Topological Dynamics And Topological Data Analysis

Author : Robert L. Devaney,Kit C. Chan,P.B. Vinod Kumar
Publisher : Springer Nature
Page : 278 pages
File Size : 40,6 Mb
Release : 2021-09-23
Category : Mathematics
ISBN : 9789811601743

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Topological Dynamics and Topological Data Analysis by Robert L. Devaney,Kit C. Chan,P.B. Vinod Kumar Pdf

This book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9–11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.

Author : Robert L. Devaney,Kit C. Chan,P.B. Vinod Kumar
Publisher : Unknown
Page : 0 pages
File Size : 51,8 Mb
Release : 2021
Category : Electronic
ISBN : 9811601755

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Topological Dynamics and Topological Data Analysis by Robert L. Devaney,Kit C. Chan,P.B. Vinod Kumar Pdf

This book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9-11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.

Author : Raul Rabadan,Andrew J. Blumberg
Publisher : Cambridge University Press
Page : 522 pages
File Size : 48,7 Mb
Release : 2019-12-19
Category : Science
ISBN : 9781108757492

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Topological Data Analysis for Genomics and Evolution by Raul Rabadan,Andrew J. Blumberg Pdf

Biology has entered the age of Big Data. A technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce comparisons of shape to a comparison of algebraic invariants, such as numbers, which are typically easier to work with. Topological data analysis is a rapidly developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer, and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology as well as mathematicians interested in applied topology.

Author : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 55,7 Mb
Release : 2022-03-10
Category : Computers
ISBN : 9781009098168

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Computational Topology for Data Analysis by Tamal Krishna Dey,Yusu Wang Pdf

This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.

Author : J. de Vries
Publisher : Springer Science & Business Media
Page : 762 pages
File Size : 49,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401581714

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Elements of Topological Dynamics by J. de Vries Pdf

This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and basic (but sufficient to understand recent research papers in this field). There are still many challenging prob lems waiting for a solution, and especially among general topologists there is a growing interest in this direction. However, the technical inaccessability of many research papers makes it almost impossible for an outsider to under stand what is going on. To a large extent, this inaccessability is caused by the lack of a good and systematic exposition of the fundamental methods and techniques of abstract TO. This book is an attempt to fill this gap. The guiding principle for the organization of the material in this book has been the exposition of methods and techniques rather than a discussion of the leading problems and their solutions. though the latter are certainly not neglected: they are used as a motivation wherever possible.

Author : Gunnar Carlsson,Mikael Vejdemo-Johansson
Publisher : Cambridge University Press
Page : 233 pages
File Size : 40,9 Mb
Release : 2021-12-16
Category : Computers
ISBN : 9781108838658

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Topological Data Analysis with Applications by Gunnar Carlsson,Mikael Vejdemo-Johansson Pdf

This timely text introduces topological data analysis from scratch, with detailed case studies.

Author : Weltausstellung (1862, London)
Publisher : Unknown
Page : 134 pages
File Size : 54,6 Mb
Release : 1862
Category : Electronic
ISBN : DMM:057002288789-150810

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Official Illustrated Catalogue by Weltausstellung (1862, London) Pdf

Author : Jan Vries
Publisher : Walter de Gruyter
Page : 513 pages
File Size : 46,7 Mb
Release : 2014-01-31
Category : Mathematics
ISBN : 9783110342406

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Topological Dynamical Systems by Jan Vries Pdf

There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and course in General Topology are sufficient.

Author : Mario A. Natiello
Publisher : World Scientific
Page : 142 pages
File Size : 44,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812771483

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The User's Approach to Topological Methods in 3D Dynamical Systems by Mario A. Natiello Pdf

This book presents the development and application of some topological methods in the analysis of data coming from 3D dynamical systems (or related objects). The aim is to emphasize the scope and limitations of the methods, what they provide and what they do not provide. Braid theory, the topology of surface homeomorphisms, data analysis and the reconstruction of phase-space dynamics are thoroughly addressed.

Author : Valerio Pascucci,Xavier Tricoche,Hans Hagen,Julien Tierny
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 50,8 Mb
Release : 2010-11-23
Category : Mathematics
ISBN : 9783642150142

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Topological Methods in Data Analysis and Visualization by Valerio Pascucci,Xavier Tricoche,Hans Hagen,Julien Tierny Pdf

Topology-based methods are of increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation of large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. . The editors have brought together the most prominent and best recognized researchers in the field of topology-based data analysis and visualization for a joint discussion and scientific exchange of the latest results in the field. This book contains the best 20 peer-reviewed papers resulting from the discussions and presentations at the third workshop on "Topological Methods in Data Analysis and Visualization", held 2009 in Snowbird, Utah, US. The 2009 "TopoInVis" workshop follows the two successful workshops in 2005 (Slovakia) and 2007 (Germany).

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,6 Mb
Release : 2024-06-07
Category : Electronic
ISBN : 9789814476553

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The User's Approach to Topological Methods in 3D Dynamical Systems by Anonim Pdf

Author : Ingrid Hotz,Talha Bin Masood,Filip Sadlo,Julien Tierny
Publisher : Springer Nature
Page : 372 pages
File Size : 51,7 Mb
Release : 2021-09-28
Category : Mathematics
ISBN : 9783030835002

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Topological Methods in Data Analysis and Visualization VI by Ingrid Hotz,Talha Bin Masood,Filip Sadlo,Julien Tierny Pdf

This book is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nyköping, Sweden. The workshop regularly gathers some of the world’s leading experts in this field. Thereby, it provides a forum for discussions on the latest advances in the field with a focus on finding practical solutions to open problems in topological data analysis for visualization. The contributions provide introductory and novel research articles including new concepts for the analysis of multivariate and time-dependent data, robust computational approaches for the extraction and approximations of topological structures with theoretical guarantees, and applications of topological scalar and vector field analysis for visualization. The applications span a wide range of scientific areas comprising climate science, material sciences, fluid dynamics, and astronomy. In addition, community efforts with respect to joint software development are reported and discussed.

Author : N. Aoki,K. Hiraide
Publisher : Elsevier
Page : 425 pages
File Size : 48,8 Mb
Release : 1994-06-03
Category : Mathematics
ISBN : 9780080887210

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Topological Theory of Dynamical Systems by N. Aoki,K. Hiraide Pdf

This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments. This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book. Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.

Author : Marco Pettini
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 48,6 Mb
Release : 2007-06-14
Category : Mathematics
ISBN : 9780387499574

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Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics by Marco Pettini Pdf

This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists.

Author : Robert Gilmore,Marc Lefranc
Publisher : John Wiley & Sons
Page : 518 pages
File Size : 42,8 Mb
Release : 2008-09-26
Category : Mathematics
ISBN : 9783527617326

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The Topology of Chaos by Robert Gilmore,Marc Lefranc Pdf

A new approach to understanding nonlinear dynamics and strange attractors The behavior of a physical system may appear irregular or chaotic even when it is completely deterministic and predictable for short periods of time into the future. How does one model the dynamics of a system operating in a chaotic regime? Older tools such as estimates of the spectrum of Lyapunov exponents and estimates of the spectrum of fractal dimensions do not sufficiently answer this question. In a significant evolution of the field of Nonlinear Dynamics, The Topology of Chaos responds to the fundamental challenge of chaotic systems by introducing a new analysis method-Topological Analysis-which can be used to extract, from chaotic data, the topological signatures that determine the stretching and squeezing mechanisms which act on flows in phase space and are responsible for generating chaotic data. Beginning with an example of a laser that has been operated under conditions in which it behaved chaotically, the authors convey the methodology of Topological Analysis through detailed chapters on: * Discrete Dynamical Systems: Maps * Continuous Dynamical Systems: Flows * Topological Invariants * Branched Manifolds * The Topological Analysis Program * Fold Mechanisms * Tearing Mechanisms * Unfoldings * Symmetry * Flows in Higher Dimensions * A Program for Dynamical Systems Theory Suitable at the present time for analyzing "strange attractors" that can be embedded in three-dimensional spaces, this groundbreaking approach offers researchers and practitioners in the discipline a complete and satisfying resolution to the fundamental questions of chaotic systems.