Weakly Precomplete Equivalence Relations in the Ershov Hierarchy
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DOI: 10.1007/s10469-019-09538-y
Abstract: We study the computable reducibility ≤c for equivalence relations in the Ershov hierarchy. For an arbitrary notation a for a nonzero computable ordinal, it is stated that there exist a $$ {\varPi}_a^{-1} $$ -universal equivalence… read more here.
Keywords: weakly precomplete; equivalence; equivalence relations; relations ershov ... See more keywords
Nodal-statistics-based equivalence relation for graph collections.
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DOI: 10.1103/physreve.107.014302
Abstract: Node role explainability in complex networks is very difficult yet is crucial in different application domains such as social science, neurosciences, or computer science. Many efforts have been made on the quantification of hubs revealing… read more here.
Keywords: graph; relation graph; nodal statistics; equivalence relation ... See more keywords
Left and right regular elements of the semigroups of transformations preserving an equivalence relation and a cross-section
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DOI: 10.1142/s179355711950058x
Abstract: Let [Formula: see text] be the semigroup of all transformations on a set [Formula: see text]. For an arbitrary equivalence relation [Formula: see text] on [Formula: see text] and a cross-section [Formula: see text] of… read more here.
Keywords: right regular; equivalence relation; formula see; see text ... See more keywords
Some Equivalence Relation between Persistent Homology and Morphological Dynamics
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DOI: 10.48550/arxiv.2205.12546
Abstract: In mathematical morphology, connected filters based on dynamics are used to filter the extrema of an image. Similarly, persistence is a concept coming from persistent homology and Morse theory that represents the stability of the… read more here.
Keywords: homology morphological; relation persistent; homology; morphological dynamics ... See more keywords