Joseph Fourier 250th Birthday

Author : Frédéric Barbaresco,Jean-Pierre Gazeau
Publisher : MDPI
Page : 260 pages
File Size : 48,6 Mb
Release : 2019-03-28
Category : Science
ISBN : 9783038977469

Get Book

Joseph Fourier 250th Birthday by Frédéric Barbaresco,Jean-Pierre Gazeau Pdf

For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 46,6 Mb
Release : 2019
Category : Electronic
ISBN : OCLC:1368419282

Get Book

Joseph Fourier 250th Birthday. Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century by Anonim Pdf

For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.

Author : Andreas Maier,Stefan Steidl,Vincent Christlein,Joachim Hornegger
Publisher : Springer
Page : 263 pages
File Size : 50,6 Mb
Release : 2018-08-02
Category : Computers
ISBN : 9783319965208

Get Book

Medical Imaging Systems by Andreas Maier,Stefan Steidl,Vincent Christlein,Joachim Hornegger Pdf

This open access book gives a complete and comprehensive introduction to the fields of medical imaging systems, as designed for a broad range of applications. The authors of the book first explain the foundations of system theory and image processing, before highlighting several modalities in a dedicated chapter. The initial focus is on modalities that are closely related to traditional camera systems such as endoscopy and microscopy. This is followed by more complex image formation processes: magnetic resonance imaging, X-ray projection imaging, computed tomography, X-ray phase-contrast imaging, nuclear imaging, ultrasound, and optical coherence tomography.

Author : Ke Chen,Carola-Bibiane Schönlieb,Xue-Cheng Tai,Laurent Younes
Publisher : Springer Nature
Page : 1981 pages
File Size : 43,5 Mb
Release : 2023-02-24
Category : Mathematics
ISBN : 9783030986612

Get Book

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging by Ke Chen,Carola-Bibiane Schönlieb,Xue-Cheng Tai,Laurent Younes Pdf

This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.

Author : Mona Sarfaty
Publisher : Jones & Bartlett Learning
Page : 139 pages
File Size : 41,8 Mb
Release : 2020-10-23
Category : Medical
ISBN : 9781284170207

Get Book

Climate Change and Population Health: A Primer by Mona Sarfaty Pdf

Climate Change and Population Health begins by explaining the global warming and climate change by looking back historically, reviewing current measurement techniques and results, and taking into consideration greenhouse gases and their origins. It then looks at the health impact as well as who is most effected by climate change, before guiding students on how to effectively communicate about climate change as a means of helping people to protect themselves. Finally, it discusses possible policy solutions that might be beneficial to help mitigate health issues caused by climate change.

Author : Frank Nielsen,Frédéric Barbaresco
Publisher : Springer Nature
Page : 929 pages
File Size : 45,6 Mb
Release : 2021-07-14
Category : Computers
ISBN : 9783030802097

Get Book

Geometric Science of Information by Frank Nielsen,Frédéric Barbaresco Pdf

This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.

Author : Fanzhang Li,Li Zhang,Zhao Zhang
Publisher : Walter de Gruyter GmbH & Co KG
Page : 533 pages
File Size : 49,6 Mb
Release : 2018-11-05
Category : Computers
ISBN : 9783110499506

Get Book

Lie Group Machine Learning by Fanzhang Li,Li Zhang,Zhao Zhang Pdf

This book explains deep learning concepts and derives semi-supervised learning and nuclear learning frameworks based on cognition mechanism and Lie group theory. Lie group machine learning is a theoretical basis for brain intelligence, Neuromorphic learning (NL), advanced machine learning, and advanced artifi cial intelligence. The book further discusses algorithms and applications in tensor learning, spectrum estimation learning, Finsler geometry learning, Homology boundary learning, and prototype theory. With abundant case studies, this book can be used as a reference book for senior college students and graduate students as well as college teachers and scientific and technical personnel involved in computer science, artifi cial intelligence, machine learning, automation, mathematics, management science, cognitive science, financial management, and data analysis. In addition, this text can be used as the basis for teaching the principles of machine learning. Li Fanzhang is professor at the Soochow University, China. He is director of network security engineering laboratory in Jiangsu Province and is also the director of the Soochow Institute of industrial large data. He published more than 200 papers, 7 academic monographs, and 4 textbooks. Zhang Li is professor at the School of Computer Science and Technology of the Soochow University. She published more than 100 papers in journals and conferences, and holds 23 patents. Zhang Zhao is currently an associate professor at the School of Computer Science and Technology of the Soochow University. He has authored and co-authored more than 60 technical papers.

Author : Claude Gasquet,Patrick Witomski
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 46,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461215981

Get Book

Fourier Analysis and Applications by Claude Gasquet,Patrick Witomski Pdf

The object of this book is two-fold -- on the one hand it conveys to mathematical readers a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations. On the other hand, it presents physics readers with a body of theory in which the well-known formulae find their justification. The basic study of fundamental notions, such as Lebesgue integration and theory of distribution, allow the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets). The whole is rounded off with a large number of exercises as well as selected worked-out solutions.

Author : Robert E. Bradley,Ed Sandifer
Publisher : Elsevier
Page : 543 pages
File Size : 49,7 Mb
Release : 2007-03-20
Category : Mathematics
ISBN : 9780080471297

Get Book

Leonhard Euler by Robert E. Bradley,Ed Sandifer Pdf

The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment’s most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world’s best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler’s life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler’s philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler’s innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science. - Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich- New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova- New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century

Author : Rodrigo A. Collazo,Christiane Goergen,Jim Q. Smith
Publisher : CRC Press
Page : 255 pages
File Size : 45,9 Mb
Release : 2018-01-29
Category : Business & Economics
ISBN : 9781498729611

Get Book

Chain Event Graphs by Rodrigo A. Collazo,Christiane Goergen,Jim Q. Smith Pdf

Written by some major contributors to the development of this class of graphical models, Chain Event Graphs introduces a viable and straightforward new tool for statistical inference, model selection and learning techniques. The book extends established technologies used in the study of discrete Bayesian Networks so that they apply in a much more general setting As the first book on Chain Event Graphs, this monograph is expected to become a landmark work on the use of event trees and coloured probability trees in statistics, and to lead to the increased use of such tree models to describe hypotheses about how events might unfold. Features: introduces a new and exciting discrete graphical model based on an event tree focusses on illustrating inferential techniques, making its methodology accessible to a very broad audience and, most importantly, to practitioners illustrated by a wide range of examples, encompassing important present and future applications includes exercises to test comprehension and can easily be used as a course book introduces relevant software packages Rodrigo A. Collazo is a methodological and computational statistician based at the Naval Systems Analysis Centre (CASNAV) in Rio de Janeiro, Brazil. Christiane Görgen is a mathematical statistician at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany. Jim Q. Smith is a professor of statistics at the University of Warwick, UK. He has published widely in the field of statistics, AI, and decision analysis and has written two other books, most recently Bayesian Decision Analysis: Principles and Practice (Cambridge University Press 2010).

Author : Conference on geometric science of information
Publisher : Unknown
Page : 790 pages
File Size : 55,9 Mb
Release : 2015
Category : Electronic
ISBN : 3319250418

Get Book

Geometric Science of Information by Conference on geometric science of information Pdf

This book constitutes the refereed proceedings of the Second International Conference on Geometric Science of Information, GSI 2015, held in Palaiseau, France, in October 2015. The 80 full papers presented were carefully reviewed and selected from 110 submissions and are organized into the following thematic sessions: Dimension reduction on Riemannian manifolds; optimal transport; optimal transport and applications in imagery/statistics; shape space and diffeomorphic mappings; random geometry/homology; Hessian information geometry; topological forms and Information; information geometry optimization; information geometry in image analysis; divergence geometry; optimization on manifold; Lie groups and geometric mechanics/thermodynamics; computational information geometry; Lie groups: novel statistical and computational frontiers; geometry of time series and linear dynamical systems; and Bayesian and information geometry for inverse problems.

Author : Frank Nielsen
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 54,8 Mb
Release : 2014-05-08
Category : Technology & Engineering
ISBN : 9783319053172

Get Book

Geometric Theory of Information by Frank Nielsen Pdf

This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition and natural language treatment which are also substantially relevant for the industry.

Author : N. Balakrishnan,Rita Aggarwala
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461213345

Get Book

Progressive Censoring by N. Balakrishnan,Rita Aggarwala Pdf

This new book offers a guide to the theory and methods of progressive censoring. In many industrial experiments involving lifetimes of machines or units, experiments have to be terminated early. Progressive Censoring first introduces progressive sampling foundations, and then discusses various properties of progressive samples. The book points out the greater efficiency gained by using this scheme instead of classical right-censoring methods.

Author : Jerome R. Busemeyer,Peter D. Bruza
Publisher : Cambridge University Press
Page : 425 pages
File Size : 42,6 Mb
Release : 2012-07-26
Category : Psychology
ISBN : 9781139536486

Get Book

Quantum Models of Cognition and Decision by Jerome R. Busemeyer,Peter D. Bruza Pdf

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modeling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.

Author : Calvin C. Moore
Publisher : American Mathematical Society(RI)
Page : 488 pages
File Size : 43,5 Mb
Release : 1973
Category : Mathematics
ISBN : STANFORD:36105031376473

Get Book

Harmonic Analysis on Homogeneous Spaces by Calvin C. Moore Pdf