Boundaries of a complex world / / Andrei Ludu

• Autore: Ludu Andrei
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Edizione: 2nd ed.
• Descrizione fisica: 1 online resource (372 pages)
• Disciplina: 515.35
• Soggetto topico: Boundary value problems
• Note generali: Includes index.
• Nota di contenuto: Intro -- Preface to the Second Edition -- Contents -- Acknowledgements -- Preface to the First Edition -- Part I Boundary in Arts and Humanities -- 1 Introduction -- 2 Boundary in Visual Perception and Arts -- 2.1 Is Our Visual Perception Two Dimensional or Three Dimensional? -- 2.2 Message of the Frame. Nonlineart -- 2.3 Importance of the Frame to the Image Inside -- 2.4 What Type of Mathematics Does Our Visual Brain Possess? -- 2.5 Framed Versus Non-framed -- 2.5.1 The Necessity of a Frame -- 2.5.2 Framed Paintings of Canvases -- 2.5.3 Eliminating Frame Effects -- 2.5.4 Frameless: Greek Pottery, Vermeer, and Feynman -- 2.6 Perception of Image Boundaries -- 2.6.1 Illusions and Frames -- 2.6.2 Bioinformatics -- 2.6.3 Representations of Boundaries in the Left and Right Cerebral Hemispheres -- 2.7 René Magritte and Bernhard Riemann -- 2.8 Appendix* -- 3 Boundary in Social Systems -- 3.1 Social Science Approach to Boundaries -- 3.1.1 Social and Collective Identity -- 3.1.2 Class, Ethnic, and Gender Inequality -- 3.1.3 Professions, Science, and Knowledge -- 3.1.4 Communities, National Identities, and Spatial Boundaries -- 3.2 Social Boundaries and Networks -- 3.3 Impact of Social Boundaries in Social Relations -- 3.4 Mathematical Approaches to Social Boundaries -- 3.5 Social Distance: Euclidean MetricSuperscript asterisk* -- 3.6 Social Distance: UltrametricSuperscript asterisk asterisk** -- 3.7 Social Topological BoundariesSuperscript asterisk asterisk** -- 3.8 Social Topological Patterns -- 3.8.1 Growth Models -- 3.8.2 Cooperation and Patterns -- 3.8.3 Multivariate NetworksSuperscript asterisk asterisk** -- 3.8.4 Pattern Formation in Unstable Social Systems -- 3.9 Epidemic Models with Moving Boundary -- 3.10 AppendixSuperscript asterisk asterisk** -- Part II Mathematical Language of Boundaries -- 310327_2_En_4_Chapter_OnlinePDF. ; 4 Boundary in Continuous Mathematics -- 4.2 Intuitive Introduction to Topology -- 4.2.1 SeparationSuperscript asterisk* -- 4.2.2 Compactness -- 4.2.3 Connectedness and Connectivity -- 4.3 Topological Boundary -- 4.4 Manifold BoundarySuperscript asterisk* -- 4.5 Forms and the Lie DerivativeSuperscript asterisk asterisk** -- 4.6 Fiber Bundles and Covariant DerivativeSuperscript asterisk asterisk** -- 4.7 Is the Lagrangian Derivative a Lie Derivative, or a Covariant Derivative? -- 4.7.1 Geometric and Physics Intuition -- 4.7.2 Mathematical ApproachSuperscript asterisk asterisk** -- 4.8 Deformation of the BoundarySuperscript asterisk* -- 4.9 Differential Topology of Boundaries. CobordismSuperscript asterisk asterisk** -- 5 Boundary in Discrete Mathematics -- 5.1 Structured Finite Sets -- 5.2 Formal Theory of Graphs* -- 5.3 Algebraic Theory and Spectra of Graphs* -- 5.3.1 Relations Between Eigenvalues and the Diameter -- 5.3.2 Relations Between Eigenvalues and Connectivity -- 5.3.3 Relations Between Eigenvalues and the Topology of a Graph -- 5.3.4 Relations Between Eigenvalues and Paths -- 5.3.5 Other Relations Between Eigenvalues -- 5.4 Graph Topology and Boundaries* -- 5.4.1 The Graph Topology and the Diameter -- 5.4.2 Embeddings -- 5.4.3 Isoperimetric Problems -- 5.4.4 Separations -- 5.4.5 Expanders -- 5.5 Algebraic Topology** -- 5.6 Classification of Continuous Structure by Discrete Criteria* -- 5.7 Triangulations and CW Complexes** -- 5.8 Connecting Discrete and Continuous -- Part III Importance of Boundary in Sciences -- 310327_2_En_6_Chapter_OnlinePDF -- 6 The Boundary in the Philosophy of Science -- 6.1 Boundaries in Epistemology -- 6.2 Triadic Classifications, Complexity, and Boundaries -- 6.3 Boundarylessness as the Philosophy of Vagueness -- 7 Networks and Their Boundaries -- 7.1 Complex Networks -- 7.2 World Networks. ; 7.3 The Shape of the Internet -- 7.4 Internet Is Its Own Boundary* -- 8 Big Data Systems -- 8.1 Data Dimensionality -- 8.2 Topology of Big Data: Persistent Homology** -- 8.3 Topology of Big Data: Regions with Holes** -- 9 Liquid Boundaries -- 9.1 Exotic Liquid Boundaries -- 9.2 Geometry of Inviscid Fluids* -- 9.3 Geometry of Viscous Fluids* -- 9.4 Soap Films with Boundary** -- 9.5 3D Drops* -- 9.6 Rotation of 3D Drops* -- 9.7 Rotation of 2D Drops* -- 9.8 Leidenfrost Drops -- 9.9 Spinning Polygons* -- 9.10 Universality in Rotating Fluid Patterns -- 9.10.1 Hollow Polygons on a Rotating Fluid Surface -- 9.10.2 Polygonal Eyewalls in Hurricanes -- 9.10.3 From the Lab to Saturn -- 9.11 Appendix: Second Fundamental Form -- 9.12 Appendix: Calculus of Variations -- 9.13 Appendix: n-Dimensional Rotating Drops -- 10 Conclusions -- 310327_2_En_BookBackmatter_OnlinePDF -- Index -- Appendix References.
• Titolo autorizzato: Boundaries of a Complex World
• ISBN: 3-031-07361-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996490349703316
• Lo trovi qui: Univ. di Salerno
• Serie: Springer Series in Synergetics