Rips repaired
نویسندگان
چکیده
منابع مشابه
Defeasible Reasoning - Adler&Rips
There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples:
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We investigate the way big rips are approached in a fully inhomogeneous description of the space-time geometry. If the pressure and energy densities are connected by a (supernegative) barotropic index, the spatial gradients and the anisotropic expansion decay as the big rip is approached. This behaviour is contrasted with the usual big-bang singularities. A similar analysis is performed in the ...
متن کاملFast construction of the Vietoris-Rips complex
The Vietoris-Rips complex characterizes the topology of a point set. This complex is popular in topological data analysis as its construction extends easily to higher dimensions. We formulate a two-phase approach for its construction that separates geometry from topology. We survey methods for the first phase, give three algorithms for the second phase, implement all algorithms, and present exp...
متن کاملVietoris-Rips Complexes of Planar Point Sets
Fix a finite set of points in Euclidean n-space En, thought of as a point-cloud sampling of a certain domain D ⊂ En. The VietorisRips complex is a combinatorial simplicial complex based on proximity of neighbors that serves as an easily-computed but high-dimensional approximation to the homotopy type of D. There is a natural “shadow” projection map from the Vietoris-Rips complex to En that has ...
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ژورنال
عنوان ژورنال: Nature
سال: 2005
ISSN: 0028-0836,1476-4687
DOI: 10.1038/436925a