arXiv subjects

Shlomo Havlin

Publications and source records attributed to Shlomo Havlin.

At least 145 records · Page 8Linked to original sources

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

How does public opinion become extreme?

We investigate the emergence of extreme opinion trends in society by employing statistical physics modeling and analysis on polls that inquire about a wide range of issues such as religion, economics, politics, abortion, extramarital sex, books, movies, and electoral vote. The surveys lay out a clear indicator of the rise of extreme views. The precursor is a nonlinear relation between the fraction of individuals holding a certain extreme view and the fraction of individuals that includes also moderates, e.g., in politics, those who are "very conservative" versus "moderate to very conservative" ones. We propose an activation model of opinion dynamics with interaction rules based on the existence of individual "stubbornness" that mimics empirical observations. According to our modeling, the onset of nonlinearity can be associated to an abrupt bootstrap-percolation transition with cascades of extreme views through society. Therefore, it represents an early-warning signal to forecast the transition from moderate to extreme views. Moreover, by means of a phase diagram we can classify societies according to the percolative regime they belong to, in terms of critical fractions of extremists and people's ties.

physics.soc-ph↗

arXiv2014

Classical mechanics of economic networks

Financial networks are dynamic. To assess their systemic importance to the world-wide economic network and avert losses we need models that take the time variations of the links and nodes into account. Using the methodology of classical mechanics and Laplacian determinism we develop a model that can predict the response of the financial network to a shock. We also propose a way of measuring the systemic importance of the banks, which we call BankRank. Using European Bank Authority 2011 stress test exposure data, we apply our model to the bipartite network connecting the largest institutional debt holders of the troubled European countries (Greece, Italy, Portugal, Spain, and Ireland). From simulating our model we can determine whether a network is in a "stable" state in which shocks do not cause major losses, or a "unstable" state in which devastating damages occur. Fitting the parameters of the model, which play the role of physical coupling constants, to Eurozone crisis data shows that before the Eurozone crisis the system was mostly in a "stable" regime, and that during the crisis it transitioned into an "unstable" regime. The numerical solutions produced by our model match closely the actual time-line of events of the crisis. We also find that, while the largest holders are usually more important, in the unstable regime smaller holders also exhibit systemic importance. Our model also proves useful for determining the vulnerability of banks and assets to shocks. This suggests that our model may be a useful tool for simulating the response dynamics of shared portfolio networks.

q-fin.RM↗

arXiv2014

Percolation of localized attack on complex networks

The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks are neither random nor hub-targeted, but localized, where a group of neighboring nodes in a network are attacked and fail. In this paper we develop a percolation framework to analytically and numerically study the robustness of complex networks against such localized attack. In particular, we investigate this robustness in Erdős-Rényi networks, random-regular networks, and scale-free networks. Our results provide insight into how to better protect networks, enhance cybersecurity, and facilitate the design of more robust infrastructures.

physics.soc-ph↗

arXiv2014

Robustness of networks with topologies of dependency links

The robustness of complex networks with dependencies has been studied in recent years. However, previous studies focused on the robustness of networks composed of dependency links without network topology. In this study, we will analyze the percolation properties of a realistic network model where dependency links follow certain network topology. We perform the theoretical analysis and numerical simulations to show the critical effects of topology of dependency links on robustness of complex networks. For Erdös-Rényi (ER) connectivity network, we find that the system with dependency of RR topology is more vulnerable than system with dependency of ER topology. And RR-RR (i.e. random-regular (RR) network with dependency of RR topology) disintegrates in an abrupt transition. In particular, we find that the system of RR-ER shows different types of phase transitions. For system of different combinations, the type of percolation depends on the interaction between connectivity topology and dependency topology.

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↗

arXiv2014

Ranking the Economic Importance of Countries and Industries

In the current era of worldwide stock market interdependencies, the global financial village has become increasingly vulnerable to systemic collapse. The recent global financial crisis has highlighted the necessity of understanding and quantifying interdependencies among the world's economies, developing new effective approaches to risk evaluation, and providing mitigating solutions. We present a methodological framework for quantifying interdependencies in the global market and for evaluating risk levels in the world-wide financial network. The resulting information will enable policy and decision makers to better measure, understand, and maintain financial stability. We use the methodology to rank the economic importance of each industry and country according to the global damage that would result from their failure. Our quantitative results shed new light on China's increasing economic dominance over other economies, including that of the USA, to the global economy.

q-fin.GN↗

arXiv2014

Influence of autocorrelation on the topology of the climate network

Different definitions of links in climate networks may lead to considerably different network topologies. We construct a network from climate records of surface level atmospheric temperature in different geographical sites around the globe using two commonly used definitions of links. Utilizing detrended fluctuation analysis, shuffled surrogates and separation analysis of maritime and continental records, we find that one of the major influences on the structure of climate networks is due to the auto-correlation in the records, that may introduce spurious links. This may explain why different methods could lead to different climate network topologies.

physics.ao-ph↗

arXiv2014

Efficiency of message transmission using biased random walks in complex networks in the presence of traps

