58,554 research outputs found
Modeling multi-cellular systems using sub-cellular elements
We introduce a model for describing the dynamics of large numbers of
interacting cells. The fundamental dynamical variables in the model are
sub-cellular elements, which interact with each other through phenomenological
intra- and inter-cellular potentials. Advantages of the model include i)
adaptive cell-shape dynamics, ii) flexible accommodation of additional
intra-cellular biology, and iii) the absence of an underlying grid. We present
here a detailed description of the model, and use successive mean-field
approximations to connect it to more coarse-grained approaches, such as
discrete cell-based algorithms and coupled partial differential equations. We
also discuss efficient algorithms for encoding the model, and give an example
of a simulation of an epithelial sheet. Given the biological flexibility of the
model, we propose that it can be used effectively for modeling a range of
multi-cellular processes, such as tumor dynamics and embryogenesis.Comment: 20 pages, 4 figure
Component sizes in networks with arbitrary degree distributions
We give an exact solution for the complete distribution of component sizes in
random networks with arbitrary degree distributions. The solution tells us the
probability that a randomly chosen node belongs to a component of size s, for
any s. We apply our results to networks with the three most commonly studied
degree distributions -- Poisson, exponential, and power-law -- as well as to
the calculation of cluster sizes for bond percolation on networks, which
correspond to the sizes of outbreaks of SIR epidemic processes on the same
networks. For the particular case of the power-law degree distribution, we show
that the component size distribution itself follows a power law everywhere
below the phase transition at which a giant component forms, but takes an
exponential form when a giant component is present.Comment: 5 pages, 1 figur
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
Community detection and graph partitioning
Many methods have been proposed for community detection in networks. Some of
the most promising are methods based on statistical inference, which rest on
solid mathematical foundations and return excellent results in practice. In
this paper we show that two of the most widely used inference methods can be
mapped directly onto versions of the standard minimum-cut graph partitioning
problem, which allows us to apply any of the many well-understood partitioning
algorithms to the solution of community detection problems. We illustrate the
approach by adapting the Laplacian spectral partitioning method to perform
community inference, testing the resulting algorithm on a range of examples,
including computer-generated and real-world networks. Both the quality of the
results and the running time rival the best previous methods.Comment: 5 pages, 2 figure
Globalisation and insecurity
We construct a simple model of the e¤ect of increased interna-tional openness on risk bearing in an environment in which the onlyrisk-sharing institutions are self-enforcing agreements. We showhow increased openness can weaken long-term relationships, andhence risk sharing, by increasing the e¤ectiveness of the market,much as some critics of globalization have argued. However, theharm thereby done is tempered by the fact that in order to havesuch a negative indirect e¤ect, openness must have a direct e¤ectthat reduces risk. It is shown that on balance, globalization reducesrisk and raises welfare for those in small countries, but increases riskand reduces welfare for those in large countries. We construct a simple model of the e¤ect of increased interna-tional openness on risk bearing in an environment in which the onlyrisk-sharing institutions are self-enforcing agreements. We showhow increased openness can weaken long-term relationships, andhence risk sharing, by increasing the e¤ectiveness of the market,much as some critics of globalization have argued. However, theharm thereby done is tempered by the fact that in order to havesuch a negative indirect e¤ect, openness must have a direct e¤ectthat reduces risk. It is shown that on balance, globalization reducesrisk and raises welfare for those in small countries, but increases riskand reduces welfare for those in large countries
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