Metric Spaces, Convexity and Nonpositive Curvature PDF Download

Author: Athanase Papadopoulos
Publisher: European Mathematical Society
ISBN: 9783037190104
Category : Computers
Languages : en
Pages : 306

View

Book Description

Author: Laurent Najman
Publisher: Springer
ISBN: 3319580027
Category : Mathematics
Languages : en
Pages : 378

View

Book Description
This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.

Author: Ignacio M. Pelayo
Publisher: Springer Science & Business Media
ISBN: 1461486998
Category : Mathematics
Languages : en
Pages : 117

View

Book Description
​​​​​​​​Geodesic Convexity in Graphs is devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph path convexities. The following chapters focus exclusively on the geodesic convexity, including motivation and background, specific definitions, discussion and examples, results, proofs, exercises and open problems. The main and most st​udied parameters involving geodesic convexity in graphs are both the geodetic and the hull number which are defined as the cardinality of minimum geodetic and hull set, respectively. This text reviews various results, obtained during the last one and a half decade, relating these two invariants and some others such as convexity number, Steiner number, geodetic iteration number, Helly number, and Caratheodory number to a wide range a contexts, including products, boundary-type vertex sets, and perfect graph families. This monograph can serve as a supplement to a half-semester graduate course in geodesic convexity but is primarily a guide for postgraduates and researchers interested in topics related to metric graph theory and graph convexity theory. ​

Author: M.L.J. van de Vel
Publisher: Elsevier
ISBN: 0080933106
Category : Mathematics
Languages : en
Pages : 556

View

Book Description
Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology.Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.

Author: Larry S. Davis
Publisher: Springer Science & Business Media
ISBN: 1461515297
Category : Computers
Languages : en
Pages : 496

View

Book Description
Computer systems that analyze images are critical to a wide variety of applications such as visual inspections systems for various manufacturing processes, remote sensing of the environment from space-borne imaging platforms, and automatic diagnosis from X-rays and other medical imaging sources. Professor Azriel Rosenfeld, the founder of the field of digital image analysis, made fundamental contributions to a wide variety of problems in image processing, pattern recognition and computer vision. Professor Rosenfeld's previous students, postdoctoral scientists, and colleagues illustrate in Foundations of Image Understanding how current research has been influenced by his work as the leading researcher in the area of image analysis for over two decades. Each chapter of Foundations of Image Understanding is written by one of the world's leading experts in his area of specialization, examining digital geometry and topology (early research which laid the foundations for many industrial machine vision systems), edge detection and segmentation (fundamental to systems that analyze complex images of our three-dimensional world), multi-resolution and variable resolution representations for images and maps, parallel algorithms and systems for image analysis, and the importance of human psychophysical studies of vision to the design of computer vision systems. Professor Rosenfeld's chapter briefly discusses topics not covered in the contributed chapters, providing a personal, historical perspective on the development of the field of image understanding. Foundations of Image Understanding is an excellent source of basic material for both graduate students entering the field and established researchers who require a compact source for many of the foundational topics in image analysis.

Author: Reinhard Klette
Publisher: Elsevier
ISBN: 0080477267
Category : Computers
Languages : en
Pages : 675

View

Book Description
Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures.*A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision*Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data*Includes exercises, examples, and references to related or more advanced work

Author: Stephanie Alexander
Publisher: Springer
ISBN: 3030053121
Category : Mathematics
Languages : en
Pages : 95

View

Book Description
Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.

Author: Gabor T. Herman
Publisher: Springer Science & Business Media
ISBN: 1461241367
Category : Mathematics
Languages : en
Pages : 221

View

Book Description
"La narraci6n literaria es la evocaci6n de las nostalgias. " ("Literary narration is the evocation of nostalgia. ") G. G. Marquez, interview in Puerta del Sol, VII, 4, 1996. A Personal Prehistory In 1972 I started cooperating with members of the Biodynamics Research Unit at the Mayo Clinic in Rochester, Minnesota, which was under the direction of Earl H. Wood. At that time, their ambitious (and eventually realized) dream was to build the Dynamic Spatial Reconstructor (DSR), a device capable of collecting data regarding the attenuation of X-rays through the human body fast enough for stop-action imaging the full extent of the beating heart inside the thorax. Such a device can be applied to study the dynamic processes of cardiopulmonary physiology, in a manner similar to the application of an ordinary cr (computerized tomography) scanner to observing stationary anatomy. The standard method of displaying the information produced by a cr scanner consists of showing two-dimensional images, corresponding to maps of the X-ray attenuation coefficient in slices through the body. (Since different tissue types attenuate X-rays differently, such maps provide a good visualization of what is in the body in those slices; bone - which attenuates X-rays a lot - appears white, air appears black, tumors typically appear less dark than the surrounding healthy tissue, etc. ) However, it seemed to me that this display mode would not be appropriate for the DSR.

Author: Franco Giannessi
Publisher: Springer Science & Business Media
ISBN: 0387280200
Category : Mathematics
Languages : en
Pages : 404

View

Book Description
Over the last twenty years, Professor Franco Giannessi, a highly respected researcher, has been working on an approach to optimization theory based on image space analysis. His theory has been elaborated by many other researchers in a wealth of papers. Constrained Optimization and Image Space Analysis unites his results and presents optimization theory and variational inequalities in their light. It presents a new approach to the theory of constrained extremum problems, including Mathematical Programming, Calculus of Variations and Optimal Control Problems. Such an approach unifies the several branches: Optimality Conditions, Duality, Penalizations, Vector Problems, Variational Inequalities and Complementarity Problems. The applications benefit from a unified theory.

Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 376438722X
Category : Mathematics
Languages : en
Pages : 333

View

Book Description
The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.