137 results on '"Lidia A. Braunstein"'
Search Results
102. Quarantine-generated phase transition in epidemic spreading
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Lidia A. Braunstein, Shlomo Havlin, Harry Eugene Stanley, P. A. Macri, M. V. Migueles, Federico Vazquez, Mark Dickison, and Cecilia Lagorio
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FOS: Computer and information sciences ,Phase transition ,Physics - Physics and Society ,Population ,FOS: Physical sciences ,Physics and Society (physics.soc-ph) ,01 natural sciences ,Complex Networks ,Models, Biological ,010305 fluids & plasmas ,law.invention ,purl.org/becyt/ford/1 [https] ,Disease susceptibility ,law ,0103 physical sciences ,Quarantine ,Disease Transmission, Infectious ,Statistical physics ,Physics - Biological Physics ,010306 general physics ,education ,Epidemics ,Condensed Matter - Statistical Mechanics ,Mathematics ,Social and Information Networks (cs.SI) ,education.field_of_study ,Degree (graph theory) ,Statistical Mechanics (cond-mat.stat-mech) ,COVID-19 ,Complex Systems ,Computer Science - Social and Information Networks ,purl.org/becyt/ford/1.3 [https] ,Biological Physics (physics.bio-ph) ,Disease Susceptibility ,Disease transmission - Abstract
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 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., Comment: 13 pages, 6 figures more...
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- 2010
103. Structural crossover of polymers in disordered media
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Shlomo Havlin, Roni Parshani, and Lidia A. Braunstein
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chemistry.chemical_classification ,Quantitative Biology::Biomolecules ,Condensed matter physics ,Crossover ,FOS: Physical sciences ,Geometry ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Function (mathematics) ,Substrate (electronics) ,Polymer ,Condensed Matter - Disordered Systems and Neural Networks ,Fractal dimension ,Condensed Matter::Soft Condensed Matter ,chemistry.chemical_compound ,Monomer ,chemistry ,Percolation ,Exponent ,Mathematics - Abstract
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 ��and a, where ��is 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*. more...
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- 2009
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104. Structure of shells in complex networks
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H. Eugene Stanley, Shlomo Havlin, Sergey V. Buldyrev, Lidia A. Braunstein, and Jia Shao
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Physics - Physics and Society ,Degree (graph theory) ,Node (networking) ,Generating function ,FOS: Physical sciences ,Function (mathematics) ,Physics and Society (physics.soc-ph) ,Complex network ,Correlation function (astronomy) ,Degree distribution ,Topology ,Models, Biological ,Combinatorics ,Distribution (mathematics) ,Physics - Data Analysis, Statistics and Probability ,Computer Simulation ,Nerve Net ,Data Analysis, Statistics and Probability (physics.data-an) ,Mathematics ,Signal Transduction - Abstract
We define shell l in a network as the set of nodes at distance l with respect to a given node and define rl as the fraction of nodes outside shell l . 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. We study the statistical properties of the shells of a randomly chosen node. For a randomly connected network with given degree distribution, we derive analytically the degree distribution and average degree of the nodes residing outside shell l as a function of rl. Further, we find that rl follows an iterative functional form rl=phi(rl-1) , where phi 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 Bl found in shells with l larger than the network diameter d , which is the average distance between all pairs of nodes. For real-world networks the theoretical prediction of rl deviates from the empirical rl. We introduce a network correlation function c(rl) identical with rl/phi(rl-1) to characterize the correlations in the network, where rl is the empirical value and phi(rl-1) is the theoretical prediction. c(rl)=1 indicates perfect agreement between empirical results and theory. We apply c(rl) to several model and real-world networks. We find that the networks fall into two distinct classes: (i) a class of poorly connected networks with c(rl)>1 , where a larger (smaller) fraction of nodes resides outside (inside) distance l from a given node than in randomly connected networks with the same degree distributions. Examples include the Watts-Strogatz model and networks characterizing human collaborations such as citation networks and the actor collaboration network; (ii) a class of well-connected networks with c(rl) more...
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- 2009
105. Discrete surface growth process as a synchronization mechanism for scale-free complex networks
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Lidia A. Braunstein, P. A. Macri, and A.L. Pastore y Piontti
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Surface (mathematics) ,Statistical Mechanics (cond-mat.stat-mech) ,Degree (graph theory) ,FOS: Physical sciences ,General Medicine ,Renormalization group ,Degree distribution ,Lambda ,Combinatorics ,Saturation (graph theory) ,Relaxation (physics) ,Scaling ,Condensed Matter - Statistical Mechanics ,Mathematics - Abstract
We consider the discrete surface growth process with relaxation to the minimum [F. Family, J. Phys. A {\bf 19} L441, (1986).] as a possible synchronization mechanism on scale-free networks, characterized by a degree distribution $P(k) \sim k^{-\lambda}$, where $k$ is the degree of a node and $\lambda$ his broadness, and compare it with the usually applied Edward-Wilkinson process [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London Ser. A {\bf 381},17 (1982) ]. In spite of both processes belong to the same universality class for Euclidean lattices, in this work we demonstrate that for scale-free networks with exponents $\lambda, Comment: 8 pages, 4 figures more...
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- 2007
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106. Transport and percolation theory in weighted networks
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H. Eugene Stanley, Guanliang Li, Shlomo Havlin, Sergey V. Buldyrev, and Lidia A. Braunstein
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Discrete mathematics ,Uniform distribution (continuous) ,Statistical Mechanics (cond-mat.stat-mech) ,Degree (graph theory) ,FOS: Physical sciences ,Conductance ,Percolation threshold ,Degree distribution ,Power law ,Kirchhoff equations ,Percolation theory ,Statistical physics ,Condensed Matter - Statistical Mechanics ,Mathematics - Abstract
We study the distribution $P(\sigma)$ of the equivalent conductance $\sigma$ for Erd\H{o}s-R\'enyi (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 $P(\sigma)$ and compare it with the traditional algorithm of solving Kirchhoff equations. We find, both analytically and numerically, that $P(\sigma)$ for ER networks exhibits two regimes. (i) A low conductance regime for $\sigma < e^{-ap_c}$ 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 $P(\sigma)$ is independent of $N$ and follows the power law $P(\sigma) \sim \sigma^{-\alpha}$, where $\alpha=1-\av{k}/a$. (ii) A high conductance regime for $\sigma >e^{-ap_c}$ in which we find that $P(\sigma)$ has strong $N$ dependence and scales as $P(\sigma) \sim f(\sigma,ap_c/N^{1/3})$. For SF networks with degree distribution $P(k)\sim k^{-\lambda}$, $k_{min} \le k \le k_{max}$, we find numerically also two regimes, similar to those found for ER networks., Comment: 4 pages, 8 figures more...
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- 2007
107. Numerical evaluation of the upper critical dimension of percolation in scale-free networks
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Zhenhua Wu, Shlomo Havlin, H. Eugene Stanley, Cecilia Lagorio, Lidia A. Braunstein, and Reuven Cohen
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Discrete mathematics ,Degree (graph theory) ,Statistical Mechanics (cond-mat.stat-mech) ,FOS: Physical sciences ,Percolation threshold ,General Medicine ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Lambda ,Condensed Matter::Disordered Systems and Neural Networks ,Combinatorics ,Percolation ,Condensed Matter::Statistical Mechanics ,Critical dimension ,Condensed Matter - Statistical Mechanics ,Mathematics - Abstract
We propose a numerical method to evaluate the upper critical dimension $d_c$ of random percolation clusters in Erd\H{o}s-R\'{e}nyi networks and in scale-free networks with degree distribution ${\cal P}(k) \sim k^{-\lambda}$, where $k$ is the degree of a node and $\lambda$ is the broadness of the degree distribution. Our results report the theoretical prediction, $d_c = 2(\lambda - 1)/(\lambda - 3)$ for scale-free networks with $3 < \lambda < 4$ and $d_c = 6$ for Erd\H{o}s-R\'{e}nyi networks and scale-free networks with $\lambda > 4$. When the removal of nodes is not random but targeted on removing the highest degree nodes we obtain $d_c = 6$ for all $\lambda > 2$. 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 $\lambda$ approaches 3 from above., Comment: 10 pages, 5 figures more...
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- 2007
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108. Competing for Attention in Social Media under Information Overload Conditions
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Yanqing Hu, Baowen Li, H. Eugene Stanley, Shlomo Havlin, Lidia A. Braunstein, and Ling Feng
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FOS: Computer and information sciences ,Competitive Behavior ,Physics - Physics and Society ,Computer science ,Population ,FOS: Physical sciences ,lcsh:Medicine ,Friends ,Physics and Society (physics.soc-ph) ,Models, Psychological ,01 natural sciences ,Social Networking ,010305 fluids & plasmas ,0103 physical sciences ,Econometrics ,Humans ,Attention ,Fraction (mathematics) ,Social media ,Social Behavior ,lcsh:Science ,010306 general physics ,education ,Probability ,Social and Information Networks (cs.SI) ,Internet ,education.field_of_study ,Multidisciplinary ,Information Dissemination ,Node (networking) ,lcsh:R ,Scale-free network ,Contrast (statistics) ,Computer Science - Social and Information Networks ,Information overload ,Zero (linguistics) ,lcsh:Q ,Research Article - Abstract
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., Comment: 11 pages, 5 figures more...
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- 2015
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109. Synchronization in scale-free networks: The role of finite-size effects
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M. A. Di Muro, D. Torres, Lidia A. Braunstein, and C. E. La Rocca
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Physics ,Ciencias Físicas ,Interfaces ,Crossover ,Scale-free network ,General Physics and Astronomy ,Function (mathematics) ,Complex network ,Otras Ciencias Físicas ,Degree distribution ,Redes Complejas ,Synchronization (computer science) ,Sincronización ,Statistical physics ,Constant (mathematics) ,Scaling ,CIENCIAS NATURALES Y EXACTAS - Abstract
Synchronization problems in complex networks are very often studied by researchers due to their 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^{-\lambda} , 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< \lambda more...
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- 2015
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110. Optimal Path and Minimal Spanning Trees in Random Weighted Networks
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Tomer Kalisky, Sameet Sreenivasan, Shlomo Havlin, Lidia A. Braunstein, Sergey V. Buldyrev, Eduardo López, Reuven Cohen, H. E. Stanley, Y. Chen, and Zhenhua Wu
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Physics - Physics and Society ,Spanning tree ,Applied Mathematics ,Scale-free network ,FOS: Physical sciences ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Physics and Society (physics.soc-ph) ,Minimum spanning tree ,Condensed Matter - Disordered Systems and Neural Networks ,Combinatorics ,Tree (descriptive set theory) ,Path length ,Modeling and Simulation ,Path (graph theory) ,Centrality ,Engineering (miscellaneous) ,Scaling ,Mathematics - Abstract
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 Erd\H{o}s-R\'enyi (ER) and scale free networks (SF), with parameter $\lambda$ ($\lambda >3$), 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 $Z=\ell_{\infty}/A$ where $A$ plays the role of the disorder strength, and $\ell_{\infty}$ is the length of the optimal path in strong disorder. The relation for $A$ is derived analytically and supported by numerical simulations. We then study the minimum spanning tree (MST) and show that it is composed of percolation clusters, which we regard as "super-nodes", connected by a scale-free tree. We furthermore show that the MST can be partitioned into two distinct components. One component the {\it superhighways}, for which the nodes with high centrality dominate, corresponds to the largest cluster at the percolation threshold which is a subset of the MST. In the other component, {\it roads}, low centrality nodes dominate. We demonstrate the significance identifying the superhighways by showing that one can improve significantly the global transport by improving a very small fraction of the network., Comment: review, accepted at IJBC more...
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- 2006
111. Optimal Paths in Complex Networks with Correlated Weights: The World-wide Airport Network
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Reuven Cohen, H. Eugene Stanley, Vittoria Colizza, Zhenhua Wu, Lidia A. Braunstein, and Shlomo Havlin
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Physics - Physics and Society ,Statistical Mechanics (cond-mat.stat-mech) ,FOS: Physical sciences ,Percolation threshold ,Physics and Society (physics.soc-ph) ,Complex network ,Computational Physics (physics.comp-ph) ,Network topology ,Topology ,Degree distribution ,Universality (dynamical systems) ,Combinatorics ,Robustness (computer science) ,Physics - Data Analysis, Statistics and Probability ,Exponent ,Physics - Computational Physics ,Scaling ,Condensed Matter - Statistical Mechanics ,Data Analysis, Statistics and Probability (physics.data-an) ,Mathematics - Abstract
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 worldwide airport network and (b) the E. Coli metabolic network. Here w(ij) approximately equals x(ij)(k(i)k(j))alpha, where k(i) and k(j) are the degrees of nodes i and j , x(ij) is a random number, and alpha represents the strength of the correlations. The case alpha0 represents correlation between weights and degree, while alpha0 represents anticorrelation and the case alpha=0 reduces to the case of no correlations. We study the scaling of the lengths of the optimal paths, l(opt), with the system size N in strong disorder for scale-free networks for different alpha. We find two different universality classes for l(opt), in strong disorder depending on alpha: (i) if alpha0 , then for lambda2 the scaling law l(opt) approximately equals N(1/3), where lambda is the power-law exponent of the degree distribution of scale-free networks, and (ii) if alphaor =0 , then l(opt) approximately equals N((nu)(opt)) with nu(opt) identical to its value for the uncorrelated case alpha=0. We calculate the robustness of correlated scale-free networks with different alpha and find the networks with alpha0 to be the most robust networks when compared to the other values of alpha. We propose an analytical method to study percolation phenomena on networks with this kind of correlation, and our numerical results suggest that for scale-free networks with alpha0 , the percolation threshold p(c) is finite for lambda3, which belongs to the same universality class as alpha=0 . We compare our simulation results with the real worldwide airport network, and we find good agreement. more...
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- 2006
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112. Transport in weighted networks: partition into superhighways and roads
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Zhenhua Wu, H. Eugene Stanley, Shlomo Havlin, and Lidia A. Braunstein
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General Physics and Astronomy ,FOS: Physical sciences ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Minimum spanning tree ,Topology ,Tree (data structure) ,Percolation ,Node (computer science) ,Exponent ,Cluster (physics) ,Partition (number theory) ,Computer Simulation ,Neural Networks, Computer ,Centrality ,Mathematics - Abstract
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., Comment: 12 pages, 5 figures more...
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- 2005
113. Scaling of optimal-path-lengths distribution in complex networks
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Sergey V. Buldyrev, H. Eugene Stanley, Tomer Kalisky, Lidia A. Braunstein, and Shlomo Havlin
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Random graph ,Discrete mathematics ,Uniform distribution (continuous) ,FOS: Physical sciences ,Percolation threshold ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Complex network ,Condensed Matter::Disordered Systems and Neural Networks ,Average path length ,Path length ,Path (graph theory) ,Statistical physics ,Scaling ,Mathematics - Abstract
We study the distribution of optimal path lengths in random graphs with random weights associated with each link (``disorder''). With each link $i$ we associate a weight $\tau_i = \exp(ar_i)$ where $r_i$ is a random number taken from a uniform distribution between 0 and 1, and the parameter $a$ controls the strength of the disorder. We suggest, in analogy with the average length of the optimal path, that the distribution of optimal path lengths has a universal form which is controlled by the expression $\frac{1}{p_c}\frac{\ell_{\infty}}{a}$, where $\ell_{\infty}$ is the optimal path length in strong disorder ($a \to \infty$) and $p_c$ is the percolation threshold. This relation is supported by numerical simulations for Erd\H{o}s-R\'enyi and scale-free graphs. We explain this phenomenon by showing explicitly the transition between strong disorder and weak disorder at different length scales in a single network. more...
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- 2005
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114. Exact scalings in competitive growth models
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Lidia A. Braunstein and Chi Hang Lam
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Mathematical model ,Continuum mechanics ,Statistical Mechanics (cond-mat.stat-mech) ,Continuum (topology) ,Surface roughness ,Order (group theory) ,Deposition (phase transition) ,FOS: Physical sciences ,Statistical physics ,Renormalization group ,Scaling ,Condensed Matter - Statistical Mechanics ,Mathematics - Abstract
A competitive growth model (CGM) describes aggregation of a single type of particle under two distinct growth rules with occurrence probabilities $p$ and $1-p$. We explain the origin of scaling behaviors of the resulting surface roughness with respect to $p$ for two CGMs which describe random deposition (RD) competing with ballistic deposition (BD) and RD competing with the Edward Wilkinson (EW) growth rule. Exact scaling exponents are derived and are in agreement with previously conjectured values. Using this analytical result we are able to derive theoretically the scaling behaviors of the coefficients of the continuous equations that describe their universality classes. We also suggest that, in some CGM, the $p-$dependence on the coefficients of the continuous equation that represents the universality class can be non trivial. In some cases the process cannot be represented by a unique universality class. In order to show this we introduce a CGM describing RD competing with a constrained EW (CEW) model. This CGM show a transition in the scaling exponents from RD to a Kardar-Parisi-Zhang behavior when $p \to 0$ and to a Edward Wilkinson one when $p \to 1$. Our simulation results are in excellent agreement with the analytic predictions., 11 pages, 6 figures more...
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- 2005
115. Scale-free networks emerging from weighted random graphs
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Lidia A. Braunstein, H. Eugene Stanley, Tomer Kalisky, Sameet Sreenivasan, Shlomo Havlin, and Sergey V. Buldyrev
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Random graph ,Discrete mathematics ,Percolation ,Random regular graph ,Scale-free network ,FOS: Physical sciences ,Percolation threshold ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Continuum percolation theory ,Condensed Matter - Disordered Systems and Neural Networks ,Degree distribution ,Supernode ,Mathematics - Abstract
We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters) into a single node. We show that this network is scale-free, i.e., the degree distribution is $P(k)\sim k^{-\lambda}$ with $\lambda=2.5$. Our results imply that the minimum spanning tree (MST) in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale-free tree with $\lambda=2.5$. We show that optimization causes the percolation threshold to emerge spontaneously, thus creating naturally a scale-free ``supernode network''. We discuss the possibility that this phenomenon is related to the evolution of several real world scale-free networks. more...
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- 2005
116. Scale-Free properties of weighted random graphs: Minimum Spanning Trees and Percolation
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Tomer Kalisky, Lidia A. Braunstein, Sameet Sreenivasan, H. Eugene Stanley, Shlomo Havlin, and Sergey V. Buldyrev
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Random graph ,Discrete mathematics ,Combinatorics ,Spanning tree ,Percolation ,Percolation threshold ,Graph theory ,Continuum percolation theory ,Minimum spanning tree ,Tree (graph theory) ,Mathematics - Abstract
We study Erdos‐Renyi random graphs with random weights associated with each link. In our approach, nodes connected by links having weights below the percolation threshold form clusters, and each cluster merges into a single node, thus generating a new “clusters network”. We show that this network is scale‐free with λ = 2.5. Furthermore, we show that optimization causes the percolation threshold to emerge spontaneously, thus creating naturally a scale‐free “clusters network”. This phenomenon may be related to the evolution of several real world scale‐free networks.Our results imply that: (i) the minimum spanning tree (MST) in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale‐free tree with λ = 2.5 (ii) the optimal path may be partitioned into segments that follow the percolation clusters, and the lengths of these segments grow exponentially with the number of clusters that are crossed (iii) the optimal path in scale‐free networks with λ < 3 sc... more...
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- 2005
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117. Possible Connection between the Optimal Path and Flow in Percolation Clusters
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Shlomo Havlin, Sergey V. Buldyrev, Eduardo López, Lidia A. Braunstein, and H. Eugene Stanley
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Percolation critical exponents ,Statistical Mechanics (cond-mat.stat-mech) ,FOS: Physical sciences ,Percolation threshold ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Power law ,Combinatorics ,Path length ,Exponent ,Probability distribution ,Continuum percolation theory ,Scaling ,Condensed Matter - Statistical Mechanics ,Mathematics - Abstract
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 $P(\ell_{\rm opt}|r,L)$ of the optimal path length $\ell_{\rm opt}$, and find for $r\ll L$ a power law decay with $\ell_{\rm opt}$, characterized by exponent $g_{\rm opt}$. We determine the scaling form of $P(\ell_{\rm opt}|r,L)$ 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 $\ell_{\rm tr}$ of tracers inside percolation through their probability distribution $P(\ell_{\rm tr}|r,L)$. 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., Comment: Accepted for publication to Physical Review E. 17 Pages, 6 Figures, 1 Table more...
