This book constitutes the refereed proceedings of the 27th International Symposium on Model Checking Software, SPIN 2021, held virtually in July 2021.The 3 full papers, 4 tool papers, and 1 case study presented together with 2 invited talks were carefully reviewed and selected from 20 submissions. Topics covered include formal verification techniques for automated analysis of software; formal analysis for modeling languages, such as UML/state charts; formal specification languages, temporal logic, design-by-contract; model checking, automated theorem proving, including SAT and SMT; verifying compilers; abstraction and symbolic execution techniques; and much more.

Iceberg semantics is a new framework of Boolean semantics for mass nouns and count nouns in which the interpretation of a noun phrase rises up from a generating base and floats with its base on its Boolean part set, like an iceberg. The framework is shown to preserve the attractive features of classical Boolean semantics for count nouns; the book argues that Iceberg semantics forms a much better framework for studying mass nouns than the classical theory does. Iceberg semantics uses its notion of base to develop a semantic theory of the differences between mass nouns and count nouns and between different types of mass nouns, in particular between prototypical mass nouns (here called mess mass nouns) like water and mud versus object mass nouns (here called neat mass nouns) like poultry and pottery. The book shows in detail how and why neat mass nouns pattern semantically both with mess mass nouns and with count nouns. Iceberg semantics is a compositional theory and in Iceberg semantics the semantic distinctions defined apply to noun phrases of any complexity. The book studies in depth the semantics of classifier noun phrases (like three glasses of wine) and measure noun phrases (like three liters of wine). The classical wisdom is that classifier interpretations are count. Recent literature has argued compellingly that measure interpretations are mass. The book shows that both connections follow from the basic architecture of Iceberg semantics. Audience: Scholars and students in linguistics - in particular semantics, pragmatics, computational linguistics and syntax - and neighbouring disciplines like logic, philosophy of language, and cognitive science.

This volume presents the refereed proceedings of the Guangzhou International Symposium on Computational Mathematics, held at the Zhongshan University, People's Republic of China. Nearly 90 international mathematicians examine numerical optimization methods, wavelet analysis, computational approximation, numerical solutions of differential and integral equations, numerical linear algebra, inverse and ill-posed problems, geometric modelling, and signal and image processing and their applications.

An introduction to computational mechanics, this textbook will enable readers to obtain numerical results to difficult problems that cannot be solved by simple computational formulae. Emphasis is placed on the numerical techniques and how they form a basis for algorithms. Numerous worked examples in structural mechanics, heat transfer, fluid flow, and biomechanics are given with the codes to illustrate how the methods are applied. Chapters complete with homework problems, proceed clearly from basic computational tools to advanced computational procedures for applications. A concluding section addresses advanced applications in such areas as finite volume methods.

This book constitutes the refereed proceedings of the 12th International Conference on the Theory and Application of Diagrams, Diagrams 2021, held virtually in September 2021. The 16 full papers and 25 short papers presented together with 16 posters were carefully reviewed and selected from 94 submissions. The papers are organized in the following topical sections: design of concrete diagrams; theory of diagrams; diagrams and mathematics; diagrams and logic; new representation systems; analysis of diagrams; diagrams and computation; cognitive analysis; diagrams as structural tools; formal diagrams; and understanding thought processes. 10 chapters are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

This book presents a set theoretical development for the foundations of the theory of atomic and finitely supported structures. It analyzes whether a classical result can be adequately reformulated by replacing a 'non-atomic structure' with an 'atomic, finitely supported structure'. It also presents many specific properties, such as finiteness, cardinality, connectivity, fixed point, order and uniformity, of finitely supported atomic structures that do not have non-atomic correspondents. In the framework of finitely supported sets, the authors analyze the consistency of various forms of choice and related results. They introduce and study the notion of 'cardinality' by presenting various order and arithmetic properties. Finitely supported partially ordered sets, chain complete sets, lattices and Galois connections are studied, and new fixed point, calculability and approximation properties are presented. In this framework, the authors study the finitely supported L-fuzzy subsets of a finitely supported set and the finitely supported fuzzy subgroups of a finitely supported group. Several pairwise non-equivalent definitions for the notion of 'infinity' (Dedekind infinity, Mostowski infinity, Kuratowski infinity, Tarski infinity, ascending infinity) are introduced, compared and studied in the new framework. Relevant examples of sets that satisfy some forms of infinity while not satisfying others are provided. Uniformly supported sets are analyzed, and certain surprising properties are presented. Finally, some variations of the finite support requirement are discussed. The book will be of value to researchers in the foundations of set theory, algebra and logic.

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.

