This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

This book examines the mismatch between discrete programs, which lie at the center of modern applied mathematics, and the continuous space phenomena they simulate. The author considers whether we can imagine continuous spaces of programs, and asks what the structure of such spaces would be and how they would be constituted. He proposes a functional analysis of program spaces focused through the lens of iterative optimization. The author begins with the observation that optimization methods such as Genetic Algorithms, Evolution Strategies, and Particle Swarm Optimization can be analyzed as Estimation of Distributions Algorithms (EDAs) in that they can be formulated as conditional probability distributions. The probabilities themselves are mathematical objects that can be compared and operated on, and thus many methods in Evolutionary Computation can be placed in a shared vector space and analyzed using techniques of functional analysis. The core ideas of this book expand from that concept, eventually incorporating all iterative stochastic search methods, including gradient-based methods. Inspired by work on Randomized Search Heuristics, the author covers all iterative optimization methods and not just evolutionary methods. The No Free Lunch Theorem is viewed as a useful introduction to the broader field of analysis that comes from developing a shared mathematical space for optimization algorithms. The author brings in intuitions from several branches of mathematics such as topology, probability theory, and stochastic processes and provides substantial background material to make the work as self-contained as possible. The book will be valuable for researchers in the areas of global optimization, machine learning, evolutionary theory, and control theory.

Matrix Analysis and Computations introduces the basics of matrix analysis and presents representative methods and their corresponding theories in matrix computations. In this textbook, readers will find: The matrix theory necessary for direct and iterative methods for solving systems of linear equations. Systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods. Current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. Exercises at the end of each chapter for applying learned methods. This book is intended for graduate students, researchers, and engineers interested in matrix analysis and matrix computations. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

This book on proof theory centers around the legacy of Kurt Schutte and its current impact on the subject. Schutte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schutte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound 0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schutte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schutte himself that have never been published before.

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.

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.

Practical Handbook of Genetic Algorithms, Volume 3: Complex Coding Systems contains computer-code examples for the development of genetic algorithm systems - compiling them from an array of practitioners in the field.
Each contribution of this singular resource includes:
unique code segments
documentation
description of the operations performed
rationale for the chosen approach
problems the code overcomes or addresses
Practical Handbook of Genetic Algorithms, Volume 3: Complex Coding Systems complements the first two volumes in the series by offering examples of computer code. The first two volumes dealt with new research and an overview of the types of applications that could be taken with GAs. This volume differs from its predecessors by specifically concentrating on specific functions in genetic algorithms, serving as the only compilation of useful and usable computer code in the field.

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 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 focuses on mathematical modeling, describes the process of constructing and evaluating models, discusses the challenges and delicacies of the modeling process, and explicitly outlines the required rules and regulations so that the reader will be able to generalize and reuse concepts in other problems by relying on mathematical logic.Undergraduate and postgraduate students of different academic disciplines would find this book a suitable option preparing them for jobs and research fields requiring modeling techniques. Furthermore, this book can be used as a reference book for experts and practitioners requiring advanced skills of model building in their jobs.

This book is dedicated to the systematization and development of models, methods, and algorithms for queuing systems with correlated arrivals. After first setting up the basic tools needed for the study of queuing theory, the authors concentrate on complicated systems: multi-server systems with phase type distribution of service time or single-server queues with arbitrary distribution of service time or semi-Markovian service. They pay special attention to practically important retrial queues, tandem queues, and queues with unreliable servers. Mathematical models of networks and queuing systems are widely used for the study and optimization of various technical, physical, economic, industrial, and administrative systems, and this book will be valuable for researchers, graduate students, and practitioners in these domains.

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.

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.

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.

"Text Mining with MATLAB" provides a comprehensive introduction to text mining using MATLAB. It's designed to help text mining practitioners, as well as those with little-to-no experience with text mining in general, familiarize themselves with MATLAB and its complex applications.

The first part provides an introduction to basic procedures for handling and operating with text strings. Then, it reviews major mathematical modeling approaches. Statistical and geometrical models are also described along with main dimensionality reduction methods. Finally, it presents some specific applications such as document clustering, classification, search and terminology extraction.

All descriptions presented are supported with practical examples that are fully reproducible. Further reading, as well as additional exercises and projects, are proposed at the end of each chapter for those readers interested in conducting further experimentation.

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.

This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.

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.

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 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 Fraisse's characterization of elementary equivalence, Lindstroem's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

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.

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.