Number of loops of size h in growing scale-free networks

The hierarchical structure of scale-free networks has been investigated focusing on the scaling of the number $N_h(t)$ of loops of size h as a function of the system size. In particular we have found the analytic expression for the scaling of $N_h(t)$ in the Barab\'asi-Albert (BA) scale-free network. We have performed numerical simulations on the scaling law for $N_h(t)$ in the BA network and in other growing scale free networks, such as the bosonic network (BN) and the aging nodes (AN) network. We show that in the bosonic network and in the aging node network the phase transitions in the topology of the network are accompained by a change in the scaling of the number of loops with the system size.Comment: 4 pages, 3 figure

Computation of the conformal algebra of 1+3 decomposable spacetimes

The conformal algebra of a 1+3 decomposable spacetime can be computed from the conformal Killing vectors (CKV) of the 3-space. It is shown that the general form of such a 3-CKV is the sum of a gradient CKV and a Killing or homothetic 3-vector. It is proved that spaces of constant curvature always admit such conformal Killing vectors. As an example, the complete conformal algebra of a G\"odel-type spacetime is computed. Finally it is shown that this method can be extended to compute the conformal algebra of more general non-decomposable spacetimes.Comment: 15 pages Latex, no figures. Minor mistakes correcte

Quantitative description and modeling of real networks

In this letter we present data analysis and modeling of two particular cases of study in the field of growing networks. We analyze WWW data set and authorship collaboration networks in order to check the presence of correlation in the data. The results are reproduced with a pretty good agreement through a suitable modification of the standard AB model of network growth. In particular, intrinsic relevance of sites plays a role in determining the future degree of the vertex.Comment: 4 pages, 3 figure

Diversification and limited information in the Kelly game

Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the classic Kelly investment game [Kelly (1956)] that incorporates these features, and use them to investigate the influence of diversification and limited information on Kelly-optimal portfolios. In particular we present approximate formulas for optimizing diversified portfolios and exact results for optimal investment in unknown games where the only available information is past outcomes.Comment: 11 pages, 4 figure

Analysis of weighted networks

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure

The Conformal Penrose Limit and the Resolution of the pp-curvature Singularities

We consider the exact solutions of the supergravity theories in various dimensions in which the space-time has the form M_{d} x S^{D-d} where M_{d} is an Einstein space admitting a conformal Killing vector and S^{D-d} is a sphere of an appropriate dimension. We show that, if the cosmological constant of M_{d} is negative and the conformal Killing vector is space-like, then such solutions will have a conformal Penrose limit: M^{(0)}_{d} x S^{D-d} where M^{(0)}_{d} is a generalized d-dimensional AdS plane wave. We study the properties of the limiting solutions and find that M^{(0)}_{d} has 1/4 supersymmetry as well as a Virasoro symmetry. We also describe how the pp-curvature singularity of M^{(0)}_{d} is resolved in the particular case of the D6-branes of D=10 type IIA supergravity theory. This distinguished case provides an interesting generalization of the plane waves in D=11 supergravity theory and suggests a duality between the SU(2) gauged d=8 supergravity of Salam and Sezgin on M^{(0)}_{8} and the d=7 ungauged supergravity theory on its pp-wave boundary.Comment: 20 pages, LaTeX; typos corrected, journal versio

Introduction

Drugs are at the centre of a complexly entangled web of science, politics, economics and culture. They are the product of scientific in- novation, and are usually brought to the bedside by private com- panies, following regulations issued by national and international authorities. These regulations are in turn the product of health poli- cies usually reflecting local cultures and ideologies

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

Cliques and duplication-divergence network growth

A population of complete subgraphs or cliques in a network evolving via duplication-divergence is considered. We find that a number of cliques of each size scales linearly with the size of the network. We also derive a clique population distribution that is in perfect agreement with both the simulation results and the clique statistic of the protein-protein binding network of the fruit fly. In addition, we show that such features as fat-tail degree distribution, various rates of average degree growth and non-averaging, revealed recently for only the particular case of a completely asymmetric divergence, are present in a general case of arbitrary divergence.Comment: 7 pages, 6 figure

Scale-Free networks from varying vertex intrinsic fitness

A new mechanism leading to scale-free networks is proposed in this Letter. It is shown that, in many cases of interest, the connectivity power-law behavior is neither related to dynamical properties nor to preferential attachment. Assigning a quenched fitness value xi to every vertex, and drawing links among vertices with a probability depending on the fitnesses of the two involved sites, gives rise to what we call a good-get-richer mechanism, in which sites with larger fitness are more likely to become hubs (i.e., to be highly connected)