Numerical assessment of the percolation threshold using complement networks

Models of percolation processes on networks currently assume locally tree-like structures at low densities, and are derived exactly only in the thermodynamic limit. Finite size effects and the presence of short loops in real systems however cause a deviation between the empirical percolation threshold $p_c$ and its model-predicted value $\pi_c$. Here we show the existence of an empirical linear relation between $p_c$ and $\pi_c$ across a large number of real and model networks. Such a putatively universal relation can then be used to correct the estimated value of $\pi_c$. We further show how to obtain a more precise relation using the concept of the complement graph, by investigating on the connection between the percolation threshold of a network, $p_c$, and that of its complement, $\bar{p}_c$

Multiple structural transitions in interacting networks

Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected networks as inter-network interactions are established. We reveal multiple structural transitions for the algebraic connectivity of such systems, between regimes in which each network layer keeps its independent identity or drives diffusive processes over the whole system, thus generalizing previous results reporting a single transition point. Furthermore we show that, at first order in perturbation theory, the growth of the algebraic connectivity of each layer depends only on the degree configuration of the interaction network (projected on the respective Fiedler vector), and not on the actual interaction topology. Our findings can have important implications in the design of robust interconnected networked system, particularly in the presence of network layers whose integrity is more crucial for the functioning of the entire system. We finally show results of perturbation theory applied to the adjacency matrix of the interconnected network, which can be useful to characterize percolation processes on such systems

Fragility and anomalous susceptibility of weakly interacting networks

Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less interlinks than the connections within each layer. For these kinds of structures, both continuous and abrupt phase transition are observed in the size of the giant component. The continuous (second-order) transition corresponds to the formation of a giant cluster inside one layer, and has a well defined percolation threshold. The abrupt transition instead corresponds to the merger of coexisting giant clusters among different layers, and is characterised by a remarkable uncertainty in the percolation threshold, which in turns causes an anomalous trend in the observed susceptibility. We develop a simple mathematical model able to describe this phenomenon and to estimate the critical threshold for which the abrupt transition is more likely to occur. Remarkably, finite-size scaling analysis in the abrupt region supports the hypothesis of a genuine first-order phase transition

Rational Fair Consensus in the GOSSIP Model

The \emph{rational fair consensus problem} can be informally defined as follows. Consider a network of $n$ (selfish) \emph{rational agents}, each of them initially supporting a \emph{color} chosen from a finite set $\Sigma$. The goal is to design a protocol that leads the network to a stable monochromatic configuration (i.e. a consensus) such that the probability that the winning color is $c$ is equal to the fraction of the agents that initially support $c$, for any $c \in \Sigma$. Furthermore, this fairness property must be guaranteed (with high probability) even in presence of any fixed \emph{coalition} of rational agents that may deviate from the protocol in order to increase the winning probability of their supported colors. A protocol having this property, in presence of coalitions of size at most $t$, is said to be a \emph{whp\,-$t$-strong equilibrium}. We investigate, for the first time, the rational fair consensus problem in the GOSSIP communication model where, at every round, every agent can actively contact at most one neighbor via a \emph{push$/$pull} operation. We provide a randomized GOSSIP protocol that, starting from any initial color configuration of the complete graph, achieves rational fair consensus within $O(\log n)$ rounds using messages of $O(\log^2n)$ size, w.h.p. More in details, we prove that our protocol is a whp\,-$t$-strong equilibrium for any $t = o(n/\log n)$ and, moreover, it tolerates worst-case permanent faults provided that the number of non-faulty agents is $\Omega(n)$. As far as we know, our protocol is the first solution which avoids any all-to-all communication, thus resulting in $o(n^2)$ message complexity.Comment: Accepted at IPDPS'1

Photometric determination of the mass accretion rates of pre-main sequence stars. VI. The case of LH 95 in the Large Magellanic Cloud

We report on the accretion properties of low-mass stars in the LH95 association within the Large Magellanic Cloud (LMC). Using non-contemporaneous wide-band and narrow-band photometry obtained with the HST, we identify 245 low-mass pre-main sequence (PMS) candidates showing H$\alpha$ excess emission above the 4$\sigma$ level. We derive their physical parameters, i.e. effective temperatures, luminosities, masses ($M_\star$), ages, accretion luminosities, and mass accretion rates ($\dot M_{\rm acc}$). We identify two different stellar populations: younger than ~8Myr with median $\dot M_{\rm acc}$~5.4x10$^{-8}M_\odot$/yr (and $M_\star$~0.15-1.8$M_\odot$) and older than ~8Myr with median $\dot M_{\rm acc}$~4.8x10$^{-9}M_\odot$/yr (and $M_\star$~0.6-1.2$M_\odot$). We find that the younger PMS candidates are assembled in groups around Be stars, while older PMS candidates are uniformly distributed within the region without evidence of clustering. We find that $\dot M_{\rm acc}$ in LH95 decreases with time more slowly than what is observed in Galactic star-forming regions (SFRs). This agrees with the recent interpretation according to which higher metallicity limits the accretion process both in rate and duration due to higher radiation pressure. The $\dot M_{\rm acc}-M_\star$ relationship shows different behaviour at different ages, becoming progressively steeper at older ages, indicating that the effects of mass and age on $\dot M_{\rm acc}$ cannot be treated independently. With the aim to identify reliable correlations between mass, age, and $\dot M_{\rm acc}$, we used for our PMS candidates a multivariate linear regression fit between these parameters. The comparison between our results with those obtained in other SFRs of our Galaxy and the MCs confirms the importance of the metallicity for the study of the $\dot M_{\rm acc}$ evolution in clusters with different environmental conditions.Comment: Accepted for publication in ApJ; 26 pages, 12 pages, 3 tables; abstract shortened. Fixed a typo in the name of a co-autho

Staggered fermions simulations on GPUs

We present our implementation of the RHMC algorithm for staggered fermions on Graphics Processing Units using the NVIDIA CUDA programming language. While previous studies exclusively deal with the Dirac matrix inversion problem, our code performs the complete MD trajectory on the GPU. After pointing out the main bottlenecks and how to circumvent them, we discuss the performance of our code.Comment: Poster presented at the XXVIII International Symposium on Lattice Field Theory, June 14-19, 2010, Villasimius, Sardinia Ital

Confinement: G2G_2 group case

The gauge group being centreless, $G_2$ gauge theory is a good laboratory for studying the role of the centre of the group for colour confinement in Yang-Mills gauge theories. In this paper, we investigate $G_2$ pure gauge theory at finite temperature on the lattice. By studying the finite size scaling of the plaquette, the Polyakov loop and their susceptibilities, we show that a deconfinement phase transition takes place. The analysis of the pseudocritical exponents give strong evidence of the deconfinement transition being first order. Implications of our findings for scenarios of colour confinement are discussed.Comment: 6 pages, 4 figures, Proceedings of the The XXV International Symposium on Lattice Field Theory, Regensburg August 200