arXiv subjects

Shlomo Havlin

Publications and source records attributed to Shlomo Havlin.

At least 163 records · Page 9Linked to original sources

arXiv2013

Anomalous biased diffusion in networks

We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the packet/particle to travel at every hop towards a site which is along the shortest path to the target node. We investigate the scaling of the mean first passage time (MFPT) with the size of the network. We find by using theoretical analysis and computer simulations that for Random Regular (RR) and Erdős-Rényi (ER) networks, there exists a threshold probability, $p_{th}$, such that for $p p_{th}$ the MFPT scales logarithmically with $N$. The threshold value $p_{th}$ of the bias parameter for which the regime transition occurs is found to depend only on the mean degree of the nodes. An exact solution for every value of $p$ is given for the scaling of the MFPT in RR networks. The regime transition is also observed for the second moment of the probability distribution function, the standard deviation.

physics.soc-ph↗

arXiv2013

Robustness of partially interdependent network formed of clustered networks

Clustering, or transitivity has been observed in real networks and its effects on their structure and function has been discussed extensively. The focus of these studies has been on clustering of single networks while the effect of clustering on the robustness of coupled networks received very little attention. Only the case of a pair of fully coupled networks with clustering has been studied recently. Here we generalize the study of clustering of a fully coupled pair of networks to the study of partially interdependent network of networks with clustering within the network components. We show both analytically and numerically, how clustering within the networks, affects the percolation properties of interdependent networks, including percolation threshold, size of giant component and critical coupling point where first order phase transition changes to second order phase transition as the coupling between the networks reduces. We study two types of clustering: one type proposed by Newman where the average degree is kept constant while changing the clustering and the other proposed by Hackett $et$ $al.$ where the degree distribution is kept constant. The first type of clustering is treated both analytically and numerically while the second one is treated only numerically.

physics.soc-ph↗

arXiv2013

Random walk with priorities in communication-like networks

We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et al., Phys. Rev. E 77, 020103 (2008); here we provide additional results. We solve analytically the diffusion coefficients of the two species in lattices for a number of protocols. In networks, we find that the probability of a B particle to be free decreases exponentially with the node degree. In scale-free networks, this leads to localization of the B's at the hubs and arrest of their motion. To remedy this, we investigate several strategies to avoid trapping of the B's: moving an A instead of the hindered B; allowing a trapped B to hop with a small probability; biased walk towards non-hub nodes; and limiting the capacity of nodes. We obtain analytic results for lattices and networks, and discuss the advantages and shortcomings of the possible strategies.

cond-mat.dis-nn↗

arXiv2013

Percolation of a general network of networks

Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that the damage in the network due to a failure is a continuous function of the fraction of failed nodes. In sharp contrast, in NetONet, due to the cascading failures, the percolation transition may be discontinuous and even a single node failure may lead to abrupt collapse of the system. We demonstrate our general framework for a NetONet composed of $n$ classic Erdős-Rényi (ER) networks, where each network depends on the same number $m$ of other networks, i.e., a random regular network of interdependent ER networks. In contrast to a \emph{treelike} NetONet in which the size of the largest connected cluster (mutual component) depends on $n$, the loops in the RR NetONet cause the largest connected cluster to depend only on $m$. We also analyzed the extremely vulnerable feedback condition of coupling. In the case of ER networks, the NetONet only exhibits two phases, a second order phase transition and collapse, and there is no first phase transition regime unlike the no feedback condition. In the case of NetONet composed of RR networks, there exists a first order phase transition when $q$ is large and second order phase transition when $q$ is small. Our results can help in designing robust interdependent systems.

physics.soc-ph↗

arXiv2013

Towards designing robust coupled networks

Natural and technological interdependent systems have been shown to be highly vulnerable due to cascading failures and an abrupt collapse of global connectivity under initial failure. Mitigating the risk by partial disconnection endangers their functionality. Here we propose a systematic strategy of selecting a minimum number of autonomous nodes that guarantee a smooth transition in robustness. Our method which is based on betweenness is tested on various examples including the famous 2003 electrical blackout of Italy. We show that, with this strategy, the necessary number of autonomous nodes can be reduced by a factor of five compared to a random choice. We also find that the transition to abrupt collapse follows tricritical scaling characterized by a set of exponents which is independent on the protection strategy.

cond-mat.stat-mech↗

arXiv2013

Improved El Niño-Forecasting by Cooperativity Detection

Although anomalous episodical warming of the eastern equatorial Pacific, dubbed El Niño by Peruvian fishermen, has major (and occasionally devastating) impacts around the globe, robust forecasting is still limited to about six months ahead. A significant extension of the pre-warming time would be instrumental for avoiding some of the worst damages such as harvest failures in developing countries. Here we introduce a novel avenue towards El Niño-prediction based on network methods inspecting emerging teleconnections. Our approach starts from the evidence that a large-scale cooperative mode - linking the El Niño-basin (equatorial Pacific corridor) and the rest of the ocean - builds up in the calendar year before the warming event. On this basis, we can develop an efficient 12 months-forecasting scheme, i.e., achieve some doubling of the early-warning period. Our method is based on high-quality observational data as available since 1950 and yields hit rates above 0.5, while false-alarm rates are below 0.1.

