1,682 research outputs found
Quartic Anharmonic Oscillator and Random Matrix Theory
In this paper the relationship between the problem of constructing the ground
state energy for the quantum quartic oscillator and the problem of computing
mean eigenvalue of large positively definite random hermitean matrices is
established. This relationship enables one to present several more or less
closed expressions for the oscillator energy. One of such expressions is given
in the form of simple recurrence relations derived by means of the method of
orthogonal polynomials which is one of the basic tools in the theory of random
matrices.Comment: 12 pages in Late
Monte Carlo study of the growth of striped domains
We analyze the dynamical scaling behavior in a two-dimensional spin model
with competing interactions after a quench to a striped phase. We measure the
growth exponents studying the scaling of the interfaces and the scaling of the
shrinking time of a ball of one phase plunged into the sea of another phase.
Our results confirm the predictions found in previous papers. The correlation
functions measured in the direction parallel and transversal to the stripes are
different as suggested by the existence of different interface energies between
the ground states of the model. Our simulations show anisotropic features for
the correlations both in the case of single-spin-flip and spin-exchange
dynamics.Comment: 15 pages, ReVTe
A blind deconvolution approach to recover effective connectivity brain networks from resting state fMRI data
A great improvement to the insight on brain function that we can get from
fMRI data can come from effective connectivity analysis, in which the flow of
information between even remote brain regions is inferred by the parameters of
a predictive dynamical model. As opposed to biologically inspired models, some
techniques as Granger causality (GC) are purely data-driven and rely on
statistical prediction and temporal precedence. While powerful and widely
applicable, this approach could suffer from two main limitations when applied
to BOLD fMRI data: confounding effect of hemodynamic response function (HRF)
and conditioning to a large number of variables in presence of short time
series. For task-related fMRI, neural population dynamics can be captured by
modeling signal dynamics with explicit exogenous inputs; for resting-state fMRI
on the other hand, the absence of explicit inputs makes this task more
difficult, unless relying on some specific prior physiological hypothesis. In
order to overcome these issues and to allow a more general approach, here we
present a simple and novel blind-deconvolution technique for BOLD-fMRI signal.
Coming to the second limitation, a fully multivariate conditioning with short
and noisy data leads to computational problems due to overfitting. Furthermore,
conceptual issues arise in presence of redundancy. We thus apply partial
conditioning to a limited subset of variables in the framework of information
theory, as recently proposed. Mixing these two improvements we compare the
differences between BOLD and deconvolved BOLD level effective networks and draw
some conclusions
Natural clustering: the modularity approach
We show that modularity, a quantity introduced in the study of networked
systems, can be generalized and used in the clustering problem as an indicator
for the quality of the solution. The introduction of this measure arises very
naturally in the case of clustering algorithms that are rooted in Statistical
Mechanics and use the analogy with a physical system.Comment: 11 pages, 5 figure enlarged versio
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
Leave-one-out prediction error of systolic arterial pressure time series under paced breathing
In this paper we show that different physiological states and pathological
conditions may be characterized in terms of predictability of time series
signals from the underlying biological system. In particular we consider
systolic arterial pressure time series from healthy subjects and Chronic Heart
Failure patients, undergoing paced respiration. We model time series by the
regularized least squares approach and quantify predictability by the
leave-one-out error. We find that the entrainment mechanism connected to paced
breath, that renders the arterial blood pressure signal more regular, thus more
predictable, is less effective in patients, and this effect correlates with the
seriousness of the heart failure. The leave-one-out error separates controls
from patients and, when all orders of nonlinearity are taken into account,
alive patients from patients for which cardiac death occurred
Visibility graphs for fMRI data: Multiplex temporal graphs and their modulations across resting-state networks.
Visibility algorithms are a family of methods that map time series into graphs, such that the tools of graph theory and network science can be used for the characterization of time series. This approach has proved a convenient tool, and visibility graphs have found applications across several disciplines. Recently, an approach has been proposed to extend this framework to multivariate time series, allowing a novel way to describe collective dynamics. Here we test their application to fMRI time series, following two main motivations, namely that (a) this approach allows vs to simultaneously capture and process relevant aspects of both local and global dynamics in an easy and intuitive way, and (b) this provides a suggestive bridge between time series and network theory that nicely fits the consolidating field of network neuroscience. Our application to a large open dataset reveals differences in the similarities of temporal networks (and thus in correlated dynamics) across resting-state networks, and gives indications that some differences in brain activity connected to psychiatric disorders could be picked up by this approach
Persistence exponent in a superantiferromagnetic quenching
We measure the persistence exponent in a phase separating two-dimensional
spin system with non-conserved dynamics quenched in a region with four
coexisting stripe phases. The system is an Ising model with nearest neighbor,
next-to-the-nearest neighbor and plaquette interactions. Due the particular
nature of the ground states, the order parameter is defined in terms of blocks
of spins. Our estimate of the persistence exponent, , differs from
those of the two-dimensional Ising and four state Potts models. Our procedure
allows the study of persistence properties also at finite temperature : our
results are compatible with the hypothesis that does not depend on
below the critical point.Comment: LaTeX file with postscript figure
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