Author : Lou Van den Dries
Publisher : Cambridge University Press
Page : 196 pages
File Size : 46,7 MB
Release : 1998-05-07
Category : Mathematics
ISBN : 0521598389
These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.
Author : L. P. D. van den Dries
Publisher :
Page : 192 pages
File Size : 23,2 MB
Release : 1998
Category : Electronic books
ISBN : 9781107367524
These notes give a self-contained treatment of the theory of o-minimal structures.
Author : Deirdre Haskell
Publisher : Cambridge University Press
Page : 244 pages
File Size : 47,86 MB
Release : 2000-07-03
Category : Mathematics
ISBN : 9780521780681
Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Author : G. O. Jones
Publisher : Cambridge University Press
Page : 235 pages
File Size : 49,23 MB
Release : 2015-08-13
Category : Mathematics
ISBN : 1107462495
This book brings the researcher up to date with recent applications of mathematical logic to number theory.
Author : Mário J. Edmundo
Publisher : Cuvillier Verlag
Page : 223 pages
File Size : 50,53 MB
Release : 2005
Category :
ISBN : 386537557X
Author : Tamal Krishna Dey
Publisher : Cambridge University Press
Page : 456 pages
File Size : 21,1 MB
Release : 2022-03-10
Category : Mathematics
ISBN : 1009103199
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
Author : Chris Miller
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 39,32 MB
Release : 2012-09-14
Category : Mathematics
ISBN : 1461440416
This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations.
Author : Pierre Simon
Publisher : Cambridge University Press
Page : 165 pages
File Size : 35,43 MB
Release : 2015-07-16
Category : Mathematics
ISBN : 1107057752
The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.
Author : Danny Calegari
Publisher : Oxford University Press on Demand
Page : 378 pages
File Size : 26,32 MB
Release : 2007-05-17
Category : Mathematics
ISBN : 0198570082
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Author : Michael Robinson
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 37,60 MB
Release : 2014-01-07
Category : Technology & Engineering
ISBN : 3642361048
Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.
