Elements Of Neurogeometry
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Elements Of Neurogeometry
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Author : Jean Petitot
language : en
Publisher: Springer
Release Date : 2017-11-08
Elements Of Neurogeometry written by Jean Petitot and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-08 with Mathematics categories.
This book describes several mathematical models of the primary visual cortex, referring them to a vast ensemble of experimental data and putting forward an original geometrical model for its functional architecture, that is, the highly specific organization of its neural connections. The book spells out the geometrical algorithms implemented by this functional architecture, or put another way, the “neurogeometry” immanent in visual perception. Focusing on the neural origins of our spatial representations, it demonstrates three things: firstly, the way the visual neurons filter the optical signal is closely related to a wavelet analysis; secondly, the contact structure of the 1-jets of the curves in the plane (the retinal plane here) is implemented by the cortical functional architecture; and lastly, the visual algorithms for integrating contours from what may be rather incomplete sensory data can be modelled by the sub-Riemannian geometry associated with this contact structure. As such, it provides readers with the first systematic interpretation of a number of important neurophysiological observations in a well-defined mathematical framework. The book’s neuromathematical exploration appeals to graduate students and researchers in integrative-functional-cognitive neuroscience with a good mathematical background, as well as those in applied mathematics with an interest in neurophysiology.
Morphology Neurogeometry Semiotics
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Author : Alessandro Sarti
language : en
Publisher: Springer Nature
Release Date : 2024-06-03
Morphology Neurogeometry Semiotics written by Alessandro Sarti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-03 with Science categories.
Jean Petitot is a polyhedric thinker whose contributions has been fundamental in a number of disciplines, such as epistemology, morphodynamics, differential geometry, structural semiotics, neurogeometry, phenomenology, linguistics, cognitive grammars, the theory of catastrophes, social sciences, literary studies, and aesthetics. This book is a homage to his huge contribution about the main concepts of morphogenesis and meaning that constitute the center of gravity around which Petitotian reflection revolves and returns. The scientific path of Jean Petitot develops between these two poles, topology and meaning. At stake it was to challenge the hiatus separating the exact sciences from the humanities that was the main point of the Petitot seminar of EHESS Epistemology of Models. By designing the appropriate qualitative dynamics between the two poles, form and meaning, it is possible to understand the Saussurian sign in structural semiotics, or the Greimasian semiotic square fordeep narrative structures or even the canonical formula of the myth of Lévi Strauss in structural anthropology. These are just few results in applying the theory of catastrophes to the emergence of meaning. The book is a collection of testimonies by distinguished authors who worked extensively with Jean Petitot in the different fields of Mathematics, Neurogeometry, Semiotics, Aesthetics, and Epistemology. An extensive bibliography of Petitot’s work is also presented.
Neuromathematics Of Vision
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Author : Giovanna Citti
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-08
Neuromathematics Of Vision written by Giovanna Citti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-08 with Mathematics categories.
This book is devoted to the study of the functional architecture of the visual cortex. Its geometrical structure is the differential geometry of the connectivity between neural cells. This connectivity is building and shaping the hidden brain structures underlying visual perception. The story of the problem runs over the last 30 years, since the discovery of Hubel and Wiesel of the modular structure of the primary visual cortex, and slowly cams towards a theoretical understanding of the experimental data on what we now know as functional architecture of the primary visual cortex. Experimental data comes from several domains: neurophysiology, phenomenology of perception and neurocognitive imaging. Imaging techniques like functional MRI and diffusion tensor MRI allow to deepen the study of cortical structures. Due to this variety of experimental data, neuromathematematics deals with modelling both cortical structures and perceptual spaces. From the mathematical point of view, neuromathematical call for new instruments of pure mathematics: sub-Riemannian geometry models horizontal connectivity, harmonic analysis in non commutative groups allows to understand pinwheels structure, as well as non-linear dimensionality reduction is at the base of many neural morphologies and possibly of the emergence of perceptual units. But at the center of the neurogeometry is the problem of harmonizing contemporary mathematical instruments with neurophysiological findings and phenomenological experiments in an unitary science of vision. The contributions to this book come from the very founders of the discipline.
Geometric Science Of Information
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Author : Frank Nielsen
language : en
Publisher: Springer Nature
Release Date : 2021-07-14
Geometric Science Of Information written by Frank Nielsen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-14 with Computers categories.
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.
Handbook Of Mathematical Models And Algorithms In Computer Vision And Imaging
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Author : Ke Chen
language : en
Publisher: Springer Nature
Release Date : 2023-02-24
Handbook Of Mathematical Models And Algorithms In Computer Vision And Imaging written by Ke Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-24 with Mathematics categories.
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.
Perceptual Organization In Computer And Biological Vision
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Author : James Elder
language : en
Publisher: Frontiers Media SA
Release Date : 2024-08-22
Perceptual Organization In Computer And Biological Vision written by James Elder 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 2024-08-22 with Science categories.
A principal challenge for both biological and machine vision systems is to integrate and organize the diversity of cues received from the environment into the coherent global representations we experience and require to make good decisions and take effective actions. Early psychological investigations date back more than 100 years to the seminal work of the Gestalt school. Yet in the last 50 years, neuroscientific and computational approaches to understanding perceptual organization have become equally important, and a full understanding requires integration of all three approaches. This highly interdisciplinary Research Topic welcomes contributions spanning Computer Science, Psychology, and Neuroscience, with the aim of presenting a single, unified collection that will encourage integration and cross-fertilization across disciplines.
The Relevance Of Ren Thom
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Author : Isabel Marcos
language : en
Publisher: Springer Nature
Release Date : 2024-08-29
The Relevance Of Ren Thom written by Isabel Marcos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-29 with Mathematics categories.
The body of work presented in this book comes from research carried out since 2017 as part of the international "Actualité de René Thom" project. This project was initially entitled "Morphology and qualitative dynamics: Knowledge of forms / Forms of knowledge". Subsequently, the name "Relevance of René Thom" was chosen for its clarity and evocative power. The aim of this research project is to promote the scientific relevance of René Thom's thinking on forms, and to demonstrate the importance of his method and discoveries. It is based on discussions of Thom's thinking and the method he proposes - i.e., to seek out dynamic structures in order to understand changes of form in nature and at the human-social level, to explain the transformation of these dynamic forms, to study the morphologies of process in various fields in order to advance scientific knowledge... The relevance of this thinker has manifested itself in the form of monthly sessions of a research seminar, held from 2017 to 2022, as well as in the form of international congresses (2018, 2019), bringing together the greatest friends and continuators, both of the work of René Thom himself, and of reflection on morphogenetic dynamics in the most diverse disciplines. This created a space for dialogue and listening between the exact sciences and the social and human sciences. Indeed, the fields of study are necessarily interdisciplinary, since, as René Thom teaches us, morphological organization, or form, in its exchanges with matter, must be considered as "independent" of its substrate, i.e. the environment in which this morphogenesis unfolds. Finally, this book marks a symbolic moment: it takes shape in the year that marks the centenary of the birth of René Thom, who was born in the French town of Montbéliard in 1923. To mark this centenary (1923-2023), a number of initiatives have been launched to celebrate the discoveries and advances of this mathematician-philosopher, ashe liked to call himself... The publication of the present book is one more, which we hope will shed light that will stimulate the morphological gaze Thom so urged us to adopt.
The Prehistory Of Mathematical Structuralism
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Author : Erich H. Reck
language : en
Publisher: Oxford University Press
Release Date : 2020
The Prehistory Of Mathematical Structuralism written by Erich H. Reck and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism.
A Critical Reflection On Automated Science
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Author : Marta Bertolaso
language : en
Publisher: Springer Nature
Release Date : 2020-02-05
A Critical Reflection On Automated Science written by Marta Bertolaso and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-05 with Philosophy categories.
This book provides a critical reflection on automated science and addresses the question whether the computational tools we developed in last decades are changing the way we humans do science. More concretely: Can machines replace scientists in crucial aspects of scientific practice? The contributors to this book re-think and refine some of the main concepts by which science is understood, drawing a fascinating picture of the developments we expect over the next decades of human-machine co-evolution. The volume covers examples from various fields and areas, such as molecular biology, climate modeling, clinical medicine, and artificial intelligence. The explosion of technological tools and drivers for scientific research calls for a renewed understanding of the human character of science. This book aims precisely to contribute to such a renewed understanding of science.
Logos And Alogon
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Author : Arkady Plotnitsky
language : en
Publisher: Springer Nature
Release Date : 2023-01-16
Logos And Alogon written by Arkady Plotnitsky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-16 with Mathematics categories.
This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book’s title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields.