Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homology and Robustness of Level and Interlevel Sets   Given a function $f: \Xspace \to \Rspace$ on a topological space, we consider
the preimages of intervals and their homology groups and show how to read the
ranks of these groups from the extended persistence diagram of $f$. In
addition, we quantify the robustness of the homology classes under
perturbations of $f$ using well groups, and we show how to read the ranks of
these groups from the same extended persistence diagram. The special case
$\Xspace = \Rspace^3$ has ramifications in the fields of medical imaging and
scientific visualization.

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The categories of this paper are: stat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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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: hep-lat
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The categories of this paper are: math-ph
18
The categories of this paper are: econ
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The categories of this paper are: mtrl-th