Systems.- Advanced modeling.- Conclusions.

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Book SynopsisSimilarity between objects plays an important role in both human cognitive processes and artificial systems for recognition and categorization. How to appropriately measure such similarities for a given task is crucial to the performance of many machine learning, pattern recognition and data mining methods. This book is devoted to metric learning, a set of techniques to automatically learn similarity and distance functions from data that has attracted a lot of interest in machine learning and related fields in the past ten years. In this book, we provide a thorough review of the metric learning literature that covers algorithms, theory and applications for both numerical and structured data. We first introduce relevant definitions and classic metric functions, as well as examples of their use in machine learning and data mining. We then review a wide range of metric learning algorithms, starting with the simple setting of linear distance and similarity learning. We show how one may scale-up these methods to very large amounts of training data. To go beyond the linear case, we discuss methods that learn nonlinear metrics or multiple linear metrics throughout the feature space, and review methods for more complex settings such as multi-task and semi-supervised learning. Although most of the existing work has focused on numerical data, we cover the literature on metric learning for structured data like strings, trees, graphs and time series. In the more technical part of the book, we present some recent statistical frameworks for analyzing the generalization performance in metric learning and derive results for some of the algorithms presented earlier. Finally, we illustrate the relevance of metric learning in real-world problems through a series of successful applications to computer vision, bioinformatics and information retrieval. Table of Contents: Introduction / Metrics / Properties of Metric Learning Algorithms / Linear Metric Learning / Nonlinear and Local Metric Learning / Metric Learning for Special Settings / Metric Learning for Structured Data / Generalization Guarantees for Metric Learning / Applications / Conclusion / Bibliography / Authors' BiographiesTable of ContentsIntroduction.- Metrics.- Properties of Metric Learning Algorithms.- Linear Metric Learning.- Nonlinear and Local Metric Learning.- Metric Learning for Special Settings.- Metric Learning for Structured Data.- Generalization Guarantees for Metric Learning.- Applications.- Conclusion.- Bibliography.- Authors' Biographies .

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