Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat and Noise on Cubes and Spheres: The Sensitivity of Randomly Rotated
  Polynomial Threshold Functions   We establish a precise relationship between spherical harmonics and Fourier
basis functions over a hypercube randomly embedded in the sphere. In
particular, we give a bound on the expected Boolean noise sensitivity of a
randomly rotated function in terms of its "spherical sensitivity," which we
define according to its evolution under the spherical heat equation. As an
application, we prove an average case of the Gotsman-Linial conjecture,
bounding the sensitivity of polynomial threshold functions subjected to a
random rotation.

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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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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: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: alg-geom