29 research outputs found
Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains
Synchronization cluster analysis is an approach to the detection of
underlying structures in data sets of multivariate time series, starting from a
matrix R of bivariate synchronization indices. A previous method utilized the
eigenvectors of R for cluster identification, analogous to several recent
attempts at group identification using eigenvectors of the correlation matrix.
All of these approaches assumed a one-to-one correspondence of dominant
eigenvectors and clusters, which has however been shown to be wrong in
important cases. We clarify the usefulness of eigenvalue decomposition for
synchronization cluster analysis by translating the problem into the language
of stochastic processes, and derive an enhanced clustering method harnessing
recent insights from the coarse-graining of finite-state Markov processes. We
illustrate the operation of our method using a simulated system of coupled
Lorenz oscillators, and we demonstrate its superior performance over the
previous approach. Finally we investigate the question of robustness of the
algorithm against small sample size, which is important with regard to field
applications.Comment: Follow-up to arXiv:0706.3375. Journal submission 9 Jul 2007.
Published 19 Dec 200
Early warning signal for interior crises in excitable systems
The ability to reliably predict critical transitions in dynamical systems is
a long-standing goal of diverse scientific communities. Previous work focused
on early warning signals related to local bifurcations (critical slowing down)
and non-bifurcation type transitions. We extend this toolbox and report on a
characteristic scaling behavior (critical attractor growth) which is indicative
of an impending global bifurcation, an interior crisis in excitable systems. We
demonstrate our early warning signal in a conceptual climate model as well as
in a model of coupled neurons known to exhibit extreme events. We observed
critical attractor growth prior to interior crises of chaotic as well as
strange-nonchaotic attractors. These observations promise to extend the classes
of transitions that can be predicted via early warning signals.Comment: 6 pages, 4 figure
Unraveling Spurious Properties of Interaction Networks with Tailored Random Networks
We investigate interaction networks that we derive from multivariate time
series with methods frequently employed in diverse scientific fields such as
biology, quantitative finance, physics, earth and climate sciences, and the
neurosciences. Mimicking experimental situations, we generate time series with
finite length and varying frequency content but from independent stochastic
processes. Using the correlation coefficient and the maximum cross-correlation,
we estimate interdependencies between these time series. With clustering
coefficient and average shortest path length, we observe unweighted interaction
networks, derived via thresholding the values of interdependence, to possess
non-trivial topologies as compared to Erd\H{o}s-R\'{e}nyi networks, which would
indicate small-world characteristics. These topologies reflect the mostly
unavoidable finiteness of the data, which limits the reliability of typically
used estimators of signal interdependence. We propose random networks that are
tailored to the way interaction networks are derived from empirical data.
Through an exemplary investigation of multichannel electroencephalographic
recordings of epileptic seizures - known for their complex spatial and temporal
dynamics - we show that such random networks help to distinguish network
properties of interdependence structures related to seizure dynamics from those
spuriously induced by the applied methods of analysis
Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data
7 pages, 4 figures Acknowledgement We are grateful to M. Riedl and G. Ansmann for fruitful discussions and critical comments on earlier versions of the manuscript. This work was supported by the Volkswagen Foundation (Grant Nos. 88461, 88462, 88463, 85390, 85391 and 85392).Peer reviewedPreprin
How important is the seizure onset zone for seizure dynamics?
Purpose: Research into epileptic networks has recently allowed deeper
insights into the epileptic process. Here we investigated the importance of
individual network nodes for seizure dynamics.
Methods: We analysed intracranial electroencephalographic recordings of 86
focal seizures with different anatomical onset locations. With time-resolved
correlation analyses, we derived a sequence of weighted epileptic networks
spanning the pre-ictal, ictal, and post-ictal period, and each recording site
represents a network node. We assessed node importance with commonly used
centrality indices that take into account different network properties.
Results: A high variability of temporal evolution of node importance was
observed, both intra- and interindividually. Nevertheless, nodes near and far
off the seizure onset zone (SOZ) were rated as most important for seizure
dynamics more often (65% of cases) than nodes from within the SOZ (35% of
cases).
Conclusion: Our findings underline the high relevance of brain outside of the
SOZ but within the large-scale epileptic network for seizure dynamics.
Knowledge about these network constituents may elucidate targets for
individualised therapeutic interventions that aim at preventing seizure
generation and spread.Comment: In press (Seizure
From brain to earth and climate systems: Small-world interaction networks or not?
We consider recent reports on small-world topologies of interaction networks
derived from the dynamics of spatially extended systems that are investigated
in diverse scientific fields such as neurosciences, geophysics, or meteorology.
With numerical simulations that mimic typical experimental situations we have
identified an important constraint when characterizing such networks:
indications of a small-world topology can be expected solely due to the spatial
sampling of the system along with commonly used time series analysis based
approaches to network characterization
Automated scoring of pre-REM sleep in mice with deep learning
Reliable automation of the labor-intensive manual task of scoring animal
sleep can facilitate the analysis of long-term sleep studies. In recent years,
deep-learning-based systems, which learn optimal features from the data,
increased scoring accuracies for the classical sleep stages of Wake, REM, and
Non-REM. Meanwhile, it has been recognized that the statistics of transitional
stages such as pre-REM, found between Non-REM and REM, may hold additional
insight into the physiology of sleep and are now under vivid investigation. We
propose a classification system based on a simple neural network architecture
that scores the classical stages as well as pre-REM sleep in mice. When
restricted to the classical stages, the optimized network showed
state-of-the-art classification performance with an out-of-sample F1 score of
0.95 in male C57BL/6J mice. When unrestricted, the network showed lower F1
scores on pre-REM (0.5) compared to the classical stages. The result is
comparable to previous attempts to score transitional stages in other species
such as transition sleep in rats or N1 sleep in humans. Nevertheless, we
observed that the sequence of predictions including pre-REM typically
transitioned from Non-REM to REM reflecting sleep dynamics observed by human
scorers. Our findings provide further evidence for the difficulty of scoring
transitional sleep stages, likely because such stages of sleep are
under-represented in typical data sets or show large inter-scorer variability.
We further provide our source code and an online platform to run predictions
with our trained network.Comment: 14 pages, 5 figure
Identifying phase synchronization clusters in spatially extended dynamical systems
We investigate two recently proposed multivariate time series analysis
techniques that aim at detecting phase synchronization clusters in spatially
extended, nonstationary systems with regard to field applications. The starting
point of both techniques is a matrix whose entries are the mean phase coherence
values measured between pairs of time series. The first method is a mean field
approach which allows to define the strength of participation of a subsystem in
a single synchronization cluster. The second method is based on an eigenvalue
decomposition from which a participation index is derived that characterizes
the degree of involvement of a subsystem within multiple synchronization
clusters. Simulating multiple clusters within a lattice of coupled Lorenz
oscillators we explore the limitations and pitfalls of both methods and
demonstrate (a) that the mean field approach is relatively robust even in
configurations where the single cluster assumption is not entirely fulfilled,
and (b) that the eigenvalue decomposition approach correctly identifies the
simulated clusters even for low coupling strengths. Using the eigenvalue
decomposition approach we studied spatiotemporal synchronization clusters in
long-lasting multichannel EEG recordings from epilepsy patients and obtained
results that fully confirm findings from well established neurophysiological
examination techniques. Multivariate time series analysis methods such as
synchronization cluster analysis that account for nonlinearities in the data
are expected to provide complementary information which allows to gain deeper
insights into the collective dynamics of spatially extended complex systems