Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Borsuk-Ulam theorem for digital images   The Borsuk-Ulam theorem states that a continuous function $f:S^n \to \R^n$
has a point $x\in S^n$ with $f(x)=f(-x)$. We give an analogue of this theorem
for digital images, which are modeled as discrete spaces of adjacent pixels
equipped with $\Z^n$-valued functions.
  In particular, for a concrete two-dimensional rectangular digital image whose
pixels all have an assigned "brightness" function, we prove that there must
exist a pair of opposite boundary points whose brightnesses are approximately
equal. This theorem applies generally to any integer-valued function on an
abstract simple graph.
  We also discuss generalizations to digital images of dimension 3 and higher.
We give some partial results for higher dimensional images, and show a counter
example which demonstrates that the full results obtained in lower dimensions
cannot hold generally.

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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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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: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th