We study the problem of a particle/message that travels as a biased random walk towards a target node in a network in the presence of traps. The bias is represented as the probability $p$ of the particle to travel along the shortest path to the target node. The efficiency of the transmission process is expressed through the fraction $f_g$ of particles that succeed to reach the target without being trapped. By relating $f_g$ with the number $S$ of nodes visited before reaching the target, we firstly show that, for the unbiased random walk, $f_g$ is inversely proportional to both the concentration $c$ of traps and the size $N$ of the network. For the case of biased walks, a simple approximation of $S$ provides an analytical solution that describes well the behavior of $f_g$, especially for $p>0.5$. Also, it is shown that for a given value of the bias $p$, when the concentration of traps is less than a threshold value equal to the inverse of the Mean First Passage Time (MFPT) between two randomly chosen nodes of the network, the efficiency of transmission is unaffected by the presence of traps and almost all the particles arrive at the target. As a consequence, for a given concentration of traps, we can estimate the minimum bias that is needed to have unaffected transmission, especially in the case of Random Regular (RR), Erdős-Rényi (ER) and Scale-Free (SF) networks, where an exact expression (RR and ER) or an upper bound (SF) of the MFPT is known analytically. We also study analytically and numerically, the fraction $f_g$ of particles that reach the target on SF networks, where a single trap is placed on the highest degree node. For the unbiased random walk, we find that $f_g \sim N^{-1/(γ-1)}$, where $γ$ is the power law exponent of the SF network.

physics.soc-ph↗

arXiv2014

Simultaneous first and second order percolation transitions in interdependent networks

In a system of interdependent networks, an initial failure of nodes invokes a cascade of iterative failures that may lead to a total collapse of the whole system in a form of an abrupt first order transition. When the fraction of initial failed nodes $1-p$ reaches criticality, $p=p_c$, the abrupt collapse occurs by spontaneous cascading failures. At this stage, the giant component decreases slowly in a plateau form and the number of iterations in the cascade, $τ$, diverges. The origin of this plateau and its increasing with the size of the system remained unclear. Here we find that simultaneously with the abrupt first order transition a spontaneous second order percolation occurs during the cascade of iterative failures. This sheds light on the origin of the plateau and on how its length scales with the size of the system. Understanding the critical nature of the dynamical process of cascading failures may be useful for designing strategies for preventing and mitigating catastrophic collapses.

cond-mat.stat-mech↗

arXiv2014

Conditions for viral influence spreading through multiplex correlated social networks

A fundamental problem in network science is to predict how certain individuals are able to initiate new networks to spring up "new ideas". Frequently, these changes in trends are triggered by a few innovators who rapidly impose their ideas through "viral" influence spreading producing cascades of followers fragmenting an old network to create a new one. Typical examples include the raise of scientific ideas or abrupt changes in social media, like the raise of Facebook.com to the detriment of Myspace.com. How this process arises in practice has not been conclusively demonstrated. Here, we show that a condition for sustaining a viral spreading process is the existence of a multiplex correlated graph with hidden "influence links". Analytical solutions predict percolation phase transitions, either abrupt or continuous, where networks are disintegrated through viral cascades of followers as in empirical data. Our modeling predicts the strict conditions to sustain a large viral spreading via a scaling form of the local correlation function between multilayers, which we also confirm empirically. Ultimately, the theory predicts the conditions for viral cascading in a large class of multiplex networks ranging from social to financial systems and markets.

physics.soc-ph↗

arXiv2014

Non-consensus opinion model on directed networks

Dynamic social opinion models have been widely studied on undirected networks, and most of them are based on spin interaction models that produce a consensus. In reality, however, many networks such as Twitter and the World Wide Web are directed and are composed of both unidirectional and bidirectional links. Moreover, from choosing a coffee brand to deciding who to vote for in an election, two or more competing opinions often coexist. In response to this ubiquity of directed networks and the coexistence of two or more opinions in decision-making situations, we study a non-consensus opinion model introduced by Shao et al. \cite{shao2009dynamic} on directed networks. We define directionality $ξ$ as the percentage of unidirectional links in a network, and we use the linear correlation coefficient $ρ$ between the indegree and outdegree of a node to quantify the relation between the indegree and outdegree. We introduce two degree-preserving rewiring approaches which allow us to construct directed networks that can have a broad range of possible combinations of directionality $ξ$ and linear correlation coefficient $ρ$ and to study how $ξ$ and $ρ$ impact opinion competitions. We find that, as the directionality $ξ$ or the indegree and outdegree correlation $ρ$ increases, the majority opinion becomes more dominant and the minority opinion's ability to survive is lowered.

physics.soc-ph↗

arXiv2014

Resilience of modular complex networks

Complex networks often have a modular structure, where a number of tightly- connected groups of nodes (modules) have relatively few interconnections. Modularity had been shown to have an important effect on the evolution and stability of biological networks, on the scalability and efficiency of large-scale infrastructure, and the development of economic and social systems. An analytical framework for understanding modularity and its effects on network vulnerability is still missing. Through recent advances in the understanding of multilayer networks, however, it is now possible to develop a theoretical framework to systematically study this critical issue. Here we study, analytically and numerically, the resilience of modular networks under attacks on interconnected nodes, which exhibit high betweenness values and are often more exposed to failure. Our model provides new understandings into the feedback between structure and function in real world systems, and consequently has important implications as diverse as developing efficient immunization strategies, designing robust large-scale infrastructure, and understanding brain function.

