10,074 research outputs found
Increment entropy as a measure of complexity for time series
Entropy has been a common index to quantify the complexity of time series in
a variety of fields. Here, we introduce increment entropy to measure the
complexity of time series in which each increment is mapped into a word of two
letters, one letter corresponding to direction and the other corresponding to
magnitude. The Shannon entropy of the words is termed as increment entropy
(IncrEn). Simulations on synthetic data and tests on epileptic EEG signals have
demonstrated its ability of detecting the abrupt change, regardless of
energetic (e.g. spikes or bursts) or structural changes. The computation of
IncrEn does not make any assumption on time series and it can be applicable to
arbitrary real-world data.Comment: 12pages,7figure,2 table
On the Von Neumann Entropy of Graphs
The von Neumann entropy of a graph is a spectral complexity measure that has
recently found applications in complex networks analysis and pattern
recognition. Two variants of the von Neumann entropy exist based on the graph
Laplacian and normalized graph Laplacian, respectively. Due to its
computational complexity, previous works have proposed to approximate the von
Neumann entropy, effectively reducing it to the computation of simple node
degree statistics. Unfortunately, a number of issues surrounding the von
Neumann entropy remain unsolved to date, including the interpretation of this
spectral measure in terms of structural patterns, understanding the relation
between its two variants, and evaluating the quality of the corresponding
approximations.
In this paper we aim to answer these questions by first analysing and
comparing the quadratic approximations of the two variants and then performing
an extensive set of experiments on both synthetic and real-world graphs. We
find that 1) the two entropies lead to the emergence of similar structures, but
with some significant differences; 2) the correlation between them ranges from
weakly positive to strongly negative, depending on the topology of the
underlying graph; 3) the quadratic approximations fail to capture the presence
of non-trivial structural patterns that seem to influence the value of the
exact entropies; 4) the quality of the approximations, as well as which variant
of the von Neumann entropy is better approximated, depends on the topology of
the underlying graph
Chaotic versus stochastic behavior in active-dissipative nonlinear systems
We study the dynamical state of the one-dimensional noisy generalized Kuramoto-Sivashinsky (gKS) equation by making use of time-series techniques based on symbolic dynamics and complex networks. We focus on analyzing temporal signals of global measure in the spatiotemporal patterns as the dispersion parameter of the gKS equation and the strength of the noise are varied, observing that a rich variety of different regimes, from high-dimensional chaos to pure stochastic behavior, emerge. Permutation entropy, permutation spectrum, and network entropy allow us to fully classify the dynamical state exposed to additive noise
Metric projection for dynamic multiplex networks
Evolving multiplex networks are a powerful model for representing the
dynamics along time of different phenomena, such as social networks, power
grids, biological pathways. However, exploring the structure of the multiplex
network time series is still an open problem. Here we propose a two-steps
strategy to tackle this problem based on the concept of distance (metric)
between networks. Given a multiplex graph, first a network of networks is built
for each time steps, and then a real valued time series is obtained by the
sequence of (simple) networks by evaluating the distance from the first element
of the series. The effectiveness of this approach in detecting the occurring
changes along the original time series is shown on a synthetic example first,
and then on the Gulf dataset of political events
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