arXiv subjects

Lidia A. Braunstein

Publications and source records attributed to Lidia A. Braunstein.

At least 37 records · Page 2Linked to original sources

arXiv2015

Epidemic spreading and immunization strategy in multiplex networks

A more connected world has brought major consequences such as facilitate the spread of diseases all over the world to quickly become epidemics, reason why researchers are concentrated in modeling the propagation of epidemics and outbreaks in Multilayer Networks. In this networks all nodes interact in different layers with different type of links. However, in many scenarios such as in the society, a Multiplex Network framework is not completely suitable since not all individuals participate in all layers. In this paper, we use a partially overlapped Multiplex Network where only a fraction of the individuals are shared by the layers. We develop a mitigation strategy for stopping a disease propagation, considering the Susceptible-Infected-Recover model, in a system consisted by two layers. We consider a random immunization in one of the layers and study the effect of the overlapping fraction in both, the propagation of the disease and the immunization strategy. Using branching theory, we study this scenario theoretically and via simulations and find a lower epidemic threshold than in the case without strategy.

physics.soc-ph↗

arXiv2015

Synchronization in Scale Free networks: The role of finite size effects

Synchronization problems in complex networks are very often studied by researchers due to its many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, Scale Free networks with degree distribution $P(k)\sim k^{-λ}$, are widely used in research since they are ubiquitous in nature and other real systems. In this paper we focus on the surface relaxation growth model in Scale Free networks with $2.5< λ<3$, and study the scaling behavior of the fluctuations, in the steady state, with the system size $N$. We find a novel behavior of the fluctuations characterized by a crossover between two regimes at a value of $N=N^*$ that depends on $λ$: a logarithmic regime, found in previous research, and a constant regime. We propose a function that describes this crossover, which is in very good agreement with the simulations. We also find that, for a system size above $N^{*}$, the fluctuations decrease with $λ$, which means that the synchronization of the system improves as $λ$ increases. We explain this crossover analyzing the role of the network's heterogeneity produced by the system size $N$ and the exponent of the degree distribution.

physics.soc-ph↗

arXiv2015

Multiple Tipping Points and Optimal Repairing in Interacting Networks

Systems that comprise many interacting dynamical networks, such as the human body with its biological networks or the global economic network consisting of regional clusters, often exhibit complicated collective dynamics. To understand the collective behavior of such systems, we investigate a model of interacting networks exhibiting the fundamental processes of failure, damage spread, and recovery. We find a very rich phase diagram that becomes exponentially more complex as the number of networks is increased. In the simplest example of $n=2$ interacting networks we find two critical points, 4 triple points, 10 allowed transitions, and two "forbidden" transitions, as well as complex hysteresis loops. Remarkably, we find that triple points play the dominant role in constructing the optimal repairing strategy in damaged interacting systems. To support our model, we analyze an example of real interacting financial networks and find evidence of rapid dynamical transitions between well-defined states, in agreement with the predictions of our model.

physics.soc-ph↗

arXiv2014

Competing for Attention in Social Media under Information Overload Conditions

Although the many forms of modern social media have become major channels for the dissemination of information, they are becoming overloaded because of the rapidly-expanding number of information feeds. We analyze the expanding user-generated content in Sina Weibo, the largest micro-blog site in China, and find evidence that popular messages often follow a mechanism that differs from that found in the spread of disease, in contrast to common believe. In this mechanism, an individual with more friends needs more repeated exposures to spread further the information. Moreover, our data suggest that in contrast to epidemics, for certain messages the chance of an individual to share the message is proportional to the fraction of its neighbours who shared it with him/her. Thus the greater the number of friends an individual has the greater the number of repeated contacts needed to spread the message, which is a result of competition for attention. We model this process using a fractional susceptible infected recovered (FSIR) model, where the infection probability of a node is proportional to its fraction of infected neighbors. Our findings have dramatic implications for information contagion. For example, using the FSIR model we find that real-world social networks have a finite epidemic threshold. This is in contrast to the zero threshold that conventional wisdom derives from disease epidemic models. This means that when individuals are overloaded with excess information feeds, the information either reaches out the population if it is above the critical epidemic threshold, or it would never be well received, leading to only a handful of information contents that can be widely spread throughout the population.

physics.soc-ph↗

arXiv2012

Competition between surface relaxation and ballistic deposition models in scale free networks

In this paper we study the scaling behavior of the fluctuations in the steady state $W_S$ with the system size $N$ for a surface growth process given by the competition between the surface relaxation (SRM) and the Ballistic Deposition (BD) models on degree uncorrelated Scale Free networks (SF), characterized by a degree distribution $P(k)\sim k^{-λ}$, where $k$ is the degree of a node. It is known that the fluctuations of the SRM model above the critical dimension ($d_c=2$) scales logarithmically with $N$ on euclidean lattices. However, Pastore y Piontti {\it et. al.} [A. L. Pastore y Piontti {\it et. al.}, Phys. Rev. E {\bf 76}, 046117 (2007)] found that the fluctuations of the SRM model in SF networks scale logarithmically with $N$ for $λ<3$ and as a constant for $λ\geq 3$. In this letter we found that for a pure ballistic deposition model on SF networks $W_S$ scales as a power law with an exponent that depends on $λ$. On the other hand when both processes are in competition, we find that there is a continuous crossover between a SRM behavior and a power law behavior due to the BD model that depends on the occurrence probability of each process and the system size. Interestingly, we find that a relaxation process contaminated by any small contribution of ballistic deposition will behave, for increasing system sizes, as a pure ballistic one. Our findings could be relevant when surface relaxation mechanisms are used to synchronize processes that evolve on top of complex networks.

physics.soc-ph↗

arXiv2012

Non-consensus opinion models on complex networks

We focus on non-consensus opinion models in which above a certain threshold two opinions coexist in a stable relationship. We revisit and extend the non-consensus opinion (NCO) model introduced by Shao. We generalize the NCO model by adding a weight factor W to individual's own opinion when determining its future opinion (NCOW model). We find that as W increases the minority opinion holders tend to form stable clusters with a smaller initial minority fraction compared to the NCO model. We also revisit another non-consensus opinion, the inflexible contrarian opinion (ICO) model, which introduces inflexible contrarians to model a competition between two opinions in the steady state. In the ICO model, the inflexible contrarians effectively decrease the size of the largest cluster of the rival opinion. All of the above models have previously been explored in terms of a single network. However opinions propagate not only within single networks but also between networks, we study here the opinion dynamics in coupled networks. We apply the NCO rule on each individual network and the global majority rule on interdependent pairs. We find that the interdependent links effectively force the system from a second order phase transition, which is characteristic of the NCO model on a single network, to a hybrid phase transition, i.e., a mix of second-order and abrupt jump-like transitions that ultimately becomes, as we increase the percentage of interdependent agents, a pure abrupt transition. We conclude that for the NCO model on coupled networks, interactions through interdependent links could push the non-consensus opinion type model to a consensus opinion type model, which mimics the reality that increased mass communication causes people to hold opinions that are increasingly similar.

physics.soc-ph↗

arXiv2012

A mechanism to synchronize fluctuations in scale free networks using growth models

In this paper we study the steady state of the fluctuations of the surface for a model of surface growth with relaxation to any of its lower nearest neighbors (SRAM) [F. Family, J. Phys. A {\bf 19}, L441 (1986)] in scale free networks. It is known that for Euclidean lattices this model belongs to the same universality class as the model of surface relaxation to the minimum (SRM). For the SRM model, it was found that for scale free networks with broadness $λ$, the steady state of the fluctuations scales with the system size $N$ as a constant for $λ\geq 3$ and has a logarithmic divergence for $λ< 3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007)]. It was also shown [La Rocca {\it et al.}, Phys. Rev. E {\bf 77}, 046120 (2008)] that this logarithmic divergence is due to non-linear terms that arises from the topology of the network. In this paper we show that the fluctuations for the SRAM model scale as in the SRM model. We also derive analytically the evolution equation for this model for any kind of complex graphs and find that, as in the SRM model, non-linear terms appear due to the heterogeneity and the lack of symmetry of the network. In spite of that, the two models have the same scaling, but the SRM model is more efficient to synchronize systems.

