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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