Dynamical Systems Analysis Using Topological Signal Processing

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Dynamical Systems Analysis Using Topological Signal Processing

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Author : Audun Myers
language : en
Publisher:
Release Date : 2022

Dynamical Systems Analysis Using Topological Signal Processing written by Audun Myers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Electronic dissertations categories.

Topological Signal Processing (TSP) is the study of time series data through the lens of Topological Data Analysis (TDA)-a process of analyzing data through its shape. This work focuses on developing novel TSP tools for the analysis of dynamical systems. A dynamical system is a term used to broadly refer to a system whose state changes in time. These systems are formally assumed to be a continuum of states whose values are real numbers. However, real-life measurements of these systems only provide finite information from which the underlying dynamics must be gleaned. This necessitates making conclusions on the continuous structure of a dynamical system using noisy finite samples or time series. The interest often lies in capturing qualitative changes in the system's behavior known as a bifurcation through changes in the shape of the state space as one or more of the system parameters vary. Current literature on time series analysis aims to study this structure by searching for a lower-dimensional representation; however, the need for user-defined inputs, the sensitivity of these inputs to noise, and the expensive computational effort limit the usability of available knowledge especially for in-situ signal processing.This research aims to use and develop TSP tools to extract useful information about the underlying dynamical system's structure. The first research direction investigates the use of sublevel set persistence-a form of persistent homology from TDA-for signal processing with applications including parameter estimation of a damped oscillator and signal complexity measures to detect bifurcations. The second research direction applies TDA to complex networks to investigate how the topology of such complex networks corresponds to the state space structure. We show how TSP applied to complex networks can be used to detect changes in signal complexity including chaotic compared to periodic dynamics in a noise-contaminated signal. The last research direction focuses on the topological analysis of dynamical networks. A dynamical network is a graph whose vertices and edges have state values driven by a highly interconnected dynamical system. We show how zigzag persistence-a modification of persistent homology-can be used to understand the changing structure of such dynamical networks.

Basics Of Representation Theory

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Author : Udayan Bhattacharya
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Basics Of Representation Theory written by Udayan Bhattacharya and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

Delve into the captivating world of "Basics of Representation Theory," a comprehensive guide designed for students, researchers, and enthusiasts eager to explore the intricate symmetries and structures that underpin modern mathematics. Our book offers a detailed introduction to foundational concepts, providing a solid understanding of group actions, linear representations, and character theory. From there, it explores the algebraic structures of irreducible representations, breaking down the decomposition into irreducible components and examining the properties of characters. Readers will journey through diverse topics, including the representation theory of symmetric groups, Lie groups, and algebraic groups, as well as advanced topics such as the representation theory of finite groups, the Langlands program, and applications in quantum mechanics and number theory. With a wealth of examples, illustrations, and exercises, "Basics of Representation Theory" ensures a hands-on approach to learning, encouraging practical exploration and problem-solving. The book also includes numerous references and further reading suggestions for those who wish to delve deeper into specific topics. Written in a clear and accessible style, this book caters to all levels, from undergraduate students encountering representation theory for the first time to experienced researchers seeking fresh insights. With its comprehensive coverage and diverse applications, "Basics of Representation Theory" is an invaluable resource for anyone interested in the beauty and depth of this field.

Applications Of Machine Intelligence In Engineering

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Author : Jyotsna Kumar Mandal
language : en
Publisher: CRC Press
Release Date : 2022-04-21

Applications Of Machine Intelligence In Engineering written by Jyotsna Kumar Mandal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-21 with Computers categories.

The Global Conference on Artificial Intelligence and Applications (GCAIA 2021) provides a prominent venue for researchers, engineers, entrepreneurs, and scholar students to share their research ideas in the area of AI. Academic researchers would reveal the results and conclusions of laboratory based investigations via the GCAIA 21 platform, which bridges the gap between academia, industry, and government ethics. The GCAIA 21 platform will also bring together regional and worldwide issues to explore current advancements in contemporary Computation Intelligence. This Conference Proceedings volume contains the written versions of most of the contributions presented during the conference of GCAIA 2021. The conference has provided an excellent chance for researchers from diverse locations to present and debate their work in the field of artificial intelligence and its applications. It includes a selection of 62 papers. All accepted papers were subjected to strict peer-review by 2–4 expert referees. The papers have been selected for this volume because of their quality and their relevance to the theme of the conference.

Signal Processing And Machine Learning For Biomedical Big Data

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Author : Ervin Sejdic
language : en
Publisher: CRC Press
Release Date : 2018-07-04

Signal Processing And Machine Learning For Biomedical Big Data written by Ervin Sejdic and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-04 with Medical categories.

Within the healthcare domain, big data is defined as any ``high volume, high diversity biological, clinical, environmental, and lifestyle information collected from single individuals to large cohorts, in relation to their health and wellness status, at one or several time points.'' Such data is crucial because within it lies vast amounts of invaluable information that could potentially change a patient's life, opening doors to alternate therapies, drugs, and diagnostic tools. Signal Processing and Machine Learning for Biomedical Big Data thus discusses modalities; the numerous ways in which this data is captured via sensors; and various sample rates and dimensionalities. Capturing, analyzing, storing, and visualizing such massive data has required new shifts in signal processing paradigms and new ways of combining signal processing with machine learning tools. This book covers several of these aspects in two ways: firstly, through theoretical signal processing chapters where tools aimed at big data (be it biomedical or otherwise) are described; and, secondly, through application-driven chapters focusing on existing applications of signal processing and machine learning for big biomedical data. This text aimed at the curious researcher working in the field, as well as undergraduate and graduate students eager to learn how signal processing can help with big data analysis. It is the hope of Drs. Sejdic and Falk that this book will bring together signal processing and machine learning researchers to unlock existing bottlenecks within the healthcare field, thereby improving patient quality-of-life. Provides an overview of recent state-of-the-art signal processing and machine learning algorithms for biomedical big data, including applications in the neuroimaging, cardiac, retinal, genomic, sleep, patient outcome prediction, critical care, and rehabilitation domains. Provides contributed chapters from world leaders in the fields of big data and signal processing, covering topics such as data quality, data compression, statistical and graph signal processing techniques, and deep learning and their applications within the biomedical sphere. This book’s material covers how expert domain knowledge can be used to advance signal processing and machine learning for biomedical big data applications.

Applied Dynamics

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Author : Francis C. Moon
language : en
Publisher: John Wiley & Sons
Release Date : 2008-09-26

Applied Dynamics written by Francis C. Moon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-26 with Technology & Engineering categories.

Applied Dynamics provides a modern and thorough examination of dynamics with specific emphasis on physical examples and applications such as: robotic systems, magnetic bearings, aerospace dynamics, and microelectromagnetic machines. Also includes the development of the method of virtual velocities based on the principle of virtual power.

Currents In Biomedical Signals Processing Methods And Applications

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Author : Aleksandra Dagmara Kawala-Sterniuk
language : en
Publisher: Frontiers Media SA
Release Date : 2022-09-05

Currents In Biomedical Signals Processing Methods And Applications written by Aleksandra Dagmara Kawala-Sterniuk 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 2022-09-05 with Science categories.

Artificial Intelligence Enabled Signal Processing Based Models For Neural Information Processing

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Author : Rajesh Kumar Tripathy
language : en
Publisher: CRC Press
Release Date : 2024-06-06

Artificial Intelligence Enabled Signal Processing Based Models For Neural Information Processing written by Rajesh Kumar Tripathy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-06 with Technology & Engineering categories.

The book provides details regarding the application of various signal processing and artificial intelligence-based methods for electroencephalography data analysis. It will help readers in understanding the use of electroencephalography signals for different neural information processing and cognitive neuroscience applications. The book: Covers topics related to the application of signal processing and machine learning-based techniques for the analysis and classification of electroencephalography signals Presents automated methods for detection of neurological disorders and other applications such as cognitive task recognition, and brain-computer interface Highlights the latest machine learning and deep learning methods for neural signal processing Discusses mathematical details for the signal processing and machine learning algorithms applied for electroencephalography data analysis Showcases the detection of dementia from electroencephalography signals using signal processing and machine learning-based techniques It is primarily written for senior undergraduates, graduate students, and researchers in the fields of electrical engineering, electronics and communications engineering, and biomedical engineering.

The Topology Of Chaos

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Author : Robert Gilmore
language : en
Publisher: John Wiley & Sons
Release Date : 2012-04-30

The Topology Of Chaos written by Robert Gilmore and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Mathematics categories.

A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep understanding of the structure of strange attractors, how they are classified, and how the information required to identify and classify a strange attractor can be extracted from experimental data. In its first edition, the Topology of Chaos has been a valuable resource for physicist and mathematicians interested in the topological analysis of dynamical systems. Since its publication in 2002, important theoretical and experimental advances have put the topological analysis program on a firmer basis. This second edition includes relevant results and connects the material to other recent developments. Following significant improvements will be included: * A gentler introduction to the topological analysis of chaotic systems for the non expert which introduces the problems and questions that one commonly encounters when observing a chaotic dynamics and which are well addressed by a topological approach: existence of unstable periodic orbits, bifurcation sequences, multistability etc. * A new chapter is devoted to bounding tori which are essential for achieving generality as well as for understanding the influence of boundary conditions. * The new edition also reflects the progress which had been made towards extending topological analysis to higher-dimensional systems by proposing a new formalism where evolving triangulations replace braids. * There has also been much progress in the understanding of what is a good representation of a chaotic system, and therefore a new chapter is devoted to embeddings. * The chapter on topological analysis program will be expanded to cover traditional measures of chaos. This will help to connect those readers who are familiar with those measures and tests to the more sophisticated methodologies discussed in detail in this book. * The addition of the Appendix with both frequently asked and open questions with answers gathers the most essential points readers should keep in mind and guides to corresponding sections in the book. This will be of great help to those who want to selectively dive into the book and its treatments rather than reading it cover to cover. What makes this book special is its attempt to classify real physical systems (e.g. lasers) using topological techniques applied to real date (e.g. time series). Hence it has become the experimenter?s guidebook to reliable and sophisticated studies of experimental data for comparison with candidate relevant theoretical models, inevitable to physicists, mathematicians, and engineers studying low-dimensional chaotic systems.

Towards A Theoretical Framework For Analyzing Complex Linguistic Networks

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Author : Alexander Mehler
language : en
Publisher: Springer
Release Date : 2015-07-07

Towards A Theoretical Framework For Analyzing Complex Linguistic Networks written by Alexander Mehler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-07 with Technology & Engineering categories.

The aim of this book is to advocate and promote network models of linguistic systems that are both based on thorough mathematical models and substantiated in terms of linguistics. In this way, the book contributes first steps towards establishing a statistical network theory as a theoretical basis of linguistic network analysis the boarder of the natural sciences and the humanities. This book addresses researchers who want to get familiar with theoretical developments, computational models and their empirical evaluation in the field of complex linguistic networks. It is intended to all those who are interested in statistical models of linguistic systems from the point of view of network research. This includes all relevant areas of linguistics ranging from phonological, morphological and lexical networks on the one hand and syntactic, semantic and pragmatic networks on the other. In this sense, the volume concerns readers from many disciplines such as physics, linguistics, computer science and information science. It may also be of interest for the upcoming area of systems biology with which the chapters collected here share the view on systems from the point of view of network analysis.

Advances In Natural Computation Fuzzy Systems And Knowledge Discovery

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Author : Yong Liu
language : en
Publisher: Springer Nature
Release Date : 2019-11-06

Advances In Natural Computation Fuzzy Systems And Knowledge Discovery written by Yong Liu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-06 with Technology & Engineering categories.

This book discusses the recent advances in natural computation, fuzzy systems and knowledge discovery. Presenting selected, peer-reviewed papers from the 15th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2019), held in Kunming, China, from 20 to 22 July 2019, it is a useful resource for researchers, including professors and graduate students, as well as R&D staff in industry.