Algebraic Foundations For Applied Topology And Data Analysis
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Algebraic Foundations For Applied Topology And Data Analysis
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Author : Hal Schenck
language : en
Publisher: Springer Nature
Release Date : 2022-11-21
Algebraic Foundations For Applied Topology And Data Analysis written by Hal Schenck and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-21 with Mathematics categories.
This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). Covering a wide range of topics at levels of sophistication varying from elementary (matrix algebra) to esoteric (Grothendieck spectral sequence), it offers a mirror of data science aimed at a general mathematical audience. The required algebraic background is developed in detail. The first third of the book reviews several core areas of mathematics, beginning with basic linear algebra and applications to data fitting and web search algorithms, followed by quick primers on algebra and topology. The middle third introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third covers key contemporary tools in TDA: persistent and multiparameter persistent homology. Also included is a user’s guide to derived functors and spectral sequences (useful but somewhat technical tools which have recently found applications in TDA), and an appendix illustrating a number of software packages used in the field. Based on a course given as part of a masters degree in statistics, the book is appropriate for graduate students.
Approximation Theory And Numerical Analysis Meet Algebra Geometry Topology
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Author : Martina Lanini
language : en
Publisher: Springer Nature
Release Date : 2024-12-22
Approximation Theory And Numerical Analysis Meet Algebra Geometry Topology written by Martina Lanini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-22 with Mathematics categories.
The book, based on the INdAM Workshop "Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology" provides a bridge between different communities of mathematicians who utilize splines in their work. Splines are mathematical objects which allow researchers in geometric modeling and approximation theory to tackle a wide variety of questions. Splines are interesting for both applied mathematicians, and also for those working in purely theoretical mathematical settings. This book contains contributions by researchers from different mathematical communities: on the applied side, those working in numerical analysis and approximation theory, and on the theoretical side, those working in GKM theory, equivariant cohomology and homological algebra.
Topological Data Analysis
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Author : Nils A. Baas
language : en
Publisher: Springer Nature
Release Date : 2020-06-25
Topological Data Analysis written by Nils A. Baas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-25 with Mathematics categories.
This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018. The symposium offered an overview of the emerging field of "Topological Data Analysis". This volume presents papers on various research directions, notably including applications in neuroscience, materials science, cancer biology, and immune response. Providing an essential snapshot of the status quo, it represents a valuable asset for practitioners and those considering entering the field.
Topology In Real World Machine Learning And Data Analysis
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Author : Kathryn Hess
language : en
Publisher: Frontiers Media SA
Release Date : 2022-11-07
Topology In Real World Machine Learning And Data Analysis written by Kathryn Hess and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-07 with Science categories.
Persistence Theory From Quiver Representations To Data Analysis
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Author : Steve Y. Oudot
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-05-17
Persistence Theory From Quiver Representations To Data Analysis written by Steve Y. Oudot and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-17 with Mathematics categories.
Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.
Handbook Of Discrete And Computational Geometry
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Author : Csaba D. Toth
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Handbook Of Discrete And Computational Geometry written by Csaba D. Toth and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Computers categories.
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
From Physics To Econophysics And Back Methods And Insights
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Author : Siew Ann Cheong
language : en
Publisher: Frontiers Media SA
Release Date : 2022-07-06
From Physics To Econophysics And Back Methods And Insights written by Siew Ann Cheong and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-06 with Science categories.
Edusemiotics A Handbook
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Author : Inna Semetsky
language : en
Publisher: Springer
Release Date : 2016-10-17
Edusemiotics A Handbook written by Inna Semetsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-17 with Education categories.
Edusemiotics is a pioneering area of study that connects semiotics – the science of signs – with educational theory and the philosophy of education. This volume reflects cutting-edge research by scholars in education and in semiotics worldwide, bridging the two discourses to present the state of the art in this new transdisciplinary field. The book’s emphasis is on educational theory as based on semiotic philosophy: as such, it challenges the current conception of semiotics in education as merely a sub-branch of applied semiotics. It presents edusemiotics as a novel unified conceptual framework at the interface of theoretical semiotics and educational philosophy, based on both theoretical and empirical studies from around the world. The chapters in this handbook also bring to the fore the intellectual legacy of Charles S. Peirce, John Dewey, Gilles Deleuze, Umberto Eco, Julia Kristeva, Mikhail Bakhtin, Paul Ricoeur, Martin Heidegger and other thinkers, pointing out the implications of edusemiotics for meaningful pedagogy and experiential learning in diverse contexts.
Data Science In Engineering Volume 9
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Author : Ramin Madarshahian
language : en
Publisher: CRC Press
Release Date : 2025-08-07
Data Science In Engineering Volume 9 written by Ramin Madarshahian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-07 with Technology & Engineering categories.
Data Science and Engineering Volume 9: Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021, the ninth volume of nine from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Data Science in Engineering, including papers on: Data Science in Engineering Applications Engineering Mathematics Computational Methods in Engineering.
The Structure And Stability Of Persistence Modules
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Author : Frédéric Chazal
language : en
Publisher: Springer
Release Date : 2016-10-08
The Structure And Stability Of Persistence Modules written by Frédéric Chazal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-08 with Mathematics categories.
This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations. Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.