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An Introduction to Artificial Intelligence Based on Reproducing Kernel Hilbert Spaces / Sergei Pereverzyev / Bâle (CHE) ; Boston, MA : Birkhäuser (2022)
Titre : An Introduction to Artificial Intelligence Based on Reproducing Kernel Hilbert Spaces Type de document : document électronique Auteurs : Sergei Pereverzyev, ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2022 Collection : Compact Textbooks in Mathematics, ISSN 2296-4568 Importance : XIV, 152 p. 8 illus., 6 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-030-98316-1 Langues : Anglais (eng) Tags : Functional analysis Operator theory Machine learning Artificial intelligence Functional Analysis Operator Theory Machine Learning Artificial Intelligence Résumé : This textbook provides an in-depth exploration of statistical learning with reproducing kernels, an active area of research that can shed light on trends associated with deep neural networks. The author demonstrates how the concept of reproducing kernel Hilbert Spaces (RKHS), accompanied with tools from regularization theory, can be effectively used in the design and justification of kernel learning algorithms, which can address problems in several areas of artificial intelligence. Also provided is a detailed description of two biomedical applications of the considered algorithms, demonstrating how close the theory is to being practically implemented. Among the book’s several unique features is its analysis of a large class of algorithms of the Learning Theory that essentially comprise every linear regularization scheme, including Tikhonov regularization as a specific case. It also provides a methodology for analyzing not only different supervised learning problems, such as regression or ranking, but also different learning scenarios, such as unsupervised domain adaptation or reinforcement learning. By analyzing these topics using the same theoretical framework, rather than approaching them separately, their presentation is streamlined and made more approachable. An Introduction to Artificial Intelligence Based on Reproducing Kernel Hilbert Spaces is an ideal resource for graduate and postgraduate courses in computational mathematics and data science Note de contenu : Introduction -- Learning in Reproducing Kernel Hilbert Spaces and related integral operators -- Selected topics of the regularization theory -- Regularized learning in RKHS -- Examples of Applications Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=172340 An Introduction to Artificial Intelligence Based on Reproducing Kernel Hilbert Spaces [document électronique] / Sergei Pereverzyev, ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2022 . - XIV, 152 p. 8 illus., 6 illus. in color : online resource. - (Compact Textbooks in Mathematics, ISSN 2296-4568) .
ISBN : 978-3-030-98316-1
Langues : Anglais (eng)
Tags : Functional analysis Operator theory Machine learning Artificial intelligence Functional Analysis Operator Theory Machine Learning Artificial Intelligence Résumé : This textbook provides an in-depth exploration of statistical learning with reproducing kernels, an active area of research that can shed light on trends associated with deep neural networks. The author demonstrates how the concept of reproducing kernel Hilbert Spaces (RKHS), accompanied with tools from regularization theory, can be effectively used in the design and justification of kernel learning algorithms, which can address problems in several areas of artificial intelligence. Also provided is a detailed description of two biomedical applications of the considered algorithms, demonstrating how close the theory is to being practically implemented. Among the book’s several unique features is its analysis of a large class of algorithms of the Learning Theory that essentially comprise every linear regularization scheme, including Tikhonov regularization as a specific case. It also provides a methodology for analyzing not only different supervised learning problems, such as regression or ranking, but also different learning scenarios, such as unsupervised domain adaptation or reinforcement learning. By analyzing these topics using the same theoretical framework, rather than approaching them separately, their presentation is streamlined and made more approachable. An Introduction to Artificial Intelligence Based on Reproducing Kernel Hilbert Spaces is an ideal resource for graduate and postgraduate courses in computational mathematics and data science Note de contenu : Introduction -- Learning in Reproducing Kernel Hilbert Spaces and related integral operators -- Selected topics of the regularization theory -- Regularized learning in RKHS -- Examples of Applications Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=172340 An Introduction to Catalan Numbers / Steven Roman / Bâle (CHE) ; Boston, MA : Birkhäuser (2015)
Titre : An Introduction to Catalan Numbers Type de document : document électronique Auteurs : Steven Roman ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2015 Collection : Compact Textbooks in Mathematics, ISSN 2296-4568 Importance : XII, 121 p. 44 illus Présentation : online resource ISBN/ISSN/EAN : 978-3-319-22144-1 Langues : Anglais (eng) Tags : Mathematics Computer science Sequences Computer mathematics Combinatorics Graph theory Graph Theory Series Summability Mathematical Applications in Computer Science Discrete Mathematics in Computer Science Résumé : This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. ?Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.? - From the foreword by Richard Stanley Note de contenu : Introduction -- Dyck Words -- The Catalan Numbers -- Catalan Numbers and Paths -- Catalan Numbers and Trees -- Catalan Numbers and Geometric Widgits -- Catalan Numbers and Algebraic Widgits -- Catalan Numbers and Interval Structures -- Catalan Numbers and Partitions -- Catalan Numbers and Permutations -- Catalan Numbers and Semiorders -- Exercises -- Solutions and Hints -- Appendix A: A Brief Introduction to Partially Ordered Sets -- Appendix B: A Brief Introduction to Graphs and Trees -- Index Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=118227 An Introduction to Catalan Numbers [document électronique] / Steven Roman ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2015 . - XII, 121 p. 44 illus : online resource. - (Compact Textbooks in Mathematics, ISSN 2296-4568) .
ISBN : 978-3-319-22144-1
Langues : Anglais (eng)
Tags : Mathematics Computer science Sequences Computer mathematics Combinatorics Graph theory Graph Theory Series Summability Mathematical Applications in Computer Science Discrete Mathematics in Computer Science Résumé : This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. ?Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.? - From the foreword by Richard Stanley Note de contenu : Introduction -- Dyck Words -- The Catalan Numbers -- Catalan Numbers and Paths -- Catalan Numbers and Trees -- Catalan Numbers and Geometric Widgits -- Catalan Numbers and Algebraic Widgits -- Catalan Numbers and Interval Structures -- Catalan Numbers and Partitions -- Catalan Numbers and Permutations -- Catalan Numbers and Semiorders -- Exercises -- Solutions and Hints -- Appendix A: A Brief Introduction to Partially Ordered Sets -- Appendix B: A Brief Introduction to Graphs and Trees -- Index Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=118227 An Introduction to the Language of Category Theory / Steven Roman / Bâle (CHE) ; Boston, MA : Birkhäuser (2017)
Titre : An Introduction to the Language of Category Theory Type de document : document électronique Auteurs : Steven Roman ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2017 Collection : Compact Textbooks in Mathematics, ISSN 2296-4568 Importance : XII, 169 p. 176 illus., 5 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-319-41917-6 Langues : Anglais (eng) Tags : Mathematics Category theory Homological algebra Algebra Ordered algebraic structures Category Theory Homological Algebra Order Lattices Ordered Algebraic Structures General Algebraic Systems Résumé : This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams, duality, initial and terminal objects, special types of morphisms, and some special types of categories, particularly comma categories and hom-set categories. Chapter 2 is devoted to functors and natural transformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions ? products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts Note de contenu : Preface -- Categories -- Functors and Natural Transformations -- Universality -- Cones and Limits -- Adjoints -- References -- Index of Symbols -- Index Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128288 An Introduction to the Language of Category Theory [document électronique] / Steven Roman ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2017 . - XII, 169 p. 176 illus., 5 illus. in color : online resource. - (Compact Textbooks in Mathematics, ISSN 2296-4568) .
ISBN : 978-3-319-41917-6
Langues : Anglais (eng)
Tags : Mathematics Category theory Homological algebra Algebra Ordered algebraic structures Category Theory Homological Algebra Order Lattices Ordered Algebraic Structures General Algebraic Systems Résumé : This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams, duality, initial and terminal objects, special types of morphisms, and some special types of categories, particularly comma categories and hom-set categories. Chapter 2 is devoted to functors and natural transformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions ? products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts Note de contenu : Preface -- Categories -- Functors and Natural Transformations -- Universality -- Cones and Limits -- Adjoints -- References -- Index of Symbols -- Index Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128288 Basic Monotonicity Methods with Some Applications / Marek Galewski / Bâle (CHE) ; Boston, MA : Birkhäuser (2021)
Titre : Basic Monotonicity Methods with Some Applications Type de document : document électronique Auteurs : Marek Galewski, ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2021 Collection : Compact Textbooks in Mathematics, ISSN 2296-4568 Importance : X, 180 p Présentation : online resource ISBN/ISSN/EAN : 978-3-030-75308-5 Langues : Anglais (eng) Tags : Operator theory Mathematical analysis Analysis (Mathematics) Operator Theory Analysis Résumé : This textbook introduces some basic tools from the theory of monotone operators together with some of their applications. Examples that work for ordinary differential equations are provided. The illustrating material is kept relatively simple, while at the same time offering inspiring applications to the reader. The material will appeal to graduate students in mathematics who want to learn some basics in the theory of monotone operators. Furthermore, it offers a smooth transition to studying more advanced topics pertaining to more refined applications by shifting to pseudomonotone operators, and next, to multivalued monotone operators Note de contenu : Preface -- Introduction to the topic of the course -- Some excerpts from functional analysis -- Monotone operators -- On the Fenchel-Young conjugate -- Potential operators -- Existence of solutions to abstract equations -- Normalized duality mapping -- On the Galerkin method -- Some selected applications Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=166003 Basic Monotonicity Methods with Some Applications [document électronique] / Marek Galewski, ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2021 . - X, 180 p : online resource. - (Compact Textbooks in Mathematics, ISSN 2296-4568) .
ISBN : 978-3-030-75308-5
Langues : Anglais (eng)
Tags : Operator theory Mathematical analysis Analysis (Mathematics) Operator Theory Analysis Résumé : This textbook introduces some basic tools from the theory of monotone operators together with some of their applications. Examples that work for ordinary differential equations are provided. The illustrating material is kept relatively simple, while at the same time offering inspiring applications to the reader. The material will appeal to graduate students in mathematics who want to learn some basics in the theory of monotone operators. Furthermore, it offers a smooth transition to studying more advanced topics pertaining to more refined applications by shifting to pseudomonotone operators, and next, to multivalued monotone operators Note de contenu : Preface -- Introduction to the topic of the course -- Some excerpts from functional analysis -- Monotone operators -- On the Fenchel-Young conjugate -- Potential operators -- Existence of solutions to abstract equations -- Normalized duality mapping -- On the Galerkin method -- Some selected applications Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=166003 A Course in Algebraic Error-Correcting Codes / Simeon Ball / Bâle (CHE) ; Boston, MA : Birkhäuser (2020)
Titre : A Course in Algebraic Error-Correcting Codes Type de document : document électronique Auteurs : Simeon Ball, ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2020 Collection : Compact Textbooks in Mathematics, ISSN 2296-4568 Importance : XIII, 177 p. 12 illus., 5 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-030-41153-4 Langues : Anglais (eng) Tags : Information theory Coding theory Commutative algebra Commutative rings Information and Communication Circuits Coding and Information Theory Commutative Rings and Algebras Résumé : This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed Note de contenu : Euclidean Plane -- Sphere -- Stereographic Projection and Inversions -- Hyperbolic Plane -- Lorentz-Minkowski Plane -- Geometry of Special Relativity -- Answers to Selected Exercises -- Index Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=149899 A Course in Algebraic Error-Correcting Codes [document électronique] / Simeon Ball, ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2020 . - XIII, 177 p. 12 illus., 5 illus. in color : online resource. - (Compact Textbooks in Mathematics, ISSN 2296-4568) .
ISBN : 978-3-030-41153-4
Langues : Anglais (eng)
Tags : Information theory Coding theory Commutative algebra Commutative rings Information and Communication Circuits Coding and Information Theory Commutative Rings and Algebras Résumé : This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed Note de contenu : Euclidean Plane -- Sphere -- Stereographic Projection and Inversions -- Hyperbolic Plane -- Lorentz-Minkowski Plane -- Geometry of Special Relativity -- Answers to Selected Exercises -- Index Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=149899 A Course on Topological Vector Spaces / Jürgen Voigt / Bâle (CHE) ; Boston, MA : Birkhäuser (2020)
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PermalinkElements of General Relativity / Piotr T. Chruściel / Bâle (CHE) ; Boston, MA : Birkhäuser (2019)
PermalinkExploring Classical Greek Construction Problems with Interactive Geometry Software / Ad Meskens / Bâle (CHE) ; Boston, MA : Birkhäuser (2017)
PermalinkFrom Groups to Categorial Algebra / Dominique Bourn / Bâle (CHE) ; Boston, MA : Birkhäuser (2017)
PermalinkGeneralized Stochastic Processes / Stefan Schäffler / Bâle (CHE) ; Boston, MA : Birkhäuser (2018)
PermalinkGeometric Multiplication of Vectors / Miroslav Josipović / Bâle (CHE) ; Boston, MA : Birkhäuser (2019)
PermalinkGetting Acquainted with Homogenization and Multiscale / Leonid Berlyand / Bâle (CHE) ; Boston, MA : Birkhäuser (2018)
PermalinkIntroduction to Algebraic Topology / Holger Kammeyer / Bâle (CHE) ; Boston, MA : Birkhäuser (2022)
PermalinkIntroduction to Functional Analysis / Christian Clason / Bâle (CHE) ; Boston, MA : Birkhäuser (2020)
PermalinkIntroduction to Geometry and Topology / Werner Ballmann / Bâle (CHE) ; Boston, MA : Birkhäuser (2018)
PermalinkIntroduction to Infinity-Categories / Markus Land / Bâle (CHE) ; Boston, MA : Birkhäuser (2021)
PermalinkIntroduction to Quantitative Methods for Financial Markets / Hansjörg Albrecher / Bâle (CHE) ; Boston, MA : Birkhäuser (2013)
PermalinkIntroduction to Quasi-Monte Carlo Integration and Applications / Gunther Leobacher / Bâle (CHE) ; Boston, MA : Birkhäuser (2014)
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