Renormalization group analysis of the small-world network model

We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a divergent correlation length as the degree of randomness tends to zero. We propose a real-space renormalization group transformation for the model and demonstrate that the transformation is exact in the limit of large system size. We use this result to calculate the exact value of the single critical exponent for the system, and to derive the scaling form for the average number of "degrees of separation" between two nodes on the network as a function of the three independent variables. We confirm our results by extensive numerical simulation.Comment: 4 pages including 3 postscript figure

Hardcore classification: identifying play styles in social games using network analysis

In the social network of a web-based online game, all players are not equal. Through network analysis, we show that the community of players in a online social game is an example of a scale free small world network and that the growth of the player-base obeys a power law. The community is centred around a minority group of ``hardcore" players who define the social environment for the game, and without whom the social network would collapse. Methods are discussed for identifying this critically important subset of players automatically through analysing social behaviours within the game

Cell cycle-related changes in the surface properties of amoebae of the cellular slime mould Dictyostelium discoideum

AbstractAmoebae of the cellular slime mould Dictyostelium discoideum were harvested during exponential, axenic growth and were partitioned in a dextran-poly(ethylene glycol) two-phase system in a countercurrent distribution apparatus. Amoebae in G1-, S- and G2-phases of the cell cycle were located in different parts of the countercurrent distribution. Since partitioning separates cells with different surface properties, it is concluded that there are cell cycle-related changes in the surface properties, and thus plasma membrane structure, of the amoebae

Statistical and Dynamical Study of Disease Propagation in a Small World Network

We study numerically statistical properties and dynamical disease propagation using a percolation model on a one dimensional small world network. The parameters chosen correspond to a realistic network of school age children. We found that percolation threshold decreases as a power law as the short cut fluctuations increase. We found also the number of infected sites grows exponentially with time and its rate depends logarithmically on the density of susceptibles. This behavior provides an interesting way to estimate the serology for a given population from the measurement of the disease growing rate during an epidemic phase. We have also examined the case in which the infection probability of nearest neighbors is different from that of short cuts. We found a double diffusion behavior with a slower diffusion between the characteristic times.Comment: 12 pages LaTex, 10 eps figures, Phys.Rev.E Vol. 64, 056115 (2001

Epidemics and percolation in small-world networks

We study some simple models of disease transmission on small-world networks, in which either the probability of infection by a disease or the probability of its transmission is varied, or both. The resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network, and we give exact solutions for the position of this threshold in a variety of cases. We confirm our analytic results by numerical simulation.Comment: 6 pages, including 3 postscript figure

Conservation of structure and mechanism in primary and secondary transporters exemplified by SiaP, a sialic acid binding virulence factor from Haemophilus influenzae

Extracytoplasmic solute receptors (ESRs) are important components of solute uptake systems in bacteria, having been studied extensively as parts of ATP binding cassette transporters. Herein we report the first crystal structure of an ESR protein from a functionally characterized electrochemical ion gradient-dependent secondary transporter. This protein, SiaP, forms part of a tripartite ATP-independent periplasmic transporter specific for sialic acid in Haemophilus influenzae. Surprisingly, the structure reveals an overall topology similar to ATP binding cassette ESR proteins, which is not apparent from the sequence, demonstrating that primary and secondary transporters can share a common structural component. The structure of SiaP in the presence of the sialic acid analogue 2,3-didehydro-2-deoxyN-acetylneuraminic acid reveals the ligand bound in a deep cavity with its carboxylate group forming a salt bridge with a highly conserved Arg residue. Sialic acid binding, which obeys simple bimolecular association kinetics as determined by stopped-flow fluorescence spectroscopy, is accompanied by domain closure about a hinge region and the kinking of an alpha-helix hinge component. The structure provides insight into the evolution, mechanism, and substrate specificity of ESR-dependent secondary transporters that are widespread in prokaryotes

Numerical Investigation of Graph Spectra and Information Interpretability of Eigenvalues

We undertake an extensive numerical investigation of the graph spectra of thousands regular graphs, a set of random Erd\"os-R\'enyi graphs, the two most popular types of complex networks and an evolving genetic network by using novel conceptual and experimental tools. Our objective in so doing is to contribute to an understanding of the meaning of the Eigenvalues of a graph relative to its topological and information-theoretic properties. We introduce a technique for identifying the most informative Eigenvalues of evolving networks by comparing graph spectra behavior to their algorithmic complexity. We suggest that extending techniques can be used to further investigate the behavior of evolving biological networks. In the extended version of this paper we apply these techniques to seven tissue specific regulatory networks as static example and network of a na\"ive pluripotent immune cell in the process of differentiating towards a Th17 cell as evolving example, finding the most and least informative Eigenvalues at every stage.Comment: Forthcoming in 3rd International Work-Conference on Bioinformatics and Biomedical Engineering (IWBBIO), Lecture Notes in Bioinformatics, 201

Topological Properties of Citation and Metabolic Networks

Topological properties of "scale-free" networks are investigated by determining their spectral dimensions $d_S$, which reflect a diffusion process in the corresponding graphs. Data bases for citation networks and metabolic networks together with simulation results from the growing network model \cite{barab} are probed. For completeness and comparisons lattice, random, small-world models are also investigated. We find that $d_S$ is around 3 for citation and metabolic networks, which is significantly different from the growing network model, for which $d_S$ is approximately 7.5. This signals a substantial difference in network topology despite the observed similarities in vertex order distributions. In addition, the diffusion analysis indicates that whereas the citation networks are tree-like in structure, the metabolic networks contain many loops.Comment: 11 pages, 3 figure

Growing dynamics of Internet providers

In this paper we present a model for the growth and evolution of Internet providers. The model reproduces the data observed for the Internet connection as probed by tracing routes from different computers. This problem represents a paramount case of study for growth processes in general, but can also help in the understanding the properties of the Internet. Our main result is that this network can be reproduced by a self-organized interaction between users and providers that can rearrange in time. This model can then be considered as a prototype model for the class of phenomena of aggregation processes in social networks