physics.ao-ph↗

arXiv2013

Origins of power-law degree distribution in the heterogeneity of human activity in social networks

The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a "maximum entropy attachment" model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.

physics.soc-ph↗

arXiv2013

The dominant imprint of Rossby waves in the climate network

The connectivity pattern of networks, which are based on a correlation between ground level temperature time series, shows a dominant dense stripe of links in the southern ocean. We show that statistical categorization of these links yields a clear association with the pattern of an atmospheric Rossby wave, one of the major mechanisms associated with the weather system and with planetary scale energy transport. It is shown that alternating densities of negative and positive links (correlations) are arranged in half Rossby wave distances around 3,500 km, 7,000 km and 10,000 km and are aligned with the expected direction of energy flow, distribution of time delays and the seasonality of these waves. It is also shown that long distance links (i.e., of distances larger than 2,000 km) that are associated with Rossby waves are the most dominant in the climate network. Climate networks may thus be used as an efficient new way to detect and analyze Rossby waves, based on reliable and available ground level measurements, in addition to the frequently used 300 hPa reanalysis meridional wind data.

physics.ao-ph↗

arXiv2013

Efficient learning strategy of Chinese characters based on network approach

Based on network analysis of hierarchical structural relations among Chinese characters, we develop an efficient learning strategy of Chinese characters. We regard a more efficient learning method if one learns the same number of useful Chinese characters in less effort or time. We construct a node-weighted network of Chinese characters, where character usage frequencies are used as node weights. Using this hierarchical node-weighted network, we propose a new learning method, the distributed node weight (DNW) strategy, which is based on a new measure of nodes' importance that takes into account both the weight of the nodes and the hierarchical structure of the network. Chinese character learning strategies, particularly their learning order, are analyzed as dynamical processes over the network. We compare the efficiency of three theoretical learning methods and two commonly used methods from mainstream Chinese textbooks, one for Chinese elementary school students and the other for students learning Chinese as a second language. We find that the DNW method significantly outperforms the others, implying that the efficiency of current learning methods of major textbooks can be greatly improved.

physics.soc-ph↗

arXiv2013

Effect of the Interconnected Network Structure on the Epidemic Threshold

Most real-world networks are not isolated. In order to function fully, they are interconnected with other networks, and this interconnection influences their dynamic processes. For example, when the spread of a disease involves two species, the dynamics of the spread within each species (the contact network) differs from that of the spread between the two species (the interconnected network). We model two generic interconnected networks using two adjacency matrices, A and B, in which A is a 2N*2N matrix that depicts the connectivity within each of two networks of size N, and B a 2N*2N matrix that depicts the interconnections between the two. Using an N-intertwined mean-field approximation, we determine that a critical susceptable-infected-susceptable (SIS) epidemic threshold in two interconnected networks is 1/λ1(A+αB), where the infection rate is βwithin each of the two individual networks and αβin the interconnected links between the two networks and λ1(A+αB) is the largest eigenvalue of the matrix A+αB. In order to determine how the epidemic threshold is dependent upon the structure of interconnected networks, we analytically derive λ1(A+αB) using perturbation approximation for small and large α, the lower and upper bound for any αas a function of the adjacency matrix of the two individual networks, and the interconnections between the two and their largest eigenvalues/eigenvectors. We verify these approximation and boundary values for λ1(A+αB) using numerical simulations, and determine how component network features affect λ1(A+αB).

physics.soc-ph↗

arXiv2013

Percolation of Partially Interdependent Scale-free Networks

We study the percolation behavior of two interdependent scale-free (SF) networks under random failure of 1-$p$ fraction of nodes. Our results are based on numerical solutions of analytical expressions and simulations. We find that as the coupling strength between the two networks $q$ reduces from 1 (fully coupled) to 0 (no coupling), there exist two critical coupling strengths $q_1$ and $q_2$, which separate three different regions with different behavior of the giant component as a function of $p$. (i) For $q \geq q_1$, an abrupt collapse transition occurs at $p=p_c$. (ii) For $q_2 3$, $q_1$ decreases with increasing $λ$. $(b)$ In the hybrid transition, at the $q_2 < q < q_1$ region, the mutual giant component $P_{\infty}$ jumps discontinuously at $p=p^{jump}_c$ to a very small but non-zero value, and when reducing $p$, $P_{\infty}$ continuously approaches to 0 at $p_c = 0$ for $λ< 3$ and at $p_c > 0$ for $λ> 3$. Thus, the known theoretical $p_c=0$ for a single network with $λ\leqslant 3$ is expected to be valid also for strictly partial interdependent networks.

physics.data-an↗

arXiv2013

Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation

As economic entities become increasingly interconnected, a shock in a financial network can provoke significant cascading failures throughout the system. To study the systemic risk of financial systems, we create a bi-partite banking network model composed of banks and bank assets and propose a cascading failure model to describe the risk propagation process during crises. We empirically test the model with 2007 US commercial banks balance sheet data and compare the model prediction of the failed banks with the real failed banks after 2007. We find that our model efficiently identifies a significant portion of the actual failed banks reported by Federal Deposit Insurance Corporation. The results suggest that this model could be useful for systemic risk stress testing for financial systems. The model also identifies that commercial rather than residential real estate assets are major culprits for the failure of over 350 US commercial banks during 2008-2011.

q-fin.GN↗

arXiv2012

Languages cool as they expand: Allometric scaling and the decreasing need for new words

We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This "cooling pattern" forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature.

physics.soc-ph↗

arXiv2012

The robustness of interdependent clustered networks

It was recently found that cascading failures can cause the abrupt breakdown of a system of interdependent networks. Using the percolation method developed for single clustered networks by Newman [Phys. Rev. Lett. {\bf 103}, 058701 (2009)], we develop an analytical method for studying how clustering within the networks of a system of interdependent networks affects the system's robustness. We find that clustering significantly increases the vulnerability of the system, which is represented by the increased value of the percolation threshold $p_c$ in interdependent 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 k-shell decomposition method for weighted networks

We present a generalized method for calculating the k-shell structure of weighted networks. The method takes into account both the weight and the degree of a network, in such a way that in the absence of weights we resume the shell structure obtained by the classic k-shell decomposition. In the presence of weights, we show that the method is able to partition the network in a more refined way, without the need of any arbitrary threshold on the weight values. Furthermore, by simulating spreading processes using the susceptible-infectious-recovered model in four different weighted real-world networks, we show that the weighted k-shell decomposition method ranks the nodes more accurately, by placing nodes with higher spreading potential into shells closer to the core. In addition, we demonstrate our new method on a real economic network and show that the core calculated using the weighted k-shell method is more meaningful from an economic perspective when compared with the unweighted one.

physics.soc-ph↗

arXiv2012

Complex networks embedded in space: Dimension and scaling relations between mass, topological distance and Euclidean distance

Many real networks are embedded in space, where in some of them the links length decay as a power law distribution with distance. Indications that such systems can be characterized by the concept of dimension were found recently. Here, we present further support for this claim, based on extensive numerical simulations for model networks embedded on lattices of dimensions $d_e=1$ and $d_e=2$. We evaluate the dimension $d$ from the power law scaling of (a) the mass of the network with the Euclidean radius $r$ and (b) the probability of return to the origin with the distance $r$ travelled by the random walker. Both approaches yield the same dimension. For networks with $δ< d_e$, $d$ is infinity, while for $δ> 2d_e$, $d$ obtains the value of the embedding dimension $d_e$. In the intermediate regime of interest $d_e \leq δ< 2 d_e$, our numerical results suggest that $d$ decreases continously from $d = \infty$ to $d_e$, with $d - d_e \sim (δ- d_e)^{-1}$ for $δ$ close to $d_e$. Finally, we discuss the scaling of the mass $M$ and the Euclidean distance $r$ with the topological distance $\ell$. Our results suggest that in the intermediate regime $d_e \leq δ< 2 d_e$, $M(\ell)$ and $r(\ell)$ do not increase with $\ell$ as a power law but with a stretched exponential, $M(\ell) \sim \exp [A \ell^{δ' (2 - δ')}]$ and $r(\ell) \sim \exp [B \ell^{δ' (2 - δ')}]$, where $δ' = δ/d_e$. The parameters $A$ and $B$ are related to $d$ by $d = A/B$, such that $M(\ell) \sim r(\ell)^d$. For $δ< d_e$, $M$ increases exponentially with $\ell$, as known for $δ=0$, while $r$ is constant and independent of $\ell$. For $δ\geq 2d_e$, we find power law scaling, $M(\ell) \sim \ell^{d_\ell}$ and $r(\ell) \sim \ell^{1/d_{min}}$, with $d_\ell \cdot d_{min} = d$.

physics.soc-ph↗

arXiv2012

Earthquake networks based on similar activity patterns

Earthquakes are a complex spatiotemporal phenomenon, the underlying mechanism for which is still not fully understood despite decades of research and analysis. We propose and develop a network approach to earthquake events. In this network, a node represents a spatial location while a link between two nodes represents similar activity patterns in the two different locations. The strength of a link is proportional to the strength of the cross-correlation in activities of two nodes joined by the link. We apply our network approach to a Japanese earthquake catalog spanning the 14-year period 1985-1998. We find strong links representing large correlations between patterns in locations separated by more than 1000 km, corroborating prior observations that earthquake interactions have no characteristic length scale. We find network characteristics not attributable to chance alone, including a large number of network links, high node assortativity, and strong stability over time.

physics.geo-ph↗