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Topics in Theoretical Computer Science: Third IFIP WG 1.8 International Conference, TTCS 2020, Tehran, Iran, July 1–2, 2020, Proceedings (Lecture Notes in Computer Science #12281)
by Luís S. Barbosa Mohammad Ali AbamThis book constitutes the refereed proceedings of the Third IFIP WG 1.8 International Conference on Topics in Theoretical Computer Science, TTCS 2020, held in Tehran, Iran, in July 2020. The conference was held virtually due to the COVID-19 pandemic. The 8 papers presented in this volume were carefully reviewed and selected from 24 submissions. They focus on novel and high-quality research in all areas of theoretical computer science, such as algorithms and complexity; logic, semantics, and programming theory; and more.
Topics in Theoretical and Applied Statistics
by Giorgio Alleva Andrea GiommiThis bookhighlights the latest research findings from the 46th International Meeting ofthe Italian Statistical Society (SIS) in Rome, during which both methodologicaland applied statistical research was discussed. This selection of fullypeer-reviewed papers, originally presented at the meeting, addresses a broadrange of topics, including the theory of statistical inference; data mining andmultivariate statistical analysis; survey methodologies; analysis of social,demographic and health data; and economic statistics and econometrics.
Topics in Theoretical and Computational Nanoscience
by Jeffrey Michael McmahonInterest in structures with nanometer-length features has significantly increased as experimental techniques for their fabrication have become possible. The study of phenomena in this area is termed nanoscience, and is a research focus of chemists, pure and applied physics, electrical engineers, and others. The reason for such a focus is the wide range of novel effects that exist at this scale, both of fundamental and practical interest, which often arise from the interaction between metallic nanostructures and light, and range from large electromagnetic field enhancements to extraordinary optical transmission of light through arrays of subwavelength holes. This dissertation is aimed at addressing some of the most fundamental and outstanding questions in nanoscience from a theoretical and computational perspective, specifically: · At the single nanoparticle level, how well do experimental and classical electrodynamics agree? · What is the detailed relationship between optical response and nanoparticle morphology, composition, and environment? · Does an optimal nanostructure exist for generating large electromagnetic field enhancements, and is there a fundamental limit to this? · Can nanostructures be used to control light, such as confining it, or causing fundamentally different scattering phenomena to interact, such as electromagnetic surface modes and diffraction effects? · Is it possible to calculate quantum effects using classical electrodynamics, and if so, how do they affect optical properties?
Topics in Topological Graph Theory
by Thomas W. Tucker Lowell W. Beineke Robin J. Wilson Jonathan L. GrossThe use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.
Topics in Uniform Approximation of Continuous Functions (Frontiers in Mathematics)
by Ileana Bucur Gavriil PaltineanuThis book presents the evolution of uniform approximations of continuous functions. Starting from the simple case of a real continuous function defined on a closed real interval, i.e., the Weierstrass approximation theorems, it proceeds up to the abstract case of approximation theorems in a locally convex lattice of (M) type. The most important generalizations of Weierstrass’ theorems obtained by Korovkin, Bohman, Stone, Bishop, and Von Neumann are also included.In turn, the book presents the approximation of continuous functions defined on a locally compact space (the functions from a weighted space) and that of continuous differentiable functions defined on ¡n. In closing, it highlights selected approximation theorems in locally convex lattices of (M) type.The book is intended for advanced and graduate students of mathematics, and can also serve as a resource for researchers in the field of the theory of functions.
Topics on Combinatorial Semigroups
by Yun Liu Yuqi Guo Shoufeng WangBy combinatorial semigroups, we mean a general term of concepts, facts and methods which are produced in investigating of algebraic and combinatorial properties, constructions, classifications and interrelations of formal languages and automata, codes, finite and infinite words by using semigroup theory and combinatorial analysis. The main research objects in this field are the elements and subsets of the free semigroups and monoids and many combinatorial properties of these objects, which are closely related to algebraic theory of semigroups. This book first introduces some basic concepts and notations in combinatorial semigroups. Since many contents involving the constructions of (generalized) disjunctive languages and regular languages are closely related to the algebraic theory of codes, some selected topics are introduced in the following chapter, including the method of defining codes by using dependence systems, the maximality and completeness of codes, and the detailed discussion of some special kinds of codes such as convex codes, semaphore codes and solid codes. Then the remaining chapters present the main topics of the book - regular languages, disjunctive languages, and their various kinds of generalizations.This book might be useful to researchers in mathematics who are interested in combinatorial semigroups.
Topics on Continua
by Sergio MaciasSpecialized as it might be, continuum theory is one of the most intriguing areas in mathematics. However, despite being popular journal fare, few books have thoroughly explored this interesting aspect of topology. In Topics on Continua, Sergio Macias, one of the field's leading scholars, presents four of his favorite continuum topics: inv
Topics on Continua
by Sergio MacíasThis book is a significant companion text to the existing literature on continuum theory. It opens with background information of continuum theory, so often missing from the preceding publications, and then explores the following topics: inverse limits, the Jones set function T, homogenous continua, and n-fold hyperspaces. In this new edition of the book, the author builds on the aforementioned topics, including the unprecedented presentation of n-fold hyperspace suspensions and induced maps on n-fold hyperspaces. The first edition of the book has had a remarkable impact on the continuum theory community. After twelve years, this updated version will also prove to be an excellent resource within the field of topology.
Topics on Methodological and Applied Statistical Inference
by Tonio Battista Elías Moreno Walter RacugnoThis book brings together selected peer-reviewed contributions from various research fields in statistics, and highlights the diverse approaches and analyses related to real-life phenomena. Major topics covered in this volume include, but are not limited to, bayesian inference, likelihood approach, pseudo-likelihoods, regression, time series, and data analysis as well as applications in the life and social sciences. The software packages used in the papers are made available by the authors. This book is a result of the 47th Scientific Meeting of the Italian Statistical Society, held at the University of Cagliari, Italy, in 2014.
Topics on Tournaments in Graph Theory (Dover Books on Mathematics)
by John W. MoonTournaments, in this context, are directed graphs - an important and interesting topic in graph theory. This concise volume collects a substantial amount of information on tournaments from throughout the mathematical literature. Suitable for advanced undergraduate students of mathematics, the straightforward treatment requires a basic familiarity with finite mathematics. The fundamental definitions and results appear in the earlier sections, and most of the later sections can be read independently of each other. Subjects include irreducible and strong tournaments, cycles and strong subtournaments of a tournament, the distribution of 3-cycles in a tournament, transitive tournaments, sets of consistent arcs in a tournament, the diameter of a tournament, and the powers of tournament matrices. Additional topics include scheduling a tournament and ranking the participants, universal tournaments, the use of oriented graphs and score vectors, and many other subjects.
Topoi: The Categorial Analysis of Logic
by Robert GoldblattA classic introduction to mathematical logic from the perspective of category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Its approach moves always from the particular to the general, following through the steps of the abstraction process until the abstract concept emerges naturally.Beginning with a survey of set theory and its role in mathematics, the text proceeds to definitions and examples of categories and explains the use of arrows in place of set-membership. The introduction to topos structure covers topos logic, algebra of subobjects, and intuitionism and its logic, advancing to the concept of functors, set concepts and validity, and elementary truth. Explorations of categorial set theory, local truth, and adjointness and quantifiers conclude with a study of logical geometry.
Topological Crystallography
by Toshikazu SunadaGeometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid's Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler's work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as "living in the logical world, not in space," leading to the question of how to place or realize them "canonically" in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.
Topological Data Analysis: The Abel Symposium 2018 (Abel Symposia #15)
by Markus Szymik Nils A. Baas Gunnar E. Carlsson Gereon Quick Marius ThauleThis book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018. The symposium offered an overview of the emerging field of "Topological Data Analysis". This volume presents papers on various research directions, notably including applications in neuroscience, materials science, cancer biology, and immune response. Providing an essential snapshot of the status quo, it represents a valuable asset for practitioners and those considering entering the field.
Topological Degree Theory and Applications (Mathematical Analysis and Applications)
by Yeol Je Cho Yu-Qing ChenSince the 1960s, many researchers have extended topological degree theory to various non-compact type nonlinear mappings, and it has become a valuable tool in nonlinear analysis. Presenting a survey of advances made in generalizations of degree theory during the past decade, this book focuses on topological degree theory in normed spaces and its ap
Topological Dimension and Dynamical Systems
by Michel CoornaertTranslated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner's characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active areas of current research in mathematics and mathematical physics, the prerequisites needed for reading it remain modest; essentially some familiarities with undergraduate point-set topology and, in order to access the final two chapters, some acquaintance with basic notions in group theory. Topological Dimension and Dynamical Systems is intended for graduate students, as well as researchers interested in topology and dynamical systems. Some of the topics treated in the book directly lead to research areas that remain to be explored.
Topological Dynamics in Metamodel Discovery with Artificial Intelligence: From Biomedical to Cosmological Technologies (Chapman & Hall/CRC Artificial Intelligence and Robotics Series)
by Ariel FernándezThe leveraging of artificial intelligence (AI) for model discovery in dynamical systems is cross-fertilizing and revolutionizing both disciplines, heralding a new era of data-driven science. This book is placed at the forefront of this endeavor, taking model discovery to the next level. Dealing with artificial intelligence, this book delineates AI’s role in model discovery for dynamical systems. With the implementation of topological methods to construct metamodels, it engages with levels of complexity and multiscale hierarchies hitherto considered off limits for data science. Key Features: Introduces new and advanced methods of model discovery for time series data using artificial intelligence Implements topological approaches to distill "machine-intuitive" models from complex dynamics data Introduces a new paradigm for a parsimonious model of a dynamical system without resorting to differential equations Heralds a new era in data-driven science and engineering based on the operational concept of "computational intuition" Intended for graduate students, researchers, and practitioners interested in dynamical systems empowered by AI or machine learning and in their biological, engineering, and biomedical applications, this book will represent a significant educational resource for people engaged in AI-related cross-disciplinary projects.
Topological Fields and Near Valuations
by Niel ShellPart I (eleven chapters) of this text for graduate students provides a Survey of topological fields, while Part II (five chapters) provides a relatively more idiosyncratic account of valuation theory.
Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications
by Afif Ben Amar Donal O'ReganThis is a monograph covering topological fixed point theory for several classes of single and multivalued maps. The authors begin by presenting basic notions in locally convex topological vector spaces. Special attention is then devoted to weak compactness, in particular to the theorems of Eberlein-Smulian, Grothendick and Dunford-Pettis. Leray-Schauder alternatives and eigenvalue problems for decomposable single-valued nonlinear weakly compact operators in Dunford-Pettis spaces are considered, in addition to some variants of Schauder, Krasnoselskii, Sadovskii, and Leray-Schauder type fixed point theorems for different classes of weakly sequentially continuous operators on general Banach spaces. The authors then proceed with an examination of Sadovskii, Furi-Pera, and Krasnoselskii fixed point theorems and nonlinear Leray-Schauder alternatives in the framework of weak topologies and involving multivalued mappings with weakly sequentially closed graph. These results are formulated in terms of axiomatic measures of weak noncompactness. The authors continue to present some fixed point theorems in a nonempty closed convex of any Banach algebras or Banach algebras satisfying a sequential condition (P) for the sum and the product of nonlinear weakly sequentially continuous operators, and illustrate the theory by considering functional integral and partial differential equations. The existence of fixed points, nonlinear Leray-Schauder alternatives for different classes of nonlinear (ws)-compact operators (weakly condensing, 1-set weakly contractive, strictly quasi-bounded) defined on an unbounded closed convex subset of a Banach space are also discussed. The authors also examine the existence of nonlinear eigenvalues and eigenvectors, as well as the surjectivity of quasibounded operators. Finally, some approximate fixed point theorems for multivalued mappings defined on Banach spaces. Weak and strong topologies play a role here and both bounded and unbounded regions are considered. The authors explicate a method developed to indicate how to use approximate fixed point theorems to prove the existence of approximate Nash equilibria for non-cooperative games. Fixed point theory is a powerful and fruitful tool in modern mathematics and may be considered as a core subject in nonlinear analysis. In the last 50 years, fixed point theory has been a flourishing area of research. As such, the monograph begins with an overview of these developments before gravitating towards topics selected to reflect the particular interests of the authors.
Topological Fixed-Point Theory in Suitable Banach Algebras with Applications (Infosys Science Foundation Series)
by Aref Jeribi Najib KaddachiThis book delves into the topics of fixed-point theory as applied to block operator matrices within the context of Banach algebras featuring multi-valued inputs. Its scope extends to a broad range of equations, encompassing nonlinear biological models as well as two-dimensional boundary value problems associated with burgeoning cell populations and functional systems of differential and integral inclusions. The book systematically introduces the principles of topological fixed-point theory, offering insights into various classes of both single-valued and multi-valued maps. The overarching goal is to disseminate key techniques and outcomes derived from fixed-point theory, with a specific emphasis on its application to both single-valued and multi-valued mappings within the framework of Banach algebras.
Topological Galois Theory
by Askold KhovanskiiThis book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in explicit form. In particular, it offers a complete exposition of the relatively new area of topological Galois theory, initiated by the author. Applications of Galois theory to solvability of algebraic equations by radicals, basics of Picard-Vessiot theory, and Liouville's results on the class of functions representable by quadratures are also discussed. A unique feature of this book is that recent results are presented in the same elementary manner as classical Galois theory, which will make the book useful and interesting to readers with varied backgrounds in mathematics, from undergraduate students to researchers. In this English-language edition, extra material has been added (Appendices A-D), the last two of which were written jointly with Yura Burda.
Topological Groups
by R.V. GamkrelidzeOffering the insights of L.S. Pontryagin, one of the foremost thinkers in modern mathematics, the second volume in this four-volume set examines the nature and processes that make up topological groups. Already hailed as the leading work in this subject for its abundance of examples and its thorough explanations, the text is arranged so that readers can follow the material either sequentially or schematically. Stand-alone chapters cover such topics as topological division rings, linear representations of compact topological groups, and the concept of a lie group.
Topological Indices and Related Descriptors in QSAR and QSPR
by James Devillers Alexandru T. BalabanTopological Indices and Related Descriptors in QSAR and QSPR reviews the state of the art in this field and highlights the important advances in the generation of descriptors calculated directly from the structure of molecules. This long-awaited comprehensive book provides all the necessary information to calculate and use these descriptors for deriving structure-activity and structure-property relationships. Written by leading experts in the field, this book discusses the physicochemical significance, strengths, and weaknesses of these indices and presents numerous examples of applications. This book will be a valuable reference for anyone involved in the use of QSAR and QSPR in the pharmaceutical, applied chemical, and environmental sciences. It is also suitable for use as a supplementary textbook on related graduate level courses.
Topological Insulators
by Shun-Qing ShenTopological insulators are insulating in the bulk, but process metallic states present around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, the first of its kind on topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological insulators and related areas. Shun-Qing Shen is a Professor at the Department of Physics, the University of Hong Kong, China.
Topological Methods for Delay and Ordinary Differential Equations: With Applications to Continuum Mechanics (Advances in Mechanics and Mathematics #51)
by Pablo Amster Pierluigi BenevieriThis volume explores the application of topological techniques in the study of delay and ordinary differential equations with a particular focus on continuum mechanics. Chapters, written by internationally recognized researchers in the field, present results on problems of existence, multiplicity localization, bifurcation of solutions, and more. Topological methods are used throughout, including degree theory, fixed point index theory, and classical and recent fixed point theorems. A wide variety of applications to continuum mechanics are provided as well, such as chemostats, non-Newtonian fluid flow, and flows in phase space. Topological Methods for Delay and Ordinary Differential Equations will be a valuable resource for researchers interested in differential equations, functional analysis, topology, and the applied sciences.
Topological Methods in Data Analysis and Visualization III
by Peer-Timo Bremer Ingrid Hotz Valerio Pascucci Ronald PeikertThis collection of peer-reviewed conference papers provides comprehensive coverage of cutting-edge research in topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The volume also features material on core research challenges such as the representation of large and complex datasets and integrating numerical methods with robust combinatorial algorithms. Reflecting the focus of the TopoInVis 2013 conference, the contributions evince the progress currently being made on finding experimental solutions to open problems in the sector. They provide an inclusive snapshot of state-of-the-art research that enables researchers to keep abreast of the latest developments and provides a foundation for future progress. With papers by some of the world's leading experts in topological techniques, this volume is a major contribution to the literature in a field of growing importance with applications in disciplines that range from engineering to medicine.