"The use of {\it dyadic interaction} between agents, in combination with {\it homophily} (the pri... more "The use of {\it dyadic interaction} between agents, in combination with {\it homophily} (the principle that
``likes attract'') in the Axelrod model for the study of cultural dissemination has two important problems: the
prediction of monoculture in large societies and an extremely narrow window of noise levels in which diversity with
local convergence is obtained. Recently, the inclusion of {\it social influence} has proven to overcome them (A. Flache
and M. W. Macey, arXiv:0808.2710). Here we extend the Axelrod model with social influence interaction for the study of
Mass Media effects through the inclusion of a super-agent which acts over the whole system and has nonnull overlap with
each agent of the society. The dependence with different parameters as the initial social diversity, size effects, Mass
Media strength and noise is outlined. Our results might be relevant in several socio-economic contexts and for the
study of the emergence of collective behavior in complex social systems."
Coupled biological and chemical systems, neural networks, social interacting species, the Interne... more Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks’ dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
Synchronization processes in populations of locally interacting elements are in the focus of inte... more Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.
We present a detailed analytical and numerical study for the spreading of infections in complex p... more We present a detailed analytical and numerical study for the spreading of infections in complex population networks with acquired immunity. We show that the large connectivity fluctuations usually found in these networks strengthen considerably the incidence of epidemic outbreaks. Scale-free networks, which are characterized by diverging connectivity fluctuations, exhibit the lack of an epidemic threshold and always show a finite fraction of infected individuals. This particular weakness, observed also in models without immunity, defines a new epidemiological framework characterized by a highly heterogeneous response of the system to the introduction of infected individuals with different connectivity. The understanding of epidemics in complex networks might deliver new insights in the spread of information and diseases in biological and technological networks that often appear to be characterized by complex heterogeneous architectures.
We derive the mean-field equations characterizing the dynamics of a rumor process that takes plac... more We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present analytical and Monte Carlo calculations for homogeneous networks and compare the results with those obtained by the numerical method. Then, we study the spreading process in detail for random scale-free networks. The time profiles for several quantities are numerically computed, which allow us to distinguish among different variants of rumor spreading algorithms. Our conclusions are directed to possible applications in replicated database maintenance, peer to peer communication networks and social spreading phenomena.
We study the tolerance to congestion failures in communication networks with scale-free topology.... more We study the tolerance to congestion failures in communication networks with scale-free topology. The traffic load carried by each damaged element in the network must be partly or totally redistributed among the remaining elements. Overloaded elements might fail on their turn, triggering the occurrence of failure cascades able to isolate large parts of the network. We find a critical traffic load above which the probability of massive traffic congestions destroying the network communication capabilities is finite. 89.75.Fb, 05.70.Jk, 05.40.a Complex heterogeneous connectivity patterns have been recently identified in several natural and technological networks . The Internet and the World-Wide-Web (WWW) networks, where nodes represent routers or web pages and edges physical connections or hyperlinks, appear to have a topology characterized by the presence of "hubs" with many connections to peripherical nodes. Empirical evidence recently collected shows that this distinctive feature finds its statistical characterization in the presence of heavy-tailed degree distributions . In the Internet, for instance, the statistical analysis reveals that the degree distribution P (k), defined as the probability that any node has k links to other nodes, is well approximated by a powerlaw behavior P (k) ∼ k −γ , with γ ≈ 2.2 . This makes the Internet a capital example of the recently identified class of scale-free (SF) networks . The statistical physics approach has been proved to be a valuable tool for the study of complex networks, and several interesting results concerning dynamical processes taking place on complex networks have been recently reported. In particular, the absence of the percolation [12, 13] and epidemic thresholds in SF networks has a large impact because of its potential practical implications. The absence of the percolating threshold, indeed, prompts to an exceptional tolerance to random damages . This is a property that assumes a great importance in communication networks, guaranteeing the connectivity capabilities of the system. Percolation properties of SF networks refer only to the static topological connectivity properties . On the other hand, in the Internet and other communications networks, many instabilities are due to traffic load congestions . The traffic load carried on the failing nodes or connections is automatically diverted to alternative paths on the networks and instabilities can spread from node to node by an avalanche of traffic congestions and overloads. For instance, route flaps have led to the transient loss of connectivity for large portions of the In-ternet. These instabilities are thus of a dynamical nature and depend on how information is routed and distributed in the network. The models proposed so far, however, deal with regular structures and do not take into account the complex topology of SF networks.
In this work, we study the synchronization of coupled phase oscillators on the underlying topolog... more In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others following the Kuramoto model. We then study the onset of global phase synchronization and fully characterize the system's dynamics. We also found that the resynchronization time of a perturbed node decays as a power law of its connectivity, providing a simple analytical explanation to this interesting behavior.
The understanding of emergent collective phenomena in natural and social systems has driven the i... more The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals or units has been intensively studied because of its ubiquity in the natural world. In this paper, we show how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks, driving the process towards a certain global synchronization degree following different paths. The dependence of the dynamics on the coupling strength and on the topology is unveiled. This study provides a new perspective and tools to understand this emerging phenomena. PACS numbers: 05.45.Xt, 89.75.Fb In 1998 Watts and Strogatz in an effort to understand the synchronization of cricket chirps, which show a high degree of coordination over long distances as though the insects where "invisibly" connected, end up with a seminal paper about the small-world effect [1] that was the seed of the modern theory of complex networks . Many natural and man-made networks have been, since then, successfully described within this framework. Nevertheless, the understanding of the synchronization dynamics in complex networks remains a challenge.
The existence or not of a percolation threshold on power law correlated graphs is a fundamental q... more The existence or not of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking. In this work we investigate the problems of site and bond percolation on graphs with degree correlations and their connection with spreading phenomena. We obtain some general expressions that allow the computation of the transition thresholds or their bounds. Using these results we study the effects of assortative and disassortative correlations on the resilience to damage of networks. PACS numbers: 89.75.Hc, The graphs representing many real networks are characterized by power law degree distributions . The origin of these power laws can be traced back to the growing nature of real networks and to some effective preferential attachment mechanism. This later mechanism implies that when new vertices are added to the graph they are more likely linked to existing vertices with large degrees . Recently, there has been a great interest in the study of processes running on top of these graphs due to their social, technological and scientific relevance. Percolation processes , spreading phenomena [5, 6, 7], the Ising model [8] and searching techniques are some examples for which analytical solutions have been found in random graphs with the only constraint given by the degree distribution. One of the fundamental results is that the threshold characterizing the percolation transition or an epidemic outbreak, depends on the ratio d 2 / d of the first two moments of the degree distribution . Hence, if d 2 diverges when increasing the graph size, there is no transition in the thermodynamic limit.
We numerically investigate jamming transitions in complex heterogeneous networks. Inspired by Int... more We numerically investigate jamming transitions in complex heterogeneous networks. Inspired by Internet routing protocols, we study a general model that incorporates local traffic information through a tunable parameter. The results show that whether the transition from a low-traffic regime to a congested phase is of first or second order type is determined by the protocol at work. The microscopic dynamics reveals that these two radically different behaviors are due to the way in which traffic jams propagate through the network. Our results are discussed in the context of Internet dynamics and other transport processes that take place on complex networks and provide insights for the design of routing policies based on traffic awareness in communication systems. 89.75.Fb, 89.20.Hh Everyday, transportation networks− airports, roads, the Internet, etc− carry on a huge amount of load in the form of passengers, vehicles or information packets delivered by millions of users when searching the World-Wide-Web (WWW), sending and receiving e-mails, or looking at stock market quotes. The globalization and the Information Era have in turn led to a continuous growth of most communication networks driven by the increase in traffic; capital examples being the Internet and main airports. The efficient performance of these systems is mainly determined by the ability of the system to avoid congestion and reduce transit times. Congestion on networked systems often comes up suddenly and provokes the breakdown of the system's functionality. Hence, it is not surprising that transport processes and information exchange have been widely studied over the last years because of potential applications in fields as diverse as sociology [1], urban planning (vehicular traffic) [2, 3], informatics and biology .
We analyze different strategies aimed at optimizing routing policies in the Internet. We first sh... more We analyze different strategies aimed at optimizing routing policies in the Internet. We first show that for a simple deterministic algorithm the local properties of the network deeply influence the time needed for packet delivery between two arbitrarily chosen nodes. We next rely on a real Internet map at the autonomous system level and introduce a score function that allows us to examine different routing protocols and their efficiency in traffic handling and packet delivery. Our results suggest that actual mechanisms are not the most efficient and that they can be integrated in a more general, though not too complex, scheme.
We introduce a numerical method to solve epidemic models on the underlying topology of complex ne... more We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field like rate equations describing the system and allows to work with very large system sizes, where Monte Carlo simulations are useless due to memory needs. We then study the SIR epidemiological model on assortative networks, providing numerical evidence of the absence of epidemic thresholds. Besides, the time profiles of the populations are analyzed. Finally, we stress that the present method would allow to solve arbitrary epidemic-like models provided that they can be described by mean-field rate equations. 89.75.Fb, 05.70.Jk, 05.40.a A few years ago, Watts and Strogatz [1] introduced a model able to produce networks with properties of both regular lattices and random graphs with small diameter. Their model soon led to a burst of activity in the field [2, 3], further spurred by Barabasi and collaborators who found that many seemingly diverse systems share several topological properties such as a power law behavior in their connectivity distributions when represented as networks . These complex networks are formed by a set of many elements (or nodes) that are linked together through edges (or links) if they interact directly. Empirical evidence supports that in notable networks, such as metabolic or communication webs, the probability P (k) that any node has k links to other nodes is distributed accordingly to a power law P (k) ∼ k −γ [5, 6, 7], with γ ≤ 3 in most cases.
We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable ... more We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function which can interpolate between the two limiting cases of load redistribution, the global and the local load sharing schemes. By varying the range of interaction several features of the model are numerically studied and a crossover from mean field to short range behavior is obtained. The properties of the two regimes and the emergence of the crossover in between are explored by numerically studying the dependence of the ultimate strength of the material on the system size, the distribution of avalanches of breakings, and of the cluster sizes of broken fibers. Finally, we analyze the moments of the cluster size distributions to accurately determine the value at which the crossover is observed.
We study the phase synchronization of Kuramoto's oscillators in small parts of networks known as ... more We study the phase synchronization of Kuramoto's oscillators in small parts of networks known as motifs. We first report on the system dynamics for the case of a scale-free network and show the existence of a non-trivial critical point. We compute the probability that network motifs synchronize, and find that the fitness for synchronization correlates well with motif's interconnectedness and structural complexity. Possible implications for present debates about network evolution in biological and other systems are discussed.
We investigate in depth the synchronization of coupled oscillators on top of complex networks wit... more We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we unveiled how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks. Here, we provide more evidence on this phenomenon extending the previous work to networks that interpolate between homogeneous and heterogeneous topologies. We also present new details on the path towards synchronization for the evolution of clustering in the synchronized patterns. Finally, we investigate the synchronization of networks with modular structure and conclude that, in these cases, local synchronization is first attained at the most internal level of organization of modules, progressively evolving to the outer levels as the coupling constant is increased. The present work introduces new parameters that are proved to be useful for the characterization of synchronization phenomena in complex networks.
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We d... more We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of three factors, respectively of dynamical, topological and statistical nature. In particular, we demonstrate that the existence of a power-law scaling characterizing the flow fluctuations at every node in the network can not be claimed for. We show the validity of this scaling breakdown under quite general topological and dynamical situations by means of different traffic algorithms and by analyzing real data.
Experiments in rupture of mercury drops have been performed recording the size distribution of th... more Experiments in rupture of mercury drops have been performed recording the size distribution of the cumulative number of drops for different conditions of rupture. A transition of the distribution from log-normal to scaling behavior is shown. To describe it, a geometric probabilistic model is proposed. Consequently, the rupture can be described as a process of percolation in a Bethe lattice. Then, the rupture process and the transition to scaling can be viewed as a problem of phase transition. Comparison with several fracture experimental data is also made showing the possibilities of this viewpoint.
We investigate by numerical simulations and analytical calculations the Bak-Sneppen model for bio... more We investigate by numerical simulations and analytical calculations the Bak-Sneppen model for biological evolution in scale-free networks. By using large scale numerical simulations, we study the avalanche size distribution and the activity time behavior at nodes with different connectivities. We argue the absence of a critical barrier and its associated critical behavior for infinite size systems. These findings are supported by a single site mean-field analytic treatment of the model.
The European Physical Journal B-Condensed …, Jan 1, 2003
We study the spreading of a disease on top of structured scale-free networks recently introduced.... more We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the network are unbounded whether the epidemic threshold exists strongly depends on the initial density of infected individuals and the type of epidemiological model considered. Analytical arguments are provided in order to account for the observed behavior. We conclude that the peculiar topological features of this network and the absence of small-world properties determine the dynamics of epidemic spreading. PACS. 89.75.-k Complex Systems -89.75.Fb Structures and organization in complex systems -05.70.Jk Critical point phenomena
"The use of {\it dyadic interaction} between agents, in combination with {\it homophily} (the pri... more "The use of {\it dyadic interaction} between agents, in combination with {\it homophily} (the principle that
``likes attract'') in the Axelrod model for the study of cultural dissemination has two important problems: the
prediction of monoculture in large societies and an extremely narrow window of noise levels in which diversity with
local convergence is obtained. Recently, the inclusion of {\it social influence} has proven to overcome them (A. Flache
and M. W. Macey, arXiv:0808.2710). Here we extend the Axelrod model with social influence interaction for the study of
Mass Media effects through the inclusion of a super-agent which acts over the whole system and has nonnull overlap with
each agent of the society. The dependence with different parameters as the initial social diversity, size effects, Mass
Media strength and noise is outlined. Our results might be relevant in several socio-economic contexts and for the
study of the emergence of collective behavior in complex social systems."
Coupled biological and chemical systems, neural networks, social interacting species, the Interne... more Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks’ dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
Synchronization processes in populations of locally interacting elements are in the focus of inte... more Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.
We present a detailed analytical and numerical study for the spreading of infections in complex p... more We present a detailed analytical and numerical study for the spreading of infections in complex population networks with acquired immunity. We show that the large connectivity fluctuations usually found in these networks strengthen considerably the incidence of epidemic outbreaks. Scale-free networks, which are characterized by diverging connectivity fluctuations, exhibit the lack of an epidemic threshold and always show a finite fraction of infected individuals. This particular weakness, observed also in models without immunity, defines a new epidemiological framework characterized by a highly heterogeneous response of the system to the introduction of infected individuals with different connectivity. The understanding of epidemics in complex networks might deliver new insights in the spread of information and diseases in biological and technological networks that often appear to be characterized by complex heterogeneous architectures.
We derive the mean-field equations characterizing the dynamics of a rumor process that takes plac... more We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present analytical and Monte Carlo calculations for homogeneous networks and compare the results with those obtained by the numerical method. Then, we study the spreading process in detail for random scale-free networks. The time profiles for several quantities are numerically computed, which allow us to distinguish among different variants of rumor spreading algorithms. Our conclusions are directed to possible applications in replicated database maintenance, peer to peer communication networks and social spreading phenomena.
