Topology With Applications Topological Spaces Via Near And Far
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Topology With Applications Topological Spaces Via Near And Far
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Author : Somashekhar A Naimpally
language : en
Publisher: World Scientific
Release Date : 2013-02-21
Topology With Applications Topological Spaces Via Near And Far written by Somashekhar A Naimpally and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-21 with Mathematics categories.
The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.
Computational Proximity
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Author : James F. Peters
language : en
Publisher: Springer
Release Date : 2016-04-20
Computational Proximity written by James F. Peters and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-20 with Technology & Engineering categories.
This book introduces computational proximity (CP) as an algorithmic approach to finding nonempty sets of points that are either close to each other or far apart. Typically in computational proximity, the book starts with some form of proximity space (topological space equipped with a proximity relation) that has an inherent geometry. In CP, two types of near sets are considered, namely, spatially near sets and descriptivelynear sets. It is shown that connectedness, boundedness, mesh nerves, convexity, shapes and shape theory are principal topics in the study of nearness and separation of physical aswell as abstract sets. CP has a hefty visual content. Applications of CP in computer vision, multimedia, brain activity, biology, social networks, and cosmology are included. The book has been derived from the lectures of the author in a graduate course on the topology of digital images taught over the past several years. Many of the students have provided important insights and valuable suggestions. The topics in this monograph introduce many forms of proximities with a computational flavour (especially, what has become known as the strong contact relation), many nuances of topological spaces, and point-free geometry.
Advances In Feature Selection For Data And Pattern Recognition
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Author : Urszula Stańczyk
language : en
Publisher: Springer
Release Date : 2017-11-16
Advances In Feature Selection For Data And Pattern Recognition written by Urszula Stańczyk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Technology & Engineering categories.
This book presents recent developments and research trends in the field of feature selection for data and pattern recognition, highlighting a number of latest advances. The field of feature selection is evolving constantly, providing numerous new algorithms, new solutions, and new applications. Some of the advances presented focus on theoretical approaches, introducing novel propositions highlighting and discussing properties of objects, and analysing the intricacies of processes and bounds on computational complexity, while others are dedicated to the specific requirements of application domains or the particularities of tasks waiting to be solved or improved. Divided into four parts – nature and representation of data; ranking and exploration of features; image, shape, motion, and audio detection and recognition; decision support systems, it is of great interest to a large section of researchers including students, professors and practitioners.
Transactions On Rough Sets Xvii
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Author : James F. Peters
language : en
Publisher: Springer
Release Date : 2014-03-03
Transactions On Rough Sets Xvii written by James F. Peters and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-03 with Computers categories.
The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence. Volume XVII is a continuation of a number of research streams which have grown out of the seminal work by Zdzislaw Pawlak during the first decade of the 21st century. The research streams represented in the papers cover both theory and applications of rough, fuzzy and near sets as well as their combinations.
On Single Valued Neutrosophic Proximity Spaces
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Author : Samed Özkan
language : en
Publisher: Infinite Study
Release Date :
On Single Valued Neutrosophic Proximity Spaces written by Samed Özkan and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this paper, the notion of single-valued neutrosophic proximity spaces which is a generalisation of fuzzy proximity spaces [Katsaras AK. Fuzzy proximity spaces. Anal and Appl. 1979;68(1):100–110.] and intuitionistic fuzzy proximity spaces [Lee SJ, Lee EP. Intuitionistic fuzzy proximity spaces. Int J Math Math Sci. 2004;49:2617–2628.] was introduced and some of their properties were investigated. Then, it was shown that a single-valued neutrosophic proximity on a set X induced a single-valued neutrosophic topology on X. Furthermore, the existence of initial single-valued neutrosophic proximity structure is proved. Finally, based on this fact, the product of single-valued neutrosophic proximity spaces was introduced.
New Trends In Applied Analysis And Computational Mathematics
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Author : Susanta Kumar Paikray
language : en
Publisher: Springer Nature
Release Date : 2021-06-28
New Trends In Applied Analysis And Computational Mathematics written by Susanta Kumar Paikray and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-28 with Technology & Engineering categories.
The volume contains original research papers as the Proceedings of the International Conference on Advances in Mathematics and Computing, held at Veer Surendra Sai University of Technology, Odisha, India, on 7-8 February, 2020. It focuses on new trends in applied analysis, computational mathematics and related areas. It also includes certain new models, image analysis technique, fluid flow problems, etc. as applications of mathematical analysis and computational mathematics. The volume should bring forward new and emerging topics of mathematics and computing having potential applications and uses in other areas of sciences. It can serve as a valuable resource for graduate students, researchers and educators interested in mathematical tools and techniques for solving various problems arising in science and engineering.
Rough Sets
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Author : Lech Polkowski
language : en
Publisher: Springer
Release Date : 2017-06-22
Rough Sets written by Lech Polkowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-22 with Computers categories.
This two-volume set LNAI 10313 and LNAI 10314 constitutes the proceedings of the International Joint Conference on Rough Sets, IJCRS 2017, held in Olsztyn, Poland, in July 2017. The 74 revised full papers presented together with 16 short papers and 16 invited talks, were carefully reviewed and selected from 130 submissions. The papers in this two set-volume of IJCRS 2017 follow the track already rutted by RSCTC and JRS conferences which aimed at unification of many facets of rough set theory from theoretical aspects of the rough set idea bordering on theory of concepts and going through algebraic structures, topological structures, logics for uncertain reasoning, decision algorithms, relations to other theories of vagueness and ambiguity, then to extensions of the rough set idea like granular structures, rough mereology, and to applications of the idea in diverse fields of applied science including hybrid methods like rough-fuzzy, neuro-rough, neuro-rough-fuzzy computing. IJCRS 2017 encompasses topics spread among four main tracks: Rough Sets and Data Science (in relation to RSCTC series organized since 1998); Rough Sets and Granular Computing (in relation to RSFDGrC series organized since 1999); Rough Sets and Knowledge Technology (in relation to RSKT series organized since 2006); and Rough Sets and Intelligent Systems (in relation to RSEISP series organized since 2007).
Foundations Of Computer Vision
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Author : James F. Peters
language : en
Publisher: Springer
Release Date : 2017-03-17
Foundations Of Computer Vision written by James F. Peters and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-17 with Technology & Engineering categories.
This book introduces the fundamentals of computer vision (CV), with a focus on extracting useful information from digital images and videos. Including a wealth of methods used in detecting and classifying image objects and their shapes, it is the first book to apply a trio of tools (computational geometry, topology and algorithms) in solving CV problems, shape tracking in image object recognition and detecting the repetition of shapes in single images and video frames. Computational geometry provides a visualization of topological structures such as neighborhoods of points embedded in images, while image topology supplies us with structures useful in the analysis and classification of image regions. Algorithms provide a practical, step-by-step means of viewing image structures. The implementations of CV methods in Matlab and Mathematica, classification of chapter problems with the symbols (easily solved) and (challenging) and its extensive glossary of key words, examples and connections with the fabric of CV make the book an invaluable resource for advanced undergraduate and first year graduate students in Engineering, Computer Science or Applied Mathematics. It offers insights into the design of CV experiments, inclusion of image processing methods in CV projects, as well as the reconstruction and interpretation of recorded natural scenes.
Elementary Topology
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Author : O. I͡A. Viro
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Elementary Topology written by O. I͡A. Viro 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 2008 with Mathematics categories.
"This textbook on elementary topologycontains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elernentary segment centered at the notions of fundamental group and covering space. The reader who has mastered the core material acquires a strong background in elementary topology and will feel at home in the environment of abstract mathemeatics."--BOOK JACKET.
Computational Geometry Topology And Physics Of Digital Images With Applications
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Author : James F. Peters
language : en
Publisher: Springer Nature
Release Date : 2019-10-03
Computational Geometry Topology And Physics Of Digital Images With Applications written by James F. Peters and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-03 with Technology & Engineering categories.
This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structures that infuse triangulated visual scenes. The book first addresses the topology of cellular complexes to provide a basis for an introductory study of the computational topology of visual scenes, exploring the fabric, shapes and structures typically found in visual scenes. The book then examines the inherent geometry and topology of visual scenes, and the fine structure of light and light caustics of visual scenes, which bring into play catastrophe theory and the appearance of light caustic folds and cusps. Following on from this, the book introduces optical vortex nerves in triangulated digital images. In this context, computational physics is synonymous with the study of the fine structure of light choreographed in video frames. This choreography appears as a sequence of snapshots of light reflected and refracted from surface shapes, providing a solid foundation for detecting, analyzing and classifying visual scene shapes.