Displaying similar documents to “Modular dynamical systems on networks”

Approximation algorithms for the design of SDH/SONET networks

Nadia Brauner, Yves Crama, Gerd Finke, Pierre Lemaire, Christelle Wynants (2010)

RAIRO - Operations Research

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In this paper, a graph partitioning problem that arises in the design of SONET/SDH networks is defined and formalized. Approximation algorithms with performance guarantees are presented. To solve this problem efficiently in practice, fast greedy algorithms and a tabu-search method are proposed and analyzed by means of an experimental study.

Using R to Build and Assess Network Models in Biology

G. Hartvigsen (2011)

Mathematical Modelling of Natural Phenomena

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In this paper we build and analyze networks using the statistical and programming environment R and the igraph package. We investigate random, small-world, and scale-free networks and test a standard problem of connectivity on a random graph. We then develop a method to study how vaccination can alter the structure of a disease transmission network. We also discuss a variety of other uses for networks in biology.

An advance in infinite graph models for the analysis of transportation networks

Martín Cera, Eugenio M. Fedriani (2016)

International Journal of Applied Mathematics and Computer Science

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This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing a given subgraph. It also relates the new results with the corresponding situations for the finite case. In particular, concepts from ‘finite' graph theory, like the average degree and the extremal number, are generalized and computed for some specific cases. Finally, some applications of infinite graphs to the transportation...

Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory

R. E. Lee DeVille, C. S. Peskin, J. H. Spencer (2010)

Mathematical Modelling of Natural Phenomena

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We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition...

Spaces of ω-limit sets of graph maps

Jie-Hua Mai, Song Shao (2007)

Fundamenta Mathematicae

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Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.