Persistence Theory From Quiver Representations To Data Analysis

Author : Steve Y. Oudot
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 51,5 Mb
Release : 2017-05-17
Category : Electronic
ISBN : 9781470434434

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Persistence Theory: From Quiver Representations to Data Analysis by Steve Y. Oudot Pdf

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.

Author : Frédéric Chazal,Vin de Silva,Marc Glisse,Steve Oudot
Publisher : Springer
Page : 120 pages
File Size : 55,9 Mb
Release : 2016-10-08
Category : Mathematics
ISBN : 9783319425450

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The Structure and Stability of Persistence Modules by Frédéric Chazal,Vin de Silva,Marc Glisse,Steve Oudot Pdf

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.

Author : Hal Schenck
Publisher : Springer Nature
Page : 231 pages
File Size : 49,6 Mb
Release : 2022-11-21
Category : Mathematics
ISBN : 9783031066641

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Algebraic Foundations for Applied Topology and Data Analysis by Hal Schenck Pdf

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.

Author : Robert L. Devaney,Kit C. Chan,P.B. Vinod Kumar
Publisher : Springer Nature
Page : 278 pages
File Size : 47,7 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 : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 52,5 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 : Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 49,6 Mb
Release : 2020-05-11
Category : Education
ISBN : 9781470454951

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Topological Persistence in Geometry and Analysis by Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang Pdf

The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.

Author : Nils A. Baas,Gunnar E. Carlsson,Gereon Quick,Markus Szymik,Marius Thaule
Publisher : Springer Nature
Page : 522 pages
File Size : 55,6 Mb
Release : 2020-06-25
Category : Mathematics
ISBN : 9783030434083

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Topological Data Analysis by Nils A. Baas,Gunnar E. Carlsson,Gereon Quick,Markus Szymik,Marius Thaule Pdf

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.

Author : Kathryn Hess,Frédéric Chazal,Umberto Lupo
Publisher : Frontiers Media SA
Page : 229 pages
File Size : 41,5 Mb
Release : 2022-11-07
Category : Science
ISBN : 9782832504123

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Topology in Real-World Machine Learning and Data Analysis by Kathryn Hess,Frédéric Chazal,Umberto Lupo Pdf

Author : Ilke Demir,Yifei Lou,Xu Wang,Kathrin Welker
Publisher : Springer Nature
Page : 374 pages
File Size : 54,6 Mb
Release : 2021-12-03
Category : Mathematics
ISBN : 9783030798918

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Advances in Data Science by Ilke Demir,Yifei Lou,Xu Wang,Kathrin Welker Pdf

This volume highlights recent advances in data science, including image processing and enhancement on large data, shape analysis and geometry processing in 2D/3D, exploration and understanding of neural networks, and extensions to atypical data types such as social and biological signals. The contributions are based on discussions from two workshops under Association for Women in Mathematics (AWM), namely the second Women in Data Science and Mathematics (WiSDM) Research Collaboration Workshop that took place between July 29 and August 2, 2019 at the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, Rhode Island, and the third Women in Shape (WiSh) Research Collaboration Workshop that took place between July 16 and 20, 2018 at Trier University in Robert-Schuman-Haus, Trier, Germany. These submissions, seeded by working groups at the conference, form a valuable source for readers who are interested in ideas and methods developed in interdisciplinary research fields. The book features ideas, methods, and tools developed through a broad range of domains, ranging from theoretical analysis on graph neural networks to applications in health science. It also presents original results tackling real-world problems that often involve complex data analysis on large multi-modal data sources.

Author : Erin Wolf Chambers,Brittany Terese Fasy,Lori Ziegelmeier
Publisher : Springer
Page : 202 pages
File Size : 50,9 Mb
Release : 2018-07-30
Category : Mathematics
ISBN : 9783319895932

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Research in Computational Topology by Erin Wolf Chambers,Brittany Terese Fasy,Lori Ziegelmeier Pdf

Based on the first Workshop for Women in Computational Topology that took place in 2016, this volume assembles new research and applications in computational topology. Featured articles range over the breadth of the discipline, including topics such as surface reconstruction, topological data analysis, persistent homology, algorithms, and surface-embedded graphs. Applications in graphics, medical imaging, and GIS are discussed throughout the book. Four of the papers in this volume are the product of working groups that were established and developed during the workshop. Additional papers were also solicited from the broader Women in Computational Topology network. The volume is accessible to a broad range of researchers, both within the field of computational topology and in related disciplines such as statistics, computational biology, and machine learning.

Author : Michael W. Mahoney,John C. Duchi,Anna C. Gilbert
Publisher : American Mathematical Soc.
Page : 325 pages
File Size : 45,9 Mb
Release : 2018-11-15
Category : Big data
ISBN : 9781470435752

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The Mathematics of Data by Michael W. Mahoney,John C. Duchi,Anna C. Gilbert Pdf

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Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1928 pages
File Size : 52,6 Mb
Release : 2017-11-22
Category : Computers
ISBN : 9781498711425

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Handbook of Discrete and Computational Geometry by Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman Pdf

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.

Author : Isao Tanaka
Publisher : Springer
Page : 298 pages
File Size : 40,9 Mb
Release : 2018-01-15
Category : Technology & Engineering
ISBN : 9789811076176

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Nanoinformatics by Isao Tanaka Pdf

This open access book brings out the state of the art on how informatics-based tools are used and expected to be used in nanomaterials research. There has been great progress in the area in which “big-data” generated by experiments or computations are fully utilized to accelerate discovery of new materials, key factors, and design rules. Data-intensive approaches play indispensable roles in advanced materials characterization. "Materials informatics" is the central paradigm in the new trend. "Nanoinformatics" is its essential subset, which focuses on nanostructures of materials such as surfaces, interfaces, dopants, and point defects, playing a critical role in determining materials properties. There have been significant advances in experimental and computational techniques to characterize individual atoms in nanostructures and to gain quantitative information. The collaboration of researchers in materials science and information science is growing actively and is creating a new trend in materials science and engineering.

Author : Raul Rabadan,Andrew J. Blumberg
Publisher : Cambridge University Press
Page : 521 pages
File Size : 50,8 Mb
Release : 2019-12-19
Category : Science
ISBN : 9781107159549

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

An introduction to geometric and topological methods to analyze large scale biological data; includes statistics and genomic applications.

Author : Luping Zhou,Nicholas Heller,Yiyu Shi,Yiming Xiao,Raphael Sznitman,Veronika Cheplygina,Diana Mateus,Emanuele Trucco,X. Sharon Hu,Danny Chen,Matthieu Chabanas,Hassan Rivaz,Ingerid Reinertsen
Publisher : Springer Nature
Page : 165 pages
File Size : 54,5 Mb
Release : 2019-11-20
Category : Computers
ISBN : 9783030336424

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Large-Scale Annotation of Biomedical Data and Expert Label Synthesis and Hardware Aware Learning for Medical Imaging and Computer Assisted Intervention by Luping Zhou,Nicholas Heller,Yiyu Shi,Yiming Xiao,Raphael Sznitman,Veronika Cheplygina,Diana Mateus,Emanuele Trucco,X. Sharon Hu,Danny Chen,Matthieu Chabanas,Hassan Rivaz,Ingerid Reinertsen Pdf

This book constitutes the refereed joint proceedings of the 4th International Workshop on Large-Scale Annotation of Biomedical Data and Expert Label Synthesis, LABELS 2019, the First International Workshop on Hardware Aware Learning for Medical Imaging and Computer Assisted Intervention, HAL-MICCAI 2019, and the Second International Workshop on Correction of Brainshift with Intra-Operative Ultrasound, CuRIOUS 2019, held in conjunction with the 22nd International Conference on Medical Imaging and Computer-Assisted Intervention, MICCAI 2019, in Shenzhen, China, in October 2019. The 8 papers presented at LABELS 2019, the 5 papers presented at HAL-MICCAI 2019, and the 3 papers presented at CuRIOUS 2019 were carefully reviewed and selected from numerous submissions. The LABELS papers present a variety of approaches for dealing with a limited number of labels, from semi-supervised learning to crowdsourcing. The HAL-MICCAI papers cover a wide set of hardware applications in medical problems, including medical image segmentation, electron tomography, pneumonia detection, etc. The CuRIOUS papers provide a snapshot of the current progress in the field through extended discussions and provide researchers an opportunity to characterize their image registration methods on newly released standardized datasets of iUS-guided brain tumor resection.