Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Persistence modules: Algebra and algorithms   Persistent homology was shown by Carlsson and Zomorodian to be homology of
graded chain complexes with coefficients in the graded ring $\kk[t]$. As such,
the behavior of persistence modules -- graded modules over $\kk[t]$ is an
important part in the analysis and computation of persistent homology.
  In this paper we present a number of facts about persistence modules; ranging
from the well-known but under-utilized to the reconstruction of techniques to
work in a purely algebraic approach to persistent homology. In particular, the
results we present give concrete algorithms to compute the persistent homology
of a simplicial complex with torsion in the chain complex.

33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph