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Topological methods in data analysis and visualization . VI Theory, applications, and software / / Ingrid Hotz [and three others] editors
| Topological methods in data analysis and visualization . VI Theory, applications, and software / / Ingrid Hotz [and three others] editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (372 pages) |
| Disciplina | 514 |
| Collana | Mathematics and Visualization |
| Soggetto topico |
Topology
Mathematical analysis Information visualization Topologia Anàlisi matemàtica Visualització de la informació |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-83500-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Part I: Scalar Field Topology - Algorithms and Applications -- W-Structures in Contour Trees -- 1 Introduction -- 2 Background -- 2.1 Contour Trees -- 2.2 Contour Tree Algorithms -- 2.3 Contour Tree Simplification -- 3 W-Structures in Contour Trees -- 3.1 Spatial Characterization -- 3.2 W-Diameter Algorithms -- 3.3 Algorithm 1-Multi BFS -- 3.4 Algorithm 2-Double BFS -- 3.5 Algorithm 3-Dynamic -- 4 Empirical Study -- 4.1 Results -- 5 W-Structure Simplification -- 5.1 Persistent Homology Overview -- 5.2 Comparison of Critical Point Pairs -- 6 Conclusion -- References -- Mergemaps: Treemaps for Scientific Data -- 1 Introduction -- 1.1 Related Work -- 1.2 Summary of Results -- 2 Background -- 2.1 Merge Tree -- 2.2 Treemap -- 3 Mergemap -- 3.1 Motivation -- 3.2 Algorithm -- 3.3 Interaction -- 3.4 Operations -- 3.5 Area Distortion -- 4 Case Studies -- 4.1 Ethane-1,2-diol -- 4.2 Fuel -- 4.3 Silicium -- 4.4 von K225rm225n Street -- 5 Conclusions -- References -- Notes on Percolation Analysis of Sampled Scalar Fields -- 1 Introduction -- 2 Related Work and Background -- 3 From Infinite to Finite -- 3.1 The Extremes of the Value Range -- 3.2 Histogram Distribution -- 4 Analysis and Visualization of Percolation Curve Ensembles -- 4.1 Analysis of a Single Percolation Curve -- 4.2 Analysis of Percolation Curve Ensembles -- 5 Experiments -- 5.1 Randomness and Structure: Gaussian Random Fields -- 5.2 Turbulent Flow: Duct Data Set -- 6 Conclusions and Future Work -- References -- Distributed Task-Parallel Topology-Controlled Volume Rendering -- 1 Introduction -- 2 Related Work -- 3 System Design -- 4 Implementation -- 4.1 Merge -- 4.2 Simplify -- 4.3 Update -- 4.4 Branch Decomposition Assembly -- 4.5 Transfer Function Assignment -- 4.6 Rendering -- 5 Results -- 5.1 Experimental Design -- 5.2 General Observations.
5.3 Algorithm Validation -- 5.4 Strong Scaling -- 5.5 Weak Scaling -- 6 Conclusion -- References -- Topology-Based Feature Design and Tracking for Multi-center Cyclones -- 1 Introduction -- 2 Background -- 3 Full Tracking Graph Computation -- 4 Feature Definition and Tracking of Cyclonic Systems -- 5 Implementation Details -- 6 Case Study -- 7 Conclusion and Discussion -- References -- Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubes -- 1 Introduction -- 2 Science Case -- 3 Technical Background -- 4 Application Development Process -- 4.1 Designing to Serve the ALMA Community -- 5 Software Design -- 5.1 Visual Elements -- 5.2 Interaction Process -- 6 Case Studies -- 6.1 Ghost of Mirach Galaxy Data Set -- 6.2 CMZ Data Set -- 7 Discussion -- References -- Part II: Topological Methods in Complex Fields - Flow Fields, Tensor Fields, and Multi-fields -- Objective Finite-Time Flow Topology from Flowmap Expansion and Contraction -- 1 Introduction -- 2 Related Work -- 2.1 Classic Steady Vector Field Topology -- 2.2 Streamlines vs. Pathlines -- 2.3 Reference Frames -- 2.4 Lagrangian Coherent Structures -- 2.5 Time-Dependent Saddles -- 3 Intuitive Approach -- 4 Theory -- 4.1 Mathematical Definition -- 4.2 Relation to the Lagrangian Definition -- 4.3 Objectivity -- 4.4 Linear Approximation -- 4.5 Strength -- 4.6 Weighting Related to FTLE -- 4.7 Separatrices -- 5 Experiments -- 6 Discussion -- 7 Conclusion -- References -- Coreline Criteria for Inertial Particle Motion -- 1 Introduction -- 2 Related Work -- 2.1 Galilean Invariance -- 2.2 Inertial Particle Motion -- 2.3 Vortex Corelines of Massless Flows -- 2.4 Vortex Corelines of Inertial Particles -- 3 Vortex Coreline Criteria for Inertial Particles -- 3.1 Generalized Inertial Particle Motion -- 3.2 Inertial Motion in Steady Frame -- 3.3 First-Order Corelines. 3.4 Second-Order Corelines -- 4 Implementation -- 5 Results -- 5.1 Comparison of Inertial Particle Parameters -- 5.2 Comparison of Inertial Particle Models -- 5.3 Second-Order Corelines in 3D -- 5.4 Memory Consumption and Performance -- 5.5 Discussion -- 6 Conclusion -- Appendix 1 - Derivation of First-order 3D Criterion -- Appendix 2 - Tracer Particles as Limit Case -- References -- Implicit Visualization of 2D Vector Field Topology for Periodic Orbit Detection -- 1 Introduction -- 2 Related Work -- 3 Motivation -- 4 Method -- 5 Algorithm -- 5.1 Integration -- 5.2 Refinement -- 5.3 Implementation -- 6 Results -- 6.1 Rotated Flow -- 6.2 Buoyant Flow -- 6.3 Buoyant Flow II -- 6.4 Discussion -- 7 Conclusion -- References -- Visually Evaluating the Topological Equivalence of Bounded Bivariate Fields -- 1 Introduction -- 2 Related Work in Visualization -- 3 Set-Up -- 3.1 The mathcalB+-Equivalence and Fiber Topology -- 3.2 Invariants -- 4 Reeb Space Visualization and Computation -- 4.1 Visualization -- 4.2 Computation -- 5 Invariants for Bounded Map Germs -- 6 Outcome -- 6.1 Comparing Forms of Equivalence Through Visual Investigation -- 6.2 Germs of Corank 2 -- 7 Discussion -- 8 Conclusion -- References -- Topological Feature Search in Time-Varying Multifield Data -- 1 Introduction -- 2 Related Work -- 3 Background -- 3.1 Histogram and Isosurface Statistics, Continuous Scatter Plot -- 3.2 Multifield Topology and Jacobi Set -- 3.3 Reeb Space and Joint Contour Net -- 3.4 Histogram Distance Measures -- 4 Our Method -- 4.1 Fiber-Component Distribution over the Range Space -- 4.2 Distance Between Two Fiber-Component Distributions -- 4.3 Weighted Distance for the Singular Values -- 4.4 Metric Space Properties of the Distance Measures -- 5 Implementation -- 6 Applications -- 6.1 Synthetic Data -- 6.2 Plutonium Atom Dataset -- 6.3 Fermium Atom Dataset. 6.4 Chemistry Data: Pt-CO Bond -- 7 Single Scalar Field vs. Multifield -- 8 Conclusions and Future Work -- References -- Tensor Fields for Data Extraction from Chart Images: Bar Charts and Scatter Plots -- 1 Introduction -- 2 Related Work -- 3 Background on Local Geometric Descriptors -- 4 Our Proposed Method -- 5 Experiments and Results -- 6 Conclusions -- References -- Part III: Topology for Geometric Data -- A Fast Approximate Skeleton with Guarantees for Any Cloud of Points in a Euclidean Space -- 1 Introduction: Reconstructions from Unorganized Clouds -- 2 Basic Definitions and a Review of the Related Past Work -- 3 A New Tree core(C) Defined for Any Point Cloud CsubsetmathbbRm -- 4 ASk(C): Approximate Skeleton of a Cloud CsubsetmathbbRm -- 5 Comparisons of Five Algorithms on Real and Synthetic Data -- 6 Conclusions and a Discussion of the Approximate Skeleton -- References -- Topologically Robust B-spline Reconstruction of Fibers from 3D Images -- 1 Introduction -- 2 Related Work -- 3 Pipeline -- 4 B-Spline Approximation -- 4.1 B-Spline Surface Notation -- 4.2 Single B-Spline Surface Approximation -- 4.3 Constructing a Continuous Surface Model -- 5 Results -- 6 Conclusions -- References -- Part IV: Overview Articles, Software and Viewpoints -- Introduction to Vector Field Topology -- 1 Introduction -- 2 Steady Vector Fields -- 2.1 Two-Dimensional Flows -- 2.2 Three-Dimensional Flows -- 2.3 Remarks -- 3 Unsteady Flows -- 3.1 Streamline-Oriented Topology -- 3.2 Pathline-Oriented Topology -- 4 Concepts -- 4.1 Reference Frame Transformation -- 4.2 Reference Frame Invariance -- 4.3 Topology in Steady Reference Frames -- 4.4 High-Dimensional Flows -- 4.5 Uncertainty -- 5 Outlook -- References -- An Overview of the Topology ToolKit -- 1 Introduction -- 2 Scalar Data -- 3 Bivariate Scalar Data -- 4 Uncertain Scalar Data -- 5 Time-Varying Scalar Data. 6 High-Dimensional Point Cloud Data -- 7 In Situ Topological Analysis -- 8 Convenience -- 9 Conclusion and Perspectives -- References -- Implementing Persistence-Based Clustering of Point Clouds in the Topology ToolKit -- 1 Introduction -- 1.1 Contributions -- 2 Related Work -- 3 Software Design Overview -- 4 Computing Scalar Fields from Point Clouds -- 4.1 Parameter Setting -- 5 Persistence-Based Clustering -- 5.1 User Options -- 5.2 Automatic Parameter Setting -- 6 Experimental Results -- 6.1 Automatic Feature Detection -- 6.2 Comparison Against Other Clustering Methods -- 7 Discussion -- References -- Report of the TopoInVis TTK Hackathon: Experiences, Lessons Learned, and Perspectives -- 1 Introduction -- 2 Organization -- 2.1 Preparation -- 2.2 Program -- 3 Results -- 3.1 Packaging -- 3.2 Vector Field Robustness Module -- 3.3 Extending the Integration of TTK in Inviwo -- 3.4 Periodic Grids -- 4 Conclusion -- 4.1 Workgroup Results -- 4.2 Organizational Aspects -- 4.3 TTK Development Directions -- References. |
| Record Nr. | UNINA-9910502997603321 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topological methods in data analysis and visualization . VI Theory, applications, and software / / Ingrid Hotz [and three others] editors
| Topological methods in data analysis and visualization . VI Theory, applications, and software / / Ingrid Hotz [and three others] editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (372 pages) |
| Disciplina | 514 |
| Collana | Mathematics and Visualization |
| Soggetto topico |
Topology
Mathematical analysis Information visualization Topologia Anàlisi matemàtica Visualització de la informació |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-83500-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Part I: Scalar Field Topology - Algorithms and Applications -- W-Structures in Contour Trees -- 1 Introduction -- 2 Background -- 2.1 Contour Trees -- 2.2 Contour Tree Algorithms -- 2.3 Contour Tree Simplification -- 3 W-Structures in Contour Trees -- 3.1 Spatial Characterization -- 3.2 W-Diameter Algorithms -- 3.3 Algorithm 1-Multi BFS -- 3.4 Algorithm 2-Double BFS -- 3.5 Algorithm 3-Dynamic -- 4 Empirical Study -- 4.1 Results -- 5 W-Structure Simplification -- 5.1 Persistent Homology Overview -- 5.2 Comparison of Critical Point Pairs -- 6 Conclusion -- References -- Mergemaps: Treemaps for Scientific Data -- 1 Introduction -- 1.1 Related Work -- 1.2 Summary of Results -- 2 Background -- 2.1 Merge Tree -- 2.2 Treemap -- 3 Mergemap -- 3.1 Motivation -- 3.2 Algorithm -- 3.3 Interaction -- 3.4 Operations -- 3.5 Area Distortion -- 4 Case Studies -- 4.1 Ethane-1,2-diol -- 4.2 Fuel -- 4.3 Silicium -- 4.4 von K225rm225n Street -- 5 Conclusions -- References -- Notes on Percolation Analysis of Sampled Scalar Fields -- 1 Introduction -- 2 Related Work and Background -- 3 From Infinite to Finite -- 3.1 The Extremes of the Value Range -- 3.2 Histogram Distribution -- 4 Analysis and Visualization of Percolation Curve Ensembles -- 4.1 Analysis of a Single Percolation Curve -- 4.2 Analysis of Percolation Curve Ensembles -- 5 Experiments -- 5.1 Randomness and Structure: Gaussian Random Fields -- 5.2 Turbulent Flow: Duct Data Set -- 6 Conclusions and Future Work -- References -- Distributed Task-Parallel Topology-Controlled Volume Rendering -- 1 Introduction -- 2 Related Work -- 3 System Design -- 4 Implementation -- 4.1 Merge -- 4.2 Simplify -- 4.3 Update -- 4.4 Branch Decomposition Assembly -- 4.5 Transfer Function Assignment -- 4.6 Rendering -- 5 Results -- 5.1 Experimental Design -- 5.2 General Observations.
5.3 Algorithm Validation -- 5.4 Strong Scaling -- 5.5 Weak Scaling -- 6 Conclusion -- References -- Topology-Based Feature Design and Tracking for Multi-center Cyclones -- 1 Introduction -- 2 Background -- 3 Full Tracking Graph Computation -- 4 Feature Definition and Tracking of Cyclonic Systems -- 5 Implementation Details -- 6 Case Study -- 7 Conclusion and Discussion -- References -- Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubes -- 1 Introduction -- 2 Science Case -- 3 Technical Background -- 4 Application Development Process -- 4.1 Designing to Serve the ALMA Community -- 5 Software Design -- 5.1 Visual Elements -- 5.2 Interaction Process -- 6 Case Studies -- 6.1 Ghost of Mirach Galaxy Data Set -- 6.2 CMZ Data Set -- 7 Discussion -- References -- Part II: Topological Methods in Complex Fields - Flow Fields, Tensor Fields, and Multi-fields -- Objective Finite-Time Flow Topology from Flowmap Expansion and Contraction -- 1 Introduction -- 2 Related Work -- 2.1 Classic Steady Vector Field Topology -- 2.2 Streamlines vs. Pathlines -- 2.3 Reference Frames -- 2.4 Lagrangian Coherent Structures -- 2.5 Time-Dependent Saddles -- 3 Intuitive Approach -- 4 Theory -- 4.1 Mathematical Definition -- 4.2 Relation to the Lagrangian Definition -- 4.3 Objectivity -- 4.4 Linear Approximation -- 4.5 Strength -- 4.6 Weighting Related to FTLE -- 4.7 Separatrices -- 5 Experiments -- 6 Discussion -- 7 Conclusion -- References -- Coreline Criteria for Inertial Particle Motion -- 1 Introduction -- 2 Related Work -- 2.1 Galilean Invariance -- 2.2 Inertial Particle Motion -- 2.3 Vortex Corelines of Massless Flows -- 2.4 Vortex Corelines of Inertial Particles -- 3 Vortex Coreline Criteria for Inertial Particles -- 3.1 Generalized Inertial Particle Motion -- 3.2 Inertial Motion in Steady Frame -- 3.3 First-Order Corelines. 3.4 Second-Order Corelines -- 4 Implementation -- 5 Results -- 5.1 Comparison of Inertial Particle Parameters -- 5.2 Comparison of Inertial Particle Models -- 5.3 Second-Order Corelines in 3D -- 5.4 Memory Consumption and Performance -- 5.5 Discussion -- 6 Conclusion -- Appendix 1 - Derivation of First-order 3D Criterion -- Appendix 2 - Tracer Particles as Limit Case -- References -- Implicit Visualization of 2D Vector Field Topology for Periodic Orbit Detection -- 1 Introduction -- 2 Related Work -- 3 Motivation -- 4 Method -- 5 Algorithm -- 5.1 Integration -- 5.2 Refinement -- 5.3 Implementation -- 6 Results -- 6.1 Rotated Flow -- 6.2 Buoyant Flow -- 6.3 Buoyant Flow II -- 6.4 Discussion -- 7 Conclusion -- References -- Visually Evaluating the Topological Equivalence of Bounded Bivariate Fields -- 1 Introduction -- 2 Related Work in Visualization -- 3 Set-Up -- 3.1 The mathcalB+-Equivalence and Fiber Topology -- 3.2 Invariants -- 4 Reeb Space Visualization and Computation -- 4.1 Visualization -- 4.2 Computation -- 5 Invariants for Bounded Map Germs -- 6 Outcome -- 6.1 Comparing Forms of Equivalence Through Visual Investigation -- 6.2 Germs of Corank 2 -- 7 Discussion -- 8 Conclusion -- References -- Topological Feature Search in Time-Varying Multifield Data -- 1 Introduction -- 2 Related Work -- 3 Background -- 3.1 Histogram and Isosurface Statistics, Continuous Scatter Plot -- 3.2 Multifield Topology and Jacobi Set -- 3.3 Reeb Space and Joint Contour Net -- 3.4 Histogram Distance Measures -- 4 Our Method -- 4.1 Fiber-Component Distribution over the Range Space -- 4.2 Distance Between Two Fiber-Component Distributions -- 4.3 Weighted Distance for the Singular Values -- 4.4 Metric Space Properties of the Distance Measures -- 5 Implementation -- 6 Applications -- 6.1 Synthetic Data -- 6.2 Plutonium Atom Dataset -- 6.3 Fermium Atom Dataset. 6.4 Chemistry Data: Pt-CO Bond -- 7 Single Scalar Field vs. Multifield -- 8 Conclusions and Future Work -- References -- Tensor Fields for Data Extraction from Chart Images: Bar Charts and Scatter Plots -- 1 Introduction -- 2 Related Work -- 3 Background on Local Geometric Descriptors -- 4 Our Proposed Method -- 5 Experiments and Results -- 6 Conclusions -- References -- Part III: Topology for Geometric Data -- A Fast Approximate Skeleton with Guarantees for Any Cloud of Points in a Euclidean Space -- 1 Introduction: Reconstructions from Unorganized Clouds -- 2 Basic Definitions and a Review of the Related Past Work -- 3 A New Tree core(C) Defined for Any Point Cloud CsubsetmathbbRm -- 4 ASk(C): Approximate Skeleton of a Cloud CsubsetmathbbRm -- 5 Comparisons of Five Algorithms on Real and Synthetic Data -- 6 Conclusions and a Discussion of the Approximate Skeleton -- References -- Topologically Robust B-spline Reconstruction of Fibers from 3D Images -- 1 Introduction -- 2 Related Work -- 3 Pipeline -- 4 B-Spline Approximation -- 4.1 B-Spline Surface Notation -- 4.2 Single B-Spline Surface Approximation -- 4.3 Constructing a Continuous Surface Model -- 5 Results -- 6 Conclusions -- References -- Part IV: Overview Articles, Software and Viewpoints -- Introduction to Vector Field Topology -- 1 Introduction -- 2 Steady Vector Fields -- 2.1 Two-Dimensional Flows -- 2.2 Three-Dimensional Flows -- 2.3 Remarks -- 3 Unsteady Flows -- 3.1 Streamline-Oriented Topology -- 3.2 Pathline-Oriented Topology -- 4 Concepts -- 4.1 Reference Frame Transformation -- 4.2 Reference Frame Invariance -- 4.3 Topology in Steady Reference Frames -- 4.4 High-Dimensional Flows -- 4.5 Uncertainty -- 5 Outlook -- References -- An Overview of the Topology ToolKit -- 1 Introduction -- 2 Scalar Data -- 3 Bivariate Scalar Data -- 4 Uncertain Scalar Data -- 5 Time-Varying Scalar Data. 6 High-Dimensional Point Cloud Data -- 7 In Situ Topological Analysis -- 8 Convenience -- 9 Conclusion and Perspectives -- References -- Implementing Persistence-Based Clustering of Point Clouds in the Topology ToolKit -- 1 Introduction -- 1.1 Contributions -- 2 Related Work -- 3 Software Design Overview -- 4 Computing Scalar Fields from Point Clouds -- 4.1 Parameter Setting -- 5 Persistence-Based Clustering -- 5.1 User Options -- 5.2 Automatic Parameter Setting -- 6 Experimental Results -- 6.1 Automatic Feature Detection -- 6.2 Comparison Against Other Clustering Methods -- 7 Discussion -- References -- Report of the TopoInVis TTK Hackathon: Experiences, Lessons Learned, and Perspectives -- 1 Introduction -- 2 Organization -- 2.1 Preparation -- 2.2 Program -- 3 Results -- 3.1 Packaging -- 3.2 Vector Field Robustness Module -- 3.3 Extending the Integration of TTK in Inviwo -- 3.4 Periodic Grids -- 4 Conclusion -- 4.1 Workgroup Results -- 4.2 Organizational Aspects -- 4.3 TTK Development Directions -- References. |
| Record Nr. | UNISA-996466401703316 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
When form becomes substance : power of gestures, diagrammatical intuition, and phenomenology of space / / edited by Luciano Boi, Carlos Lobo
| When form becomes substance : power of gestures, diagrammatical intuition, and phenomenology of space / / edited by Luciano Boi, Carlos Lobo |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2022] |
| Descrizione fisica | 1 online resource (607 pages) |
| Disciplina | 001.4226 |
| Soggetto topico |
Charts, diagrams, etc
Information visualization Science - Philosophy Visualització de la informació Diagrames Filosofia de la ciència Fenomenologia |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-83125-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Introduction -- Topological Visualisation, or How to Apprehend the Invisible -- Feynman Diagrams: A New Way Forward in Theoretical Physics -- Diagrammatics and Invariants in Knot and Braid Theory -- Philosophical and Scientific Implications -- Diagrammatics and Category Theory -- A French Singularity in Epistemological Field: Gilles Châtelet -- Phenomenology of Space (and Time) and Diagrammatic Epistemology -- Towards a "Diagrammatic Critique of Aesthetics" -- Acknowledgments -- Contents -- Part I Logic, Forms and Diagrams -- The Semiotics of Laws of Form -- Introduction -- Finding Distinction -- Finding Primary Arithmetic -- Finding Logic -- Finding Mathematics -- The Arctic Essay -- Epilogue -- References -- Can We "Show" the Correctness of Reasoning? On the Role of Diagrammatic Spatialization in Logical Justification -- Introduction -- The Eulerian Thesis: The Logical Correctness of the Diagrams "Jumps to the Eyes" -- Determining the Logical Framework of Our Research -- The Late Emergence of "Analytical" Logic Diagrams in a Pedagogical Context -- First Section: The Cognitive Advantages of the Diagrammatic Method -- Second Section: Can Diagrams Be Given the Task of Validating Reasoning? -- Third Section: Can a Diagram Show ("donner à voir") the Nature of a Proposition or the Correctness of a Reasoning? -- Back to Euler -- Showing the Nature of a Proposition -- Showing the Correctness of a Reasoning -- Some Remarks on the Relationship Between the Principles of Logic and Spatiality in Syllogistic (From Aristotle to Hamilton) -- Conclusion: Summary and Discussion -- References -- Articles and Monographs -- Proceedings of International Colloquia -- Catégorification et méthode -- Le polynôme de Jones -- La catégorification du polynôme de Jones -- La méthode de catégorification -- La théorie topologique quantique des champs.
Diagrammes et méthode -- Référenes -- Part II Geometrical Spaces and Topological Knots, Old and New -- Which Came First, the Circle or the Wheel? From Idea (δεα) to Concrete Construction -- Introduction -- Geometric Ideas and their Diagrams -- Digital Fabrication -- Geometry in Higher Dimension -- Bibliography -- Sitography -- The Classical Style in Contemporary Geometry: Views from a Person Working in the Field -- Introduction -- Fragments of Basic Algebraic Geometry -- Sterographic Projections in Dimension 1 and 2 (Figs. 4 and 5) -- Origins of Birational Geometry and Classification -- Cremona Transformations (Fig. 6) -- de Jonquiéres Transformations (Fig. 8) -- Classical Problems and Rational Parametrizations: Curves and Surfaces -- Classical Problems and Rational Parametrizations: Cubics -- The Classical Turn in Algebraic Geometry -- References -- Knots, Diagrams and Kids' Shoelaces. On Space and their Forms -- Introductive Remarks: Shoelaces, Knots, and the Intuition of Space -- Exploring and Visualizing 3-manifols and the Importance of Topology -- Equivalence of Images and of Forms: Manifolds, Knots and Diagrams -- Embeddings and Isotopies -- Mathematical Propaedeutic for the Understanding of Knots -- Knots and Links: Equivalence, Invariants and the Knot Complement -- The Alexander and Jones Polynomials -- Crossing Changes of Knots -- Back to Classical Invariants of Knots and Links -- Historical Note on Knots and their Diagrams -- Equivalence of Knots and Links -- From the Alexander Polynomial to Seifert Surfaces for Knots -- Reidemeister Moves and Classical Knot Invariants -- Dehn Surgery of Knots and his Work on Knot Theory and 3-dimensional Manifolds -- The Fundamental Group of Knots and Links -- Invariants of 3-manifolds and Hyperbolic Knots -- The Importance of the Linking Number in Molecular Biology. Geometrical and Topological Properties of the Double Helix and Supercoiling -- Knots, Links, and Topological Quantum Field Theories: An Overview -- Knots and Dynamics Systems -- The Energy of Knots -- References -- Part III Diagrams, Graphs and Representation -- Diagrammes planaires qui représentent des objets de dimension 1, 2, 3 et 4 -- Problème de classification -- Approche combinatoire -- Noeuds (dimension 1) -- Surfaces (dimension 2) -- Codage planaire des surfaces -- Variétés de dimension 3 -- Polyèdres spéciaux -- Polyèdres spéciaux épaississable -- Reconstruction -- Codage graphique -- Mouvements locaux -- Calcul graphique -- Variétés de dimension 4 -- Codage graphique des ombres -- References -- From Singularities to Graphs -- Introduction -- What Is the Meaning of Such Graphs? -- What Does it Mean to Resolve the Singularities of an Algebraic Surface? -- Representations of Surface Singularities Around 1900 -- Du Val's Singularities, Coxeter's Diagrams and the Birth of Dual Graphs -- Mumford's Paper on the Links of Surface Singularities -- Waldhausen's Graph Manifolds and Neumann's Calculus with Graphs -- Conclusion -- References -- Part IV Diagrams, Physical Forces and Path Integrals -- Mathematical Aspects of Feynman Path Integrals, Divergences, Quantum Fields and Diagrams, and Some More General Reflections -- Introduction -- The Case of Quantum Fields -- Divergences and Diagrams -- Some Conclusions, Philosophical Remarks and Reflections -- References -- Some Remarks on Penrose Diagrams -- Introduction -- Reflexions on the Different Notions of Dimensions -- The Notion of a Function -- A Second Kind of Diagram -- The Introduction of Infinity -- Some Complements to Conformal Geometry and General Relativity -- Cosmology and Conformal Diagrams -- Philosophical Comments -- Final Complements -- References. Part V Phenomenology in and of Mathematical Diagrams -- Phénoménologie, représentations, combinatoire -- Représentations géométriques: une approche classique -- Représentations géométriques: l'approche mathématique -- Représentations géométriques: l'approche phénoménologique -- Partitions non croisées -- Représentations graphiques -- De l'usage des représentations diagrammatiques. -- De la portée des représentations diagrammatiques -- Références -- Husserl, Intentionality and Mathematics: Geometry and Category Theory -- Intentionality and Space -- The Idea of a Mannigfaltigkeitslehre -- Space and Time in Phenomenology -- Issues of Foundation in Phenomenology through Category Theory -- References -- Diagrams of Time and Syntaxes of Consciousness: A Contribution to the Phenomenology of Visualization -- The Time Diagram Has Been Touched Upon (Varela, Weyl) -- Phenomenological Elucidation of the Subjective Resources of the Mathematical Construction of Linear Time -- The Specious Time of Neurophenomenology -- Phenomenology of the Use of Diagrams in Science Including Phenomenology -- Diagrammatic Underpinnings of Scientific Knowledge -- The Use of Diagrams in Phenomenology -- A Second Example: Intersubjective Constitution and Relativisation of the Original Coordinate System -- Symbolisation and Formal Writing in Phenomenology -- Symbolisation and Diagrammatisation of Intentional Analysis -- Intentionality as a System of Modification and Its Symbolism -- Analysis of the System of Continuous, i.e. Temporal Changes in 1913 -- An Example of Moving from an Analysis to a Mathematical Model -- Phenomenology and Diagrammatic of Lived Time -- The Dialectic of Phenomenological Reflection, Symbolisation and Diagram Construction Between 1905 and 1918 -- Diagrams of Retentions and Drafts of a Chronometry. From Infinitesimal Analysis to Complex Analysis of Phenomenological Time -- Gaps in the 1905 Diagrams -- An Important Gap in the Initial Retention Diagram: The Meaning of the Zero -- Diagrams of the on-in-the-Other (or Nesting) and Intertwining of Retentions and Protentions -- Diagrams in Reflection -- Conclusion: Perspectives for a General Theory of Possible Times -- References -- Part VI Diagrams, Gestures and Subjectivity -- A Topological Analysis of Space-Time-Consciousness: Self, Self-Self, Self-Other -- Knot Logic: Linking as Mutuality -- Belongingness: Not-I, Knot-I -- Self-Mutuality as Mutuality: Mutuality as Self-Mutuality -- Plurality of Now's -- Music -- Kauffman's Universe and HYK's Self -- References -- Gestes, diagrammes et subjectivité -- Un exemple de diagramme social (et ses gestes) -- Prendre sur soi, le 0-milieu -- Rapport à soi, la verticale -- Tourner autour de soi, le trou -- Le virtuel-Temps événementiel -- Some Prolegomena for a Contemporary "Critique of Imagination" -- Six Guiding Theses -- Imagination: Common Sense Notions -- Imagination: Philosophic Insights from Leibniz, Hume, Kant and Husserl -- Imagination: Hints from Neuroscience -- Bibliography -- Le langage diagrammatique au-delà de la différencephénoménologique -- Introduction -- La première forme canonique de notre rapport au monde : la signifiance -- De la signifiance au calcul : brève histoire de la différence phénoménologique -- Conclusion -- Part VII Diagrams: from Mathematics to Aesthetics -- Ars diagrammaticae -- Le phénomène de compactification -- Du diagramme comme preuve par l'image -- Quelques précisions maintenant concernant la désintrication des concepts d'Image, de Figure & -- de Diagramme. -- Grid Diagram: Deleuze's Aesthetics Applied to Maggs's Photographs -- Grid as Diagram in Portraits -- Faciality of Portraits -- Grid and Virtuality. Dada Diagrams/Dada Portraits. |
| Record Nr. | UNINA-9910633938303321 |
| Cham, Switzerland : , : Birkhäuser, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
When form becomes substance : power of gestures, diagrammatical intuition, and phenomenology of space / / edited by Luciano Boi, Carlos Lobo
| When form becomes substance : power of gestures, diagrammatical intuition, and phenomenology of space / / edited by Luciano Boi, Carlos Lobo |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2022] |
| Descrizione fisica | 1 online resource (607 pages) |
| Disciplina | 001.4226 |
| Soggetto topico |
Charts, diagrams, etc
Information visualization Science - Philosophy Visualització de la informació Diagrames Filosofia de la ciència Fenomenologia |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-83125-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Introduction -- Topological Visualisation, or How to Apprehend the Invisible -- Feynman Diagrams: A New Way Forward in Theoretical Physics -- Diagrammatics and Invariants in Knot and Braid Theory -- Philosophical and Scientific Implications -- Diagrammatics and Category Theory -- A French Singularity in Epistemological Field: Gilles Châtelet -- Phenomenology of Space (and Time) and Diagrammatic Epistemology -- Towards a "Diagrammatic Critique of Aesthetics" -- Acknowledgments -- Contents -- Part I Logic, Forms and Diagrams -- The Semiotics of Laws of Form -- Introduction -- Finding Distinction -- Finding Primary Arithmetic -- Finding Logic -- Finding Mathematics -- The Arctic Essay -- Epilogue -- References -- Can We "Show" the Correctness of Reasoning? On the Role of Diagrammatic Spatialization in Logical Justification -- Introduction -- The Eulerian Thesis: The Logical Correctness of the Diagrams "Jumps to the Eyes" -- Determining the Logical Framework of Our Research -- The Late Emergence of "Analytical" Logic Diagrams in a Pedagogical Context -- First Section: The Cognitive Advantages of the Diagrammatic Method -- Second Section: Can Diagrams Be Given the Task of Validating Reasoning? -- Third Section: Can a Diagram Show ("donner à voir") the Nature of a Proposition or the Correctness of a Reasoning? -- Back to Euler -- Showing the Nature of a Proposition -- Showing the Correctness of a Reasoning -- Some Remarks on the Relationship Between the Principles of Logic and Spatiality in Syllogistic (From Aristotle to Hamilton) -- Conclusion: Summary and Discussion -- References -- Articles and Monographs -- Proceedings of International Colloquia -- Catégorification et méthode -- Le polynôme de Jones -- La catégorification du polynôme de Jones -- La méthode de catégorification -- La théorie topologique quantique des champs.
Diagrammes et méthode -- Référenes -- Part II Geometrical Spaces and Topological Knots, Old and New -- Which Came First, the Circle or the Wheel? From Idea (δεα) to Concrete Construction -- Introduction -- Geometric Ideas and their Diagrams -- Digital Fabrication -- Geometry in Higher Dimension -- Bibliography -- Sitography -- The Classical Style in Contemporary Geometry: Views from a Person Working in the Field -- Introduction -- Fragments of Basic Algebraic Geometry -- Sterographic Projections in Dimension 1 and 2 (Figs. 4 and 5) -- Origins of Birational Geometry and Classification -- Cremona Transformations (Fig. 6) -- de Jonquiéres Transformations (Fig. 8) -- Classical Problems and Rational Parametrizations: Curves and Surfaces -- Classical Problems and Rational Parametrizations: Cubics -- The Classical Turn in Algebraic Geometry -- References -- Knots, Diagrams and Kids' Shoelaces. On Space and their Forms -- Introductive Remarks: Shoelaces, Knots, and the Intuition of Space -- Exploring and Visualizing 3-manifols and the Importance of Topology -- Equivalence of Images and of Forms: Manifolds, Knots and Diagrams -- Embeddings and Isotopies -- Mathematical Propaedeutic for the Understanding of Knots -- Knots and Links: Equivalence, Invariants and the Knot Complement -- The Alexander and Jones Polynomials -- Crossing Changes of Knots -- Back to Classical Invariants of Knots and Links -- Historical Note on Knots and their Diagrams -- Equivalence of Knots and Links -- From the Alexander Polynomial to Seifert Surfaces for Knots -- Reidemeister Moves and Classical Knot Invariants -- Dehn Surgery of Knots and his Work on Knot Theory and 3-dimensional Manifolds -- The Fundamental Group of Knots and Links -- Invariants of 3-manifolds and Hyperbolic Knots -- The Importance of the Linking Number in Molecular Biology. Geometrical and Topological Properties of the Double Helix and Supercoiling -- Knots, Links, and Topological Quantum Field Theories: An Overview -- Knots and Dynamics Systems -- The Energy of Knots -- References -- Part III Diagrams, Graphs and Representation -- Diagrammes planaires qui représentent des objets de dimension 1, 2, 3 et 4 -- Problème de classification -- Approche combinatoire -- Noeuds (dimension 1) -- Surfaces (dimension 2) -- Codage planaire des surfaces -- Variétés de dimension 3 -- Polyèdres spéciaux -- Polyèdres spéciaux épaississable -- Reconstruction -- Codage graphique -- Mouvements locaux -- Calcul graphique -- Variétés de dimension 4 -- Codage graphique des ombres -- References -- From Singularities to Graphs -- Introduction -- What Is the Meaning of Such Graphs? -- What Does it Mean to Resolve the Singularities of an Algebraic Surface? -- Representations of Surface Singularities Around 1900 -- Du Val's Singularities, Coxeter's Diagrams and the Birth of Dual Graphs -- Mumford's Paper on the Links of Surface Singularities -- Waldhausen's Graph Manifolds and Neumann's Calculus with Graphs -- Conclusion -- References -- Part IV Diagrams, Physical Forces and Path Integrals -- Mathematical Aspects of Feynman Path Integrals, Divergences, Quantum Fields and Diagrams, and Some More General Reflections -- Introduction -- The Case of Quantum Fields -- Divergences and Diagrams -- Some Conclusions, Philosophical Remarks and Reflections -- References -- Some Remarks on Penrose Diagrams -- Introduction -- Reflexions on the Different Notions of Dimensions -- The Notion of a Function -- A Second Kind of Diagram -- The Introduction of Infinity -- Some Complements to Conformal Geometry and General Relativity -- Cosmology and Conformal Diagrams -- Philosophical Comments -- Final Complements -- References. Part V Phenomenology in and of Mathematical Diagrams -- Phénoménologie, représentations, combinatoire -- Représentations géométriques: une approche classique -- Représentations géométriques: l'approche mathématique -- Représentations géométriques: l'approche phénoménologique -- Partitions non croisées -- Représentations graphiques -- De l'usage des représentations diagrammatiques. -- De la portée des représentations diagrammatiques -- Références -- Husserl, Intentionality and Mathematics: Geometry and Category Theory -- Intentionality and Space -- The Idea of a Mannigfaltigkeitslehre -- Space and Time in Phenomenology -- Issues of Foundation in Phenomenology through Category Theory -- References -- Diagrams of Time and Syntaxes of Consciousness: A Contribution to the Phenomenology of Visualization -- The Time Diagram Has Been Touched Upon (Varela, Weyl) -- Phenomenological Elucidation of the Subjective Resources of the Mathematical Construction of Linear Time -- The Specious Time of Neurophenomenology -- Phenomenology of the Use of Diagrams in Science Including Phenomenology -- Diagrammatic Underpinnings of Scientific Knowledge -- The Use of Diagrams in Phenomenology -- A Second Example: Intersubjective Constitution and Relativisation of the Original Coordinate System -- Symbolisation and Formal Writing in Phenomenology -- Symbolisation and Diagrammatisation of Intentional Analysis -- Intentionality as a System of Modification and Its Symbolism -- Analysis of the System of Continuous, i.e. Temporal Changes in 1913 -- An Example of Moving from an Analysis to a Mathematical Model -- Phenomenology and Diagrammatic of Lived Time -- The Dialectic of Phenomenological Reflection, Symbolisation and Diagram Construction Between 1905 and 1918 -- Diagrams of Retentions and Drafts of a Chronometry. From Infinitesimal Analysis to Complex Analysis of Phenomenological Time -- Gaps in the 1905 Diagrams -- An Important Gap in the Initial Retention Diagram: The Meaning of the Zero -- Diagrams of the on-in-the-Other (or Nesting) and Intertwining of Retentions and Protentions -- Diagrams in Reflection -- Conclusion: Perspectives for a General Theory of Possible Times -- References -- Part VI Diagrams, Gestures and Subjectivity -- A Topological Analysis of Space-Time-Consciousness: Self, Self-Self, Self-Other -- Knot Logic: Linking as Mutuality -- Belongingness: Not-I, Knot-I -- Self-Mutuality as Mutuality: Mutuality as Self-Mutuality -- Plurality of Now's -- Music -- Kauffman's Universe and HYK's Self -- References -- Gestes, diagrammes et subjectivité -- Un exemple de diagramme social (et ses gestes) -- Prendre sur soi, le 0-milieu -- Rapport à soi, la verticale -- Tourner autour de soi, le trou -- Le virtuel-Temps événementiel -- Some Prolegomena for a Contemporary "Critique of Imagination" -- Six Guiding Theses -- Imagination: Common Sense Notions -- Imagination: Philosophic Insights from Leibniz, Hume, Kant and Husserl -- Imagination: Hints from Neuroscience -- Bibliography -- Le langage diagrammatique au-delà de la différencephénoménologique -- Introduction -- La première forme canonique de notre rapport au monde : la signifiance -- De la signifiance au calcul : brève histoire de la différence phénoménologique -- Conclusion -- Part VII Diagrams: from Mathematics to Aesthetics -- Ars diagrammaticae -- Le phénomène de compactification -- Du diagramme comme preuve par l'image -- Quelques précisions maintenant concernant la désintrication des concepts d'Image, de Figure & -- de Diagramme. -- Grid Diagram: Deleuze's Aesthetics Applied to Maggs's Photographs -- Grid as Diagram in Portraits -- Faciality of Portraits -- Grid and Virtuality. Dada Diagrams/Dada Portraits. |
| Record Nr. | UNISA-996499866903316 |
| Cham, Switzerland : , : Birkhäuser, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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