cond-mat.stat-mech↗

arXiv2012

Synchronization in Scale Free networks with degree correlation

In this paper we study a model of synchronization process on scale free networks with degree-degree correlations. This model was already studied on this kind of networks without correlations by Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007). Here, we study the effects of the degree-degree correlation on the behavior of the load fluctuations $W_s$ in the steady state. We found that for assortative networks there exist a specific correlation where the system is optimal synchronized. In addition, we found that close to this optimally value the fluctuations does not depend on the system size and therefore the system becomes fully scalable. This result could be very important for some technological applications. On the other hand, far from the optimal correlation, $W_s$ scales logarithmically with the system size.

physics.soc-ph↗

arXiv2012

Conservative model for synchronization problems in complex networks

In this paper we study the scaling behavior of the interface fluctuations (roughness) for a discrete model with conservative noise on complex networks. Conservative noise is a noise which has no external flux of deposition on the surface and the whole process is due to the diffusion. It was found that in Euclidean lattices the roughness of the steady state $W_s$ does not depend on the system size. Here, we find that for Scale-Free networks of $N$ nodes, characterized by a degree distribution $P(k)\sim k^{-λ}$, $W_s$ is independent of $N$ for any $λ$. This behavior is very different than the one found by Pastore y Piontti {\it et. al} [Phys. Rev. E {\bf 76}, 046117 (2007)] for a discrete model with non-conservative noise, that implies an external flux, where $W_s \sim \ln N$ for $λ< 3$, and was explained by non-linear terms in the analytical evolution equation for the interface [La Rocca {\it et. al}, Phys. Rev. E {\bf 77}, 046120 (2008)]. In this work we show that in this processes with conservative noise the non-linear terms are not relevant to describe the scaling behavior of $W_s$.

cond-mat.stat-mech↗

arXiv2011

Disorder Induced Limited Path Percolation

We introduce a model of percolation induced by disorder, where an initially homogeneous network with links of equal weight is disordered by the introduction of heterogeneous weights for the links. We consider a pair of nodes i and j to be mutually reachable when the ratio α_{ij} of length of the optimal path between them before and after the introduction of disorder does not increase beyond a tolerance ratio τ. These conditions reflect practical limitations of reachability better than the usual percolation model, which entirely disregards path length when defining connectivity and, therefore, communication. We find that this model leads to a first order phase transition in both 2-dimensional lattices and in Erdos-Renyi networks, and in the case of the latter, the size of the discontinuity implies that the transition is effectively catastrophic, with almost all system pairs undergoing the change from reachable to unreachable. Using the theory of optimal path lengths under disorder, we are able to predict the percolation threshold. For real networks subject to changes while in operation, this model should perform better in predicting functional limits than current percolation models.

cond-mat.dis-nn↗

arXiv2011

Strategy of Competition between Two Groups based on a Contrarian Opinion Model

We introduce a contrarian opinion (CO) model in which a fraction p of contrarians within a group holds a strong opinion opposite to the opinion held by the rest of the group. At the initial stage, stable clusters of two opinions, A and B exist. Then we introduce contrarians which hold a strong B opinion into the opinion A group. Through their interactions, the contrarians are able to decrease the size of the largest A opinion cluster, and even destroy it. We see this kind of method in operation, e.g when companies send free new products to potential customers in order to convince them to adopt the product and influence others. We study the CO model, using two different strategies, on both ER and scale-free networks. In strategy I, the contrarians are positioned at random. In strategy II, the contrarians are chosen to be the highest degrees nodes. We find that for both strategies the size of the largest A cluster decreases to zero as p increases as in a phase transition. At a critical threshold value p_c the system undergoes a second-order phase transition that belongs to the same universality class of mean field percolation. We find that even for an ER type model, where the degrees of the nodes are not so distinct, strategy II is significantly more effctive in reducing the size of the largest A opinion cluster and, at very small values of p, the largest A opinion cluster is destroyed.

physics.data-an↗

arXiv2010

Jamming in complex networks with degree correlation

We study the effects of the degree-degree correlations on the pressure congestion J when we apply a dynamical process on scale free complex networks using the gradient network approach. We find that the pressure congestion for disassortative (assortative) networks is lower (bigger) than the one for uncorrelated networks which allow us to affirm that disassortative networks enhance transport through them. This result agree with the fact that many real world transportation networks naturally evolve to this kind of correlation. We explain our results showing that for the disassortative case the clusters in the gradient network turn out to be as much elongated as possible, reducing the pressure congestion J and observing the opposite behavior for the assortative case. Finally we apply our model to real world networks, and the results agree with our theoretical model.

physics.soc-ph↗

arXiv2009

Structural crossover of polymers in disordered media

We present a unified scaling theory for the structural behavior of polymers embedded in a disordered energy substrate. An optimal polymer configuration is defined as the polymer configuration that minimizes the sum of interacting energies between the monomers and the substrate. The fractal dimension of the optimal polymer in the limit of strong disorder (SD) was found earlier to be larger than the fractal dimension in weak disorder (WD). We introduce a scaling theory for the crossover between the WD and SD limits. For polymers of various sizes in the same disordered substrate we show that polymers with a small number of monomers, N << N*, will behave as in SD, while large polymers with length N >> N* will behave as in WD. This implies that small polymers will be relatively more compact compared to large polymers even in the same substrate. The crossover length N* is a function of νand a, where νis the percolation correlation length exponent and a is the parameter which controls the broadness of the disorder. Furthermore, our results show that the crossover between the strong and weak disorder limits can be seen even within the same polymer configuration. If one focuses on a segment of size n << N* within a long polymer (N >> N*) that segment will have a higher fractal dimension compared to a segment of size n >> N*.

cond-mat.dis-nn↗

arXiv2009

Structure of shells in complex networks

In a network, we define shell $\ell$ as the set of nodes at distance $\ell$ with respect to a given node and define $r_\ell$ as the fraction of nodes outside shell $\ell$. In a transport process, information or disease usually diffuses from a random node and reach nodes shell after shell. Thus, understanding the shell structure is crucial for the study of the transport property of networks. For a randomly connected network with given degree distribution, we derive analytically the degree distribution and average degree of the nodes residing outside shell $\ell$ as a function of $r_\ell$. Further, we find that $r_\ell$ follows an iterative functional form $r_\ell=ϕ(r_{\ell-1})$, where $ϕ$ is expressed in terms of the generating function of the original degree distribution of the network. Our results can explain the power-law distribution of the number of nodes $B_\ell$ found in shells with $\ell$ larger than the network diameter $d$, which is the average distance between all pairs of nodes. For real world networks the theoretical prediction of $r_\ell$ deviates from the empirical $r_\ell$. We introduce a network correlation function $c(r_\ell)\equiv r_{\ell+1}/ϕ(r_\ell)$ to characterize the correlations in the network, where $r_{\ell+1}$ is the empirical value and $ϕ(r_\ell)$ is the theoretical prediction. $c(r_\ell)=1$ indicates perfect agreement between empirical results and theory. We apply $c(r_\ell)$ to several model and real world networks. We find that the networks fall into two distinct classes: (i) a class of {\it poorly-connected} networks with $c(r_\ell)>1$, which have larger average distances compared with randomly connected networks with the same degree distributions; and (ii) a class of {\it well-connected} networks with $c(r_\ell)<1$.

physics.data-an↗

arXiv2007

Numerical evaluation of the upper critical dimension of percolation in scale-free networks

We propose a numerical method to evaluate the upper critical dimension $d_c$ of random percolation clusters in Erdős-Rényi networks and in scale-free networks with degree distribution ${\cal P}(k) \sim k^{-λ}$, where $k$ is the degree of a node and $λ$ is the broadness of the degree distribution. Our results report the theoretical prediction, $d_c = 2(λ- 1)/(λ- 3)$ for scale-free networks with $3 < λ< 4$ and $d_c = 6$ for Erdős-Rényi networks and scale-free networks with $λ> 4$. When the removal of nodes is not random but targeted on removing the highest degree nodes we obtain $d_c = 6$ for all $λ> 2$. Our method also yields a better numerical evaluation of the critical percolation threshold, $p_c$, for scale-free networks. Our results suggest that the finite size effects increases when $λ$ approaches 3 from above.

cond-mat.dis-nn↗

arXiv2007

Transport and Percolation Theory in Weighted Networks

We study the distribution $P(σ)$ of the equivalent conductance $σ$ for Erdős-Rényi (ER) and scale-free (SF) weighted resistor networks with $N$ nodes. Each link has conductance $g\equiv e^{-ax}$, where $x$ is a random number taken from a uniform distribution between 0 and 1 and the parameter $a$ represents the strength of the disorder. We provide an iterative fast algorithm to obtain $P(σ)$ and compare it with the traditional algorithm of solving Kirchhoff equations. We find, both analytically and numerically, that $P(σ)$ for ER networks exhibits two regimes. (i) A low conductance regime for $σ< e^{-ap_c}$ where $p_c=1/\av{k}$ is the critical percolation threshold of the network and $\av{k}$ is average degree of the network. In this regime $P(σ)$ is independent of $N$ and follows the power law $P(σ) \sim σ^{-α}$, where $α=1-\av{k}/a$. (ii) A high conductance regime for $σ>e^{-ap_c}$ in which we find that $P(σ)$ has strong $N$ dependence and scales as $P(σ) \sim f(σ,ap_c/N^{1/3})$. For SF networks with degree distribution $P(k)\sim k^{-λ}$, $k_{min} \le k \le k_{max}$, we find numerically also two regimes, similar to those found for ER networks.

cond-mat.stat-mech↗

arXiv2006

Optimal Paths in Complex Networks with Correlated Weights: The World-wide Airport Network

We study complex networks with weights, $w_{ij}$, associated with each link connecting node $i$ and $j$. The weights are chosen to be correlated with the network topology in the form found in two real world examples, (a) the world-wide airport network, and (b) the {\it E. Coli} metabolic network. Here $w_{ij} \sim x_{ij} (k_i k_j)^α$, where $k_i$ and $k_j$ are the degrees of nodes $i$ and $j$, $x_{ij}$ is a random number and $α$ represents the strength of the correlations. The case $α> 0$ represents correlation between weights and degree, while $α< 0$ represents anti-correlation and the case $α= 0$ reduces to the case of no correlations. We study the scaling of the lengths of the optimal paths, $\ell_{\rm opt}$, with the system size $N$ in strong disorder for scale-free networks for different $α$. We calculate the robustness of correlated scale-free networks with different $α$, and find the networks with $α< 0$ to be the most robust networks when compared to the other values of $α$. We propose an analytical method to study percolation phenomena on networks with this kind of correlation. We compare our simulation results with the real world-wide airport network, and we find good agreement.

physics.soc-ph↗

arXiv2006

Transport in weighted networks: Partition into superhighways and roads

Transport in weighted networks is dominated by the minimum spanning tree (MST), the tree connecting all nodes with the minimum total weight. We find that the MST can be partitioned into two distinct components, having significantly different transport properties, characterized by centrality -- number of times a node (or link) is used by transport paths. One component, the {\it superhighways}, is the infinite incipient percolation cluster; for which we find that nodes (or links) with high centrality dominate. For the other component, {\it roads}, which includes the remaining nodes, low centrality nodes dominate. We find also that the distribution of the centrality for the infinite incipient percolation cluster satisfies a power law, with an exponent smaller than that for the entire MST. The significance of this finding is that one can improve significantly the global transport by improving a tiny fraction of the network, the superhighways.

cond-mat.dis-nn↗