physics.soc-ph↗

arXiv2014

Robustness of a Network Formed of Spatially Embedded Networks

We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent links and $(ii)$ interdependent links restricted to a maximum length, $r$. Analytic results are given for each network of networks with unconstrained dependency links and compared with simulations. For the case of two spatially embedded networks it was found that only for $r>r_c\approx8$ does the system undergo a first order phase transition. We find that for treelike networks of networks $r_c$ significantly decreases as $n$ increases and rapidly reaches its limiting value, $r=1$. For cases where the dependencies form loops, such as in random regular networks, we show analytically and confirm through simulations, that there is a certain fraction of dependent nodes, $q_{max}$, above which the entire network structure collapses even if a single node is removed. This $q_{max}$ decreases quickly with $m$, the degree of the random regular network of networks. Our results show the extreme sensitivity of coupled spatial networks and emphasize the susceptibility of these networks to sudden collapse. The theory derived here can be used to find the robustness of any network of networks where the profile of percolation of a single network is known.

physics.soc-ph↗

arXiv2014

Partial correlation analysis: Applications for financial markets

The presence of significant cross-correlations between the synchronous time evolution of a pair of equity returns is a well-known empirical fact. The Pearson correlation is commonly used to indicate the level of similarity in the price changes for a given pair of stocks, but it does not measure whether other stocks influence the relationship between them. To explore the influence of a third stock on the relationship between two stocks, we use a partial correlation measurement to determine the underlying relationships between financial assets. Building on previous work, we present a statistically robust approach to extract the underlying relationships between stocks from four different financial markets: the United States, the United Kingdom, Japan, and India. This methodology provides new insights into financial market dynamics and uncovers implicit influences in play between stocks. To demonstrate the capabilities of this methodology, we (i) quantify the influence of different companies and, by studying market similarity across time, present new insights into market structure and market stability, and (ii) we present a practical application, which provides information on the how a company is influenced by different economic sectors, and how the sectors interact with each other. These examples demonstrate the effectiveness of this methodology in uncovering information valuable for a range of individuals, including not only investors and traders but also regulators and policy makers.

q-fin.ST↗

arXiv2013

Spatially localized attacks on interdependent networks: the existence of a finite critical attack size

Many real world complex systems such as infrastructure, communication and transportation networks are embedded in space, where entities of one system may depend on entities of other systems. These systems are subject to geographically localized failures due to malicious attacks or natural disasters. Here we study the resilience of a system composed of two interdependent spatially embedded networks to localized geographical attacks. We find that if an attack is larger than a finite (zero fraction of the system) critical size, it will spread through the entire system and lead to its complete collapse. If the attack is below the critical size, it will remain localized. In contrast, under random attack a finite fraction of the system needs to be removed to initiate system collapse. We present both numerical simulations and a theoretical approach to analyze and predict the effect of local attacks and the critical attack size. Our results demonstrate the high risk of local attacks on interdependent spatially embedded infrastructures and can be useful for designing more resilient systems.

physics.soc-ph↗

arXiv2013

Global Climate network evolves with North Atlantic Oscillation phases: Coupling to Southern Pacific Ocean

We construct a network from climate records of atmospheric temperature at surface level, at different geographical sites in the globe, using reanalysis data from years 1948-2010. We find that the network correlates with the North Atlantic Oscillation (NAO), both locally in the north Atlantic, and through coupling to the southern Pacific Ocean. The existence of tele-connection links between those areas and their stability over time allows us to suggest a possible physical explanation for this phenomenon.

physics.ao-ph↗

arXiv2013

Percolation of Interdependent Networks with Inter-similarity

Real data show that interdependent networks usually involve inter-similarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent (Parshani et al \cite{PAR10B}). For example, the coupled world wide port network and the global airport network are intersimilar since many pairs of linked nodes (neighboring cities), by direct flights and direct shipping lines exist in both networks. Nodes in both networks in the same city are regarded as interdependent. If two neighboring nodes in one network depend on neighboring nodes in the another we call these links common links. The fraction of common links in the system is a measure of intersimilarity. Previous simulation results suggest that intersimilarity has considerable effect on reducing the cascading failures, however, a theoretical understanding on this effect on the cascading process is currently missing. Here, we map the cascading process with inter-similarity to a percolation of networks composed of components of common links and non common links. This transforms the percolation of inter-similar system to a regular percolation on a series of subnetworks, which can be solved analytically. We apply our analysis to the case where the network of common links is an Erdős-Rényi (ER) network with the average degree $K$, and the two networks of non-common links are also ER networks. We show for a fully coupled pair of ER networks, that for any $K\geq0$, although the cascade is reduced with increasing $K$, the phase transition is still discontinuous. Our analysis can be generalized to any kind of interdependent random networks system.

physics.soc-ph↗