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- 2005
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118. Nucleation model for multiparticle reactions with finite reaction rates in one dimension
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R. C. Buceta and Lidia A. Braunstein
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Reaction rate ,Physics ,Mean field theory ,Dimension (graph theory) ,Monte Carlo method ,Nucleation ,Dynamic Monte Carlo method ,Rate equation ,Statistical physics ,Particle density ,Mathematical physics - Abstract
We study one-dimensional reactions $\ensuremath{\mu}A\ensuremath{\rightarrow}\ensuremath{\nu}A$ ($\ensuremath{\mu}g\ensuremath{\nu}$)with nucleation and finite reaction rate ($k\ensuremath{\ll}$) in one dimension for the particle density decay by means of a Monte Carlo simulation and analytic modeling. The anomalous case $\ensuremath{\mu}=2$ was studied in our previous work. The marginal case $\ensuremath{\mu}=3$ is described without logaritmic corrections in the mean field approach. The case $\ensuremath{\mu}g3$ is well described by classical rate equations. The rate equation for the particle density is derived for all $\ensuremath{\mu}$. We present a mean field approach for the early time regime (reaction-controlled limit) for any initial density. Also, the mean field aproximation is derived in a simple way from the rate equation for any time at low densities. more...
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- 1996
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119. Effect of disorder strength on optimal paths in complex networks
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Sameet Sreenivasan, Shlomo Havlin, Sergey V. Buldyrev, H. Eugene Stanley, Lidia A. Braunstein, and Tomer Kalisky
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Random graph ,Uniform distribution (continuous) ,Statistical Mechanics (cond-mat.stat-mech) ,Crossover ,FOS: Physical sciences ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,General Medicine ,Condensed Matter - Disordered Systems and Neural Networks ,Complex network ,Measure (mathematics) ,Combinatorics ,Limit (mathematics) ,Statistical physics ,Scaling ,Condensed Matter - Statistical Mechanics ,Ansatz ,Mathematics - Abstract
We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path $\ell_{\rm opt}$ in a disordered Erd\H{o}s-R\'enyi (ER) random network and scale-free (SF) network. Each link $i$ is associated with a weight $\tau_i\equiv\exp(a r_i)$, where $r_i$ is a random number taken from a uniform distribution between 0 and 1 and the parameter $a$ controls the strength of the disorder. We find that for any finite $a$, there is a crossover network size $N^*(a)$ at which the transition occurs. For $N \ll N^*(a)$ the scaling behavior of $\ell_{\rm opt}$ is in the strong disorder regime, with $\ell_{\rm opt} \sim N^{1/3}$ for ER networks and for SF networks with $\lambda \ge 4$, and $\ell_{\rm opt} \sim N^{(\lambda-3)/(\lambda-1)}$ for SF networks with $3 < \lambda < 4$. For $N \gg N^*(a)$ the scaling behavior is in the weak disorder regime, with $\ell_{\rm opt}\sim\ln N$ for ER networks and SF networks with $\lambda > 3$. In order to study the transition we propose a measure which indicates how close or far the disordered network is from the limit of strong disorder. We propose a scaling ansatz for this measure and demonstrate its validity. We proceed to derive the scaling relation between $N^*(a)$ and $a$. We find that $N^*(a)\sim a^3$ for ER networks and for SF networks with $\lambda\ge 4$, and $N^*(a)\sim a^{(\lambda-1)/(\lambda-3)}$ for SF networks with $3 < \lambda < 4$., Comment: 6 pages, 6 figures. submitted to Phys. Rev. E more...
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- 2004
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120. The Optimal Pathin an Erdős-Rényi Random Graph
- Author
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Lidia A. Braunstein, Sergey V. Buldyrev, Sameet Sreenivasan, Reuven Cohen, Shlomo Havlin, and H. Eugene Stanley
- Subjects
Random graph ,Discrete mathematics ,Combinatorics ,Random regular graph ,Voltage graph ,Strength of a graph ,Null graph ,Butterfly graph ,Random geometric graph ,Simplex graph ,Mathematics - Published
- 2004
- Full Text
- View/download PDF
121. Universal Behavior of the Coefficients of the Continuous Equation in Competitive Growth Models
- Author
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Lidia A. Braunstein, R. C. Buceta, and Diego Muraca
- Subjects
Quadratic equation ,Regularization (physics) ,Competitive growth ,Mathematical analysis ,FOS: Physical sciences ,Analytical equations ,Statistical physics ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Scaling ,Mathematics ,Universality (dynamical systems) - Abstract
The competitive growth models involving only one kind of particles (CGM), are a mixture of two processes one with probability $p$ and the other with probability $1-p$. The $p-$dependance produce crossovers between two different regimes. We demonstrate that the coefficients of the continuous equation, describing their universality classes, are quadratic in $p$ (or $1-p$). We show that the origin of such dependance is the existence of two different average time rates. Thus, the quadratic $p-$dependance is an universal behavior of all the CGM. We derive analytically the continuous equations for two CGM, in 1+1 dimensions, from the microscopic rules using a regularization procedure. We propose generalized scalings that reproduce the scaling behavior in each regime. In order to verify the analytic results and the scalings, we perform numerical integrations of the derived analytical equations. The results are in excellent agreement with those of the microscopic CGM presented here and with the proposed scalings., Comment: 9 pages, 3 figures more...
