Luciano R. da Silva

Spreading gossip in social networks

We study a simple model of information propagation in social networks, where two quantities are introduced: the spread factor, which measures the average maximal reachability of the neighbors of a given node that interchange information among each other, and the spreading time needed for the information to reach such a fraction of nodes. When the information refers to a particular node at which both quantities are measured, the model can be taken as a model for gossip propagation. In this context, we apply the model to real empirical networks of social acquaintances and compare the underlying spreading dynamics with different types of scale-free and small-world networks. We find that the number of friendship connections strongly influences the probability of being gossiped. Finally, we discuss how the spread factor is able to be applied to other situations.

Connection between energy spectrum, self-similarity, and specific heat log-periodicity

As a first step towards the understanding of the thermodynamical properties of quasiperiodic structures, we have performed both analytical and numerical calculations of the specific heats associated with successive hierarchical approximations to multiscale fractal energy spectra. We show that, in a certain range of temperatures, the specific heat displays log-periodic oscillations as a function of the temperature. We exhibit scaling arguments that allow for relating the mean value as well as the amplitude and the period of the oscillations to the characteristic scales of the spectrum.

Crossover from extensive to nonextensive behavior driven by long-range d=1 bond percolation

We present a Monte Carlo study of a linear chain (d=1) with long-range bonds whose occupancy probabilities are given by pij=p/rijα(0⩽p⩽1;α⩾0) where rij=1,2,… is the distance between sites. The α→∞(α=0) corresponds to the first-neighbor (“mean field”) particular case. We exhibit that the order parameter P∞ equals unity ∀p>0 for 0⩽α⩽1, presents a familiar behavior (i.e., 0 for p⩽pc(α) and finite otherwise) for 1 2. Our results confirm recent conjecture, namely that the nonextensive region (0⩽α⩽1) can be meaningfully unfolded, as well as unified with the extensive region (α>1), by exhibiting P∞ as a function of p∗ where (1−p∗)=(1−p)N∗(N∗≡(N1−α/d−1)/(1−α/d),N being the number of sites of the chain). A corollary of this conjecture, now numerically verified, is that pc∝(α−1) in the α→1+0 limit.

Minimal Path on the Hierarchical Diamond Lattice

We consider the minimal paths on a hierarchical diamond lattice, where bonds are assigned a random weight. Depending on the initial distribution of weights, we find all possible asymptotic scaling properties. The different cases found are the small-disorder case, the analog of Lévys distributions with a power-law decay at-∞, and finally a limit of large disorder which can be identified as a percolation problem. The asymptotic shape of the stable distributions of weights of the minimal path are obtained, as well as their scaling properties. As a side result, we obtain the asymptotic form of the distribution of effective percolation thresholds for finite-size hierarchical lattices.

Preferential Attachment Scale-Free Growth Model with Random Fitness and Connection with Tsallis Statistics

We introduce a network growth model in which the preferential attachment probability includes the fitness vertex and the Euclidean distance between nodes. We grow a planar network around its barycenter. Each new site is fixed in space by obeying a power law distribution.

Faceted-to-rough transition in a branching growth model

A growth model, introduced to describe the development of branched polymers in an heterogeneous environment, gives rise to clusters whose boundary is either faceted or rough. We study the transition between these two morphologies as a function of the parameters of the model. The phase diagram is obtained by direct numerical simulations. The nature of the transition is discussed.

THREE-DIMENSIONAL APOLLONIAN NETWORKS

We discuss the three-dimensional Apollonian network introduced by Andrade et al.1 for the two-dimensional case. These networks are simultaneously scale-free, small world, Euclidean, space-filling and matching graphs and have a wide range of applications going from the description of force chains in polydisperse granular packings to the geometry of fully fragmented porous media. Some of the properties of these networks, namely, the connectivity exponent, the clustering coefficient, the shortest path, and vertex betweenness are calculated and found to be particularly rich.

Self-organized percolation in multi-layered structures

We present a self-organized model for the growth of two- and three-dimensional percolation clusters in multi-layered structures. Anisotropy in the medium is modeled by randomly allocating layers of different physical properties. A controlling mechanism for the growing aggregate perimeter is introduced in such a manner that the system self-tunes to a stationary regime that corresponds to the percolation threshold. The critical probability for infinite growth is studied as a function of the anisotropy of the medium.

Do the simple and 2/3 majority models belong to the same universality class?: A monte carlo approach

We extend the majority model (introduced by Tsallis in 1982) in the sense that the required majority might be different from the simple majority. We simulate these models for typical cases which include simple and 2/3 majorities. We exhibit the average cluster size as well as the order parameter as functions ofp, the concentration of one of the two possible constituents. No crossover exists between the simple- and non-simple-majority models.

Role of dimensionality in preferential attachment growth in the Bianconi–Barabási model

Scale-free networks are quite popular nowadays since many systems are well represented by such structures. In order to study these systems, several models were proposed. However, most of them do not take into account the node-to-node Euclidean distance, i.e. the geographical distance. In real networks, the distance between sites can be very relevant, e.g. those cases where it is intended to minimize costs. Within this scenario we studied the role of dimensionality d in the Bianconi–Barabasi model with a preferential attachment growth involving Euclidean distances. The preferential attachment in this model follows the rule , where characterizes the fitness of the ith site and is randomly chosen within the interval. We verified that the degree distribution for dimensions are well fitted by , where is the q-exponential function naturally emerging within nonextensive statistical mechanics. We determine the index q and κ as functions of the quantities and d, and numerically verify that both present a universal behavior with respect to the scaled variable . The same behavior also has been displayed by the dynamical β exponent which characterizes the steadily growing number of links of a given site.