Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multidimensional Persistence and Noise   In this paper we study multidimensional persistence modules [5,13] via what
we call tame functors and noise systems. A noise system leads to a
pseudo-metric topology on the category of tame functors. We show how this
pseudo-metric can be used to identify persistent features of compact
multidimensional persistence modules. To count such features we introduce the
feature counting invariant and prove that assigning this invariant to compact
tame functors is a 1-Lipschitz operation. For 1-dimensional persistence, we
explain how, by choosing an appropriate noise system, the feature counting
invariant identifies the same persistent features as the classical barcode
construction.

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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc