Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lexis: An Optimization Framework for Discovering the Hierarchical
  Structure of Sequential Data   Data represented as strings abounds in biology, linguistics, document mining,
web search and many other fields. Such data often have a hierarchical
structure, either because they were artificially designed and composed in a
hierarchical manner or because there is an underlying evolutionary process that
creates repeatedly more complex strings from simpler substrings. We propose a
framework, referred to as "Lexis", that produces an optimized hierarchical
representation of a given set of "target" strings. The resulting hierarchy,
"Lexis-DAG", shows how to construct each target through the concatenation of
intermediate substrings, minimizing the total number of such concatenations or
DAG edges. The Lexis optimization problem is related to the smallest grammar
problem. After we prove its NP-Hardness for two cost formulations, we propose
an efficient greedy algorithm for the construction of Lexis-DAGs. We also
consider the problem of identifying the set of intermediate nodes (substrings)
that collectively form the "core" of a Lexis-DAG, which is important in the
analysis of Lexis-DAGs. We show that the Lexis framework can be applied in
diverse applications such as optimized synthesis of DNA fragments in genomic
libraries, hierarchical structure discovery in protein sequences,
dictionary-based text compression, and feature extraction from a set of
documents.

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The categories of this paper are: stat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
10
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: hep-lat
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
18
The categories of this paper are: econ