2,877 research outputs found
Alumni of Note
Key Player - Maryland Stadium Authority\u27s Alison Asti; Big Hitters: Percival\u27s Winning Softball Team; Fitting Tributes: Newly Endowed Scholarships
Resilience of Complex Networks to Random Breakdown
Using Monte Carlo simulations we calculate , the fraction of nodes which
are randomly removed before global connectivity is lost, for networks with
scale-free and bimodal degree distributions. Our results differ with the
results predicted by an equation for proposed by Cohen, et al. We discuss
the reasons for this disagreement and clarify the domain for which the proposed
equation is valid
Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities
Many complex networks display a mesoscopic structure with groups of nodes
sharing many links with the other nodes in their group and comparatively few
with nodes of different groups. This feature is known as community structure
and encodes precious information about the organization and the function of the
nodes. Many algorithms have been proposed but it is not yet clear how they
should be tested. Recently we have proposed a general class of undirected and
unweighted benchmark graphs, with heterogenous distributions of node degree and
community size. An increasing attention has been recently devoted to develop
algorithms able to consider the direction and the weight of the links, which
require suitable benchmark graphs for testing. In this paper we extend the
basic ideas behind our previous benchmark to generate directed and weighted
networks with built-in community structure. We also consider the possibility
that nodes belong to more communities, a feature occurring in real systems,
like, e. g., social networks. As a practical application, we show how
modularity optimization performs on our new benchmark.Comment: 9 pages, 13 figures. Final version published in Physical Review E.
The code to create the benchmark graphs can be freely downloaded from
http://santo.fortunato.googlepages.com/inthepress
Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks
In this work we investigate the spectra of Laplacian matrices that determine
many dynamic properties of scale-free networks below and at the percolation
threshold. We use a replica formalism to develop analytically, based on an
integral equation, a systematic way to determine the ensemble averaged
eigenvalue spectrum for a general type of tree-like networks. Close to the
percolation threshold we find characteristic scaling functions for the density
of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic
power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for
small lambda, where alpha_1 holds below and alpha_2 at the percolation
threshold. In the range where the spectra are accessible from a numerical
diagonalization procedure the two methods lead to very similar results.Comment: 9 pages, 6 figure
A weighted configuration model and inhomogeneous epidemics
A random graph model with prescribed degree distribution and degree dependent
edge weights is introduced. Each vertex is independently equipped with a random
number of half-edges and each half-edge is assigned an integer valued weight
according to a distribution that is allowed to depend on the degree of its
vertex. Half-edges with the same weight are then paired randomly to create
edges. An expression for the threshold for the appearance of a giant component
in the resulting graph is derived using results on multi-type branching
processes. The same technique also gives an expression for the basic
reproduction number for an epidemic on the graph where the probability that a
certain edge is used for transmission is a function of the edge weight. It is
demonstrated that, if vertices with large degree tend to have large (small)
weights on their edges and if the transmission probability increases with the
edge weight, then it is easier (harder) for the epidemic to take off compared
to a randomized epidemic with the same degree and weight distribution. A recipe
for calculating the probability of a large outbreak in the epidemic and the
size of such an outbreak is also given. Finally, the model is fitted to three
empirical weighted networks of importance for the spread of contagious diseases
and it is shown that can be substantially over- or underestimated if the
correlation between degree and weight is not taken into account
New Research on the Cowling and Cooling of Radial Engines
An extensive series of wind-tunnel tests on a half-scale conventional, nacelle model were made by the United Aircraft Corporation to determine and correlate the effects of many variables on cooling air flow and nacelle drag. The primary investigation was concerned with the reaction of these factors to varying conditions ahead of, across, and behind the engine. In the light of this investigation, common misconceptions and factors which are frequently overlooked in the cooling and cowling of radial engines are considered in some detail. Data are presented to support certain design recommendations and conclusions which should lead toward the improvement of present engine installations. Several charts are included to facilitate the estimation of cooling drag, available cooling pressure, and cowl exit area
Spin Glass Phase Transition on Scale-Free Networks
We study the Ising spin glass model on scale-free networks generated by the
static model using the replica method. Based on the replica-symmetric solution,
we derive the phase diagram consisting of the paramagnetic (P), ferromagnetic
(F), and spin glass (SG) phases as well as the Almeida-Thouless line as
functions of the degree exponent , the mean degree , and the
fraction of ferromagnetic interactions . To reflect the inhomogeneity of
vertices, we modify the magnetization and the spin glass order parameter
with vertex-weights. The transition temperature () between the
P-F (P-SG) phases and the critical behaviors of the order parameters are found
analytically. When , and are infinite, and the
system is in the F phase or the mixed phase for , while it is in the
SG phase at . and decay as power-laws with increasing
temperature with different -dependent exponents. When ,
the and are finite and related to the percolation threshold. The
critical exponents associated with and depend on for () at the P-F (P-SG) boundary.Comment: Phys. Rev. E in pres
Predicting the size and probability of epidemics in a population with heterogeneous infectiousness and susceptibility
We analytically address disease outbreaks in large, random networks with
heterogeneous infectivity and susceptibility. The transmissibility
(the probability that infection of causes infection of ) depends on the
infectivity of and the susceptibility of . Initially a single node is
infected, following which a large-scale epidemic may or may not occur. We use a
generating function approach to study how heterogeneity affects the probability
that an epidemic occurs and, if one occurs, its attack rate (the fraction
infected). For fixed average transmissibility, we find upper and lower bounds
on these. An epidemic is most likely if infectivity is homogeneous and least
likely if the variance of infectivity is maximized. Similarly, the attack rate
is largest if susceptibility is homogeneous and smallest if the variance is
maximized. We further show that heterogeneity in infectious period is
important, contrary to assumptions of previous studies. We confirm our
theoretical predictions by simulation. Our results have implications for
control strategy design and identification of populations at higher risk from
an epidemic.Comment: 5 pages, 3 figures. Submitted to Physical Review Letter
Upper bounds for number of removed edges in the Erased Configuration Model
Models for generating simple graphs are important in the study of real-world
complex networks. A well established example of such a model is the erased
configuration model, where each node receives a number of half-edges that are
connected to half-edges of other nodes at random, and then self-loops are
removed and multiple edges are concatenated to make the graph simple. Although
asymptotic results for many properties of this model, such as the limiting
degree distribution, are known, the exact speed of convergence in terms of the
graph sizes remains an open question. We provide a first answer by analyzing
the size dependence of the average number of removed edges in the erased
configuration model. By combining known upper bounds with a Tauberian Theorem
we obtain upper bounds for the number of removed edges, in terms of the size of
the graph. Remarkably, when the degree distribution follows a power-law, we
observe three scaling regimes, depending on the power law exponent. Our results
provide a strong theoretical basis for evaluating finite-size effects in
networks
- …