arXiv subjects

Romualdo Pastor-Satorras

Publications and source records attributed to Romualdo Pastor-Satorras.

At least 73 records · Page 4Linked to original sources

arXiv2013

The Biological Origin of Linguistic Diversity

In contrast with animal communication systems, diversity is characteristic of almost every aspect of human language. Languages variously employ tones, clicks, or manual signs to signal differences in meaning; some languages lack the noun-verb distinction (e.g., Straits Salish), whereas others have a proliferation of fine-grained syntactic categories (e.g., Tzeltal); and some languages do without morphology (e.g., Mandarin), while others pack a whole sentence into a single word (e.g., Cayuga). A challenge for evolutionary biology is to reconcile the diversity of languages with the high degree of biological uniformity of their speakers. Here, we model processes of language change and geographical dispersion and find a consistent pressure for flexible learning, irrespective of the language being spoken. This pressure arises because flexible learners can best cope with the observed high rates of linguistic change associated with divergent cultural evolution following human migration. Thus, rather than genetic adaptations for specific aspects of language, such as recursion, the coevolution of genes and fast-changing linguistic structure provides the biological basis for linguistic diversity. Only biological adaptations for flexible learning combined with cultural evolution can explain how each child has the potential to learn any human language.

physics.soc-ph↗

arXiv2013

Phase transitions with infinitely many absorbing states in complex networks

We instigate the properties of the threshold contact process (TCP), a process showing an absorbing-state phase transition with infinitely many absorbing states, on random complex networks. The finite size scaling exponents characterizing the transition are obtained in a heterogeneous mean field (HMF) approximation and compared with extensive simulations, particularly in the case of heterogeneous scale-free networks. We observe that the TCP exhibits the same critical properties as the contact process (CP), which undergoes an absorbing-state phase transition to a single absorbing state. The accordance among the critical exponents of different models and networks leads to conjecture that the critical behavior of the contact process in a HMF theory is a universal feature of absorbing state phase transitions in complex networks, depending only on the locality of the interactions and independent of the number of absorbing states. The conditions for the applicability of the conjecture are discussed considering a parallel with the susceptible-infected-susceptible epidemic spreading model, which in fact belongs to a different universality class in complex networks.

cond-mat.stat-mech↗

arXiv2013

Mean-field analysis of the q-voter model on networks

We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations.

physics.soc-ph↗

arXiv2013

Random walks and search in time-varying networks

The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale. We consider a model for time varying networks created from the activity potential of the nodes, and derive solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks. Our findings show striking differences with respect to the well known results obtained in quenched and annealed networks, emphasizing the effects of dynamical connectivity patterns in the definition of proper strategies for search, retrieval and diffusion processes in time-varying networks

cond-mat.stat-mech↗

arXiv2012

Universal and non-universal features of the generalized voter class for ordering dynamics

By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [I. Dornic, \textit{et al.} Phys. Rev. Lett. \textbf{87}, 045701 (2001)], we show that they behave differently from the linear voter model when the initial configuration is an unbalanced mixture up and down spins. In particular we show that for nonlinear voter models the exit probability (probability to end with all spins up when starting with an initial fraction $x$ of them) assumes a nontrivial shape. The change is traced back to the strong nonconservation of the average magnetization during the early stages of dynamics. Also the time needed to reach the final consensus state $T_N(x)$ has an anomalous nonuniversal dependence on $x$.

cond-mat.stat-mech↗

arXiv2012

Ordering dynamics of the multi-state voter model

The voter model is a paradigm of ordering dynamics. At each time step, a random node is selected and copies the state of one of its neighbors. Traditionally, this state has been considered as a binary variable. Here, we relax this assumption and address the case in which the number of states is a parameter that can assume any value, from 2 to \infty, in the thermodynamic limit. We derive mean-field analytical expressions for the exit probability and the consensus time for the case of an arbitrary number of states. We then perform a numerical study of the model in low dimensional lattices, comparing the case of multiple states with the usual binary voter model. Our work generalizes the well-known results for the voter model, and sheds light on the role of the so far almost neglected parameter accounting for the number of states.

cond-mat.stat-mech↗

arXiv2012

Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results

Recent work has shown that different theoretical approaches to the dynamics of the Susceptible-Infected-Susceptible (SIS) model for epidemics lead to qualitatively different estimates for the position of the epidemic threshold in networks. Here we present large-scale numerical simulations of the SIS dynamics on various types of networks, allowing the precise determination of the effective threshold for systems of finite size N. We compare quantitatively the numerical thresholds with theoretical predictions of the heterogeneous mean-field theory and of the quenched mean-field theory. We show that the latter is in general more accurate, scaling with N with the correct exponent, but often failing to capture the correct prefactor.

cond-mat.stat-mech↗

arXiv2012

Slow dynamics and rare-region effects in the contact process on weighted tree networks

We show that generic, slow dynamics can occur in the contact process on complex networks with a tree-like structure and a superimposed weight pattern, in the absence of additional (non-topological) sources of quenched disorder. The slow dynamics is induced by rare-region effects occurring on correlated subspaces of vertices connected by large weight edges, and manifests in the form of a smeared phase transition. We conjecture that more sophisticated network motifs could be able to induce Griffiths phases, as a consequence of purely topological disorder.

cond-mat.stat-mech↗

arXiv2012

Activity driven modeling of time varying networks

Network modeling plays a critical role in identifying statistical regularities and structural principles common to many systems. The large majority of recent modeling approaches are connectivity driven. The structural patterns of the network are at the basis of the mechanisms ruling the network formation. Connectivity driven models necessarily provide a time-aggregated representation that may fail to describe the instantaneous and fluctuating dynamics of many networks. We address this challenge by defining the activity potential, a time invariant function characterizing the agents' interactions and constructing an activity driven model capable of encoding the instantaneous time description of the network dynamics. The model provides an explanation of structural features such as the presence of hubs, which simply originate from the heterogeneous activity of agents. Within this framework, highly dynamical networks can be described analytically, allowing a quantitative discussion of the biases induced by the time-aggregated representations in the analysis of dynamical processes.

physics.soc-ph↗

arXiv2012

Generalized voter-like models on heterogeneous networks

We describe a generalization of the voter model on complex networks that encompasses different sources of degree-related heterogeneity and that is amenable to direct analytical solution by applying the standard methods of heterogeneous mean-field theory. Our formalism allows for a compact description of previously proposed heterogeneous voter-like models, and represents a basic framework within which we can rationalize the effects of heterogeneity in voter-like models, as well as implement novel sources of heterogeneity, not previously considered in the literature.

physics.soc-ph↗

arXiv2012

Competing activation mechanisms in epidemics on networks

In contrast to previous common wisdom that epidemic activity in heterogeneous networks is dominated by the hubs with the largest number of connections, recent research has pointed out the role that the innermost, dense core of the network plays in sustaining epidemic processes. Here we show that the mechanism responsible of spreading depends on the nature of the process. Epidemics with a transient state are boosted by the innermost core. Contrarily, epidemics allowing a steady state present a dual scenario, where either the hub independently sustains activity and propagates it to the rest of the system, or, alternatively, the innermost network core collectively turns into the active state, maintaining it globally. In uncorrelated networks the former mechanism dominates if the degree distribution decays with an exponent larger than 5/2, and the latter otherwise. Topological correlations, rife in real networks, may perturb this picture, mixing the role of both mechanisms.

physics.soc-ph↗

arXiv2012

Heterogenous mean-field analysis of a generalized voter-like model on networks

We propose a generalized framework for the study of voter models in complex networks at the the heterogeneous mean-field (HMF) level that (i) yields a unified picture for existing copy/invasion processes and (ii) allows for the introduction of further heterogeneity through degree-selectivity rules. In the context of the HMF approximation, our model is capable of providing straightforward estimates for central quantities such as the exit probability and the consensus/fixation time, based on the statistical properties of the complex network alone. The HMF approach has the advantage of being readily applicable also in those cases in which exact solutions are difficult to work out. Finally, the unified formalism allows one to understand previously proposed voter-like processes as simple limits of the generalized model.

physics.soc-ph↗

arXiv2012

Random walks on temporal networks

Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis of the temporal patterns characterizing dynamic networks are still recent, so that many questions remain open. Here, we study how random walks, as paradigm of dynamical processes, unfold on temporally evolving networks. To this aim, we use empirical dynamical networks of contacts between individuals, and characterize the fundamental quantities that impact any general process taking place upon them. Furthermore, we introduce different randomizing strategies that allow us to single out the role of the different properties of the empirical networks. We show that the random walk exploration is slower on temporal networks than it is on the aggregate projected network, even when the time is properly rescaled. In particular, we point out that a fundamental role is played by the temporal correlations between consecutive contacts present in the data. Finally, we address the consequences of the intrinsically limited duration of many real world dynamical networks. Considering the fundamental prototypical role of the random walk process, we believe that these results could help to shed light on the behavior of more complex dynamics on temporally evolving networks.

cond-mat.stat-mech↗

arXiv2012

Percolation analysis of force networks in anisotropic granular matter

We study the percolation properties of force networks in an anisotropic model for granular packings, the so-called q-model. Following the original recipe of Ostojic et al. [Nature 439, 828 (2006)], we consider a percolation process in which forces smaller than a given threshold f are deleted in the network. For a critical threshold f_c, the system experiences a transition akin to percolation. We determine the point of this transition and its characteristic critical exponents applying a finite-size scaling analysis that takes explicitly into account the directed nature of the q-model. By means of extensive numerical simulations, we show that this percolation transition is strongly affected by the anisotropic nature of the model, yielding characteristic exponents which are neither those found in isotropic granular systems nor those in the directed version of standard percolation. The differences shown by the computed exponents can be related to the presence of strong directed correlations and mass conservation laws in the model under scrutiny.

cond-mat.stat-mech↗

arXiv2011

Quasi-stationary simulations of the contact process on quenched networks

We present high-accuracy quasi-stationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the anomalous finite size scaling which was recently shown to hold for the contact process on annealed networks. It turns out that the quenched topology does not qualitatively change the critical behavior, leading only (as expected) to a shift of the transition point. The anomalous finite size scaling holds with exactly the same exponents of the annealed case, so that we can conclude that heterogeneous mean-field theory works for the contact process on quenched networks, at odds with previous claims. Interestingly, topological correlations induced by the presence of the natural cutoff do not alter the picture.

cond-mat.stat-mech↗

arXiv2011

Voter models on weighted networks

We study the dynamics of the voter and Moran processes running on top of complex network substrates where each edge has a weight depending on the degree of the nodes it connects. For each elementary dynamical step the first node is chosen at random and the second is selected with probability proportional to the weight of the connecting edge. We present a heterogeneous mean-field approach allowing to identify conservation laws and to calculate exit probabilities along with consensus times. In the specific case when the weight is given by the product of nodes' degree raised to a power theta, we derive a rich phase-diagram, with the consensus time exhibiting various scaling laws depending on theta and on the exponent of the degree distribution gamma. Numerical simulations give very good agreement for small values of |theta|. An additional analytical treatment (heterogeneous pair approximation) improves the agreement with numerics, but the theoretical understanding of the behavior in the limit of large |theta| remains an open challenge.

cond-mat.stat-mech↗

arXiv2011

Quasi-stationary analysis of the contact process on annealed scale-free networks

We present an analysis of the quasi-stationary (QS) state of the contact process (CP) on annealed scale-free networks using a mapping of the CP dynamics in a one-step processes and analyzing numerically and analytically the corresponding master equation. The relevant QS quantities determined via the master equation exhibit an excellent agreement with direct QS stochastic simulations of the CP. The high accuracy of the resulting data allows to probe the strong corrections to scaling present in both the critical and supercritical regions, corrections that mask the correct finite size scaling obtained analytically by applying an exact heterogeneous mean-field approach. {Our results represent a promising starting point for a deeper understanding of the contact process and absorbing phase transitions on real (quenched) complex networks

cond-mat.stat-mech↗

arXiv2011

Complex networks and glassy dynamics: walks in the energy landscape

We present a simple mathematical framework for the description of the dynamics of glassy systems in terms of a random walk in a complex energy landscape pictured as a network of minima. We show how to use the tools developed for the study of dynamical processes on complex networks, in order to go beyond mean-field models that consider that all minima are connected to each other. We consider several possibilities for the transition rates between minima, and show that in all cases the existence of a glassy phase depends on a delicate interplay between the network's topology and the relationship between energy and degree of a minimum. Interestingly, the network's degree correlations and the details of the transition rates do not play any role in the existence (nor in the value) of the transition temperature, but have an impact only on more involved properties. For Glauber or Metropolis rates in particular, we find that the low-temperature phase can be further divided into two regions with different scaling properties of the average trapping time. Overall, our results rationalize and link the empirical findings about correlations between the energy of the minima and their degree, and should stimulate further investigations on this issue.

cond-mat.stat-mech↗