Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Slipknotting in Random Diagrams   The presence of slipknots in configurations of proteins and DNA has been
shown to affect their functionality, or alter it entirely. Historically,
polymers are modeled as polygonal chains in space. As an alternative to space
curves, we provide a framework for working with subknots inside of knot
diagrams via knotoid diagrams. We prove using a pattern theorem for knot
diagrams that not only are almost all knot diagrams slipknotted, almost all
unknot diagrams are slipknotted. This proves in the random diagram model a
conjecture yet unproven in random space curve models. We also discuss
conjectures on the enumeration of knotoid diagrams.

33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
14
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: chem-ph
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The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs