Dynamical Properties of Interaction Data

Network dynamics are typically presented as a time series of network properties captured at each period. The current approach examines the dynamical properties of transmission via novel measures on an integrated, temporally extended network representation of interaction data across time. Because it encodes time and interactions as network connections, static network measures can be applied to this "temporal web" to reveal features of the dynamics themselves. Here we provide the technical details and apply it to agent-based implementations of the well-known SEIR and SEIS epidemiological models.Comment: 29 pages, 15 figure

X-ray sources as tracers of the large-scale structure in the Universe

We review the current status of studies of large-scale structure in the X-ray Universe. After motivating the use X-rays for cosmological purposes, we discuss the various approaches used on different angular scales including X-ray background multipoles, cross-correlations of the X-ray background with galaxy catalogues, clustering of X-ray selected sources and small-scale fluctuations and anisotropies in the X-ray background. We discuss the implications of the above studies for the bias parameter of X-ray sources, which is likely to be moderate for X-ray selected AGN and the X-ray background (~1-2). We finally outline how all-sky X-ray maps at hard X-rays and medium surveys with large sky coverage could provide important tests for the cosmological models.Comment: Invited review presented at the Workshop X-ray Astronomy'99: Stellar endpoints, AGN and the diffuse X-ray background (Astrophys Lett and Comm

Bulk Viscosity driven clusterization of quark-gluon plasma and early freeze-out in relativistic heavy-ion collisions

We introduce a new scenario for heavy ion collisions that could solve the lingering problems associated with the so-called HBT puzzle. We postulate that the system starts expansion as the perfect quark-gluon fluid but close to freeze-out it splits into clusters, due to a sharp rise of bulk viscosity in the vicinity of the hadronization transition. We then argue that the characteristic cluster size is determined by the viscosity coefficient and the expansion rate. Typically it is much smaller and independent of the total system volume. These clusters maintain the pre-existing outward-going flow, as a spray of droplets, but develop no flow of their own, and hadronize by evaporation. We provide an ansatz for converting the hydrodynamic output into clusters.Comment: Accepted for publication, Phys. Rev. C. Arguments considerably expanded, refined and reworde

Router-level community structure of the Internet Autonomous Systems

The Internet is composed of routing devices connected between them and organized into independent administrative entities: the Autonomous Systems. The existence of different types of Autonomous Systems (like large connectivity providers, Internet Service Providers or universities) together with geographical and economical constraints, turns the Internet into a complex modular and hierarchical network. This organization is reflected in many properties of the Internet topology, like its high degree of clustering and its robustness. In this work, we study the modular structure of the Internet router-level graph in order to assess to what extent the Autonomous Systems satisfy some of the known notions of community structure. We show that the modular structure of the Internet is much richer than what can be captured by the current community detection methods, which are severely affected by resolution limits and by the heterogeneity of the Autonomous Systems. Here we overcome this issue by using a multiresolution detection algorithm combined with a small sample of nodes. We also discuss recent work on community structure in the light of our results

Complex networks of earthquakes and aftershocks

We invoke a metric to quantify the correlation between any two earthquakes. This provides a simple and straightforward alternative to using space-time windows to detect aftershock sequences and obviates the need to distinguish main shocks from aftershocks. Directed networks of earthquakes are constructed by placing a link, directed from the past to the future, between pairs of events that are strongly correlated. Each link has a weight giving the relative strength of correlation such that the sum over the incoming links to any node equals unity for aftershocks, or zero if the event had no correlated predecessors. A correlation threshold is set to drastically reduce the size of the data set without losing significant information. Events can be aftershocks of many previous events, and also generate many aftershocks. The probability distribution for the number of incoming and outgoing links are both scale free, and the networks are highly clustered. The Omori law holds for aftershock rates up to a decorrelation time that scales with the magnitude, $m$, of the initiating shock as $t_{\rm cutoff} \sim 10^{\beta m}$ with $\beta \simeq 3/4$. Another scaling law relates distances between earthquakes and their aftershocks to the magnitude of the initiating shock. Our results are inconsistent with the hypothesis of finite aftershock zones. We also find evidence that seismicity is dominantly triggered by small earthquakes. Our approach, using concepts from the modern theory of complex networks, together with a metric to estimate correlations, opens up new avenues of research, as well as new tools to understand seismicity.Comment: 12 pages, 12 figures, revtex

Effects of receptor clustering on ligand dissociation: Theory and simulations

Receptor-ligand binding is a critical first step in signal transduction and the duration of the interaction can impact signal generation. In mammalian cells, clustering of receptors may be facilitated by heterogeneous zones of lipids, known as lipid rafts. In vitro experiments show that disruption of rafts significantly alters the dissociation of fibroblast growth factor-2 (FGF-2) from heparan sulfate proteoglycans, co-receptors for FGF-2. In this paper, we develop a continuum stochastic formalism in order to (i) study how rebinding affects the dissociation of ligands from a planar substrate, and (ii) address the question of how receptor clustering influences ligand rebinding. We find that clusters reduce the effective dissociation rate dramatically when the clusters are dense and the overall surface density of receptors is low. The effect is much less pronounced in the case of high receptor density and shows non-monotonic behavior with time. These predictions are verified via lattice Monte Carlo simulations. Comparison with experimental results suggests that the theory does not capture the complete biological system. We speculate that additional co-operative mechanisms might be present in order to increase ligand retention, and present one possible ``internal diffusion'' model.Comment: Expanded text and added figures, revised version to appear in Biophys.