We study the tolerance to congestion failures in communication networks with scale-free topology.... more We study the tolerance to congestion failures in communication networks with scale-free topology. The traffic load carried by each damaged element in the network must be partly or totally redistributed among the remaining elements. Overloaded elements might fail on their turn, triggering the occurrence of failure cascades able to isolate large parts of the network. We find a critical traffic load above which the probability of massive traffic congestions destroying the network communication capabilities is finite. 89.75.Fb, 05.70.Jk, 05.40.a Complex heterogeneous connectivity patterns have been recently identified in several natural and technological networks . The Internet and the World-Wide-Web (WWW) networks, where nodes represent routers or web pages and edges physical connections or hyperlinks, appear to have a topology characterized by the presence of "hubs" with many connections to peripherical nodes. Empirical evidence recently collected shows that this distinctive feature finds its statistical characterization in the presence of heavy-tailed degree distributions . In the Internet, for instance, the statistical analysis reveals that the degree distribution P (k), defined as the probability that any node has k links to other nodes, is well approximated by a powerlaw behavior P (k) ∼ k −γ , with γ ≈ 2.2 . This makes the Internet a capital example of the recently identified class of scale-free (SF) networks . The statistical physics approach has been proved to be a valuable tool for the study of complex networks, and several interesting results concerning dynamical processes taking place on complex networks have been recently reported. In particular, the absence of the percolation [12, 13] and epidemic thresholds in SF networks has a large impact because of its potential practical implications. The absence of the percolating threshold, indeed, prompts to an exceptional tolerance to random damages . This is a property that assumes a great importance in communication networks, guaranteeing the connectivity capabilities of the system. Percolation properties of SF networks refer only to the static topological connectivity properties . On the other hand, in the Internet and other communications networks, many instabilities are due to traffic load congestions . The traffic load carried on the failing nodes or connections is automatically diverted to alternative paths on the networks and instabilities can spread from node to node by an avalanche of traffic congestions and overloads. For instance, route flaps have led to the transient loss of connectivity for large portions of the In-ternet. These instabilities are thus of a dynamical nature and depend on how information is routed and distributed in the network. The models proposed so far, however, deal with regular structures and do not take into account the complex topology of SF networks.
In this work, we study the synchronization of coupled phase oscillators on the underlying topolog... more In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others following the Kuramoto model. We then study the onset of global phase synchronization and fully characterize the system's dynamics. We also found that the resynchronization time of a perturbed node decays as a power law of its connectivity, providing a simple analytical explanation to this interesting behavior.
The understanding of emergent collective phenomena in natural and social systems has driven the i... more The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals or units has been intensively studied because of its ubiquity in the natural world. In this paper, we show how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks, driving the process towards a certain global synchronization degree following different paths. The dependence of the dynamics on the coupling strength and on the topology is unveiled. This study provides a new perspective and tools to understand this emerging phenomena. PACS numbers: 05.45.Xt, 89.75.Fb In 1998 Watts and Strogatz in an effort to understand the synchronization of cricket chirps, which show a high degree of coordination over long distances as though the insects where "invisibly" connected, end up with a seminal paper about the small-world effect [1] that was the seed of the modern theory of complex networks . Many natural and man-made networks have been, since then, successfully described within this framework. Nevertheless, the understanding of the synchronization dynamics in complex networks remains a challenge.
The existence or not of a percolation threshold on power law correlated graphs is a fundamental q... more The existence or not of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking. In this work we investigate the problems of site and bond percolation on graphs with degree correlations and their connection with spreading phenomena. We obtain some general expressions that allow the computation of the transition thresholds or their bounds. Using these results we study the effects of assortative and disassortative correlations on the resilience to damage of networks. PACS numbers: 89.75.Hc, The graphs representing many real networks are characterized by power law degree distributions . The origin of these power laws can be traced back to the growing nature of real networks and to some effective preferential attachment mechanism. This later mechanism implies that when new vertices are added to the graph they are more likely linked to existing vertices with large degrees . Recently, there has been a great interest in the study of processes running on top of these graphs due to their social, technological and scientific relevance. Percolation processes , spreading phenomena [5, 6, 7], the Ising model [8] and searching techniques are some examples for which analytical solutions have been found in random graphs with the only constraint given by the degree distribution. One of the fundamental results is that the threshold characterizing the percolation transition or an epidemic outbreak, depends on the ratio d 2 / d of the first two moments of the degree distribution . Hence, if d 2 diverges when increasing the graph size, there is no transition in the thermodynamic limit.
We numerically investigate jamming transitions in complex heterogeneous networks. Inspired by Int... more We numerically investigate jamming transitions in complex heterogeneous networks. Inspired by Internet routing protocols, we study a general model that incorporates local traffic information through a tunable parameter. The results show that whether the transition from a low-traffic regime to a congested phase is of first or second order type is determined by the protocol at work. The microscopic dynamics reveals that these two radically different behaviors are due to the way in which traffic jams propagate through the network. Our results are discussed in the context of Internet dynamics and other transport processes that take place on complex networks and provide insights for the design of routing policies based on traffic awareness in communication systems. 89.75.Fb, 89.20.Hh Everyday, transportation networks− airports, roads, the Internet, etc− carry on a huge amount of load in the form of passengers, vehicles or information packets delivered by millions of users when searching the World-Wide-Web (WWW), sending and receiving e-mails, or looking at stock market quotes. The globalization and the Information Era have in turn led to a continuous growth of most communication networks driven by the increase in traffic; capital examples being the Internet and main airports. The efficient performance of these systems is mainly determined by the ability of the system to avoid congestion and reduce transit times. Congestion on networked systems often comes up suddenly and provokes the breakdown of the system's functionality. Hence, it is not surprising that transport processes and information exchange have been widely studied over the last years because of potential applications in fields as diverse as sociology [1], urban planning (vehicular traffic) [2, 3], informatics and biology .
We analyze different strategies aimed at optimizing routing policies in the Internet. We first sh... more We analyze different strategies aimed at optimizing routing policies in the Internet. We first show that for a simple deterministic algorithm the local properties of the network deeply influence the time needed for packet delivery between two arbitrarily chosen nodes. We next rely on a real Internet map at the autonomous system level and introduce a score function that allows us to examine different routing protocols and their efficiency in traffic handling and packet delivery. Our results suggest that actual mechanisms are not the most efficient and that they can be integrated in a more general, though not too complex, scheme.
We introduce a numerical method to solve epidemic models on the underlying topology of complex ne... more We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field like rate equations describing the system and allows to work with very large system sizes, where Monte Carlo simulations are useless due to memory needs. We then study the SIR epidemiological model on assortative networks, providing numerical evidence of the absence of epidemic thresholds. Besides, the time profiles of the populations are analyzed. Finally, we stress that the present method would allow to solve arbitrary epidemic-like models provided that they can be described by mean-field rate equations. 89.75.Fb, 05.70.Jk, 05.40.a A few years ago, Watts and Strogatz [1] introduced a model able to produce networks with properties of both regular lattices and random graphs with small diameter. Their model soon led to a burst of activity in the field [2, 3], further spurred by Barabasi and collaborators who found that many seemingly diverse systems share several topological properties such as a power law behavior in their connectivity distributions when represented as networks . These complex networks are formed by a set of many elements (or nodes) that are linked together through edges (or links) if they interact directly. Empirical evidence supports that in notable networks, such as metabolic or communication webs, the probability P (k) that any node has k links to other nodes is distributed accordingly to a power law P (k) ∼ k −γ [5, 6, 7], with γ ≤ 3 in most cases.
We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable ... more We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function which can interpolate between the two limiting cases of load redistribution, the global and the local load sharing schemes. By varying the range of interaction several features of the model are numerically studied and a crossover from mean field to short range behavior is obtained. The properties of the two regimes and the emergence of the crossover in between are explored by numerically studying the dependence of the ultimate strength of the material on the system size, the distribution of avalanches of breakings, and of the cluster sizes of broken fibers. Finally, we analyze the moments of the cluster size distributions to accurately determine the value at which the crossover is observed.
We study the phase synchronization of Kuramoto's oscillators in small parts of networks known as ... more We study the phase synchronization of Kuramoto's oscillators in small parts of networks known as motifs. We first report on the system dynamics for the case of a scale-free network and show the existence of a non-trivial critical point. We compute the probability that network motifs synchronize, and find that the fitness for synchronization correlates well with motif's interconnectedness and structural complexity. Possible implications for present debates about network evolution in biological and other systems are discussed.
We investigate in depth the synchronization of coupled oscillators on top of complex networks wit... more We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we unveiled how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks. Here, we provide more evidence on this phenomenon extending the previous work to networks that interpolate between homogeneous and heterogeneous topologies. We also present new details on the path towards synchronization for the evolution of clustering in the synchronized patterns. Finally, we investigate the synchronization of networks with modular structure and conclude that, in these cases, local synchronization is first attained at the most internal level of organization of modules, progressively evolving to the outer levels as the coupling constant is increased. The present work introduces new parameters that are proved to be useful for the characterization of synchronization phenomena in complex networks.
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We d... more We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of three factors, respectively of dynamical, topological and statistical nature. In particular, we demonstrate that the existence of a power-law scaling characterizing the flow fluctuations at every node in the network can not be claimed for. We show the validity of this scaling breakdown under quite general topological and dynamical situations by means of different traffic algorithms and by analyzing real data.
Experiments in rupture of mercury drops have been performed recording the size distribution of th... more Experiments in rupture of mercury drops have been performed recording the size distribution of the cumulative number of drops for different conditions of rupture. A transition of the distribution from log-normal to scaling behavior is shown. To describe it, a geometric probabilistic model is proposed. Consequently, the rupture can be described as a process of percolation in a Bethe lattice. Then, the rupture process and the transition to scaling can be viewed as a problem of phase transition. Comparison with several fracture experimental data is also made showing the possibilities of this viewpoint.
We investigate by numerical simulations and analytical calculations the Bak-Sneppen model for bio... more We investigate by numerical simulations and analytical calculations the Bak-Sneppen model for biological evolution in scale-free networks. By using large scale numerical simulations, we study the avalanche size distribution and the activity time behavior at nodes with different connectivities. We argue the absence of a critical barrier and its associated critical behavior for infinite size systems. These findings are supported by a single site mean-field analytic treatment of the model.
The European Physical Journal B-Condensed …, Jan 1, 2003
We study the spreading of a disease on top of structured scale-free networks recently introduced.... more We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the network are unbounded whether the epidemic threshold exists strongly depends on the initial density of infected individuals and the type of epidemiological model considered. Analytical arguments are provided in order to account for the observed behavior. We conclude that the peculiar topological features of this network and the absence of small-world properties determine the dynamics of epidemic spreading. PACS. 89.75.-k Complex Systems -89.75.Fb Structures and organization in complex systems -05.70.Jk Critical point phenomena
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Papers by yamir moreno
``likes attract'') in the Axelrod model for the study of cultural dissemination has two important problems: the
prediction of monoculture in large societies and an extremely narrow window of noise levels in which diversity with
local convergence is obtained. Recently, the inclusion of {\it social influence} has proven to overcome them (A. Flache
and M. W. Macey, arXiv:0808.2710). Here we extend the Axelrod model with social influence interaction for the study of
Mass Media effects through the inclusion of a super-agent which acts over the whole system and has nonnull overlap with
each agent of the society. The dependence with different parameters as the initial social diversity, size effects, Mass
Media strength and noise is outlined. Our results might be relevant in several socio-economic contexts and for the
study of the emergence of collective behavior in complex social systems."
``likes attract'') in the Axelrod model for the study of cultural dissemination has two important problems: the
prediction of monoculture in large societies and an extremely narrow window of noise levels in which diversity with
local convergence is obtained. Recently, the inclusion of {\it social influence} has proven to overcome them (A. Flache
and M. W. Macey, arXiv:0808.2710). Here we extend the Axelrod model with social influence interaction for the study of
Mass Media effects through the inclusion of a super-agent which acts over the whole system and has nonnull overlap with
each agent of the society. The dependence with different parameters as the initial social diversity, size effects, Mass
Media strength and noise is outlined. Our results might be relevant in several socio-economic contexts and for the
study of the emergence of collective behavior in complex social systems."