17,649 research outputs found
Second look at the spread of epidemics on networks
In an important paper, M.E.J. Newman claimed that a general network-based
stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to
a bond percolation model, where the bonds are the edges of the contact network
and the bond occupation probability is equal to the marginal probability of
transmission from an infected node to a susceptible neighbor. In this paper, we
show that this isomorphism is incorrect and define a semi-directed random
network we call the epidemic percolation network that is exactly isomorphic to
the SIR epidemic model in any finite population. In the limit of a large
population, (i) the distribution of (self-limited) outbreak sizes is identical
to the size distribution of (small) out-components, (ii) the epidemic threshold
corresponds to the phase transition where a giant strongly-connected component
appears, (iii) the probability of a large epidemic is equal to the probability
that an initial infection occurs in the giant in-component, and (iv) the
relative final size of an epidemic is equal to the proportion of the network
contained in the giant out-component. For the SIR model considered by Newman,
we show that the epidemic percolation network predicts the same mean outbreak
size below the epidemic threshold, the same epidemic threshold, and the same
final size of an epidemic as the bond percolation model. However, the bond
percolation model fails to predict the correct outbreak size distribution and
probability of an epidemic when there is a nondegenerate infectious period
distribution. We confirm our findings by comparing predictions from percolation
networks and bond percolation models to the results of simulations. In an
appendix, we show that an isomorphism to an epidemic percolation network can be
defined for any time-homogeneous stochastic SIR model.Comment: 29 pages, 5 figure
The main transition in the Pink membrane model: finite-size scaling and the influence of surface roughness
We consider the main transition in single-component membranes using computer
simulations of the Pink model [D. Pink {\it et al.}, Biochemistry {\bf 19}, 349
(1980)]. We first show that the accepted parameters of the Pink model yield a
main transition temperature that is systematically below experimental values.
This resolves an issue that was first pointed out by Corvera and co-workers
[Phys. Rev. E {\bf 47}, 696 (1993)]. In order to yield the correct transition
temperature, the strength of the van der Waals coupling in the Pink model must
be increased; by using finite-size scaling, a set of optimal values is
proposed. We also provide finite-size scaling evidence that the Pink model
belongs to the universality class of the two-dimensional Ising model. This
finding holds irrespective of the number of conformational states. Finally, we
address the main transition in the presence of quenched disorder, which may
arise in situations where the membrane is deposited on a rough support. In this
case, we observe a stable multi-domain structure of gel and fluid domains, and
the absence of a sharp transition in the thermodynamic limit.Comment: submitted to PR
Identifying the starting point of a spreading process in complex networks
When dealing with the dissemination of epidemics, one important question that
can be asked is the location where the contamination began. In this paper, we
analyze three spreading schemes and propose and validate an effective
methodology for the identification of the source nodes. The method is based on
the calculation of the centrality of the nodes on the sampled network,
expressed here by degree, betweenness, closeness and eigenvector centrality. We
show that the source node tends to have the highest measurement values. The
potential of the methodology is illustrated with respect to three theoretical
complex network models as well as a real-world network, the email network of
the University Rovira i Virgili
Local Algorithms for Block Models with Side Information
There has been a recent interest in understanding the power of local
algorithms for optimization and inference problems on sparse graphs. Gamarnik
and Sudan (2014) showed that local algorithms are weaker than global algorithms
for finding large independent sets in sparse random regular graphs. Montanari
(2015) showed that local algorithms are suboptimal for finding a community with
high connectivity in the sparse Erd\H{o}s-R\'enyi random graphs. For the
symmetric planted partition problem (also named community detection for the
block models) on sparse graphs, a simple observation is that local algorithms
cannot have non-trivial performance.
In this work we consider the effect of side information on local algorithms
for community detection under the binary symmetric stochastic block model. In
the block model with side information each of the vertices is labeled
or independently and uniformly at random; each pair of vertices is
connected independently with probability if both of them have the same
label or otherwise. The goal is to estimate the underlying vertex
labeling given 1) the graph structure and 2) side information in the form of a
vertex labeling positively correlated with the true one. Assuming that the
ratio between in and out degree is and the average degree , we characterize three different regimes under which a
local algorithm, namely, belief propagation run on the local neighborhoods,
maximizes the expected fraction of vertices labeled correctly. Thus, in
contrast to the case of symmetric block models without side information, we
show that local algorithms can achieve optimal performance for the block model
with side information.Comment: Due to the limitation "The abstract field cannot be longer than 1,920
characters", the abstract here is shorter than that in the PDF fil
Linking urban design to sustainability : formal indicators of social urban sustainability field research in Perth, Western Australia
The making of a livable urban community is a complex endeavor. For much of the 20th Century plannersand engineers believed that modern and rational decision-making would create successful cities. Today, political leaders across the globe are considering ways to promote sustainable development and the concepts of New Urbanism are making their way from the drawing board to the ground. While much has changed in the world, the creation of a successful street is as much of an art today as it was in the 1960s.Our work seeks to investigate 'street life' in cities as a crucial factor towards community success. What arethe components of the neighborhood and street form that contributes to the richness of street life? To answer this question we rely on the literature. The aim of the Formal Indicators of Social Urban Sustainability studyis to measure the formal components of a neighborhood and street that theorists have stated important in promoting sustainability. This paper will describe how this concept helps to bridge urban design and sustainability. It will describe the tool and show how this was applied in a comparative assessment of Joondalup and Fremantle, two urban centers in the Perth metropolitan area
Entropy in Spin Foam Models: The Statistical Calculation
Recently an idea for computing the entropy of black holes in the spin foam
formalism has been introduced. Particularly complete calculations for the three
dimensional euclidean BTZ black hole were done. The whole calculation is based
on observables living at the horizon of the black hole universe. Departing from
this idea of observables living at the horizon, we now go further and compute
the entropy of BTZ black hole in the spirit of statistical mechanics. We
compare both calculations and show that they are very interrelated and equally
valid. This latter behaviour is certainly due to the importance of the
observables.Comment: 11 pages, 1 figur
Complete trails of co-authorship network evolution
The rise and fall of a research field is the cumulative outcome of its
intrinsic scientific value and social coordination among scientists. The
structure of the social component is quantifiable by the social network of
researchers linked via co-authorship relations, which can be tracked through
digital records. Here, we use such co-authorship data in theoretical physics
and study their complete evolutionary trail since inception, with a particular
emphasis on the early transient stages. We find that the co-authorship networks
evolve through three common major processes in time: the nucleation of small
isolated components, the formation of a tree-like giant component through
cluster aggregation, and the entanglement of the network by large-scale loops.
The giant component is constantly changing yet robust upon link degradations,
forming the network's dynamic core. The observed patterns are successfully
reproducible through a new network model
Fast Simulation of Facilitated Spin Models
We show how to apply the absorbing Markov chain Monte Carlo algorithm of
Novotny to simulate kinetically constrained models of glasses. We consider in
detail one-spin facilitated models, such as the East model and its
generalizations to arbitrary dimensions. We investigate how to maximise the
efficiency of the algorithms, and show that simulation times can be improved on
standard continuous time Monte Carlo by several orders of magnitude. We
illustrate the method with equilibrium and aging results. These include a study
of relaxation times in the East model for dimensions d=1 to d=13, which
provides further evidence that the hierarchical relaxation in this model is
present in all dimensions. We discuss how the method can be applied to other
kinetically constrained models.Comment: 8 pages, 4 figure
Random pinning limits the size of membrane adhesion domains
Theoretical models describing specific adhesion of membranes predict (for
certain parameters) a macroscopic phase separation of bonds into adhesion
domains. We show that this behavior is fundamentally altered if the membrane is
pinned randomly due to, e.g., proteins that anchor the membrane to the
cytoskeleton. Perturbations which locally restrict membrane height fluctuations
induce quenched disorder of the random-field type. This rigorously prevents the
formation of macroscopic adhesion domains following the Imry-Ma argument [Y.
Imry and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1975)]. Our prediction of
random-field disorder follows from analytical calculations, and is strikingly
confirmed in large-scale Monte Carlo simulations. These simulations are based
on an efficient composite Monte Carlo move, whereby membrane height and bond
degrees of freedom are updated simultaneously in a single move. The application
of this move should prove rewarding for other systems also.Comment: revised and extended versio
Network robustness and fragility: Percolation on random graphs
Recent work on the internet, social networks, and the power grid has
addressed the resilience of these networks to either random or targeted
deletion of network nodes. Such deletions include, for example, the failure of
internet routers or power transmission lines. Percolation models on random
graphs provide a simple representation of this process, but have typically been
limited to graphs with Poisson degree distribution at their vertices. Such
graphs are quite unlike real world networks, which often possess power-law or
other highly skewed degree distributions. In this paper we study percolation on
graphs with completely general degree distribution, giving exact solutions for
a variety of cases, including site percolation, bond percolation, and models in
which occupation probabilities depend on vertex degree. We discuss the
application of our theory to the understanding of network resilience.Comment: 4 pages, 2 figure
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