37,097 research outputs found
Optimization in Gradient Networks
Gradient networks can be used to model the dominant structure of complex
networks. Previous works have focused on random gradient networks. Here we
study gradient networks that minimize jamming on substrate networks with
scale-free and Erd\H{o}s-R\'enyi structure. We introduce structural
correlations and strongly reduce congestion occurring on the network by using a
Monte Carlo optimization scheme. This optimization alters the degree
distribution and other structural properties of the resulting gradient
networks. These results are expected to be relevant for transport and other
dynamical processes in real network systems.Comment: 5 pages, 4 figure
Quantifying metastatic inefficiency:rare genotypes versus rare dynamics
abstract: We introduce and solve a ânull modelâ of stochastic metastatic colonization. The model is described by a single parameter θ: the ratio of the rate of cell division to the rate of cell death for a disseminated tumour cell in a given secondary tissue environment. We are primarily interested in the case in which colonizing cells are poorly adapted for proliferation in the local tissue environment, so that cell death is more likely than cell division, i.e. θ 1), i.e. the statistics show a duality mapping (1 â θ) â (θ â 1). We conclude our analysis with a study of heterogeneity in the fitness of colonising cells, and describe a phase diagram delineating parameter regions in which metastatic colonization is dominated either by low or high fitness cells, showing that both are plausible given our current knowledge of physiological conditions in human cancer
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
A tutorial task and tertiary courseware model for collaborative learning communities
RAED provides a computerised infrastructure to support the development and administration of Vicarious Learning in collaborative learning communities spread across multiple universities and workplaces. The system is based on the OASIS middleware for Role-based Access Control. This paper describes the origins of the model and the approach to implementation and outlines some of its benefits to collaborative teachers and learners
The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V
We construct a braided version of Thompson's group V.Comment: 27 page
Mean-field solution of the small-world network model
The small-world network model is a simple model of the structure of social
networks, which simultaneously possesses characteristics of both regular
lattices and random graphs. The model consists of a one-dimensional lattice
with a low density of shortcuts added between randomly selected pairs of
points. These shortcuts greatly reduce the typical path length between any two
points on the lattice. We present a mean-field solution for the average path
length and for the distribution of path lengths in the model. This solution is
exact in the limit of large system size and either large or small number of
shortcuts.Comment: 14 pages, 2 postscript figure
Clustering and preferential attachment in growing networks
We study empirically the time evolution of scientific collaboration networks
in physics and biology. In these networks, two scientists are considered
connected if they have coauthored one or more papers together. We show that the
probability of scientists collaborating increases with the number of other
collaborators they have in common, and that the probability of a particular
scientist acquiring new collaborators increases with the number of his or her
past collaborators. These results provide experimental evidence in favor of
previously conjectured mechanisms for clustering and power-law degree
distributions in networks.Comment: 13 pages, 2 figure
Characterizing the structure of small-world networks
We give exact relations which are valid for small-world networks (SWN's) with
a general `degree distribution', i.e the distribution of nearest-neighbor
connections. For the original SWN model, we illustrate how these exact
relations can be used to obtain approximations for the corresponding basic
probability distribution. In the limit of large system sizes and small
disorder, we use numerical studies to obtain a functional fit for this
distribution. Finally, we obtain the scaling properties for the mean-square
displacement of a random walker, which are determined by the scaling behavior
of the underlying SWN
The first-mover advantage in scientific publication
Mathematical models of the scientific citation process predict a strong
"first-mover" effect under which the first papers in a field will, essentially
regardless of content, receive citations at a rate enormously higher than
papers published later. Moreover papers are expected to retain this advantage
in perpetuity -- they should receive more citations indefinitely, no matter how
many other papers are published after them. We test this conjecture against
data from a selection of fields and in several cases find a first-mover effect
of a magnitude similar to that predicted by the theory. Were we wearing our
cynical hat today, we might say that the scientist who wants to become famous
is better off -- by a wide margin -- writing a modest paper in next year's
hottest field than an outstanding paper in this year's. On the other hand,
there are some papers, albeit only a small fraction, that buck the trend and
attract significantly more citations than theory predicts despite having
relatively late publication dates. We suggest that papers of this kind, though
they often receive comparatively few citations overall, are probably worthy of
our attention.Comment: 7 pages, 3 figure
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