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J F Mendes

Publications and source records attributed to J F Mendes.

13 recordsLinked to original sources
PubMed2001

Language as an evolving word web.

Human language may be described as a complex network of linked words. In such a treatment, each distinct word in language is a vertex of this web, and interacting words in sentences are connected by edges. The empirical distribution of the number of connections of words in this network is of a peculiar form that includes two pronounced power-law regions. Here we propose a theory of the evolution of language, which treats language as a self-organizing network of interacting words. In the framework of this concept, we completely describe the observed word web structure without any fitting. We show that the two regimes in the distribution naturally emerge from the evolutionary dynamics of the word web. It follows from our theory that the size of the core part of language, the 'kernel lexicon', does not vary as language evolves.

Humans↗
PubMed2001

Anomalous percolation properties of growing networks.

We describe the anomalous phase transition of the emergence of the giant connected component in scale-free networks growing under mechanism of preferential linking. We obtain exact results for the size of the giant connected component and the distribution of vertices among connected components. We show that all the derivatives of the giant connected component size S over the rate b of the emergence of new edges are zero at the percolation threshold b(c), and S infinity exp[-d(gamma)(b-b(c))(-1/2)], where the coefficient d is a function of the degree distribution exponent gamma. In the entire phase without the giant component, these networks are in a "critical state." The probability P(k) that a vertex belongs to a connected component of a size k is of a power-law form. At the phase transition point, P(k) approximately 1/(k ln k)(2). In the phase with the giant component, P(k) has an exponential cutoff at k(c) approximately 1/S. In the simplest particular case, we present exact results for growing exponential networks.

Journal Article↗
PubMed2001

Giant strongly connected component of directed networks.

We describe how to calculate the sizes of all giant connected components of a directed graph, including the strongly connected one. In particular, the World Wide Web is a directed network. The results are obtained for graphs with statistically uncorrelated vertices and an arbitrary joint in and out-degree distribution P(k(i),k(o)). We show that if P(k(i),k(o)) does not factorize, the relative size of the giant strongly connected component deviates from the product of the relative sizes of the giant in- and out-components. The calculations of the relative sizes of all the giant components are demonstrated using the simplest examples. We explain that the giant strongly connected component may be less resilient to random damage than the giant weakly connected one.

Journal Article↗
PubMed2001

Size-dependent degree distribution of a scale-free growing network.

We propose the simplest model of scale-free growing networks and obtain the exact form of its degree distribution for any size of the network (degree is a number of connections of a node). We demonstrate that a trace of initial conditions - a hump near cutoff of the degree distribution at k(cut) approximately t(beta)--may be found for any network size. Here beta=1/(gamma-1), where gamma is the exponent of the degree distribution of the network. These size effects implement a natural boundary for the observation of the scale-free networks.

Journal Article↗
PubMed2001

Scaling properties of scale-free evolving networks: continuous approach.

The scaling behavior of scale-free evolving networks, arising in areas such as communications, scientific citations, collaborations, etc., is studied. We derive universal scaling relations describing properties of such networks, and indicate the limits of their validity. We show that the main properties of scale-free evolving networks may be described in the framework of a simple continuous approach. The simplest models of networks, growing according to a mechanism of preferential attachment of links to nodes, are used. We consider different forms of this preference, and demonstrate that the range of preferential attachments producing scale-free networks is wide. We also obtain scaling relations for networks with nonlinear, accelerating growth, and describe the temporal evolution of the arising distributions. Size effects-the cutoffs of these distributions-introduce restrictions for the observation of power-law dependences. Mainly we discuss the so-called degree distribution, i.e., the distribution of the number of connections of nodes. A scaling form of the distribution of links between pairs of individual nodes for a growing network of citations is also studied. We describe the effects of differences between nodes. The "aging" of nodes changes the exponents of the distributions. The appearance of a single node with high fitness changes the degree distribution of a network dramatically. If its fitness exceeds some threshold value, this node captures a finite part of all links of the network. We show that permanent random damage to a growing scale-free network-a permanent deletion of some links-radically changes the values of the scaling exponents. Results of other kinds of permanent damage are described.

Journal Article↗
PubMed2001

Anomalous behavior of the contact process with aging.

The effect of power-law aging on a contact process is studied by simulation and using a mean-field approach. The introduced type of aging accounts for, e.g., the growth of the virus fitness (HIV infection). We find that the system may approach its stationary state in a nontrivial, nonmonotonous way. For the particular value of the aging exponent alpha=1 we observe a rich set of behaviors: depending on the process parameters, the relaxation to the stationary state proceeds as 1/ln t or via a power law with a nonuniversal exponent. Simulation results suggest that for 0<alpha<1, the absorbing-state phase transition is in the universality class of directed percolation.

Journal Article↗
PubMed2001

Effect of the accelerating growth of communications networks on their structure.

Motivated by data on the evolution of the Internet and World Wide Web we consider scenarios of self-organization of nonlinearly growing networks into free-scale structures. We find that the accelerating growth of networks establishes their structure. For growing networks with preferential linking and increasing density of links, two scenarios are possible. In one of them, the value of the exponent gamma of the distribution of the number of incoming links is between 3/2 and 2. In the other scenario, gamma>2 and the distribution is necessarily nonstationary.

Journal Article↗
PubMed2000

Structure of growing networks with preferential linking.

The model of growing networks with the preferential attachment of new links is generalized to include initial attractiveness of sites. We find the exact form of the stationary distribution of the number of incoming links of sites in the limit of long times, P(q), and the long-time limit of the average connectivity q(s,t) of a site s at time t (one site is added per unit of time). At long times, P(q) approximately q(-gamma) at q-->infinity and q(s,t) approximately (s/t)(-beta) at s/t-->0, where the exponent gamma varies from 2 to infinity depending on the initial attractiveness of sites. We show that the relation beta(gamma-1) = 1 between the exponents is universal.

Algorithms↗
PubMed1999

Vortex dynamics in a three-state model under cyclic dominance.

The evolution of domain structure is investigated in a two-dimensional voter model with three states under cyclic dominance. The study focus on the dynamics of vortices, defined by the points where the three states (domains) meet. We can distinguish vortices and antivortices which walk randomly and annihilate each other. The domain wall motion can create vortex-antivortex pairs at a rate that is increased by the spiral formation due to cyclic dominance. This mechanism is contrasted with a branching annihilating random walk (BARW) in a particle-antiparticle system with density-dependent pair creation rate. Numerical estimates for the critical indices of the vortex density [beta=0.29(4)] and of its fluctuation [gamma=0.34(6)] improve an earlier Monte Carlo study [K. Tainaka and Y. Itoh, Europhys. Lett. 15, 399 (1991)] of the three-state cyclic model in two dimensions.

Journal Article↗