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Nature Communications, ISSN 2041-1723, 05/2017, Volume 8
In most applications of nanoporous materials the pore structure is as important as the chemical composition as a determinant of performance. For example, one... 
applied mathematics | structural properties | MATERIALS SCIENCE | theory and computation | metal-organic frameworks
Journal Article
02/2018
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D... 
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 01/2013, Volume 253, pp. 530 - 542
► We present a novel algorithm for the computation of cohomology generators. ► The algorithm is based on a number of combinatorial and semi-algebraic... 
(Co) homology generators | Definition of potentials | Eddy-currents | Thick cuts | (Co) homology computation | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MESHES | ENGINEERING, MULTIDISCIPLINARY | ALGORITHM | MAGNETIC SCALAR POTENTIALS | CUTS | Graphics software | Methods | Algorithms
Journal Article
Homology, Homotopy and Applications, ISSN 1532-0073, 2014, Volume 16, Issue 1, pp. 49 - 63
In this paper we focus on preprocessing for persistent homology computations. We adapt some techniques that were successfully used for standard homology... 
Persistence | Homology | Reduction algorithm | MATHEMATICS | MATHEMATICS, APPLIED | homology | COREDUCTION HOMOLOGY | reduction algorithm | ALGORITHM | persistence | 55-04 | 68R05 | 57M15 | 55U05
Journal Article
The European Physical Journal - Applied Physics, ISSN 1286-0042, 2/2011, Volume 53, Issue 2
A technique based on a tree-cotree decomposition, called Spanning Tree Technique (STT) in this paper, has been shown to be simple and efficient to compute the... 
ELEMENTS | PHYSICS, APPLIED | EDDY-CURRENT FORMULATION | CUTS
Journal Article
01/2019
Topological data analysis provides a collection of tools to encapsulate and summarize the shape of data. Currently it is mainly restricted to \emph{mapper... 
Mathematics - Algebraic Topology
Journal Article
Applicable Algebra in Engineering, Communication and Computing, ISSN 0938-1279, 4/2012, Volume 23, Issue 1, pp. 29 - 58
Journal Article
07/2018
This is a tutorial in applied and computational topology and topological data analysis. It is illustrated with numerous computational examples that utilize... 
Journal Article
IEEE Transactions on Magnetics, ISSN 0018-9464, 08/2010, Volume 46, Issue 8, pp. 3069 - 3072
Journal Article
2016 IEEE Conference on Electromagnetic Field Computation (CEFC), 11/2016, pp. 1 - 1
This paper extends the T-Ω formulation for eddy currents based on higher order hierarchical basis functions so that it can deal with conductors of arbitrary... 
Manifolds | high order | cohomology | Computer architecture | Benchmark testing | Conductors | Generators | Topology | Eddy currents | cuts | Cuts | Cohomology | High order
Conference Proceeding
Applicable Algebra in Engineering, Communications and Computing, ISSN 0938-1279, 2015, Volume 26, Issue 1-2, pp. 27 - 48
We describe an algorithm for computing a finite, and typically small, presentation of the fundamental group of a finite regular CW-space. The algorithm is... 
Regular cw-complex | Discrete Morse theory | Computation | Finite presentation | Fundamental group | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CELL COMPLEXES | COMPUTER SCIENCE, THEORY & METHODS | Algorithms
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 9/2011, Volume 46, Issue 2, pp. 361 - 388
Journal Article
2012, Lecture Notes in Computer Science, ISBN 9783642302374, Volume 7309
In this paper we present our ongoing research on applying computational topology to analysis of structure of similarities within a collection of text... 
Computer Graphics | Pattern Recognition | Algebraic Topology | Computer Science | Image Processing and Computer Vision | Simulation and Modeling | Algorithm Analysis and Problem Complexity | Text mining | Computational homology | Vector space model | Discrete Morse theory | Flag Complex | Computational topology
Book Chapter
10/2016
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences.... 
Mathematics - Numerical Analysis
Journal Article
05/2019
Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying... 
Journal Article
10/2014
Modern applications of algebraic topology to point cloud data analysis have motivated active investigation of combinatorial clique complexes --... 
Mathematics - Algebraic Topology
Journal Article
12/2018
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit,... 
Journal Article
2011, Lecture Notes in Computer Science, ISBN 9783642236716, Volume 6854, Issue 1
In this paper, we investigate the problem of analyzing the shape of obstacle-avoiding paths in a space. Given a d-dimensional space with holes, representing... 
Biometrics | Pattern Recognition | Computer Science | Data Mining and Knowledge Discovery | Computer Imaging, Vision, Pattern Recognition and Graphics | Document Preparation and Text Processing | Artificial Intelligence (incl. Robotics) | cohomology generators | trajectory planning problem | obstacle-avoidance
Book Chapter
04/2013
In this paper we focus on preprocessing for persistent homology computations. We adapt some techniques which were successfully used for standard homology... 
Mathematics - Geometric Topology
Journal Article
12/2012
The issue of computing (co)homology generators of a cell complex is gaining a pivotal role in various branches of science. While this issue can be rigorously... 
Journal Article
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