3,482 research outputs found
Universality of the Tearing Phase in Matrix Models
The spontaneous symmetry breaking associated to the tearing of a random
surface, where large dynamical holes fill the surface, was recently analized
obtaining a non-universal critical exponent on a border phase. Here the issue
of universality is explained by an independent analysis. The one hole sector of
the model is useful to manifest the origin of the (limited) non-universal
behaviour, that is the existence of two inequivalent critical points.Comment: 9 pages, 1 figure non include
Synergy and redundancy in the Granger causal analysis of dynamical networks
We analyze by means of Granger causality the effect of synergy and redundancy
in the inference (from time series data) of the information flow between
subsystems of a complex network. Whilst we show that fully conditioned Granger
causality is not affected by synergy, the pairwise analysis fails to put in
evidence synergetic effects.
In cases when the number of samples is low, thus making the fully conditioned
approach unfeasible, we show that partially conditioned Granger causality is an
effective approach if the set of conditioning variables is properly chosen. We
consider here two different strategies (based either on informational content
for the candidate driver or on selecting the variables with highest pairwise
influences) for partially conditioned Granger causality and show that depending
on the data structure either one or the other might be valid. On the other
hand, we observe that fully conditioned approaches do not work well in presence
of redundancy, thus suggesting the strategy of separating the pairwise links in
two subsets: those corresponding to indirect connections of the fully
conditioned Granger causality (which should thus be excluded) and links that
can be ascribed to redundancy effects and, together with the results from the
fully connected approach, provide a better description of the causality pattern
in presence of redundancy. We finally apply these methods to two different real
datasets. First, analyzing electrophysiological data from an epileptic brain,
we show that synergetic effects are dominant just before seizure occurrences.
Second, our analysis applied to gene expression time series from HeLa culture
shows that the underlying regulatory networks are characterized by both
redundancy and synergy
Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
We compare numerical evolutions performed with the BSSNOK formulation and a
conformal decomposition of a Z4-like formulation of General Relativity. The
important difference between the two formulations is that the Z4 formulation
has a propagating Hamiltonian constraint, whereas BSSNOK has a zero-speed
characteristic variable in the constraint subsystem. In spherical symmetry we
evolve both puncture and neutron star initial data. We demonstrate that the
propagating nature of the Z4 constraints leads to results that compare
favorably with BSSNOK evolutions, especially when matter is present in the
spacetime. From the point of view of implementation the new system is a simple
modification of BSSNOK.Comment: Published in PR
The Effect of EDTA in Attachment Gain and Root Coverage
Root surface biomodification using low pH agents such as citric acid and tetracycline has been proposed to enhance root coverage following connective tissue grafting. The authors hypothesized that root conditioning with neutral pH edetic acid would improve vertical recession depth, root surface coverage, pocket depth, and clinical attachment levels. Twenty teeth in 10 patients with Miller class I and II recession were treated with connective tissue grafting. The experimental sites received 24% edetic acid in sterile distilled water applied to the root surface for 2 minutes before grafting. Controls were pretreated with only sterile distilled water. Measurements were evaluated before surgery and 6 months after surgery. Analysis of variance was used to determine differences between experimental and control groups. We found significant postoperative improvements in vertical recession depth, root surface coverage, and clinical attachment levels in test and control groups, compared to postoperative data. Pocket depth differences were not significant (P\u3c.01)
Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis
Building up on previous work, we present a new calculation of the
gravitational wave (GW) emission generated during the transition from
quasi-circular inspiral to plunge, merger and ringdown by a binary system of
nonspinning black holes, of masses and , in the extreme mass ratio
limit, . The relative dynamics of the system is computed
{\it without making any adiabatic approximation} by using an effective one body
(EOB) description, namely by representing the binary by an effective particle
of mass moving in a (quasi-)Schwarzschild background of
mass and submitted to an \O(\nu) 5PN-resummed analytical
radiation reaction force, with . The gravitational wave emission is
calculated via a multipolar Regge-Wheeler-Zerilli type perturbative approach
(valid in the limit ). We consider three mass ratios,
,and we compute the multipolar waveform up to
. We estimate energy and angular momentum losses during the
quasi-universal and quasi-geodesic part of the plunge phase and we analyze the
structure of the ringdown. We calculate the gravitational recoil, or "kick",
imparted to the merger remnant by the gravitational wave emission and we
emphasize the importance of higher multipoles to get a final value of the
recoil . We finally show that there is an {\it excellent
fractional agreement} () (even during the plunge) between the 5PN
EOB analytically-resummed radiation reaction flux and the numerically computed
gravitational wave angular momentum flux. This is a further confirmation of the
aptitude of the EOB formalism to accurately model extreme-mass-ratio inspirals,
as needed for the future space-based LISA gravitational wave detector.Comment: 20 pages, 12 figures. Version published in Phys. Rev.
Constraint preserving boundary conditions for the Z4c formulation of general relativity
We discuss high order absorbing constraint preserving boundary conditions for
the Z4c formulation of general relativity coupled to the moving puncture family
of gauges. We are primarily concerned with the constraint preservation and
absorption properties of these conditions. In the frozen coefficient
approximation, with an appropriate first order pseudo-differential reduction,
we show that the constraint subsystem is boundary stable on a four dimensional
compact manifold. We analyze the remainder of the initial boundary value
problem for a spherical reduction of the Z4c formulation with a particular
choice of the puncture gauge. Numerical evidence for the efficacy of the
conditions is presented in spherical symmetry.Comment: 18 pages, 8 figure
Synergetic and redundant information flow detected by unnormalized Granger causality: application to resting state fMRI
Objectives: We develop a framework for the analysis of synergy and redundancy
in the pattern of information flow between subsystems of a complex network.
Methods: The presence of redundancy and/or synergy in multivariate time series
data renders difficult to estimate the neat flow of information from each
driver variable to a given target. We show that adopting an unnormalized
definition of Granger causality one may put in evidence redundant multiplets of
variables influencing the target by maximizing the total Granger causality to a
given target, over all the possible partitions of the set of driving variables.
Consequently we introduce a pairwise index of synergy which is zero when two
independent sources additively influence the future state of the system,
differently from previous definitions of synergy. Results: We report the
application of the proposed approach to resting state fMRI data from the Human
Connectome Project, showing that redundant pairs of regions arise mainly due to
space contiguity and interhemispheric symmetry, whilst synergy occurs mainly
between non-homologous pairs of regions in opposite hemispheres. Conclusions:
Redundancy and synergy, in healthy resting brains, display characteristic
patterns, revealed by the proposed approach. Significance: The pairwise synergy
index, here introduced, maps the informational character of the system at hand
into a weighted complex network: the same approach can be applied to other
complex systems whose normal state corresponds to a balance between redundant
and synergetic circuits.Comment: 6 figures. arXiv admin note: text overlap with arXiv:1403.515
Accuracy of numerical relativity waveforms from binary neutron star mergers and their comparison with post-Newtonian waveforms
We present numerical relativity simulations of nine-orbit equal-mass binary
neutron star covering the quasicircular late inspiral and merger. The extracted
gravitational waveforms are analyzed for convergence and accuracy. Second order
convergence is observed up to contact, i.e. about 3-4 cycles to merger; error
estimates can be made up to this point. The uncertainties on the phase and the
amplitude are dominated by truncation errors and can be minimized to 0.13 rad
and less then 1%, respectively, by using several simulations and extrapolating
in resolution. In the latter case finite-radius extraction uncertainties become
a source of error of the same order and have to be taken into account. The
waveforms are tested against accuracy standards for data analysis. The
uncertainties on the waveforms are such that accuracy standards are generically
not met for signal-to-noise ratios relevant for detection, except for some best
cases using extrapolation from several runs. A detailed analysis of the errors
is thus imperative for the use of numerical relativity waveforms from binary
neutron stars in quantitative studies. The waveforms are compared with the
post-Newtonian Taylor T4 approximants both for point-particle and including the
analytically known tidal corrections. The T4 approximants accumulate
significant phase differences of 2 rad at contact and 4 rad at merger,
underestimating the influence of finite size effects. Tidal signatures in the
waveforms are thus important at least during the last six orbits of the merger
process.Comment: Physical Review D (Vol.85, No.10) 201
Information transfer of an Ising model on a brain network
We implement the Ising model on a structural connectivity matrix describing
the brain at a coarse scale. Tuning the model temperature to its critical
value, i.e. at the susceptibility peak, we find a maximal amount of total
information transfer between the spin variables. At this point the amount of
information that can be redistributed by some nodes reaches a limit and the net
dynamics exhibits signature of the law of diminishing marginal returns, a
fundamental principle connected to saturated levels of production. Our results
extend the recent analysis of dynamical oscillators models on the connectome
structure, taking into account lagged and directional influences, focusing only
on the nodes that are more prone to became bottlenecks of information. The
ratio between the outgoing and the incoming information at each node is related
to the number of incoming links
Consensus clustering approach to group brain connectivity matrices
A novel approach rooted on the notion of consensus clustering, a strategy
developed for community detection in complex networks, is proposed to cope with
the heterogeneity that characterizes connectivity matrices in health and
disease. The method can be summarized as follows:
(i) define, for each node, a distance matrix for the set of subjects by
comparing the connectivity pattern of that node in all pairs of subjects; (ii)
cluster the distance matrix for each node; (iii) build the consensus network
from the corresponding partitions; (iv) extract groups of subjects by finding
the communities of the consensus network thus obtained.
Differently from the previous implementations of consensus clustering, we
thus propose to use the consensus strategy to combine the information arising
from the connectivity patterns of each node. The proposed approach may be seen
either as an exploratory technique or as an unsupervised pre-training step to
help the subsequent construction of a supervised classifier. Applications on a
toy model and two real data sets, show the effectiveness of the proposed
methodology, which represents heterogeneity of a set of subjects in terms of a
weighted network, the consensus matrix
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