• Corpus ID: 15697801

Physics inspired algorithms for (co)homology computation

@article{Dlotko2012PhysicsIA,
  title={Physics inspired algorithms for (co)homology computation},
  author={Pawel Dlotko and Ruben Specogna},
  journal={ArXiv},
  year={2012},
  volume={abs/1212.1360}
}
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 solved in polynomial time, it is still overly demanding for large scale problems. Drawing inspiration from low-frequency electrodynamics, this paper presents a physics inspired algorithm for first cohomology group computations on three-dimensional complexes. The algorithm is general and exhibits orders of magnitude speed up with respect to… 

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References

SHOWING 1-10 OF 43 REFERENCES
Cohomology in electromagnetic modeling
Electromagnetic modeling provides an interesting context to present a link between physical phenomena and homology and cohomology theories. Over the past twenty-five years, a considerable effort has
Efficient Cohomology Computation for Electromagnetic Modeling
TLDR
An automatic, computationally efficient and provably general algorithm based on a rigorous algorithm to compute a cohomology basis of the insulating region with state-of-art reductions techniquesexpressly designed for cohomological computations over simplicial complexes is presented.
Cohomology in 3D Magneto-Quasistatics Modeling
TLDR
Several definitions of cuts are surveyed, defined as generators of the first cohomology group over integers of a finite CW-complex, which has the virtue of providing an automatic, general and efficient algorithm for the computation of cuts.
Greedy optimal homotopy and homology generators
TLDR
It is shown that the shortest set of loops that generate the fundamental group of any oriented combinatorial 2-manifold, with any given basepoint, can be constructed in O(n log n) time using a straightforward application of Dijkstra's shortest path algorithm.
Extensive scaling from computational homology and Karhunen-Loève decomposition analysis of Rayleigh-Bénard convection experiments.
TLDR
Spatiotemporally chaotic dynamics in laboratory experiments on convection are characterized using a new dimension, D(CH), determined from computational homology, which scales in the same manner as D(KLD), a dimension determined from experimental data using Karhuenen-Loéve decomposition.
Critical Analysis of the Spanning Tree Techniques
TLDR
The aim of this paper is to give a rigorous description of the GSTT in terms of homology and cohomology theories, together with an analysis of its termination.
A basic course in algebraic topology
1: Two-Dimensional Manifolds. 2: The Fundamental Group. 3: Free Groups and Free Products of Groups. 4: Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces.
Efficient generalized source field computation for h-oriented magnetostatic formulations
TLDR
The aim of this paper is to present a generalization of STT called Extended Spanning Tree Technique (ESTT), which is provably general and it retains the STT computational efficiency.
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