Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical framework for recurrence-network analysis of time series   Recurrence networks are a powerful nonlinear tool for time series analysis of
complex dynamical systems. {While there are already many successful
applications ranging from medicine to paleoclimatology, a solid theoretical
foundation of the method has still been missing so far. Here, we interpret an
$\varepsilon$-recurrence network as a discrete subnetwork of a "continuous"
graph with uncountably many vertices and edges corresponding to the system's
attractor. This step allows us to show that various statistical measures
commonly used in complex network analysis can be seen as discrete estimators of
newly defined continuous measures of certain complex geometric properties of
the attractor on the scale given by $\varepsilon$.} In particular, we introduce
local measures such as the $\varepsilon$-clustering coefficient, mesoscopic
measures such as $\varepsilon$-motif density, path-based measures such as
$\varepsilon$-betweennesses, and global measures such as
$\varepsilon$-efficiency. This new analytical basis for the so far
heuristically motivated network measures also provides an objective criterion
for the choice of $\varepsilon$ via a percolation threshold, and it shows that
estimation can be improved by so-called node splitting invariant versions of
the measures. We finally illustrate the framework for a number of archetypical
chaotic attractors such as those of the Bernoulli and logistic maps, periodic
and two-dimensional quasi-periodic motions, and for hyperballs and hypercubes,
by deriving analytical expressions for the novel measures and comparing them
with data from numerical experiments. More generally, the theoretical framework
put forward in this work describes random geometric graphs and other networks
with spatial constraints which appear frequently in disciplines ranging from
biology to climate science.

28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math