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Link de la búsquedaMathematical Modeling of Biological Systems, Volume I / SpringerLink (Online service) ; Andreas Deutsch ; Lutz Brusch ; Helen Byrne ; Gerda de Vries ; Hanspeter Herzel (2007)
Título : Mathematical Modeling of Biological Systems, Volume I : Cellular Biophysics, Regulatory Networks, Development, Biomedicine, and Data Analysis Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Andreas Deutsch ; Lutz Brusch ; Helen Byrne ; Gerda de Vries ; Hanspeter Herzel Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2007 Colección: Modeling and Simulation in Science, Engineering and Technology, ISSN 2164-3679 Número de páginas: XVIII, 382 p. 120 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4558-8 Idioma : Inglés (eng) Palabras clave: Mathematics Cell biology Mathematical models Biomathematics Biophysics Biological physics Statistics Modeling and Industrial Computational Biology Physics Biomedicine general for Life Sciences, Medicine, Health Sciences Clasificación: 51 Matemáticas Resumen: This two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout both works are mathematical and computational approaches to examine central problems in the life sciences, ranging from the organizational principles of individual cells to the dynamics of large populations. Volume I covers a number of areas, including: * Cellular Biophysics * Regulatory Networks * Developmental Biology * Biomedical Applications * Data Analysis and Model Validation Volume II examines a diverse range of subjects, including: * Epidemiology * Evolution and Ecology * Immunology * Neural Systems and the Brain * Innovative Mathematical Methods and Education Both volumes will be excellent reference texts for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics Nota de contenido: Cellular Biophysics -- Multiparticle Direct Simulation of Photosynthetic Electron Transport Processes -- Selective Regulation of Protein Activity by Complex Ca2+ Oscillations: A Theoretical Study -- Phase Separation in Eukaryotic Directional Sensing -- Protein Domains of GTPases on Membranes: Do They Rely on Turing’s Mechanism? -- In Vitro Tubulogenesis of Endothelial Cells: Analysis of a Bifurcation Process Controlled by a Mechanical Switch -- Nonexponential Time Distributions in Biocatalytic Systems: Mass Service Replacing Mass Action -- Regulatory Networks -- A Stochastic Model of Gene Regulation Using the Chemical Master Equation -- Piecewise-Linear Models of Genetic Regulatory Networks: Analysis of the Carbon Starvation Response in Escherichia coli -- Predicting Gene Expression from Combined Expression and Promoter Profile Similarity with Application to Missing Value Imputation -- Chemical Organizations in the Central Sugar Metabolism of Escherichia coli -- Transition Networks: A Unifying Theme for Molecular Simulation and Computer Science -- Development -- Pigmentation Pattern Formation in Butterfly Wings: Global Patterns on Fore- and Hindwing -- Agent-Based Model for Developmental Pattern Formation with Multiscale Dynamics and Varying Cell Geometry -- Bacterial Swarming Driven by Rod Shape -- Stability Properties of Some Tissue-Growth Models -- A Modified Backward Euler Scheme for Advection-Reaction-Diffusion Systems -- Biomedical Applications -- Fractional Transport of Cancer Cells Due to Self-Entrapment by Fission -- Mathematical Modelling of Vascular Tumour Growth and Implications for Therapy -- A Stochastic Model of Glioblastoma Invasion -- Morphology of Tumor Vasculature A Theoretical Model -- A Mathematical Model of the Cell Cycle and Its Circadian Control -- Bone Turnover Cycle Model with a Torus-Like Steady State -- Modelling the Early Stages of Atherosclerosis -- Magnetic Nanoparticles for In Vivo Applications: A Numerical Modeling Study -- Fluid Transport in Peritoneal Dialysis: A Mathematical Model and Numerical Solutions -- Relevance of Intracellular Replication to the Evolution of Chagas Disease -- A Finite Volume Spatial Discretisation for Taxis-Diffusion-Reaction Systems with Axi-Symmetry: Application to Fracture Healing -- Information Content Toward a Neonatal Disease Severity Score System -- Data Analysis and Model Validation -- Statistical Analysis and Physical Modelling of Oligonucleotide Microarrays -- Validation of Human Alternative Splice Forms Using the EASED Platform and Multiple Splice Site Discriminating Features -- Gaussian Mixture Decomposition of Time-Course DNA Microarray Data -- SVD Analysis of Gene Expression Data En línea: http://dx.doi.org/10.1007/978-0-8176-4558-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34552 Mathematical Modeling of Biological Systems, Volume I : Cellular Biophysics, Regulatory Networks, Development, Biomedicine, and Data Analysis [documento electrónico] / SpringerLink (Online service) ; Andreas Deutsch ; Lutz Brusch ; Helen Byrne ; Gerda de Vries ; Hanspeter Herzel . - Boston, MA : Birkhäuser Boston, 2007 . - XVIII, 382 p. 120 illus : online resource. - (Modeling and Simulation in Science, Engineering and Technology, ISSN 2164-3679) .
ISBN : 978-0-8176-4558-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Cell biology Mathematical models Biomathematics Biophysics Biological physics Statistics Modeling and Industrial Computational Biology Physics Biomedicine general for Life Sciences, Medicine, Health Sciences Clasificación: 51 Matemáticas Resumen: This two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout both works are mathematical and computational approaches to examine central problems in the life sciences, ranging from the organizational principles of individual cells to the dynamics of large populations. Volume I covers a number of areas, including: * Cellular Biophysics * Regulatory Networks * Developmental Biology * Biomedical Applications * Data Analysis and Model Validation Volume II examines a diverse range of subjects, including: * Epidemiology * Evolution and Ecology * Immunology * Neural Systems and the Brain * Innovative Mathematical Methods and Education Both volumes will be excellent reference texts for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics Nota de contenido: Cellular Biophysics -- Multiparticle Direct Simulation of Photosynthetic Electron Transport Processes -- Selective Regulation of Protein Activity by Complex Ca2+ Oscillations: A Theoretical Study -- Phase Separation in Eukaryotic Directional Sensing -- Protein Domains of GTPases on Membranes: Do They Rely on Turing’s Mechanism? -- In Vitro Tubulogenesis of Endothelial Cells: Analysis of a Bifurcation Process Controlled by a Mechanical Switch -- Nonexponential Time Distributions in Biocatalytic Systems: Mass Service Replacing Mass Action -- Regulatory Networks -- A Stochastic Model of Gene Regulation Using the Chemical Master Equation -- Piecewise-Linear Models of Genetic Regulatory Networks: Analysis of the Carbon Starvation Response in Escherichia coli -- Predicting Gene Expression from Combined Expression and Promoter Profile Similarity with Application to Missing Value Imputation -- Chemical Organizations in the Central Sugar Metabolism of Escherichia coli -- Transition Networks: A Unifying Theme for Molecular Simulation and Computer Science -- Development -- Pigmentation Pattern Formation in Butterfly Wings: Global Patterns on Fore- and Hindwing -- Agent-Based Model for Developmental Pattern Formation with Multiscale Dynamics and Varying Cell Geometry -- Bacterial Swarming Driven by Rod Shape -- Stability Properties of Some Tissue-Growth Models -- A Modified Backward Euler Scheme for Advection-Reaction-Diffusion Systems -- Biomedical Applications -- Fractional Transport of Cancer Cells Due to Self-Entrapment by Fission -- Mathematical Modelling of Vascular Tumour Growth and Implications for Therapy -- A Stochastic Model of Glioblastoma Invasion -- Morphology of Tumor Vasculature A Theoretical Model -- A Mathematical Model of the Cell Cycle and Its Circadian Control -- Bone Turnover Cycle Model with a Torus-Like Steady State -- Modelling the Early Stages of Atherosclerosis -- Magnetic Nanoparticles for In Vivo Applications: A Numerical Modeling Study -- Fluid Transport in Peritoneal Dialysis: A Mathematical Model and Numerical Solutions -- Relevance of Intracellular Replication to the Evolution of Chagas Disease -- A Finite Volume Spatial Discretisation for Taxis-Diffusion-Reaction Systems with Axi-Symmetry: Application to Fracture Healing -- Information Content Toward a Neonatal Disease Severity Score System -- Data Analysis and Model Validation -- Statistical Analysis and Physical Modelling of Oligonucleotide Microarrays -- Validation of Human Alternative Splice Forms Using the EASED Platform and Multiple Splice Site Discriminating Features -- Gaussian Mixture Decomposition of Time-Course DNA Microarray Data -- SVD Analysis of Gene Expression Data En línea: http://dx.doi.org/10.1007/978-0-8176-4558-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34552 Ejemplares
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Título : Killer Cell Dynamics : Mathematical and Computational Approaches to Immunology Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Dominik Wodarz Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Interdisciplinary Applied Mathematics, ISSN 0939-6047 num. 32 Número de páginas: XIII, 220 p Il.: online resource ISBN/ISSN/DL: 978-0-387-68733-9 Idioma : Inglés (eng) Palabras clave: Mathematics Immunology Cell biology Ecology Evolutionary Biomathematics Mathematical and Computational Biology Theoretical Ecology/Statistics Clasificación: 51 Matemáticas Resumen: This book reviews how mathematics can be used in combination with biological data in order to improve understanding of how the immune system works. This is illustrated largely in the context of viral infections. Mathematical models allow scientists to capture complex biological interactions in a clear mathematical language and to follow them to their precise logical conclusions. This can give rise to counter-intuitive insights which would not be attained by experiments alone, and can be used for the design of further experiments in order to address the mathematical results. This book provides both an introduction to the field of mathematical immunology, and an overview of many topics which are the subject of current research, covering a broad variety of immunological topics. It starts with basic principles of immunology and covers the dynamical interactions between the immune system and specific viral infections, including important human pathogens such as HIV. General biological and mathematical background material to both virus infection and immune system dynamics is provided, and each chapter begins with a simple introduction to the biological questions examined. This book is intended for an interdisciplinary audience. It explains the concept of mathematical modeling in immunology and shows how modeling has been used to address specific questions. It is intended both for the mathematical biologists who are interested in immunology, and for the biological readership that is interested in the use of mathematical models in immunology. Dominik Wodarz is an Associate Professor at the Department of Ecology and Evolutionary Biology at the University of California, Irvine Nota de contenido: Viruses and Immune Responses: A Dynamical View -- Models of CTL Responses and Correlates of Virus Control -- CTL Memory -- CD4 T Cell Help -- Immunodominance -- Multiple Infections and CTL Dynamics -- Control versus CTL-Induced Pathology -- Lytic versus Nonlytic Activity -- Dynamical Interactions between CTL and Antibody Responses -- Effector Molecules and CTL Homeostasis -- Virus-Induced Subversion of CTL Responses -- Boosting Immunity against Immunosuppressive Infections -- Evolutionary Aspects of Immunity En línea: http://dx.doi.org/10.1007/978-0-387-68733-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34509 Killer Cell Dynamics : Mathematical and Computational Approaches to Immunology [documento electrónico] / SpringerLink (Online service) ; Dominik Wodarz . - New York, NY : Springer New York, 2007 . - XIII, 220 p : online resource. - (Interdisciplinary Applied Mathematics, ISSN 0939-6047; 32) .
ISBN : 978-0-387-68733-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Immunology Cell biology Ecology Evolutionary Biomathematics Mathematical and Computational Biology Theoretical Ecology/Statistics Clasificación: 51 Matemáticas Resumen: This book reviews how mathematics can be used in combination with biological data in order to improve understanding of how the immune system works. This is illustrated largely in the context of viral infections. Mathematical models allow scientists to capture complex biological interactions in a clear mathematical language and to follow them to their precise logical conclusions. This can give rise to counter-intuitive insights which would not be attained by experiments alone, and can be used for the design of further experiments in order to address the mathematical results. This book provides both an introduction to the field of mathematical immunology, and an overview of many topics which are the subject of current research, covering a broad variety of immunological topics. It starts with basic principles of immunology and covers the dynamical interactions between the immune system and specific viral infections, including important human pathogens such as HIV. General biological and mathematical background material to both virus infection and immune system dynamics is provided, and each chapter begins with a simple introduction to the biological questions examined. This book is intended for an interdisciplinary audience. It explains the concept of mathematical modeling in immunology and shows how modeling has been used to address specific questions. It is intended both for the mathematical biologists who are interested in immunology, and for the biological readership that is interested in the use of mathematical models in immunology. Dominik Wodarz is an Associate Professor at the Department of Ecology and Evolutionary Biology at the University of California, Irvine Nota de contenido: Viruses and Immune Responses: A Dynamical View -- Models of CTL Responses and Correlates of Virus Control -- CTL Memory -- CD4 T Cell Help -- Immunodominance -- Multiple Infections and CTL Dynamics -- Control versus CTL-Induced Pathology -- Lytic versus Nonlytic Activity -- Dynamical Interactions between CTL and Antibody Responses -- Effector Molecules and CTL Homeostasis -- Virus-Induced Subversion of CTL Responses -- Boosting Immunity against Immunosuppressive Infections -- Evolutionary Aspects of Immunity En línea: http://dx.doi.org/10.1007/978-0-387-68733-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34509 Ejemplares
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Título : Introduction to Topological Manifolds Tipo de documento: documento electrónico Autores: John M. Lee ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Otro editor: Imprint: Springer Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 202 Número de páginas: XVII, 433 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7940-7 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Topology Clasificación: 51 Matemáticas Resumen: This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness. This text is designed to be used for an introductory graduate course on the geometry and topology of manifolds. It should be accessible to any student who has completed a solid undergraduate degree in mathematics. The author’s book Introduction to Smooth Manifolds is meant to act as a sequel to this book Nota de contenido: Preface -- 1 Introduction -- 2 Topological Spaces -- 3 New Spaces from Old -- 4 Connectedness and Compactness -- 5 Cell Complexes -- 6 Compact Surfaces -- 7 Homotopy and the Fundamental Group -- 8 The Circle -- 9 Some Group Theory -- 10 The Seifert-Van Kampen Theorem -- 11 Covering Maps -- 12 Group Actions and Covering Maps -- 13 Homology -- Appendix A: Review of Set Theory -- Appendix B: Review of Metric Spaces -- Appendix C: Review of Group Theory -- References -- Notation Index -- Subject Index En línea: http://dx.doi.org/10.1007/978-1-4419-7940-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33177 Introduction to Topological Manifolds [documento electrónico] / John M. Lee ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2011 . - XVII, 433 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 202) .
ISBN : 978-1-4419-7940-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Topology Clasificación: 51 Matemáticas Resumen: This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness. This text is designed to be used for an introductory graduate course on the geometry and topology of manifolds. It should be accessible to any student who has completed a solid undergraduate degree in mathematics. The author’s book Introduction to Smooth Manifolds is meant to act as a sequel to this book Nota de contenido: Preface -- 1 Introduction -- 2 Topological Spaces -- 3 New Spaces from Old -- 4 Connectedness and Compactness -- 5 Cell Complexes -- 6 Compact Surfaces -- 7 Homotopy and the Fundamental Group -- 8 The Circle -- 9 Some Group Theory -- 10 The Seifert-Van Kampen Theorem -- 11 Covering Maps -- 12 Group Actions and Covering Maps -- 13 Homology -- Appendix A: Review of Set Theory -- Appendix B: Review of Metric Spaces -- Appendix C: Review of Group Theory -- References -- Notation Index -- Subject Index En línea: http://dx.doi.org/10.1007/978-1-4419-7940-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33177 Ejemplares
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Título : The Mathematics of Knots : Theory and Application Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Markus Banagl ; Denis Vogel Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: Contributions in Mathematical and Computational Sciences, ISSN 2191-303X num. 1 Número de páginas: X, 357 p Il.: online resource ISBN/ISSN/DL: 978-3-642-15637-3 Idioma : Inglés (eng) Palabras clave: Mathematics Differential geometry Topology Manifolds (Mathematics) Complex manifolds Biomathematics Physics and Cell Complexes (incl. Diff.Topology) Geometry Physiological, Cellular Medical Topics Numerical Computational Clasificación: 51 Matemáticas Resumen: The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands Nota de contenido: Preface -- 1 Knots, Singular Embeddings, and Monodromy -- 2 Lower Bounds on Virtual Crossing Number and Minimal Surface Genus -- 3 A Survey of Twisted Alexander Polynomials -- 4 On Two Categorifications of the Arrow Polynomial for Virtual Knots -- 5 An Adelic Extension of the Jones Polynomial -- 6 Legendrian Grid Number One Knots and Augmentations of their Differential Algebras -- 7 Embeddings of Four-Valent Framed Graphs into 2-Surfaces -- 8 Geometric Topology and Field Theory on 3-Manifolds -- 9 From Goeritz Matrices to Quasi-Alternating Links -- 10 An Overview of Property 2R -- 11 DNA, Knots and Tangles En línea: http://dx.doi.org/10.1007/978-3-642-15637-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33383 The Mathematics of Knots : Theory and Application [documento electrónico] / SpringerLink (Online service) ; Markus Banagl ; Denis Vogel . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - X, 357 p : online resource. - (Contributions in Mathematical and Computational Sciences, ISSN 2191-303X; 1) .
ISBN : 978-3-642-15637-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Differential geometry Topology Manifolds (Mathematics) Complex manifolds Biomathematics Physics and Cell Complexes (incl. Diff.Topology) Geometry Physiological, Cellular Medical Topics Numerical Computational Clasificación: 51 Matemáticas Resumen: The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands Nota de contenido: Preface -- 1 Knots, Singular Embeddings, and Monodromy -- 2 Lower Bounds on Virtual Crossing Number and Minimal Surface Genus -- 3 A Survey of Twisted Alexander Polynomials -- 4 On Two Categorifications of the Arrow Polynomial for Virtual Knots -- 5 An Adelic Extension of the Jones Polynomial -- 6 Legendrian Grid Number One Knots and Augmentations of their Differential Algebras -- 7 Embeddings of Four-Valent Framed Graphs into 2-Surfaces -- 8 Geometric Topology and Field Theory on 3-Manifolds -- 9 From Goeritz Matrices to Quasi-Alternating Links -- 10 An Overview of Property 2R -- 11 DNA, Knots and Tangles En línea: http://dx.doi.org/10.1007/978-3-642-15637-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33383 Ejemplares
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Título : Algebraic Operads Tipo de documento: documento electrónico Autores: Jean-Louis Loday ; SpringerLink (Online service) ; Bruno Vallette Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, ISSN 0072-7830 num. 346 Número de páginas: XXIV, 636 p Il.: online resource ISBN/ISSN/DL: 978-3-642-30362-3 Idioma : Inglés (eng) Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Nonassociative rings Rings (Algebra) Algebraic topology Manifolds Complex manifolds Theory, Algebra Non-associative and Algebras Topology Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: In many areas of mathematics some “higher operations” are arising. These have become so important that several research projects refer to such expressions. Higher operations form new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After an elementary chapter on classical algebra, accessible to undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers. Nota de contenido: Preface -- 1.Algebras, coalgebras, homology -- 2.Twisting morphisms -- 3.Koszul duality for associative algebras -- 4.Methods to prove Koszulity of an algebra -- 5.Algebraic operad -- 6 Operadic homological algebra -- 7.Koszul duality of operads -- 8.Methods to prove Koszulity of an operad -- 9.The operads As and A\infty -- 10.Homotopy operadic algebras -- 11.Bar and cobar construction of an algebra over an operad -- 12.(Co)homology of algebras over an operad -- 13.Examples of algebraic operads -- Apendices: A.The symmetric group -- B.Categories -- C.Trees -- References -- Index -- List of Notation En línea: http://dx.doi.org/10.1007/978-3-642-30362-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32989 Algebraic Operads [documento electrónico] / Jean-Louis Loday ; SpringerLink (Online service) ; Bruno Vallette . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012 . - XXIV, 636 p : online resource. - (Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, ISSN 0072-7830; 346) .
ISBN : 978-3-642-30362-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Nonassociative rings Rings (Algebra) Algebraic topology Manifolds Complex manifolds Theory, Algebra Non-associative and Algebras Topology Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: In many areas of mathematics some “higher operations” are arising. These have become so important that several research projects refer to such expressions. Higher operations form new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After an elementary chapter on classical algebra, accessible to undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers. Nota de contenido: Preface -- 1.Algebras, coalgebras, homology -- 2.Twisting morphisms -- 3.Koszul duality for associative algebras -- 4.Methods to prove Koszulity of an algebra -- 5.Algebraic operad -- 6 Operadic homological algebra -- 7.Koszul duality of operads -- 8.Methods to prove Koszulity of an operad -- 9.The operads As and A\infty -- 10.Homotopy operadic algebras -- 11.Bar and cobar construction of an algebra over an operad -- 12.(Co)homology of algebras over an operad -- 13.Examples of algebraic operads -- Apendices: A.The symmetric group -- B.Categories -- C.Trees -- References -- Index -- List of Notation En línea: http://dx.doi.org/10.1007/978-3-642-30362-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32989 Ejemplares
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