Papers by Lidia Braunstein
Many models of market dynamics make use of the idea of conservative wealth exchanges among econom... more Many models of market dynamics make use of the idea of conservative wealth exchanges among economic agents. A few years ago an exchange model using extremal dynamics was developed and a very interesting result was obtained: a self-generated minimum wealth or poverty line. On the other hand, the wealth distribution exhibited an exponential shape as a function of the square of the wealth. These results have been obtained both considering exchanges between nearest neighbors or in a mean field scheme. In the present paper we study the effect of distributing the agents on a complex network. We have considered archetypical complex networks: Erdös-Rényi random networks and scale-free networks. The presence of a poverty line with finite wealth is preserved but spatial correlations are important, particularly between the degree of the node and the wealth. We present a detailed study of the correlations, as well as the changes in the Gini coefficient, that measures the inequality, as a function of the type and average degree of the considered networks.
Physical Review E, 1999
An error occurs on p. 4244 of our paper in the sentence four lines below the unnumbered equation.... more An error occurs on p. 4244 of our paper in the sentence four lines below the unnumbered equation. The sentence ''The height in the site i is increased by ͑i͒ 1 if h i уmin(h iϩ1 ,h iϪ1) and F i (h i ϩ1)ϭ1, and ͑ii͒ Y i if h i Ͻmin(h iϩ1 ,h iϪ1) and F i (h i ϩY i)ϭ1'' must be replaced by ''The height in the site i is increased by ͑i͒ 1 if h i уmax(h iϩ1 ,h iϪ1) and F i (h i ϩ1)ϭ1, or ͑ii͒ Y i if h i Ͻmax(h iϩ1 ,h iϪ1) and F i (h i ϩY i)ϭ1.''
We present the microscopic equation for the growing interface with quenched noise for the model f... more We present the microscopic equation for the growing interface with quenched noise for the model first presented by Buldyrev et al. [Phys. Rev. A 45, R8313 (1992)]. The evolution equation for the height, the mean height, and the roughness are reached in a simple way. The microscopic equation allows us to express these equations in two contributions: the contact and the local one. We compare this two contributions with the ones obtained for the Tang and Leschhorn model [Phys. Rev A 45, R8309 (1992)] by Braunstein et al. Even when the microscopic mechanisms are quiet different in both model, the two contribution are qualitatively similar. An interesting result is that the diffusion contribution, in the Tang and Leschhorn model, and the contact one, in the Buldyrev model, leads to an increase of the roughness near the criticality.
We review results on the scaling of the optimal path length in random networks with weighted link... more We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for the minimum distance. For Erdős-Rényi (ER) and scale free networks (SF), with parameter λ (λ >3), we find that the small-world nature is destroyed. We also find numerically that for weak disorder the length of the optimal path scales logaritmically with the size of the networks studied. We also review the transition between the strong and weak disorder regimes in the scaling properties of the length of the optimal path for ER and SF networks and for a general distribution of weights, and suggest that for any distribution of weigths, the distribution of optimal path lengths has a universal form which is controlled by the scaling parameter Z=ℓ_∞/A where A plays the role of the disorder strength, and ℓ_∞ is the length of the optimal path in strong...
journal homepage: www.elsevier.com/locate/physa Study of a market model with conservative exchang... more journal homepage: www.elsevier.com/locate/physa Study of a market model with conservative exchanges on
This thesis employs methods of statistical mechanics and numerical simulations to study some aspe... more This thesis employs methods of statistical mechanics and numerical simulations to study some aspects of dynamic and interacting complex networks. The mapping of various social and physical phenomena to complex networks has been a rich field in the past few decades. Subjects as broad as petroleum engineering, scientific collaborations, and the structure of the internet have all been analyzed in a network physics context, with useful and universal results. In the first chapter we introduce basic concepts in networks, including the two types of network configurations that are studied and the statistical physics and epidemiological models that form the framework of the network research, as well as covering various previously-derived results in network theory that are used in the work in the following chapters. In the second chapter we introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to ...
Scientific reports, 2015
The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order ... more The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order to quantify the effectiveness of different strategies for controlling the spread, we develop a mathematical model in which the propagation of the Ebola virus through Liberia is caused by travel between counties. For the initial months in which the Ebola virus spreads, we find that the arrival times of the disease into the counties predicted by our model are compatible with World Health Organization data, but we also find that reducing mobility is insufficient to contain the epidemic because it delays the arrival of Ebola virus in each county by only a few weeks. We study the effect of a strategy in which safe burials are increased and effective hospitalisation instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii) one in mid-August--which was the actual time that strong interventions began in Liberia. We find that if scenario (i) had been pursued the lifetime of th...
EPL (Europhysics Letters), 2014
We present a model that explores the influence of persuasion in a population of agents with posit... more We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number k that expresses its level of agreement on a given issue, from totally against k = −M to totally in favor k = M. Same-orientation agents persuade each other with probability p, becoming more extreme, while opposite-orientation agents become more moderate as they reach a compromise with probability q. The population initially evolves to (a) a polarized state for r = p/q > 1, where opinions' distribution is peaked at the extreme values k = ±M , or (b) a centralized state for r < 1, with most opinions around k = ±1. When r ≫ 1, polarization lasts for a time that diverges as r M ln N , where N is the population's size. Finally, an extremist consensus (k = M or −M) is reached in a time that scales as r −1 for r ≪ 1.
Physical Review Letters, 2003
We study the optimal distance in networks, ' opt , defined as the length of the path minimizing t... more We study the optimal distance in networks, ' opt , defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For strong disorder, where the maximal weight along the path dominates the sum, we find that ' opt N 1=3 in both Erdős-Rényi (ER) and Watts-Strogatz (WS) networks. For scale-free (SF) networks, with degree distribution Pk k ÿ , we find that ' opt scales as N ÿ3=ÿ1 for 3 < < 4 and as N 1=3 for 4. Thus, for these networks, the small-world nature is destroyed. For 2 < < 3, our numerical results suggest that ' opt scales as ln ÿ1 N. We also find numerically that for weak disorder ' opt lnN for both the ER and WS models as well as for SF networks.
Physical Review E, 2013
We explore how heterogeneity in the intensity of interactions between people affects epidemic spr... more We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals i and j is endowed with an infection rate β ij = λw ij proportional to the intensity of their contact w ij , with a distribution P (w ij) taken from face-to-face experiments analyzed in Cattuto et al. (PLoS ONE 5, e11596, 2010). We find an extremely slow decay of the fraction of infected individuals, for a wide range of the control parameter λ. Using a distribution of width a we identify two large regions in the a − λ space with anomalous behaviors, which are reminiscent of rare region effects (Griffiths phases) found in models with quenched disorder. We show that the slow approach to extinction is caused by isolated small groups of highly interacting individuals, which keep epidemic alive for very long times. A mean-field approximation and a percolation approach capture with very good accuracy the absorbing-active transition line for weak (small a) and strong (large a) disorder, respectively.
Physical Review E, 2011
We study the critical effect of quarantine on the propagation of epidemics on an adaptive network... more We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered (SIR) model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w, and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold w c separating a phase (w < w c) where the disease reaches a large fraction of the population, from a phase (w ≥ w c) where the disease does not spread out. We find that in our model the topology of the network strongly affects the size of the propagation, and that w c increases with the mean degree and heterogeneity of the network. We also find that w c is reduced if we perform a preferential rewiring, in which the rewiring probability is proportional to the degree of infected nodes.
Physical Review E, 2005
We study the behavior of the optimal path between two sites separated by a distance r on a d-dime... more We study the behavior of the optimal path between two sites separated by a distance r on a d-dimensional lattice of linear size L with weight assigned to each site. We focus on the strong disorder limit, i.e., when the weight of a single site dominates the sum of the weights along each path. We calculate the probability distribution P͑ᐉ opt ͉ r , L͒ of the optimal path length ᐉ opt , and find for r Ӷ L a power-law decay with ᐉ opt , characterized by exponent g opt. We determine the scaling form of P͑ᐉ opt ͉ r , L͒ in two-and three-dimensional lattices. To test the conjecture that the optimal paths in strong disorder and flow in percolation clusters belong to the same universality class, we study the tracer path length ᐉ tr of tracers inside percolation through their probability distribution P͑ᐉ tr ͉ r , L͒. We find that, because the optimal path is not constrained to belong to a percolation cluster, the two problems are different. However, by constraining the optimal paths to remain inside the percolation clusters in analogy to tracers in percolation, the two problems exhibit similar scaling properties.
The roughening of interfaces moving in inhomogeneous media is investigated by numerical integrati... more The roughening of interfaces moving in inhomogeneous media is investigated by numerical integration of the phenomenological stochastic differential equation proposed by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889, (1986)] with quenched noise (QKPZ). We express the evolution equations for the mean height and the roughness into two contributions: the local and the lateral one. We compare this two contributions with the ones obtained for two directed percolation deppining models (DPD): the Tang and Leschhorn model [Phys. Rev A 45, R8309 (1992)] and the Buldyrev et al. model [Phys. Rev. A 45, R8313 (1992)] by Braunstein al. [J. Phys. A 32, 1801 (1999); Phys. Rev. E 59, 4243 (1999)]. Even these models have being classified in the same universality class that the QKPZ the contributions to the growing mechanisms are quite different. The lateral contribution in the DPD models, leads to an increasing of the roughness near the criticality while in the QKPZ equation this contribution a...
Reports on progress in physics. Physical Society (Great Britain), Mar 8, 2017
Models of epidemic spreading on complex networks have attracted great attention among researchers... more Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical message-passing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into dev...
PloS one, 2017
Through years, the use of vaccines has always been a controversial issue. People in a society may...
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Papers by Lidia Braunstein