- Published
- 2004
- Full Text
- View/download PDF
122. Current Flow in Random Resistor Networks: The Role of Percolation in Weak and Strong Disorder
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Lidia A. Braunstein, Zhenhua Wu, Shlomo Havlin, Sergey V. Buldyrev, Eduardo López, and H. Eugene Stanley
- Subjects
Length scale ,Condensed Matter - Materials Science ,Condensed matter physics ,Materials Science (cond-mat.mtrl-sci) ,FOS: Physical sciences ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Square lattice ,Distribution (mathematics) ,Path length ,Percolation ,Exponent ,Limit (mathematics) ,Random variable ,Mathematics - Abstract
We study the current flow paths between two edges in a random resistor network on a $L\times L$ square lattice. Each resistor has resistance $e^{ax}$, where $x$ is a uniformly-distributed random variable and $a$ controls the broadness of the distribution. We find (a) the scaled variable $u\equiv L/a^\nu$, where $\nu$ is the percolation connectedness exponent, fully determines the distribution of the current path length $\ell$ for all values of $u$. For $u\gg 1$, the behavior corresponds to the weak disorder limit and $\ell$ scales as $\ell\sim L$, while for $u\ll 1$, the behavior corresponds to the strong disorder limit with $\ell\sim L^{d_{\scriptsize opt}}$, where $d_{\scriptsize opt} = 1.22\pm0.01$ is the optimal path exponent. (b) In the weak disorder regime, there is a length scale $\xi\sim a^\nu$, below which strong disorder and critical percolation characterize the current path., Comment: 9 pages, 4 figures more...
- Published
- 2004
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123. Optimal Paths in Disordered Complex Networks
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Shlomo Havlin, Sergey V. Buldyrev, Reuven Cohen, H. Eugene Stanley, and Lidia A. Braunstein
- Subjects
Physics ,Combinatorics ,Communication ,Path (graph theory) ,General Physics and Astronomy ,Social Support ,Soft Condensed Matter (cond-mat.soft) ,FOS: Physical sciences ,Condensed Matter - Soft Condensed Matter ,Complex network ,Models, Theoretical ,Degree distribution ,Models, Biological - Abstract
We study the optimal distance in networks, $\ell_{\scriptsize opt}$, 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 $\ell_{\scriptsize opt}\sim N^{1/3}$ in both Erd\H{o}s-R\'enyi (ER) and Watts-Strogatz (WS) networks. For scale free (SF) networks, with degree distribution $P(k) \sim k^{-\lambda}$, we find that $\ell_{\scriptsize opt}$ scales as $N^{(\lambda - 3)/(\lambda - 1)}$ for $3, Comment: 5 pages, 4 figures, accepted for publication in Physical Review Letters more...
- Published
- 2003
- Full Text
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124. Universality classes for self-avoiding walks in a strongly disordered system
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H. Eugene Stanley, Lidia A. Braunstein, Shlomo Havlin, and Sergey V. Buldyrev
- Subjects
Combinatorics ,Fractal ,Lattice (order) ,Probability distribution ,Statistical physics ,Fixed length ,Renormalization group ,Condensed Matter::Disordered Systems and Neural Networks ,Fractal dimension ,Mathematics ,Universality (dynamical systems) - Abstract
We study the behavior of self-avoiding walks (SAWs) on square and cubic lattices in the presence of strong disorder. We simulate the disorder by assigning random energy epsilon taken from a probability distribution P(epsilon) to each site (or bond) of the lattice. We study the strong disorder limit for an extremely broad range of energies with P(epsilon) is proportional to 1/epsilon. For each configuration of disorder, we find by exact enumeration the optimal SAW of fixed length N and fixed origin that minimizes the sum of the energies of the visited sites (or bonds). We find the fractal dimension of the optimal path to be d(opt)=1.52+/-0.10 in two dimensions (2D) and d(opt)=1.82+/-0.08 in 3D. Our results imply that SAWs in strong disorder with fixed N are much more compact than SAWs in disordered media with a uniform distribution of energies, optimal paths in strong disorder with fixed end-to-end distance R, and SAWs on a percolation cluster. Our results are also consistent with the possibility that SAWs in strong disorder belong to the same universality class as the maximal SAW on a percolation cluster at criticality, for which we calculate the fractal dimension d(max)=1.64+/-0.02 for 2D and d(max)=1.87+/-0.05 for 3D, values very close to the fractal dimensions of the percolation backbone in 2D and 3D. more...
- Published
- 2002
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125. When a Text Is Translated Does the Complexity of Its Vocabulary Change? Translations and Target Readerships
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Sasuke Miyazima, Gregorio D' Agostino, Lidia A. Braunstein, Henio H. A. Rego, H. Eugene Stanley, and D'Agostino, G.
- Subjects
Computer and Information Sciences ,Vocabulary ,Science ,media_common.quotation_subject ,Energy (esotericism) ,Social Sciences ,Research and Analysis Methods ,computer.software_genre ,Semantics ,Systems Science ,01 natural sciences ,010305 fluids & plasmas ,Computational Techniques ,0103 physical sciences ,Humans ,Translations ,010306 general physics ,media_common ,Multidisciplinary ,Zipf's law ,business.industry ,Linguistics ,Complex Systems ,16. Peace & justice ,Computational Linguistics ,Physical Sciences ,Medicine ,Probability distribution ,Artificial intelligence ,Computational linguistics ,business ,computer ,Mathematics ,Natural language processing ,Word (computer architecture) ,Research Article - Abstract
In linguistic studies, the academic level of the vocabulary in a text can be described in terms of statistical physics by using a ''temperature'' concept related to the text's word-frequency distribution. We propose a ''comparative thermo-linguistic'' technique to analyze the vocabulary of a text to determine its academic level and its target readership in any given language. We apply this technique to a large number of books by several authors and examine how the vocabulary of a text changes when it is translated from one language to another. Unlike the uniform results produced using the Zipf law, using our ''word energy'' distribution technique we find variations in the power-law behavior. We also examine some common features that span across languages and identify some intriguing questions concerning how to determine when a text is suitable for its intended readership. Copyright more...
- Published
- 2014
- Full Text
- View/download PDF
126. Theoretical Continuous Equation Derived from the Microscopic Dynamics for Growing Interfaces in Quenched Media
- Author
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C. D. Archubi, R. C. Buceta, Lidia A. Braunstein, and G. Costanza
- Subjects
Statistical Mechanics (cond-mat.stat-mech) ,Multiplicative function ,Mathematical analysis ,FOS: Physical sciences ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Directed percolation ,Noise (electronics) ,Numerical integration ,Nonlinear system ,Regularization (physics) ,Condensed Matter::Statistical Mechanics ,Statistical physics ,Scaling ,Condensed Matter - Statistical Mechanics ,Mathematics - Abstract
We present an analytical continuous equation for the Tang and Leschhorn model [Phys. Rev A {\bf 45}, R8309 (1992)] derived from his microscopic rules using a regularization procedure. As well in this approach the nonlinear term $(\nabla h)^2$ arises naturally from the microscopic dynamics even if the continuous equation is not the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. {\bf 56}, 889 (1986)] with quenched noise (QKPZ). Our equation looks like a QKPZ but with multiplicative quenched and thermal noise. The numerical integration of our equation reproduce the scaling exponents of the roughness of this directed percolation depinning model., 8 pages, 4 figures. Submitted to Phys. Rev. E (Rapid Comunication) more...
- Published
- 1999
127. Microscopic equation for growing interfaces in quenched disordered media
- Author
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R. C. Buceta, Anastasio Díaz-Sánchez, and Lidia A. Braunstein
- Subjects
Physics ,Condensed matter physics ,Statistical Mechanics (cond-mat.stat-mech) ,General Physics and Astronomy ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Surface finish ,Function (mathematics) ,Noise (electronics) ,Evolution equation ,Condensed Matter::Statistical Mechanics ,Diffusion (business) ,Mathematical Physics ,Condensed Matter - Statistical Mechanics - Abstract
We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [L. H. Tang and H. Leschhorn, Phys. Rev. A {\bf 45}, R8309 (1992)]. The evolution equation for the height, the mean height, and the roughness are reached in a simple way. An equation for the interface activity density (or free sites density) as function of time is obtained. The microscopic equation allows us to express these equations into two contributions: the diffusion and the substratum contributions. All these equations shows the strong interplay between the diffusion and the substratum contribution in the dynamics., 10 pages and 8 figures more...
- Published
- 1999
128. Growing interfaces in quenched disordered media
- Author
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Lidia A. Braunstein, Anastasio Díaz-Sánchez, and R. C. Buceta
- Subjects
Statistics and Probability ,Physics ,Condensed matter physics ,Statistical Mechanics (cond-mat.stat-mech) ,Monte Carlo method ,FOS: Physical sciences ,Function (mathematics) ,Surface finish ,Condensed Matter Physics ,Noise (electronics) ,Simple (abstract algebra) ,Evolution equation ,Exponent ,Diffusion (business) ,Condensed Matter - Statistical Mechanics - Abstract
We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [{\em Phys. Rev.} {\bf A 45}, R8309 (1992)]. The evolution equations for the mean heigth and the roughness are reached in a simple way. Also, an equation for the interface activity density (i.e. interface density of free sites) as function of time is obtained. The microscopic equation allows us to express these equations in two contributions: the diffusion and the substratum one. All the equation shows the strong interplay between both contributions in the dynamics. A macroscopic evolution equation for the roughness is presented for this model for the critical pressure $p=0.461$. The dynamical exponent $\beta=0.629$ is analitically obtained in a simple way. Theoretical results are in excellent agreement with the Monte Carlo simulation., Comment: 6 pages and 3 figures. Conference on Percolation and disordered systems: theory and applications, Giessen, Germany, (July, 1998) more...
- Published
- 1999
- Full Text
- View/download PDF
129. Effect of degree correlations above the first shell on the percolation transition
- Author
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Lidia A. Braunstein, Camila Buono, L. D. Valdez, and P. A. Macri
- Subjects
Physics - Physics and Society ,Statistical Mechanics (cond-mat.stat-mech) ,Degree (graph theory) ,Generalization ,Shell (structure) ,FOS: Physical sciences ,General Physics and Astronomy ,Observable ,Physics and Society (physics.soc-ph) ,Correlation ,Percolation ,Node (circuits) ,Statistical physics ,Condensed Matter - Statistical Mechanics ,Mathematics - Abstract
The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on processes on top of them, has not yet been discussed. In this letter, using different correlation algorithms to generate assortative networks, we show that for very assortative networks the behavior of the main observables in percolation processes depends on the algorithm used to build the network. The different alghoritms used here introduce different inner structures that are missed in Pearson's coefficient. We explain the different behaviors through a generalization of Pearson's coefficient that allows to study the correlations at chemical distances l from a root node. We apply our findings to real networks., In press EPL more...
- Published
- 2011
- Full Text
- View/download PDF
130. Erratum: Directed percolation depinning models: Evolution equations [Phys. Rev. E 59, 4243 (1999)]
- Author
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R. C. Buceta, Lidia A. Braunstein, N. Giovambattista, and Anastasio Díaz-Sánchez
- Subjects
Physics ,Condensed matter physics ,Statistical physics ,Diffusion (business) ,Directed percolation - Published
- 1999
- Full Text
- View/download PDF
131. Braunstein, Buceta, and Giovambattista Reply
- Author
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R. C. Buceta, Lidia A. Braunstein, and N. Giovambattista
- Subjects
Physics ,Quantum mechanics ,Lattice (order) ,General Physics and Astronomy - Abstract
We argue that the fail in reproducing theearly time regime until the correlations are generated (t ≃ 1 at the depinning transition) isbecause the density of active sites of the interface is not a constant p. This density dependson time as we will show below. At time t a site i, of a one dimensional lattice of size L, ischosen at random with probability 1/L. Let us denote by h more...
- Published
- 1999
- Full Text
- View/download PDF
132. Optimal resource diffusion for suppressing disease spreading in multiplex networks.
- Author
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Xiaolong Chen, Wei Wang, Shimin Cai, H Eugene Stanley, and Lidia A Braunstein
- Published
- 2018
- Full Text
- View/download PDF
133. Cascading failure and recovery of spatially interdependent networks.
- Author
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Sheng Hong, Juxing Zhu, Lidia A Braunstein, Tingdi Zhao, and Qiuju You
- Published
- 2017
- Full Text
- View/download PDF
134. Promoting information spreading by using contact memory.
- Author
-
Lei Gao, Wei Wang, Panpan Shu, Hui Gao, and Lidia A. Braunstein
- Abstract
Promoting information spreading is a booming research topic in network science community. However, the existing studies about promoting information spreading seldom took into account the human memory, which plays an important role in the spreading dynamics. In this letter we propose a non-Markovian information spreading model on complex networks, in which every informed node contacts a neighbor by using the memory of neighbor's accumulated contact numbers in the past. We systematically study the information spreading dynamics on uncorrelated configuration networks and a group of 22 real-world networks, and find an effective contact strategy of promoting information spreading, i.e., the informed nodes preferentially contact neighbors with a small number of accumulated contacts. According to the effective contact strategy, the high-degree nodes are more likely to be chosen as the contacted neighbors in the early stage of the spreading, while in the late stage of the dynamics, the nodes with small degrees are preferentially contacted. We also propose a mean-field theory to describe our model, which qualitatively agrees well with the stochastic simulations on both artificial and real-world networks. [ABSTRACT FROM AUTHOR] more...
- Published
- 2017
- Full Text
- View/download PDF
135. Epidemic spreading and immunization strategy in multiplex networks.
- Author
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Lucila G Alvarez Zuzek, Camila Buono, and Lidia A Braunstein
- Published
- 2015
- Full Text
- View/download PDF
136. When a text is translated does the complexity of its vocabulary change? Translations and target readerships.
- Author
-
Hênio Henrique Aragão Rêgo, Lidia A Braunstein, Gregorio D'Agostino, H Eugene Stanley, and Sasuke Miyazima
- Subjects
Medicine ,Science - Abstract
In linguistic studies, the academic level of the vocabulary in a text can be described in terms of statistical physics by using a "temperature" concept related to the text's word-frequency distribution. We propose a "comparative thermo-linguistic" technique to analyze the vocabulary of a text to determine its academic level and its target readership in any given language. We apply this technique to a large number of books by several authors and examine how the vocabulary of a text changes when it is translated from one language to another. Unlike the uniform results produced using the Zipf law, using our "word energy" distribution technique we find variations in the power-law behavior. We also examine some common features that span across languages and identify some intriguing questions concerning how to determine when a text is suitable for its intended readership. more...
- Published
- 2014
- Full Text
- View/download PDF
137. Epidemics in partially overlapped multiplex networks.
- Author
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Camila Buono, Lucila G Alvarez-Zuzek, Pablo A Macri, and Lidia A Braunstein
- Subjects
Medicine ,Science - Abstract
Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction [Formula: see text] of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted [Formula: see text]. We also theoretically determine the dependence of the epidemic threshold on the fraction [Formula: see text] of shared nodes in a system composed of two layers. We find that in the limit of [Formula: see text] the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network. more...
- Published
- 2014
- Full Text
- View/download PDF
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