Publications

Correlations In Scale-Free Networks

Bruno Miguel Tavares Gonçalves
Departamento de Física
Universidade de Aveiro

Abstract:

The study of connectivity correlations between nodes has been somewhat neglected in the study of Complex Networks. We try to correct this by using the correlation function, combined with the concept of shell to calculate the connectivity distribution, $ P^{(d)}(k)$ and the average connectivity for the neighbours, $ \langle k_{nn}^{(d)}(k)\rangle$ of a node as a function of distance $ d$. With these results we create a better idea of how the Internet is organized and structured. We also determine that the time evolution of the Internet is coherent with the results obtained in the literature for the case of accelerated growth by the process of edge copying with a probability $ p=0.58$.

Crescimentos Epitaxiais e Interacções Elásticas

Bruno Miguel Tavares Gonçalves
Departamento de Física
Faculdade de Ciências da Universidade do Porto

 

Monte Carlo study of the elastic interaction in heteropitaxial growth

B. M. T. Gonçalves$^\ast$ and J. F. F. Mendes$^\dagger$

Departamento de Física da Universidade do Porto
Centro de Física do Porto, Rua do Campo Alegre, 687

4169-007 Porto, Portugal

 

Abstract

We have studied the island size distribution and spatial correlation function of an island growth model under the effect of an elastic interaction of the form $1/r^{3}$. The mass distribution $P_n(t)$ that was obtained presents a pronounced peak that widens with the increase of the total coverage of the system, $\theta$. The presence of this peak is an indication of the self-organization of the system, since it demonstrates that some sizes are more frequent than others. We have treated exactly the energy of the system using periodic boundary conditions which were used in the Monte-Carlo simulations. A discussion about the effect of different factors is presented.

 

Ensemble inequivalence in random graphs

Julien Barré1 and B. Gonçalves2

1Laboratoire J.-A. Dieudonne, Universite de Nice-Sophia Antipolis
Parc Valrose, 06108 Nice Cedex 02, France

2Physics Department, Emory Univeristy
Atlanta, Georgia, 30322, USA

 

AbstractTop

We present a complete analytical solution of a system of Potts spins on a random $ k$ -regular graph in both the canonical and microcanonical ensembles, using the Large Deviation Cavity Method (LDCM). The solution is shown to be composed of three different branches, resulting in an non-concave entropy function.The analytical solution is confirmed with numerical Metropolis and Creutz simulations and our results clearly demonstrate the presence of a region with negative specific heat and, consequently, ensemble inequivalence between the canonical and microcanonical ensembles.

 

Transport on weighted Networks:
when the correlations are independent of the degree<

José J. Ramasco1 and Bruno Gonçalves2
1CNLL, ISI Foundation, Viale S. Severo 65, I-10133 Torino, Italy
2Physics Department, Emory University, Atlanta, Georgia 30322, USA

AbstractTop

Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the correlations beyond the degree dependent case. We propose a simple method to introduce weight-weight correlations in topologically uncorrelated graphs. This allows us to test different measures to discriminate between the different correlation types and to quantify their intensity. We also discuss here the effect of weight correlations on the transport properties of the networks, showing that positive correlations dramatically improve transport. Finally, we give two examples of real-world networks (social and transport graphs) in which weight-weight correlations are present.

 

Hysteretic Optimization For Spin Glasses

B. Gonçalves and S. Boettcher

Emory University, Atlanta, Ga 30322

AbstractTop

The recently proposed Hysteretic Optimization (HO) procedure is applied to the $1D$ Ising spin chain with long range interactions. To study its effectiveness , the quality of ground state energies found as a function of the distance dependence exponent, $\sigma $, is assessed. It is found that the transition from an infinite-range to a long-range interaction at $\sigma=0.5$ is accompanied by a sharp decrease in the performance . The transition is signaled by a change in the scaling behavior of the average avalanche size observed during the hysteresis process. This indicates that HO requires the system to be infinite-range, with a high degree of interconnectivity between variables leading to large avalanches, in order to function properly. An analysis of the way auto-correlations evolve during the optimization procedure confirm that the search of phase space is less efficient, with the system becoming effectively stuck in suboptimal configurations much earlier. These observations explain the poor performance that HO obtained for the Edwards-Anderson spin glass on finite-dimensional lattices, and suggest that its usefulness might be limited in many combinatorial optimization problems.

Magnetic Reversal Time in Open Long Range Systems

F. Borgonovi1,2, G. L. Celardo3, B. Goncalves4 and L. Spadafora1

1Dipartimento di Matematica e Fisica, Università Cattolica, via Musei 41, 25121, Brescia, Italy
2I.N.F.N., Sezione di Pavia, Italy
3Instituto de Fisica, Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
4Emory University, Atlanta USA

AbstractTop

Topological phase space disconnection has been recently found to be a general phenomenon in isolated anisotropic spin systems. It sets a general framework to understand the emergence of ferromagnetism in finite magnetic systems starting from microscopic models without phenomenological on-site barriers. Here we study its relevance for finite systems with long range interacting potential in contact with a thermal bath. We show that, even in this case, the induced magnetic reversal time is exponentially large in the number of spins, thus determining stable (to any experimental observation time) ferromagnetic behavior. Moreover, the explicit temperature dependence of the magnetic reversal time obtained from the microcanonical results, is found to be in good agreement with numerical simulations. Also, a simple and suggestive expression, indicating the Topological Energy Threshold at which the disconnection occurs, as a real energy barrier for many body systems, is obtained analytically for low temperature.

 



 

© Copyright 2004-2007 Bruno Goncalves - All rights reserved

Valid XhtmlValid CSS