Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Embedded Homology of Hypergraphs and Applications   Hypergraphs are mathematical models for many problems in data sciences. In
recent decades, the topological properties of hypergraphs have been studied and
various kinds of (co)homologies have been constructed (cf. [3, 4, 12]). In this
paper, generalising the usual homology of simplicial complexes, we define the
embedded homology of hypergraphs as well as the persistent embedded homology of
sequences of hypergraphs. As a generalisation of the Mayer-Vietoris sequence
for the homology of simplicial complexes, we give a Mayer-Vietoris sequence for
the embedded homology of hypergraphs. Moreover, as applications of the embedded
homology, we study acyclic hypergraphs and construct some indices for the data
analysis of hyper-networks.

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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg