Results 51 to 60 of about 6,556,269 (259)
A Novel Robust Topological Denoising Method Based on Homotopy Theory for Virtual Colonoscopy
Axioms, 2023 Virtual colonoscopy plays an important role in polyp detection of colorectal cancer. Noise in the colon data acquisition process can result in topological errors during surface reconstruction.
Ming Ma, Wei Chen, Na Lei, Xianfeng Gu
doaj +1 more source
Journal of Applied and Computational Topology, 2023 AbstractWe implement an algorithm RSHT (random simple-homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higher-dimensional complexes. The algorithm combines elementary simplicial collapses with pure elementary expansions. For triangulated d-manifolds with
Benedetti, Bruno +3 more
openaire +4 more sources
n-relative categories: a model for the homotopy theory of n-fold homotopy theories [PDF]
, 2013 We introduce, for every integer n ≥ 1, the notion of an n-relative category and show that the category of the small n-relative categories is a model for the homotopy theory of n-fold homotopy theories, i.e., homotopy theories of… homotopy ...
Barwick, Clark Edward, Kan, D. M.
core +1 more source
Towards a directed homotopy type theory [PDF]
Mathematical Foundations of Programming Semantics, 2018 In this paper, we present a directed homotopy type theory for reasoning synthetically about (higher) categories, directed homotopy theory, and its applications to concurrency. We specify a new `homomorphism' type former for Martin-L\"of type theory which
P. North
semanticscholar +1 more source
Cellular structures in Topology [PDF]
, 1990 This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type.
Renzo Piccinini +4 more
core +1 more source
The higher topological complexity in digital images
Applied General Topology, 2020 Y. Rudyak develops the concept of the topological complexity TC(X) defined by M. Farber. We study this notion in digital images by using the fundamental properties of the digital homotopy.
Melih İs, İsmet Karaca
doaj +1 more source
T-Homotopy and Refinement of Observation—Part II: Adding New T-Homotopy Equivalences
International Journal of Mathematics and Mathematical Sciences, 2007 This paper is the second part of a series of papers about a new notion of T-homotopy of flows. It is proved that the old definition of T-homotopy equivalence does not allow the identification of the directed segment with the 3-dimensional cube.
Philippe Gaucher
doaj +1 more source
Higher Groups in Homotopy Type Theory [PDF]
Logic in Computer Science, 2018 We present a development of the theory of higher groups, including infinity groups and connective spectra, in homotopy type theory. An infinity group is simply the loops in a pointed, connected type, where the group structure comes from the structure ...
U. Buchholtz, Floris van Doorn, E. Rijke
semanticscholar +1 more source
Quadratic corrections to the higher-spin equations by the differential homotopy approach
Nuclear Physics BThe recently proposed differential homotopy approach to the analysis of nonlinear higher-spin theory is developed. The Ansatz is extended to the form applicable in the second order of the perturbation theory and general star-multiplication formulae are ...
P.T. Kirakosiants +2 more
doaj +1 more source
Motivic and real étale stable homotopy theory [PDF]
Compositio Mathematica, 2016 Let $S$ be a Noetherian scheme of finite dimension and denote by $\unicode[STIX]{x1D70C}\in [\unicode[STIX]{x1D7D9},\mathbb{G}_{m}]_{\mathbf{SH}(S)}$ the (additive inverse of the) morphism corresponding to $-1\in {\mathcal{O}}^{\times }(S)$ .
Tom Bachmann
semanticscholar +1 more source