Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Persistent homology of time-dependent functional networks constructed
  from coupled time series   We use topological data analysis to study "functional networks" that we
construct from time-series data from both experimental and synthetic sources.
We use persistent homology with a weight rank clique filtration to gain
insights into these functional networks, and we use persistence landscapes to
interpret our results. Our first example uses time-series output from networks
of coupled Kuramoto oscillators. Our second example consists of biological data
in the form of functional magnetic resonance imaging (fMRI) data that was
acquired from human subjects during a simple motor-learning task in which
subjects were monitored on three days in a five-day period. With these
examples, we demonstrate that (1) using persistent homology to study functional
networks provides fascinating insights into their properties and (2) the
position of the features in a filtration can sometimes play a more vital role
than persistence in the interpretation of topological features, even though
conventionally the latter is used to distinguish between signal and noise. We
find that persistent homology can detect differences in synchronization
patterns in our data sets over time, giving insight both on changes in
community structure in the networks and on increased synchronization between
brain regions that form loops in a functional network during motor learning.
For the motor-learning data, persistence landscapes also reveal that on average
the majority of changes in the network loops take place on the second of the
three days of the learning process.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin