263 research outputs found
Diffusion dynamics on multiplex networks
We study the time scales associated to diffusion processes that take place on
multiplex networks, i.e. on a set of networks linked through interconnected
layers. To this end, we propose the construction of a supra-Laplacian matrix,
which consists of a dimensional lifting of the Laplacian matrix of each layer
of the multiplex network. We use perturbative analysis to reveal analytically
the structure of eigenvectors and eigenvalues of the complete network in terms
of the spectral properties of the individual layers. The spectrum of the
supra-Laplacian allows us to understand the physics of diffusion-like processes
on top of multiplex networks.Comment: 6 Pages including supplemental material. To appear in Physical Review
Letter
Assortativity Decreases the Robustness of Interdependent Networks
It was recently recognized that interdependencies among different networks
can play a crucial role in triggering cascading failures and hence system-wide
disasters. A recent model shows how pairs of interdependent networks can
exhibit an abrupt percolation transition as failures accumulate. We report on
the effects of topology on failure propagation for a model system consisting of
two interdependent networks. We find that the internal node correlations in
each of the two interdependent networks significantly changes the critical
density of failures that triggers the total disruption of the two-network
system. Specifically, we find that the assortativity (i.e. the likelihood of
nodes with similar degree to be connected) within a single network decreases
the robustness of the entire system. The results of this study on the influence
of assortativity may provide insights into ways of improving the robustness of
network architecture, and thus enhances the level of protection of critical
infrastructures
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
Patient-specific image-based computer simulation for theprediction of valve morphology and calcium displacement after TAVI with the Medtronic CoreValve and the Edwards SAPIEN valve
AIMS:
Our aim was to validate patient-specific software integrating baseline anatomy and biomechanical properties of both the aortic root and valve for the prediction of valve morphology and aortic leaflet calcium displacement after TAVI.
METHODS AND RESULTS:
Finite element computer modelling was performed in 39 patients treated with a Medtronic CoreValve System (MCS; n=33) or an Edwards SAPIEN XT (ESV; n=6). Quantitative axial frame morphology at inflow (MCS, ESV) and nadir, coaptation and commissures (MCS) was compared between multislice computed tomography (MSCT) post TAVI and a computer model as well as displacement of the aortic leaflet calcifications, quantified by the distance between the coronary ostium and the closest calcium nodule. Bland-Altman analysis revealed a strong correlation between the observed (MSCT) and predicted frame dimensions, although small differences were detected for, e.g., Dmin at the inflow (mean±SD MSCT vs.
MODEL:
21.6±2.4 mm vs. 22.0±2.4 mm; difference±SD: -0.4±1.3 mm, p<0.05) and Dmax (25.6±2.7 mm vs. 26.2±2.7 mm; difference±SD: -0.6±1.0 mm, p<0.01). The observed and predicted calcium displacements were highly correlated for the left and right coronary ostia (R2=0.67 and R2=0.71, respectively p<0.001).
CONCLUSIONS:
Dedicated software allows accurate prediction of frame morphology and calcium displacement after valve implantation, which may help to improve outcome
Self-Similar Bootstrap of Divergent Series
A method is developed for calculating effective sums of divergent series.
