Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Persistent Homology of Complex Networks for Dynamic State Detection   In this paper we develop a novel Topological Data Analysis (TDA) approach for
studying graph representations of time series of dynamical systems.
Specifically, we show how persistent homology, a tool from TDA, can be used to
yield a compressed, multi-scale representation of the graph that can
distinguish between dynamic states such as periodic and chaotic behavior. We
show the approach for two graph constructions obtained from the time series. In
the first approach the time series is embedded into a point cloud which is then
used to construct an undirected $k$-nearest neighbor graph. The second
construct relies on the recently developed ordinal partition framework. In
either case, a pairwise distance matrix is then calculated using the shortest
path between the graph's nodes, and this matrix is utilized to define a
filtration of a simplicial complex that enables tracking the changes in
homology classes over the course of the filtration. These changes are
summarized in a persistence diagram---a two-dimensional summary of changes in
the topological features. We then extract existing as well as new geometric and
entropy point summaries from the persistence diagram and compare to other
commonly used network characteristics. Our results show that persistence-based
point summaries yield a clearer distinction of the dynamic behavior and are
more robust to noise than existing graph-based scores, especially when combined
with ordinal graphs.

7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex