Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Persistent homology of convection cycles in network flows   Convection is a well-studied topic in fluid dynamics, yet it is less
understood in the context of networks flows. Here, we incorporate techniques
from topological data analysis (namely, persistent homology) to automate the
detection and characterization of convective/cyclic/chiral flows over networks,
particularly those that arise for irreversible Markov chains (MCs). As two
applications, we study convection cycles arising under the PageRank algorithm,
and we investigate chiral edges flows for a stochastic model of a bi-monomer's
configuration dynamics. Our experiments highlight how system parameters --
e.g., the teleportation rate for PageRank and the transition rates of external
and internal state changes for a monomer -- can act as homology regularizers of
convection, which we summarize with persistence barcodes and homological
bifurcation diagrams. Our approach establishes a new connection between the
study of convection cycles and homology, the branch of mathematics that
formally studies cycles, which has diverse potential applications throughout
the sciences and engineering.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex