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Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences #147)
by Gilles Aubert Pierre KornprobstPartial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences. The first is the mathematical community, to show the contribution of mathematics to this domain and to highlight some unresolved theoretical questions. The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems.The book is divided into five main parts. Chapter 1 is a detailed overview. Chapter 2 describes and illustrates most of the mathematical notions found throughout the work. Chapters 3 and 4 examine how PDEs and variational methods can be successfully applied in image restoration and segmentation processes. Chapter 5, which is more applied, describes some challenging computer vision problems, such as sequence analysis or classification. This book will be useful to researchers and graduate students in mathematics and computer vision.
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences #147)
by Gilles Aubert Pierre KornprobstThe updated 2nd edition of this book presents a variety of image analysis applications, reviews their precise mathematics and shows how to discretize them. For the mathematical community, the book shows the contribution of mathematics to this domain, and highlights unsolved theoretical questions. For the computer vision community, it presents a clear, self-contained and global overview of the mathematics involved in image procesing problems. The second edition offers a review of progress in image processing applications covered by the PDE framework, and updates the existing material. The book also provides programming tools for creating simulations with minimal effort.
Mathematical Problems in Data Science: Theoretical and Practical Methods
by Li M. Chen Zhixun Su Bo JiangThis book describes current problems in data science and Big Data. Key topics are data classification, Graph Cut, the Laplacian Matrix, Google Page Rank, efficient algorithms, hardness of problems, different types of big data, geometric data structures, topological data processing, and various learning methods. For unsolved problems such as incomplete data relation and reconstruction, the book includes possible solutions and both statistical and computational methods for data analysis. Initial chapters focus on exploring the properties of incomplete data sets and partial-connectedness among data points or data sets. Discussions also cover the completion problem of Netflix matrix; machine learning method on massive data sets; image segmentation and video search. This book introduces software tools for data science and Big Data such MapReduce, Hadoop, and Spark. This book contains three parts. The first part explores the fundamental tools of data science. It includes basic graph theoretical methods, statistical and AI methods for massive data sets. In second part, chapters focus on the procedural treatment of data science problems including machine learning methods, mathematical image and video processing, topological data analysis, and statistical methods. The final section provides case studies on special topics in variational learning, manifold learning, business and financial data recovery, geometric search, and computing models. Mathematical Problems in Data Science is a valuable resource for researchers and professionals working in data science, information systems and networks. Advanced-level students studying computer science, electrical engineering and mathematics will also find the content helpful.
Mathematical Problems from Applied Logic I: Logics for the XXIst Century (International Mathematical Series #4)
by Dov M. Gabbay Michael Zakharyaschev Sergei S. GoncharovThis is an overview of the current state of knowledge along with open problems and perspectives, clarified in such fields as non-standard inferences in description logics, logic of provability, logical dynamics and computability theory. The book includes contributions concerning the role of logic today, including unexpected aspects of contemporary logic and the application of logic. This book will be of interest to logicians and mathematicians in general.
Mathematical Problem Solving and New Information Technologies: Research in Contexts of Practice (NATO ASI Subseries F: #89)
by Joao P. Ponte Joao F. Matos José M. Matos Domingos FernandesA strong and fluent competency in mathematics is a necessary condition for scientific, technological and economic progress. However, it is widely recognized that problem solving, reasoning, and thinking processes are critical areas in which students' performance lags far behind what should be expected and desired. Mathematics is indeed an important subject, but is also important to be able to use it in extra-mathematical contexts. Thinking strictly in terms of mathematics or thinking in terms of its relations with the real world involve quite different processes and issues. This book includes the revised papers presented at the NATO ARW "Information Technology and Mathematical Problem Solving Research", held in April 1991, in Viana do Castelo, Portugal, which focused on the implications of computerized learning environments and cognitive psychology research for these mathematical activities. In recent years, several committees, professional associations, and distinguished individuals throughout the world have put forward proposals to renew mathematics curricula, all emphasizing the importance of problem solving. In order to be successful, these reforming intentions require a theory-driven research base. But mathematics problem solving may be considered a "chaotic field" in which progress has been quite slow.
Mathematical Principles of Topological and Geometric Data Analysis (Mathematics of Data #2)
by Parvaneh Joharinad Jürgen JostThis book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information.In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately.Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use.
Mathematical Principles of the Internet, Volume 2: Mathematics (Chapman & Hall/CRC Computer and Information Science Series)
by Nirdosh BhatnagarThis two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.
Mathematical Principles of the Internet, Volume 2: Mathematics (Chapman & Hall/CRC Computer and Information Science Series)
by Nirdosh BhatnagarThis two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.
Mathematical Principles of the Internet, Volume 1: Engineering (Chapman & Hall/CRC Computer and Information Science Series)
by Nirdosh BhatnagarThis two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.
Mathematical Principles of the Internet, Volume 1: Engineering (Chapman & Hall/CRC Computer and Information Science Series)
by Nirdosh BhatnagarThis two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.
Mathematical Principles of the Internet, Two Volume Set (Chapman & Hall/CRC Computer and Information Science Series)
by Nirdosh BhatnagarThis two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, these cover only a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.
Mathematical Principles of Human Conceptual Behavior: The Structural Nature of Conceptual Representation and Processing (Scientific Psychology Series)
by Ronaldo VigoThe ability to learn concepts lies at the very core of human cognition, enabling us to efficiently classify, organize, identify, and store complex information. In view of the basic role that concepts play in our everyday physical and mental lives, the fields of cognitive science and psychology face three long standing challenges: discovering the laws that govern concept learning and categorization behavior in organisms, showing how they inform other areas of cognitive research, and describing them with the mathematical systematicity and precision found in the physical sciences. In light of these theoretical and methodological shortcomings, this volume will introduce a set of general mathematical principles for predicting and explaining conceptual behavior. The author’s theory is based on seven fundamental constructs of universal science: invariance, complexity, information, similarity, dissimilarity, pattern, and representation. These constructs are joined by a novel mathematical framework that does not depend on probability theory, and derives key results from conceptual behavior research with other key areas of cognitive research such as pattern perception, similarity assessment, and contextual choice. The result is a unique and systematic unifying foundation for cognitive science in the tradition of classical physics.
Mathematical Principles of Human Conceptual Behavior: The Structural Nature of Conceptual Representation and Processing (Scientific Psychology Series)
by Ronaldo VigoThe ability to learn concepts lies at the very core of human cognition, enabling us to efficiently classify, organize, identify, and store complex information. In view of the basic role that concepts play in our everyday physical and mental lives, the fields of cognitive science and psychology face three long standing challenges: discovering the laws that govern concept learning and categorization behavior in organisms, showing how they inform other areas of cognitive research, and describing them with the mathematical systematicity and precision found in the physical sciences. In light of these theoretical and methodological shortcomings, this volume will introduce a set of general mathematical principles for predicting and explaining conceptual behavior. The author’s theory is based on seven fundamental constructs of universal science: invariance, complexity, information, similarity, dissimilarity, pattern, and representation. These constructs are joined by a novel mathematical framework that does not depend on probability theory, and derives key results from conceptual behavior research with other key areas of cognitive research such as pattern perception, similarity assessment, and contextual choice. The result is a unique and systematic unifying foundation for cognitive science in the tradition of classical physics.
Mathematical Principles of Fuzzy Logic (The Springer International Series in Engineering and Computer Science #517)
by Vilém Novák Irina Perfilieva J. MockorMathematical Principles of Fuzzy Logic provides a systematic study of the formal theory of fuzzy logic. The book is based on logical formalism demonstrating that fuzzy logic is a well-developed logical theory. It includes the theory of functional systems in fuzzy logic, providing an explanation of what can be represented, and how, by formulas of fuzzy logic calculi. It also presents a more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter. This book presents fuzzy logic as the mathematical theory of vagueness as well as the theory of commonsense human reasoning, based on the use of natural language, the distinguishing feature of which is the vagueness of its semantics.
Mathematical Principles for Scientific Computing and Visualization
by Gerald FarinThis non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coo
Mathematical Optimization Theory and Operations Research: 18th International Conference, MOTOR 2019, Ekaterinburg, Russia, July 8 - 12, 2019, Revised Selected Papers (Communications in Computer and Information Science #1090)
by Igor Bykadorov Vitaly Strusevich Tatiana TchemisovaThis book constitutes revised and selected papers from the 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019, held in Ekaterinburg, Russia, in July 2019. The 40 full papers and 4 short papers presented in this volume were carefully reviewed and selected from a total of 170 submissions. The papers in the volume are organised according to the following topical headings: combinatorial optimization; game theory and mathematical economics; data mining and computational geometry; integer programming; mathematical programming; operations research; optimal control and applications.
Mathematical Optimization Theory and Operations Research: 22nd International Conference, MOTOR 2023, Ekaterinburg, Russia, July 2–8, 2023, Proceedings (Lecture Notes in Computer Science #13930)
by Michael Khachay Yury Kochetov Anton Eremeev Oleg Khamisov Vladimir Mazalov Panos PardalosThis book constitutes the refereed proceedings of the 22nd International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2023, held in Ekaterinburg, Russia, during July 2–8, 2023. The 28 full papers and 1 short paper included in this book were carefully reviewed and selected from 89 submissions. They were organized in topical sections as follows: Mathematical programming and applications; discrete and combinatorial optimization; stochastic optimization; scheduling; game theory; and optimal control and mathematical economics. The book also contains one invited talk in full paper length.
Mathematical Optimization Theory and Operations Research: 22nd International Conference, MOTOR 2023, Ekaterinburg, Russia, July 2–8, 2023, Revised Selected Papers (Communications in Computer and Information Science #1881)
by Michael Khachay Yury Kochetov Anton Eremeev Oleg Khamisov Vladimir Mazalov Panos PardalosThis book constitutes refereed proceedings of the 22nd International Conference on Mathematical Optimization Theory and Operations Research: Recent Trends, MOTOR 2023, held in Ekaterinburg, Russia, during July 2–8, 2023. The 28 full papers and one invited paper presented in this volume were carefully reviewed and selected from a total of 61 submissions. The papers in the volume are organized according to the following topical headings: mathematical programming; stochastic optimization; discrete and combinatorial optimization; operations research; optimal control and mathematical economics; and optimization in machine learning.
Mathematical Optimization Theory and Operations Research: 18th International Conference, MOTOR 2019, Ekaterinburg, Russia, July 8-12, 2019, Proceedings (Lecture Notes in Computer Science #11548)
by Michael Khachay Yury Kochetov Panos PardalosThis book constitutes the proceedings of the 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019, held in Ekaterinburg, Russia, in July 2019.The 48 full papers presented in this volume were carefully reviewed and selected from 170 submissions. MOTOR 2019 is a successor of the well-known International and All-Russian conference series, which were organized in Ural, Siberia, and the Far East for a long time. The selected papers are organized in the following topical sections: mathematical programming; bi-level optimization; integer programming; combinatorial optimization; optimal control and approximation; data mining and computational geometry; games and mathematical economics.
Mathematical Optimization Theory and Operations Research: 19th International Conference, MOTOR 2020, Novosibirsk, Russia, July 6–10, 2020, Revised Selected Papers (Communications in Computer and Information Science #1275)
by Yury Kochetov Igor Bykadorov Tatiana GruzdevaThis book constitutes refereed proceedings of the 19th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2020, held in July 2020. Due to the COVID-19 pandemic the conference was held online. The 25 full papers and 8 short papers presented in this volume were carefully reviewed and selected from a total of 102 submissions. The papers in the volume are organised according to the following topical headings: combinatorial optimization; mathematical programming; global optimization; game theory and mathematical economics; heuristics and metaheuristics; machine learning and data analysis.
Mathematical Optimization Theory and Operations Research: 21st International Conference, MOTOR 2022, Petrozavodsk, Russia, July 2–6, 2022, Revised Selected Papers (Communications in Computer and Information Science #1661)
by Yury Kochetov Anton Eremeev Oleg Khamisov Anna RettievaThis book constitutes refereed proceedings of the 21st International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2022, held in Petrozavodsk, Russia, in July 2022. The 21 full papers and 3 short papers presented in this volume were carefully reviewed and selected from a total of 88 submissions. The papers in the volume are organised according to the following topical headings: invited talks; integer programming and combinatorial optimization; mathematical programming; game theory and optimal control; operational research applications.
Mathematical Optimization Theory and Operations Research: 19th International Conference, MOTOR 2020, Novosibirsk, Russia, July 6–10, 2020, Proceedings (Lecture Notes in Computer Science #12095)
by Alexander Kononov Michael Khachay Valery A Kalyagin Panos PardalosThis book constitutes the proceedings of the 19th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2020, held in Novosibirsk, Russia, in July 2020. The 31 full papers presented in this volume were carefully reviewed and selected from 102 submissions. The papers are grouped in these topical sections: discrete optimization; mathematical programming; game theory; scheduling problem; heuristics and metaheuristics; and operational research applications.
Mathematical Optimization Theory and Operations Research: 20th International Conference, MOTOR 2021, Irkutsk, Russia, July 5–10, 2021, Proceedings (Lecture Notes in Computer Science #12755)
by Panos Pardalos Michael Khachay Alexander KazakovThis book constitutes the proceedings of the 20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021, held in Irkutsk, Russia, in July 2021. The 29 full papers and 1 short paper presented in this volume were carefully reviewed and selected from 102 submissions. Additionally, 2 full invited papers are presented in the volume. The papers are grouped in the following topical sections: combinatorial optimization; mathematical programming; bilevel optimization; scheduling problems; game theory and optimal control; operational research and mathematical economics; data analysis.
Mathematical Optimization Theory and Operations Research: 21st International Conference, MOTOR 2022, Petrozavodsk, Russia, July 2–6, 2022, Proceedings (Lecture Notes in Computer Science #13367)
by Panos Pardalos Michael Khachay Vladimir MazalovThis book constitutes the proceedings of the 21st International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2022, held in Petrozavodsk, Russia, in July 2022. The 21 full papers presented together with 6 invited abstracts lectures and 2 tutorial abstracts in this volume were carefully reviewed and selected from 88 submissions. The conference focuses on the following topics: Mathematical programming, bi-level and global optimization, integer programming and combinatorial optimization, approximation algorithms with theoretical guarantees and approximation schemes, heuristics and meta-heuristics, game theory, optimal control, optimization in machine learning and data analysis, and their valuable applications in operations research and economics.
Mathematical Optimization Theory and Operations Research: 20th International Conference, MOTOR 2021, Irkutsk, Russia, July 5–10, 2021, Revised Selected Papers (Communications in Computer and Information Science #1476)
by Alexander Strekalovsky Yury Kochetov Tatiana Gruzdeva Andrei OrlovThis book constitutes refereed proceedings of the 20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021, held in Irkutsk, Russia, in July 2021. Due to the COVID-19 pandemic the conference was held online. The 31 full papers and 3 short papers presented in this volume were carefully reviewed and selected from a total of 102 submissions. The papers in the volume are organised according to the following topical headings: continuous optimization; integer programming and combinatorial optimization; operational research applications; optimal control.