This text provides deep and comprehensive coverage of the mathematical background for data science, including machine learning, optimal recovery, compressed sensing, optimization, and neural networks. In the past few decades, heuristic methods adopted by big tech companies have complemented existing scientific disciplines to form the new field of Data Science. This text embarks the readers on an engaging itinerary through the theory supporting the field. Altogether, twenty-seven lecture-length chapters with exercises provide all the details necessary for a solid understanding of key topics in data science. While the book covers standard material on machine learning and optimization, it also includes distinctive presentations of topics such as reproducing kernel Hilbert spaces, spectral clustering, optimal recovery, compressed sensing, group testing, and applications of semidefinite programming. Students and data scientists with less mathematical background will appreciate the appendices that provide more background on some of the more abstract concepts.

This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Caratheodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Henon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.

This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.

The volume contains original research papers as the Proceedings of the International Conference on Advances in Mathematics and Computing, held at Veer Surendra Sai University of Technology, Odisha, India, on 7-8 February, 2020. It focuses on new trends in applied analysis, computational mathematics and related areas. It also includes certain new models, image analysis technique, fluid flow problems, etc. as applications of mathematical analysis and computational mathematics. The volume should bring forward new and emerging topics of mathematics and computing having potential applications and uses in other areas of sciences. It can serve as a valuable resource for graduate students, researchers and educators interested in mathematical tools and techniques for solving various problems arising in science and engineering.

A new class of methods, termed "group explicit methods," is introduced in this text. Their applications to solve parabolic, hyperbolic and elliptic equations are outlined, and the advantages for their implementation on parallel computers clearly portrayed. Also included are the introductory and fundamental concepts from which the new methods are derived, and on which they are dependent. With the increasing advent of parallel computing into all aspects of computational mathematics, there is no doubt that the new methods will be widely used.

Arguably the strongest addition to numerical finance of the past decade, Algorithmic Adjoint Differentiation (AAD) is the technology implemented in modern financial software to produce thousands of accurate risk sensitivities, within seconds, on light hardware. AAD recently became a centerpiece of modern financial systems and a key skill for all quantitative analysts, developers, risk professionals or anyone involved with derivatives. It is increasingly taught in Masters and PhD programs in finance. Danske Bank's wide scale implementation of AAD in its production and regulatory systems won the In-House System of the Year 2015 Risk award. The Modern Computational Finance books, written by three of the very people who designed Danske Bank's systems, offer a unique insight into the modern implementation of financial models. The volumes combine financial modelling, mathematics and programming to resolve real life financial problems and produce effective derivatives software. This volume is a complete, self-contained learning reference for AAD, and its application in finance. AAD is explained in deep detail throughout chapters that gently lead readers from the theoretical foundations to the most delicate areas of an efficient implementation, such as memory management, parallel implementation and acceleration with expression templates. The book comes with professional source code in C++, including an efficient, up to date implementation of AAD and a generic parallel simulation library. Modern C++, high performance parallel programming and interfacing C++ with Excel are also covered. The book builds the code step-by-step, while the code illustrates the concepts and notions developed in the book.

This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems.

Sparse grids are a popular tool for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different flavors, are frequently the method of choice. This volume of LNCSE presents selected papers from the proceedings of the fifth workshop on sparse grids and applications, and demonstrates once again the importance of this numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including uncertainty quantification, plasma physics simulations, and computational chemistry, to name but a few.

This book on optimization includes forewords by Michael I. Jordan, Zongben Xu and Zhi-Quan Luo. Machine learning relies heavily on optimization to solve problems with its learning models, and first-order optimization algorithms are the mainstream approaches. The acceleration of first-order optimization algorithms is crucial for the efficiency of machine learning. Written by leading experts in the field, this book provides a comprehensive introduction to, and state-of-the-art review of accelerated first-order optimization algorithms for machine learning. It discusses a variety of methods, including deterministic and stochastic algorithms, where the algorithms can be synchronous or asynchronous, for unconstrained and constrained problems, which can be convex or non-convex. Offering a rich blend of ideas, theories and proofs, the book is up-to-date and self-contained. It is an excellent reference resource for users who are seeking faster optimization algorithms, as well as for graduate students and researchers wanting to grasp the frontiers of optimization in machine learning in a short time.

This book constitutes the refereed proceedings of the 18th International Semantic Web Conference, ESWC 2021, held virtually in June 2021. The 41 full papers and 2 short papers presented were carefully reviewed and selected from 167 submissions. The papers were submitted to three tracks: the research track, the resource track and the in-use track. These tracks showcase research and development activities, services and applications, and innovative research outcomes making their way into industry. The research track caters to both long-standing and emerging research topics in the form of the following subtracks: ontologies and reasoning; knowledge graphs (understanding, creating, and exploiting); semantic data management, querying and distributed data; data dynamics, quality, and trust; matching, integration, and fusion; NLP and information retrieval; machine learning; science data and scholarly communication; and problems to solve before you die.

A compact and easily accessible book, it guides the reader in unravelling the apparent mysteries found in doing mathematical proofs. Simply written, it introduces the art and science of proving mathematical theorems and propositions and equips students with the skill required to tackle the task of proving mathematical assertions. Theoremus - A Student's Guide to Mathematical Proofs is divided into two parts. Part 1 provides a grounding in the notion of mathematical assertions, arguments and fallacies and Part 2, presents lessons learned in action by applying them into the study of logic itself. The book supplies plenty of examples and figures, gives some historical background on personalities that gave rise to the topic and provides reflective problems to try and solve. The author aims to provide the reader with the confidence to take a deep dive into some more advanced work in mathematics or logic.

This textbook tackles the problem of formulating AI systems by combining probabilistic modeling and deep learning. Moreover, it goes beyond typical predictive modeling and brings together supervised learning and unsupervised learning. The resulting paradigm, called deep generative modeling, utilizes the generative perspective on perceiving the surrounding world. It assumes that each phenomenon is driven by an underlying generative process that defines a joint distribution over random variables and their stochastic interactions, i.e., how events occur and in what order. The adjective "deep" comes from the fact that the distribution is parameterized using deep neural networks. There are two distinct traits of deep generative modeling. First, the application of deep neural networks allows rich and flexible parameterization of distributions. Second, the principled manner of modeling stochastic dependencies using probability theory ensures rigorous formulation and prevents potential flaws in reasoning. Moreover, probability theory provides a unified framework where the likelihood function plays a crucial role in quantifying uncertainty and defining objective functions. Deep Generative Modeling is designed to appeal to curious students, engineers, and researchers with a modest mathematical background in undergraduate calculus, linear algebra, probability theory, and the basics in machine learning, deep learning, and programming in Python and PyTorch (or other deep learning libraries). It will appeal to students and researchers from a variety of backgrounds, including computer science, engineering, data science, physics, and bioinformatics, who wish to become familiar with deep generative modeling. To engage the reader, the book introduces fundamental concepts with specific examples and code snippets. The full code accompanying the book is available on github. The ultimate aim of the book is to outline the most important techniques in deep generative modeling and, eventually, enable readers to formulate new models and implement them.

This textbook offers theoretical, algorithmic and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems. It provides an overview of recent advances in control and systems theory, numerical line algebra, numerical optimization, scientific computations and software engineering.

This book features selected papers presented at the 2nd International Conference on Advanced Computing Technologies and Applications, held at SVKM's Dwarkadas J. Sanghvi College of Engineering, Mumbai, India, from 28 to 29 February 2020. Covering recent advances in next-generation computing, the book focuses on recent developments in intelligent computing, such as linguistic computing, statistical computing, data computing and ambient applications.

This book covers applications of machine learning in artificial intelligence. The specific topics covered include human language, heterogeneous and streaming data, unmanned systems, neural information processing, marketing and the social sciences, bioinformatics and robotics, etc. It also provides a broad range of techniques that can be successfully applied and adopted in different areas. Accordingly, the book offers an interesting and insightful read for scholars in the areas of computer vision, speech recognition, healthcare, business, marketing, and bioinformatics.

The mathematics employed by genetic algorithms (GAs)are among the most exciting discoveries of the last few decades. But what exactly is a genetic algorithm? A genetic algorithm is a problem-solving method that uses genetics as its model of problem solving. It applies the rules of reproduction, gene crossover, and mutation to pseudo-organisms so those "organisms" can pass beneficial and survival-enhancing traits to new generations. GAs are useful in the selection of parameters to optimize a system's performance. A second potential use lies in testing and fitting quantitative models. Unlike any other book available, this interesting new text/reference takes you from the construction of a simple GA to advanced implementations. As you come to understand GAs and their processes, you will begin to understand the power of the genetic-based problem-solving paradigms that lie behind them.
The Practical Handbook of Genetic Algorithms presents for the first time new areas of research and implementation. Problems that for many have been considered intractable are shown to be solvable using the techniques described in this work. Specific solution descriptions to real-world problems are provided, or use these as examples to develop solutions to unique problems.
Volume II picks up where the first book leaves off and presents the topic from more of an applications point of view. The focus of the book is to show the reader how to develop their own genetic algorithm coding schemes and how and when to employ the GA to solve problems.

This two-volume set constitutes the refereed post-conference proceedings of the 12th International Conference on Simulation Tools and Techniques, SIMUTools 2020, held in Guiyang, China, in August 2020. Due to COVID-19 pandemic the conference was held virtually. The 125 revised full papers were carefully selected from 354 submissions. The papers focus on simulation methods, simulation techniques, simulation software, simulation performance, modeling formalisms, simulation verification and widely used frameworks.

This is an introduction to mathematical computation that examines a broad array of techniques in the area, from scientific to symbolic to graphical. The book also introduces topics such as implicit and parametric representations, interpolation, approximation, sampling, filtering, reconstruction and integration. Although it is targeted to students in the pure and applied sciences, mathematics and computer science, the book is designed to be accessible to undergraduates at all levels, having a minimum of prerequisites (essentially single-variable calculus).