This approach is a variant of the self-similar approximation theory. The
novelty here is in using an algebraic transformation with a power providing the
maximal stability of the self-similar renormalization procedure. The latter is
to be repeated as many times as it is necessary in order to convert into closed
self-similar expressions all sums from the series considered. This multiple and
complete renormalization is called self-similar bootstrap. The method is
illustrated by several examples from statistical physics.Comment: 1 file, 22 pages, RevTe
Towards designing robust coupled networks
Natural and technological interdependent systems have been shown to be highly
vulnerable due to cascading failures and an abrupt collapse of global
connectivity under initial failure. Mitigating the risk by partial
disconnection endangers their functionality. Here we propose a systematic
strategy of selecting a minimum number of autonomous nodes that guarantee a
smooth transition in robustness. Our method which is based on betweenness is
tested on various examples including the famous 2003 electrical blackout of
Italy. We show that, with this strategy, the necessary number of autonomous
nodes can be reduced by a factor of five compared to a random choice. We also
find that the transition to abrupt collapse follows tricritical scaling
characterized by a set of exponents which is independent on the protection
strategy
Correlation between centrality metrics and their application to the opinion model
In recent decades, a number of centrality metrics describing network
properties of nodes have been proposed to rank the importance of nodes. In
order to understand the correlations between centrality metrics and to
approximate a high-complexity centrality metric by a strongly correlated
low-complexity metric, we first study the correlation between centrality
metrics in terms of their Pearson correlation coefficient and their similarity
in ranking of nodes. In addition to considering the widely used centrality
metrics, we introduce a new centrality measure, the degree mass. The m order
degree mass of a node is the sum of the weighted degree of the node and its
neighbors no further than m hops away. We find that the B_{n}, the closeness,
and the components of x_{1} are strongly correlated with the degree, the
1st-order degree mass and the 2nd-order degree mass, respectively, in both
network models and real-world networks. We then theoretically prove that the
Pearson correlation coefficient between x_{1} and the 2nd-order degree mass is
larger than that between x_{1} and a lower order degree mass. Finally, we
investigate the effect of the inflexible antagonists selected based on
different centrality metrics in helping one opinion to compete with another in
the inflexible antagonists opinion model. Interestingly, we find that selecting
the inflexible antagonists based on the leverage, the B_{n}, or the degree is
more effective in opinion-competition than using other centrality metrics in
all types of networks. This observation is supported by our previous
observations, i.e., that there is a strong linear correlation between the
degree and the B_{n}, as well as a high centrality similarity between the
leverage and the degree.Comment: 20 page
Discordant severity criteria in patients with moderate aortic stenosis: prognostic implications
Background The criteria to define the grade of aortic stenosis (AS)-aortic valve area (AVA) and mean gradient (MG) or peak jet velocity-do not always coincide into one grade. Although in severe AS, this discrepancy is well characterised, in moderate AS, the phenomenon of discordant grading has not been investigated and its prognostic implications are unknown.Objectives To investigate the occurrence of discordant grading in patients with moderate AS (defined by an AVA between 1.0 cm(2) and 1.5 cm(2) but with an MG = 20 mm Hg) in terms of clinical outcomes.Methods From an ongoing registry of patients with AS, patients with moderate AS based on AVA were selected and classified into discordant or concordant grading (MG = 20 mm Hg, respectively). The clinical endpoint was all-cause mortality.Results Of 790 patients with moderate AS, 150 (19.0%) had discordant grading, moderate AS. Patients with discordant grading were older, had higher prevalence of previous myocardial infarction and left ventricular (LV) hypertrophy, larger LV end-diastolic and end-systolic volume index, higher LV filling pressure and lower LV ejection fraction and stroke volume index as compared with their counterparts. After a median follow-up of 4.9 years (IQR 3.0-8.2), patients with discordant grading had lower aortic valve replacement rates (26.7% vs 44.1%, p<0.001) and higher mortality rates (60.0% vs 43.1%, p<0.001) as compared with patients with concordant grading. Discordant grading moderate AS, combined with low LV ejection fraction, presented the higher risk of mortality (HR 2.78 (2.00-3.87), p<0.001).Conclusion Discordant-grading moderate AS is not uncommon and, when combined with low LV ejection fraction, is associated with high risk of mortality.Cardiolog
Josephson Coupling, Phase Correlations, and Josephson Plasma Resonance in Vortex Liquid Phase
Josephson plasma resonance has been introduced recently as a powerful tool to
probe interlayer Josephson coupling in different regions of the vortex phase
diagram in layered superconductors. In the liquid phase, the high temperature
expansion with respect to the Josephson coupling connects the Josephson plasma
frequency with the phase correlation function. This function, in turn, is
directly related to the pair distribution function of the liquid. We develop a
recipe to extract the phase and density correlation functions from the
dependencies of the plasma resonance frequency and the
axis conductivity on the {\it ab}-component of the
magnetic field at fixed {\it c} -component. Using Langevin dynamic simulations
of two-dimensional vortex arrays we calculate density and phase correlation
functions at different temperatures. Calculated phase correlations describe
very well the experimental angular dependence of the plasma resonance field. We
also demonstrate that in the case of weak damping in the liquid phase,
broadening of the JPR line is caused mainly by random Josephson coupling
arising from the density fluctuations of pancake vortices. In this case the JPR
line has a universal shape, which is determined only by parameters of the
superconductors and temperature.Comment: 22 pages, 6 figures, to appear in Phys. Rev. B, December
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