Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Signed Positive Semidefinite Matrix Completion Problem for Odd-$K_4$
  Minor Free Signed Graphs   We give a signed generalization of Laurent's theorem that characterizes
feasible positive semidefinite matrix completion problems in terms of metric
polytopes. Based on this result, we give a characterization of the maximum rank
completions of the signed positive semidefinite matrix completion problem for
odd-$K_4$ minor free signed graphs. The analysis can also be used to bound the
minimum rank over the completions and to characterize uniquely solvable
completion problems for odd-$K_4$ minor free signed graphs. As a corollary we
derive a characterization of the universal rigidity of odd-$K_4$ minor free
spherical tensegrities, and also a characterization of signed graphs whose
signed Colin de Verdi\`ere parameter $\nu$ is bounded by two, recently shown by
Arav et al.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an