Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum Number of Modes of Gaussian Mixtures   Gaussian mixture models are widely used in Statistics. A fundamental aspect
of these distributions is the study of the local maxima of the density, or
modes. In particular, it is not known how many modes a mixture of $k$ Gaussians
in $d$ dimensions can have. We give a brief account of this problem's history.
Then, we give improved lower bounds and the first upper bound on the maximum
number of modes, provided it is finite.

25
The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: ao-sci