Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry...

to be confused with algorithmic or computational topology, which studies the application of computation to topology. As shown by Alan Turing and Alonzo...

geometry Computational group theory Computational geometry Computational number theory Computational topology Computational statistics Algorithmic information...

conjecture for large classes of groups. Carlsson has worked in computational topology, especially as it applies to the analysis of high dimensional and...

study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry...

Edelsbrunner and Harer's book gives general guidance on computational topology. One issue that arises in computation is the choice of complex. The Čech complex and...

Čech cohomology Computational geometry Simplicial complex Simplicial homology Ghrist, Robert W. (2014). Elementary applied topology (1st ed.). [United...

In computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and...

{\displaystyle Q} is a facet or primary face of P {\displaystyle P} . In algebraic topology, cubical complexes are often useful for concrete calculations. In particular...

Geometric and Topological Inference is a monograph in computational geometry, computational topology, geometry processing, and topological data analysis...

captures all the topological information in a filtration. In algebraic topology, the persistence barcodes were first introduced by Sergey Barannikov in...

location missing publisher (link) Moraleda, Rodrigo Rojas (2020). Computational topology for biomedical image and data analysis : theory and applications...

computations. Computational statistics Computational synthetic geometry Computational topology Computer algebra see symbolic computation Conformal geometry...

persistence intervals of a finite filtration. Computational topology Carlsson, Gunnar (2009). "Topology and data". Bulletin of the American Mathematical...

The region connection calculus (RCC) is intended to serve for qualitative spatial representation and reasoning. RCC abstractly describes regions (in Euclidean...

2012-04-26. "the Topology ToolKit". GitHub.io. Mischaikow, Konstantin; Nanda, Vidit (2013). "Morse Theory for Filtrations and Efficient computation of Persistent...

Combinatorial topology Computational geometry Computational topology Topological data analysis Topology Discrete mathematics Geospatial topology Chen, Li;...

NeuroEvolution of Augmenting Topologies (NEAT) is a genetic algorithm (GA) for generating evolving artificial neural networks (a neuroevolution technique)...

Department of Applied and Computational Mathematics and Statistics. Her research concerns computational geometry and computational topology Chambers was a student...

https://doi.org/10.1093/mnras/stw2862 Edelsbrunner, Herbert (2010). Computational topology : an introduction. J. Harer. Providence, R.I.: American Mathematical...

Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions...

offset filtration has become a primary example in the study of computational topology and data analysis. Let X {\displaystyle X} be a finite set in a...

Cusped census Closed census Regina incorporates aspects of SnapPea. Computational topology Thurston's 24 questions Weeks, Jeffrey R., SnapPea C source code...

persistent homology theory". Journal of Symbolic Computation. Algorithms and Software for Computational Topology. 78: 61–75. doi:10.1016/j.jsc.2015.11.020....

ISBN 9781605580715. S2CID 1020710. Ghrist, Robert (2007). "Barcodes: The persistent topology of data". Bulletin of the American Mathematical Society. 45: 61–76. doi:10...

NP-hard. It has been argued that the UGC is essentially a question of computational topology, involving local-global principles (the latter are also evident...

dynamics Topological entropy Topological mixing Computational topology Digital topology Network topology Topological computing Topological Quantum Computing...

general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It...

Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric...

In algebraic topology, simplicial homology is the sequence of homology groups of a simplicial complex. It formalizes the idea of the number of holes of...