The Strong-Coupling Expansion in Simplicial Quantum Gravity

We construct the strong-coupling series in 4d simplicial quantum gravity up to volume 38. It is used to calculate estimates for the string susceptibility exponent gamma for various modifications of the theory. It provides a very efficient way to get a first view of the phase structure of the models.Comment: LATTICE98(surfaces), 3 pages, 4 eps figure

Random manifolds and quantum gravity

The non-perturbative, lattice field theory approach towards the quantization of Euclidean gravity is reviewed. Included is a tentative summary of the most significant results and a presentation of the current state of art.Comment: invited plenary talk at LATTICE '99 (Pisa), latex 5p

Phase transition and topology in 4d simplicial gravity

We present data indicating that the recent evidence for the phase transition being of first order does not result from a breakdown of the ergodicity of the algorithm. We also present data showing that the thermodynamical limit of the model is independent of topology.Comment: 3 latex pages + 4 ps fig. + espcrc2.sty. Talk presented at LATTICE(gravity

4d Simplicial Quantum Gravity Interacting with Gauge Matter Fields

The effect of coupling non-compact $U(1)$ gauge fields to four dimensional simplicial quantum gravity is studied using strong coupling expansions and Monte Carlo simulations. For one gauge field the back-reaction of the matter on the geometry is weak. This changes, however, as more matter fields are introduced. For more than two gauge fields the degeneracy of random manifolds into branched polymers does not occur, and the branched polymer phase seems to be replaced by a new phase with a negative string susceptibility exponent $\gamma$ and fractal dimension $d_H \approx 4$.Comment: latex2e, 10 pages incorporating 2 tables and 3 figures (using epsf

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

Crumpled triangulations and critical points in 4D simplicial quantum gravity

This is an expanded and revised version of our geometrical analysis of the strong coupling phase of 4D simplicial quantum gravity. The main differences with respect to the former version is a full discussion of singular triangulations with singular vertices connected by a subsingular edge. In particular we provide analytical arguments which characterize the entropical properties of triangulations with a singular edge connecting two singular vertices. The analytical estimate of the location of the critical coupling at k_2\simeq 1.3093 is presented in more details. Finally we also provide a model for pseudo-criticality at finite N_4(S^4).Comment: 44 page

The Strange Man in Random Networks of Automata

We have performed computer simulations of Kauffman's automata on several graphs such as the regular square lattice and invasion percolation clusters in order to investigate phase transitions, radial distributions of the mean total damage (dynamical exponent $z$) and propagation speeds of the damage when one adds a damaging agent, nicknamed "strange man". Despite the increase in the damaging efficiency, we have not observed any appreciable change at the transition threshold to chaos neither for the short-range nor for the small-world case on the square lattices when the strange man is added in comparison to when small initial damages are inserted in the system. The propagation speed of the damage cloud until touching the border of the system in both cases obeys a power law with a critical exponent $\alpha$ that strongly depends on the lattice. Particularly, we have ckecked the damage spreading when some connections are removed on the square lattice and when one considers special invasion percolation clusters (high boundary-saturation clusters). It is seen that the propagation speed in these systems is quite sensible to the degree of dilution.Comment: AMS-LaTeX v1.2, 7 pages with 14 figures Encapsulated Postscript, to be publishe

The Kauffman model on Small-World Topology

We apply Kauffman's automata on small-world networks to study the crossover between the short-range and the infinite-range case. We perform accurate calculations on square lattices to obtain both critical exponents and fractal dimensions. Particularly, we find an increase of the damage propagation and a decrease in the fractal dimensions when adding long-range connections.Comment: AMS-LaTeX v1.2, 8 pages with 8 figures Encapsulated Postscript, to be published in Physica

Detecting Community Structure in Dynamic Social Networks Using the Concept of Leadership

Detecting community structure in social networks is a fundamental problem empowering us to identify groups of actors with similar interests. There have been extensive works focusing on finding communities in static networks, however, in reality, due to dynamic nature of social networks, they are evolving continuously. Ignoring the dynamic aspect of social networks, neither allows us to capture evolutionary behavior of the network nor to predict the future status of individuals. Aside from being dynamic, another significant characteristic of real-world social networks is the presence of leaders, i.e. nodes with high degree centrality having a high attraction to absorb other members and hence to form a local community. In this paper, we devised an efficient method to incrementally detect communities in highly dynamic social networks using the intuitive idea of importance and persistence of community leaders over time. Our proposed method is able to find new communities based on the previous structure of the network without recomputing them from scratch. This unique feature, enables us to efficiently detect and track communities over time rapidly. Experimental results on the synthetic and real-world social networks demonstrate that our method is both effective and efficient in discovering communities in dynamic social networks

Focusing on the Fixed Point of 4D Simplicial Gravity

Our earlier renormalization group analysis of simplicial gravity is extended. A high statistics study of the volume and coupling constant dependence of the cumulants of the node distribution is carried out. It appears that the phase transition of the theory is of first order, contrary to what is generally believed.Comment: Latex, 20 pages, 6 postscript figures, published versio