Distribution of return intervals of extreme events

The distribution of return intervals of extreme events is studied in time series characterized by finite-term correlations with non-exponential decay. Precisely, it has been analyzed the statistics of the return intervals of extreme values of the resistance fluctuations displayed by resistors with granular structure in nonequilibrium stationary states. The resistance fluctuations are calculated by Monte Carlo simulations using a resistor network approach. It has been found that for highly disordered networks, when the auto-correlation function displays a non-exponential and non-power-law decay, the distribution of return intervals of the extreme values is a stretched exponential, with exponent independent of the threshold.     

Global fluctuations and Gumbel statistics

We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution Ga(x), with a real index a, in the study of global fluctuations. To illustrate these findings, we introduce an exactly solvable nonequilibrium model describing an energy flux on a lattice, with local dissipation, in which the fluctuations of the global energy are precisely described by the generalized Gumbel distribution.     

Experimental evidence of extreme value statistics in Raman fiber lasers

We present an experiment in which the intracavity broadened spectrum of a Raman fiber laser is sliced by using a narrow-bandwidth optical filter. High-contrast fast fluctuations of the Stokes power are observed at the output of the optical filter. The statistics of the power fluctuations strongly change with the central wavelength of the filter, and rare extreme events are found to be generated in the far wings of the spectrum.     

Generalized synchronization of coupled chaotic systems

In this paper we briefly report some recent developments on generalized synchronization. We discuss different methods of detecting generalized synchronization. We first consider two unidirectionally coupled systems and then two mutually coupled systems. We then extend the study to a network of coupled systems. In the study of generalized synchronization of coupled nonidentical systems we discuss the Master Stability Function (MSF) formalism for coupled nearly identical systems. Later we use this MSF to construct synchronized optimized networks. In the optimized networks the nodes which have parameter value at one extreme are chosen as hubs and the pair of nodes with larger difference in parameter are chosen to create links.     

Modular networks with hierarchical organization: The dynamical implications of complex structure

Several networks occurring in real life have modular structures that are arranged in a hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that, the scaling relation between the clustering and degree of the nodes is not a necessary property of hierarchical modular networks, as had previously been suggested on the basis of a deterministically constructed model. We also look at dynamics on such networks, in particular, the stability of equilibria of network dynamics and of synchronized activity in the network. For both of these, we find that, increasing modularity or the number of hierarchical levels tends to increase the probability of instability. As both hierarchy and modularity are seen in natural systems, which necessarily have to be robust against environmental fluctuations, we conclude that additional constraints are necessary for the emergence of hierarchical structure, similar to the occurrence of modularity through multi-constraint optimization as shown by us previously.      

Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces

We investigate the statistics of the maximal fluctuation of two-dimensional Gaussian interfaces. Its relation to the entropic repulsion between rigid walls and a confined interface is used to derive the average maximal [EQUATION: SEE TEXT]and the asymptotic behavior of the whole distribution for [EQUATION: SEE TEXT] for m finite with N2 and K the interface size and tension, respectively. The standardized form of P(m) does not depend on N or K, but shows a good agreement with Gumbel's first asymptote distribution with a particular noninteger parameter. The effects of the correlations among individual fluctuations on the extreme value statistics are discussed in our findings.     

Extremum statistics in scale-free network models

We investigate the statistics of the most connected node in scale-free networks. For a scale-free network model with homogeneous nodes, we show by means of extensive simulations that the exponential truncation, due to the finite size of the network, of the degree distribution governs the scaling of the extreme values and that the distribution of maxima follows the Gumbel statistics. For a scale-free network model with heterogeneous nodes, we show that scaling no longer holds and that the truncation of the degree distribution no longer controls the maxima distribution.     

Symmetry-based structure entropy of complex networks

Precisely quantifying the heterogeneity or disorder of network systems is important and desired in studies of behaviors and functions of network systems. Although various degree-based entropies have been available to measure the heterogeneity of real networks, heterogeneity implicated in the structures of networks can not be precisely quantified yet. Hence, we propose a new structure entropy based on automorphism partition. Analysis of extreme cases shows that entropy based on automorphism partition can quantify the structural heterogeneity of networks more precisely than degree-based entropies. We also summarized symmetry and heterogeneity statistics of many real networks, finding that real networks are more heterogeneous in the view of automorphism partition than what have been depicted under the measurement of degree-based entropies; and that structural heterogeneity is strongly negatively correlated to symmetry of real networks.     

The near-extreme density of intraday log-returns

The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge amount of records to obtain significant statistics, and thus limiting its practical applications. Focussing, instead, on the closely related density of “near-extremes”–the distance between a record and the maximal value–can render the statistical methods to be more suitable in the practical applications and/or validations of models. We apply this recently proposed method in the empirical validation of an adapted financial market model of the intraday market fluctuations.     

Fluctuations in Wikipedia access-rate and edit-event data

Internet-based social networks often reflect extreme events in nature and society by drastic increases in user activity. We study and compare the dynamics of the two major complex processes necessary for information spread via the online encyclopedia ‘Wikipedia’, i.e., article editing (information upload) and article access (information viewing) based on article edit-event time series and (hourly) user access-rate time series for all articles. Daily and weekly activity patterns occur in addition to fluctuations and bursting activity. The bursts (i.e., significant increases in activity for an extended period of time) are characterized by a power-law distribution of durations of increases and decreases. For describing the recurrence and clustering of bursts we investigate the statistics of the return intervals between them. We find stretched exponential distributions of return intervals in access-rate time series, while edit-event time series yield simple exponential distributions. To characterize the fluctuation behavior we apply detrended fluctuation analysis (DFA), finding that most article access-rate time series are characterized by strong long-term correlations with fluctuation exponents α≈0.9$\alpha \approx 0.9$. The results indicate significant differences in the dynamics of information upload and access and help in understanding the complex process of collecting, processing, validating, and distributing information in self-organized social networks.     

Synchronization in scale free networks with degree correlation

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

Synchronization of networks

We study the synchronization of coupled dynamical systems on networks. The dynamics is governed by a local nonlinear oscillator for each node of the network and interactions connecting different nodes via the links of the network. We consider existence and stability conditions for both single- and multi-cluster synchronization. For networks with time-varying topology we compare the synchronization properties of these networks with the corresponding time-average network. We find that if the different coupling matrices corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand, for non-commuting coupling matrices the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.      

Synchronized state of coupled dynamics on time-varying networks

We consider synchronization properties of coupled dynamics on time-varying networks and the corresponding time-average network. We find that if the different Laplacians corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand for noncommuting Laplacians the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.     

Statistical properties of Er/Yb co-doped random Rayleigh feedback fiber laser

In this Letter, we experimentally investigate fast temporal intensity dynamics and statistical properties of the claddingpumped Er/Yb co-doped random Rayleigh feedback fiber laser(EYRFL) for the first time, to the best of our knowledge. By using the optical spectral filtering method, strong and fast intensity fluctuations with the generation of extreme events are revealed at the output of EYRFL. The statistics of the intensity fluctuations strongly depends on the wavelength of the filtered radiation, and the intensity probability density function(PDF) with a heavy tail is observed in the far wings of the spectrum. We also find that the PDF of the intensity in the central part of the spectrum deviates from the exponential distribution and has the dependence on the laser operating regimes, which indicates some correlations among different frequency components exist in the EYRFL radiation and may play an important role in the random lasing spectrum stabilization process.     

Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology

We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the coupling delay along the network links and time scale at which the topology changes. Concentrating on a linearized model, we develop an analytical theory for the stability of a synchronized solution. In two limit cases, the system can be reduced to an “effective” topology: in the fast switching approximation, when the network fluctuations are much faster than the internal time scale and the coupling delay, the effective network topology is the arithmetic mean over the different topologies. In the slow network limit, when the network fluctuation time scale is equal to the coupling delay, the effective adjacency matrix is the geometric mean over the adjacency matrices of the different topologies. In the intermediate regime, the system shows a sensitive dependence on the ratio of time scales, and on the specific topologies, reproduced as well by numerical simulations. Our results are shown to describe the synchronization properties of fluctuating networks of delay-coupled chaotic maps.     

Formation of electrically active clusterized neural networks

Ordinarily, in vitro neurons self-organize into homogeneous networks of single neurons linked by dendrites and axons. We show that under special conditions they can also self-organize into neuronal clusters, which are linked by bundles of axons. Multielectrode array measurement reveals that the clusterized networks are also electrically active and exhibit synchronized bursting events similar to those observed in the homogeneous networks. From time-lapse recording, we deduced the features required for the neuronal clusterized versus homogeneous self-organization and developed a simple model for testing their validity.     

Synchronization structure of evolving epileptic networks using cross-entropy

In this paper we present connectivity patterns of evolving large scale epileptic networks. We employed a cross-entropy measure in the frequency domain on EEG signals to infer the networks, before and during episodes of epileptic seizures. This measure allowed us to make a richer portrait about the node interactions on the graph and to identify emergent structures associated with the synchronization of brain activity. Our results points to a more complex scenario of network organization than the synchronized/unsynchronized dichotomy, with two main results: first, showing regions with unsynchronized (or independent) behavior, even during absence seizures, contradicting the concept of hypersynchrony. Furthermore, we explore the cross-entropy fluctuations along the seizure: a group of nodes became more similar over time while another group became more different, showing a complementary behaviour and different local brain activities. These results bring new questions about the spreading and the sustenance of the epileptic seizures and others synchronization phenomena in living systems.     

Correlations of the States of Non-Entrained Oscillators in the Kuramoto Ensemble with Noise in the Mean Field

Radiophysics and Quantum Electronics - We consider the dynamics of the Kuramoto ensemble oscillators not included in a common synchronized cluster, where the mean field is subject to fluctuations....     

Epidemic outbreaks in complex heterogeneous networks

We present a detailed analytical and numerical study for the spreading of infections with acquired immunity in complex population networks. 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 in the limit of a very large number of nodes, 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. Received 20 September 2001 and Received in final form 4 February 2002     

Synchronization interfaces and overlapping communities in complex networks

We show that a complex network of phase oscillators may display interfaces between domains (clusters) of synchronized oscillations. The emergence and dynamics of these interfaces are studied for graphs composed of either dynamical domains (influenced by different forcing processes), or structural domains (modular networks). The obtained results allow us to give a functional definition of overlapping structures in modular networks, and suggest a practical method able to give information on overlapping clusters in both artificially constructed and real world modular networks.