96 research outputs found
Identification of network modules by optimization of ratio association
We introduce a novel method for identifying the modular structures of a
network based on the maximization of an objective function: the ratio
association. This cost function arises when the communities detection problem
is described in the probabilistic autoencoder frame. An analogy with kernel
k-means methods allows to develop an efficient optimization algorithm, based on
the deterministic annealing scheme. The performance of the proposed method is
shown on a real data set and on simulated networks
Conserved Ising Model on the Human Connectome
Dynamical models implemented on the large scale architecture of the human
brain may shed light on how function arises from the underlying structure. This
is the case notably for simple abstract models, such as the Ising model. We
compare the spin correlations of the Ising model and the empirical functional
brain correlations, both at the single link level and at the modular level, and
show that their match increases at the modular level in anesthesia, in line
with recent results and theories. Moreover, we show that at the peak of the
specific heat (the \it{critical state}) the spin correlations are minimally
shaped by the underlying structural network, explaining how the best match
between structure and function is obtained at the onset of criticality, as
previously observed. These findings confirm that brain dynamics under
anesthesia shows a departure from criticality and could open the way to novel
perspectives when the conserved magnetization is interpreted in terms of an
homeostatic principle imposed to neural activity
Expanding the Transfer Entropy to Identify Information Subgraphs in Complex Systems
We propose a formal expansion of the transfer entropy to put in evidence
irreducible sets of variables which provide information for the future state of
each assigned target. Multiplets characterized by a large contribution to the
expansion are associated to informational circuits present in the system, with
an informational character which can be associated to the sign of the
contribution. For the sake of computational complexity, we adopt the assumption
of Gaussianity and use the corresponding exact formula for the conditional
mutual information. We report the application of the proposed methodology on
two EEG data sets
Phase shifts of synchronized oscillators and the systolic/diastolic blood pressure relation
We study the phase-synchronization properties of systolic and diastolic
arterial pressure in healthy subjects. We find that delays in the oscillatory
components of the time series depend on the frequency bands that are
considered, in particular we find a change of sign in the phase shift going
from the Very Low Frequency band to the High Frequency band. This behavior
should reflect a collective behavior of a system of nonlinear interacting
elementary oscillators. We prove that some models describing such systems, e.g.
the Winfree and the Kuramoto models offer a clue to this phenomenon. For these
theoretical models there is a linear relationship between phase shifts and the
difference of natural frequencies of oscillators and a change of sign in the
phase shift naturally emerges.Comment: 8 figures, 9 page
Variational method and duality in the 2D square Potts model
The ferromagnetic q-state Potts model on a square lattice is analyzed, for
q>4, through an elaborate version of the operatorial variational method. In the
variational approach proposed in the paper, the duality relations are exactly
satisfied, involving at a more fundamental level, a duality relationship
between variational parameters. Besides some exact predictions, the approach is
very effective in the numerical estimates over the whole range of temperature
and can be systematically improved.Comment: 20 pages, 5 EPS figure
Phase diagram of a generalized Winfree model
We study the phase diagram of a generalized Winfree model. The modification
is such that the coupling depends on the fraction of synchronized oscillators,
a situation which has been noted in some experiments on coupled Josephson
junctions and mechanical systems. We let the global coupling k be a function of
the Kuramoto order parameter r through an exponent z such that z=1 corresponds
to the standard Winfree model, z<1 strengthens the coupling at low r (low
amount of synchronization) and, at z>1, the coupling is weakened for low r.
Using both analytical and numerical approaches, we find that z controls the
size of the incoherent phase region, and one may make the incoherent behavior
less typical by choosing z<1. We also find that the original Winfree model is a
rather special case, indeed the partial locked behavior disappears for z>1. At
fixed k and varying gamma, the stability boundary of the locked phase
corresponds to a transition that is continuous for z1.
This change in the nature of the transition is in accordance with a previous
study on a similarly modified Kuramoto model.Comment: 9 pages, 3 figure
Phase ordering in chaotic map lattices with conserved dynamics
Dynamical scaling in a two-dimensional lattice model of chaotic maps, in
contact with a thermal bath, is numerically studied. The model here proposed is
equivalent to a conserved Ising model with coupligs which fluctuate over the
same time scale as spin moves. When couplings fluctuations and thermal
fluctuations are both important, this model does not belong to the class of
universality of a Langevin equation known as model B; the scaling exponents are
continuously varying with the temperature and depend on the map used. The
universal behavior of model B is recovered when thermal fluctuations are
dominant.Comment: 6 pages, 4 figures. Revised version accepted for publication on
Physical Review E as a Rapid Communicatio
Kernel Granger causality and the analysis of dynamical networks
We propose a method of analysis of dynamical networks based on a recent
measure of Granger causality between time series, based on kernel methods. The
generalization of kernel Granger causality to the multivariate case, here
presented, shares the following features with the bivariate measures: (i) the
nonlinearity of the regression model can be controlled by choosing the kernel
function and (ii) the problem of false-causalities, arising as the complexity
of the model increases, is addressed by a selection strategy of the
eigenvectors of a reduced Gram matrix whose range represents the additional
features due to the second time series. Moreover, there is no {\it a priori}
assumption that the network must be a directed acyclic graph. We apply the
proposed approach to a network of chaotic maps and to a simulated genetic
regulatory network: it is shown that the underlying topology of the network can
be reconstructed from time series of node's dynamics, provided that a
sufficient number of samples is available. Considering a linear dynamical
network, built by preferential attachment scheme, we show that for limited data
use of bivariate Granger causality is a better choice w.r.t methods using
minimization. Finally we consider real expression data from HeLa cells, 94
genes and 48 time points. The analysis of static correlations between genes
reveals two modules corresponding to well known transcription factors; Granger
analysis puts in evidence nineteen causal relationships, all involving genes
related to tumor development.Comment: 14 pages, 10 figure
Clustering data by inhomogeneous chaotic map lattices
A new approach to clustering, based on the physical properties of
inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to
each data-point and short range couplings are introduced. The stationary regime
of the system corresponds to a macroscopic attractor independent of the initial
conditions. The mutual information between couples of maps serves to partition
the data set in clusters, without prior assumptions about the structure of the
underlying distribution of the data. Experiments on simulated and real data
sets show the effectiveness of the proposed algorithm.Comment: 8 pages, 6 figures. Revised version accepted for publication on
Physical Review Letter
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