Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New methods to find patches of invisible integer lattice points   It is a surprising fact that the proportion of integer lattice points visible
from the origin is exactly $\frac{6}{\pi^2}$, or approximately 60 percent.
Hence, approximately 40 percent of the integer lattice is hidden from the
origin. Since 1971, many have studied a variety of problems involving lattice
point visibility, in particular, searching for patterns in that 40 percent of
the lattice comprised of invisible points. One such pattern is a square patch,
an $n \times n$ grid of $n^2$ invisible points, which we call a hidden forest.
It is known that there exist arbitrarily large hidden forests in the integer
lattice. However, the methods up to now involve the Chinese Remainder Theorem
(CRT) on the rows and columns of matrices with prime number entries, and they
have only been able to locate hidden forests very far from the origin. For
example, using this method the closest known $4 \times 4$ hidden forest is over
3 quintillion, or $3 \times 10^{18}$, units away from the origin. We introduce
the concept of quasiprime matrices and utilize a variety of computational and
theoretical techniques to find some of the closest known hidden forests to this
date. Using these new techniques, we find a $4 \times 4$ hidden forest that is
merely 184 million units away from the origin. We conjecture that every hidden
forest can be found via the CRT-algorithm on a quasiprime matrix.

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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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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: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph