Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Capacity and Expressiveness of Genomic Tandem Duplication   The majority of the human genome consists of repeated sequences. An important
type of repeated sequences common in the human genome are tandem repeats, where
identical copies appear next to each other. For example, in the sequence
$AGTC\underline{TGTG}C$, $TGTG$ is a tandem repeat, that may be generated from
$AGTCTGC$ by a tandem duplication of length $2$. In this work, we investigate
the possibility of generating a large number of sequences from a \textit{seed},
i.e.\ a small initial string, by tandem duplications of bounded length. We
study the capacity of such a system, a notion that quantifies the system's
generating power. Our results include \textit{exact capacity} values for
certain tandem duplication string systems. In addition, motivated by the role
of DNA sequences in expressing proteins via RNA and the genetic code, we define
the notion of the \textit{expressiveness} of a tandem duplication system as the
capability of expressing arbitrary substrings. We then \textit{completely}
characterize the expressiveness of tandem duplication systems for general
alphabet sizes and duplication lengths. In particular, based on a celebrated
result by Axel Thue from 1906, presenting a construction for ternary
square-free sequences, we show that for alphabets of size 4 or larger, bounded
tandem duplication systems, regardless of the seed and the bound on duplication
length, are not fully expressive, i.e. they cannot generate all strings even as
substrings of other strings. Note that the alphabet of size 4 is of particular
interest as it pertains to the genomic alphabet. Building on this result, we
also show that these systems do not have full capacity. In general, our results
illustrate that duplication lengths play a more significant role than the seed
in generating a large number of sequences for these systems.

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The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
3
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: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph