Showing papers in "Physica A-statistical Mechanics and Its Applications in 2004"
TL;DR: This work represents communication/transportation systems as networks and studies their ability to resist failures simulated as the breakdown of a group of nodes of the network chosen at random (chosen accordingly to degree or load).
Abstract: Communication/transportation systems are often subjected to failures and attacks. Here we represent such systems as networks and we study their ability to resist failures (attacks) simulated as the breakdown of a group of nodes of the network chosen at random (chosen accordingly to degree or load). We consider and compare the results for two different network topologies: the Erdos–Renyi random graph and the Barabasi–Albert scale-free network. We also discuss briefly a dynamical model recently proposed to take into account the dynamical redistribution of loads after the initial damage of a single node of the network.
2,352 citations
TL;DR: In this paper, the authors numerically studied the chaotic behaviors in the fractional-order Rossler equations and found that chaos and hyperchaos exist in such systems with order less than 3.
Abstract: The dynamics of fractional-order systems have attracted increasing attentions in recent years. In this paper, we numerically study the chaotic behaviors in the fractional-order Rossler equations. We found that chaotic behaviors exist in the fractional-order Rossler equation with orders less than 3, and hyperchaos exists in the fractional-order Rossler hyperchaotic equation with order less than 4. The lowest orders we found for chaos and hyperchaos to exist in such systems are 2.4 and 3.8, respectively. Period doubling routes to chaos in the fractional-order Rossler equation are also found.
617 citations
TL;DR: This paper introduces complex dynamical network models with coupling delays for both continuous- and discrete-time cases and investigates their synchronization phenomena and criteria, and derives synchronization conditions for both delay-independent and delay-dependent asymptotical stabilities in terms of linear matrix inequalities (LMI).
Abstract: Complex networks have attracted increasing attention from various fields of science and engineering today. Due to the finite speeds of transmission and spreading as well as traffic congestions, a signal or influence travelling through a complex network often is associated with time delays, and this is very common in biological and physical networks. In this paper, we introduce complex dynamical network models with coupling delays for both continuous- and discrete-time cases and then investigate their synchronization phenomena and criteria. Based on these new complex network models, we derive synchronization conditions for both delay-independent and delay-dependent asymptotical stabilities in terms of linear matrix inequalities (LMI). We finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results.
583 citations
TL;DR: This work analyzes the structural vulnerability of the Italian GRTN power grid by using a model for cascading failures recently proposed in Crucitti et al. (2004).
Abstract: Large-scale blackouts are an intrinsic drawback of electric power transmission grids. Here we analyze the structural vulnerability of the Italian GRTN power grid by using a model for cascading failures recently proposed in Crucitti et al. (Phys. Rev. E 69 (2004)).
482 citations
TL;DR: In this article, the inner coupled link matrix, the eigenvalues and the corresponding eigenvectors of the coupled configuration matrix, rather than the conventional eigen values of a uniform network, are determined by means of the chaos synchronization of a time-varying complex network.
Abstract: Recently, it has been demonstrated that many large-scale complex dynamical networks display a collective synchronization motion. Here, we introduce a time-varying complex dynamical network model and further investigate its synchronization phenomenon. Based on this new complex network model, two network chaos synchronization theorems are proved. We show that the chaos synchronization of a time-varying complex network is determined by means of the inner coupled link matrix, the eigenvalues and the corresponding eigenvectors of the coupled configuration matrix, rather than the conventional eigenvalues of the coupled configuration matrix for a uniform network. Especially, we do not assume that the coupled configuration matrix is symmetric and its off-diagonal elements are nonnegative, which in a way generalizes the related results existing in the literature.
419 citations
TL;DR: In this paper, a three-stage approach combining novel and traditional algorithms for the segmentation of images of porous and composite materials obtained from X-ray tomography is presented. But this approach is not suitable for large-scale images.
Abstract: This article presents a three-stage approach, combining novel and traditional algorithms, for the segmentation of images of porous and composite materials obtained from X-ray tomography. The first stage is an anisotropic diffusion filter which removes noise while preserving significant features. The second stage applies the unsharp mask sharpening filter which enhances edges and partially reverses the smoothing that is often a consequence of tomographic reconstruction. The final stage uses a combination of watershed and active contour methods for segmentation of the grey-scale data. For the data sets we have analysed, this approach gives the highest quality results. In addition, it has been implemented on cluster-type parallel computers and applied to cubic images comprising up to 20003 voxels.
395 citations
TL;DR: In this article, the authors propose the calculation of the Hurst exponent over time using a time window with 4 years of data and show that the assertion that emerging markets are becoming more efficient over time does not hold for countries such as Brazil, The Philippines and Thailand.
Abstract: This paper is concerned with the assertion found in the financial literature that emerging markets are becoming more efficient over time. To verify whether this assertion is true or not, we propose the calculation of the Hurst exponent over time using a time window with 4 years of data. The data used here comprises the bulk of emerging markets for Latin America and Asia. Our empirical results show that this assertion seems to be true for most countries, but it does not hold for countries such as Brazil, The Philippines and Thailand. Moreover, in order to check whether or not these results depend on the short term memory and the volatility of returns common in such financial asset return data, we filter the data by an AR-GARCH procedure and present the Hurst exponents for this filtered data.
377 citations
TL;DR: In this article, the detrending moving average (DMA) scaling technique is used to calculate the Hurst exponent H( t ) of several time series by dynamical implementation of a recently proposed scaling technique.
Abstract: We calculate the Hurst exponent H ( t ) of several time series by dynamical implementation of a recently proposed scaling technique: the detrending moving average (DMA). In order to assess the accuracy of the technique, we calculate the exponent H ( t ) for artificial series, simulating monofractal Brownian paths, with assigned Hurst exponents H. We next calculate the exponent H ( t ) for the return of high-frequency (tick-by-tick sampled every minute) series of the German market. We find a much more pronounced time-variability in the local scaling exponent of financial series compared to the artificial ones. The DMA algorithm allows the calculation of the exponent H ( t ) , without any a priori assumption on the stochastic process and on the probability distribution function of the random variables, as happens, for example, in the case of the Kitagawa grid and the extended Kalmann filtering methods. The present technique examines the local scaling exponent H ( t ) around a given instant of time. This is a significant advance with respect to the standard wavelet transform or to the higher-order power spectrum technique, which instead operate on the global properties of the series by Legendre or Fourier transform of qth-order moments.
368 citations
TL;DR: In this paper, a deformed algebra related to the q-exponential and q-logarithm functions is presented, and a q-derivative for which the qexponential is an eigenfunction is presented.
Abstract: We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an eigenfunction. The q-derivative and the q-integral have a dual nature, that is also presented.
359 citations
TL;DR: It is demonstrated that the clustering in a network is very sensitive to both the degree distribution and its correlation profile and compared to the appropriate null model.
Abstract: A general scheme for detecting and analyzing topological patterns in large complex networks is presented. In this scheme the network in question is compared with its properly randomized version that preserves some of its low-level topological properties. Statistically significant deviation of any topological property of a network from this null model likely reflects its design principles and/or evolutionary history. We illustrate this basic scheme using the example of the correlation profile of the Internet quantifying correlations between degrees of its neighboring nodes. This profile distinguishes the Internet from previously studied molecular networks with a similar scale-free degree distribution. We finally demonstrate that the clustering in a network is very sensitive to both the degree distribution and its correlation profile and compare the clustering in the Internet to the appropriate null model.
351 citations
TL;DR: A study of information flow that takes into account the observation that an item relevant to one person is more likely to be of interest to individuals in the same social circle than those outside of it due to the fact that the similarity of node attributes in social networks decreases as a function of the graph distance.
Abstract: We present a study of information flow that takes into account the observation that an item relevant to one person is more likely to be of interest to individuals in the same social circle than those outside of it. This is due to the fact that the similarity of node attributes in social networks decreases as a function of the graph distance. An epidemic model on a scale-free network with this property has a finite threshold, implying that the spread of information is limited. We tested our predictions by measuring the spread of messages in an organization and also by numerical experiments that take into consideration the organizational distance among individuals.
TL;DR: A detailed investigation of the coupling architecture of this network reveals that the overall dynamics emerge from the interaction of two interweaved subnetworks, which may lead to new insights about the dynamics of the climate system but of other spatially extended complex systems with a large number of degrees of freedom.
Abstract: We consider climate as a network of many dynamical systems and apply ideas from graph theory to a global data set to study its collective behavior. We find that the network has properties of ‘small-world’ networks (Nature 393 (1999) 440). A detailed investigation of the coupling architecture of this network reveals that the overall dynamics emerge from the interaction of two interweaved subnetworks. One subnetwork operates in the tropics and the other at higher latitudes with the equatorial one acting as an agent that establishes links between the two hemispheres. Both subsystems are ‘small-world’ networks, but there are distinct differences between the two subsystems. The tropical one is an almost fully connected network, whereas the mid-latitude one is more like a scale-free network characterized by dominant super nodes, and multifractal properties. This unique architecture may lead to new insights not only about the dynamics of the climate system but of other spatially extended complex systems with a large number of degrees of freedom.
TL;DR: In this article, the authors have numerically simulated the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving two-body collision.
Abstract: We have numerically simulated the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving two-body collision. Unlike in the ideal gas, we introduce (quenched) saving propensity of the agents, distributed widely between the agents (0⩽λ
TL;DR: In this paper, the effects of contrarians on the dynamics of opinion forming using the 2-state Galam opinion dynamics model were studied and it was shown that contrarians can lead to interesting new dynamics properties.
Abstract: We study the effects of contrarians on the dynamics of opinion forming using the 2-state Galam opinion dynamics model. In a single update step, groups of a given size are defined and all agents in each group adopt the state of the local majority. In the absence of contrarians, the dynamics is fast and leads to a total polarization always along the initial majority (for groups of odd sizes). The introduction of contrarians is then shown to give rise to interesting new dynamics properties. First, at low concentration a, a new mixed phase is stabilized with a coexistence of both states. This is an ordered phase with a clear cut majority–minority splitting (non zero order parameter). Second, there is a phase transition into a new disordered phase at a c = 1 6 , 0.23, 0.30… 1 2 for groups of respective sizes 3, 5, 9 and infinite. For a⩾ac the disordered phase has no opinion dominating with both state densities equal (zero order parameter). In this phase agents keep shifting states but no global symmetry breaking, i.e., the appearance of a majority, takes place. Our results may shed a new light on the phenomenon of “hung elections” as occured in the 2000 American presidential elections and that of the 2002 German parliamentary elections.
TL;DR: In this article, the Jensen-Shannon divergence is used to measure the complexity of probability distributions, and a measure of complexity called nontriviality is proposed to distinguish different degrees of periodicity.
Abstract: We discuss a way of characterizing probability distributions, complementing that provided by the celebrated notion of information measure, with reference to a measure of complexity that we call a “nontriviality measure”. Our starting point is the “LMC” measure of complexity advanced by Lopez-Ruiz et al. (Phys. Lett. A 209 (1995) 321) and its analysis by Anteneodo and Plastino (Phys. Lett. A 223 (1997) 348). An improvement of some of their troublesome characteristics is thereby achieved. Basically, we replace the Euclidean distance to equilibrium by the Jensen–Shannon divergence. The resulting measure turns out to be (i) an intensive quantity and (ii) allows one to distinguish between different degrees of periodicity. We apply the “cured” measure to the logistic map so as to clearly exhibit its advantages.
TL;DR: This work discusses the idea put forward by Per Bak that the working brain stays at an intermediate regime characterized by power-law correlations, and produces synchronized states with no behavioral value.
Abstract: Highly correlated brain dynamics produces synchronized states with no behavioral value, while weakly correlated dynamics prevents information flow. We discuss the idea put forward by Per Bak that the working brain stays at an intermediate (critical) regime characterized by power-law correlations.
TL;DR: In this paper, a detailed study of the relaxation towards equilibrium in the Hamiltonian Mean-Field model, a prototype for long-range interactions in N -particle dynamics, is performed.
Abstract: We perform a detailed study of the relaxation towards equilibrium in the Hamiltonian Mean-Field model, a prototype for long-range interactions in N -particle dynamics. In particular, we point out the role played by the infinity of stationary states of the associated N →∞ Vlasov dynamics. In this context, we derive a new general criterion for the stability of any spatially homogeneous distribution, and compare its analytical predictions with numerical simulations of the Hamiltonian, finite N , dynamics. We then propose, and verify numerically, a scenario for the relaxation process, relying on the Vlasov equation. When starting from a nonstationary or a Vlasov unstable stationary state, the system shows initially a rapid convergence towards a stable stationary state of the Vlasov equation via nonstationary states: we characterize numerically this dynamical instability in the finite N system by introducing appropriate indicators. This first step of the evolution towards Boltzmann–Gibbs equilibrium is followed by a slow quasi-stationary process, that proceeds through different stable stationary states of the Vlasov equation. If the finite N system is initialized in a Vlasov stable homogeneous state, it remains trapped in a quasi-stationary state for times that increase with the nontrivial power law N 1.7 . Single particle momentum distributions in such a quasi-stationary regime do not have power-law tails, and hence cannot be fitted by the q -exponential distributions derived from Tsallis statistics.
TL;DR: In this article, the authors address the issue of modeling spot electricity prices and present a number of models proposed in the literature to fit a jump diffusion and a regime switching model to spot prices from the Nordic power exchange.
Abstract: In this paper we address the issue of modeling spot electricity prices. After summarizing the stylized facts about spot electricity prices, we review a number of models proposed in the literature. Afterwards we fit a jump diffusion and a regime switching model to spot prices from the Nordic power exchange and discuss the pros and cons of each one.
TL;DR: In this paper, the authors apply the Hurst exponent idea for investigation of DJIA index time-series data and analyze the behavior of the local Hurst expander prior to drastic changes in financial series signal.
Abstract: We apply the Hurst exponent idea for investigation of DJIA index time-series data. The behavior of the local Hurst exponent prior to drastic changes in financial series signal is analyzed. The optimal length of the time-window over which this exponent can be calculated in order to make some meaningful predictions is discussed. Our prediction hypothesis is verified with examples of 1929 and 1987 crashes, as well as with more recent phenomena in stock market from the period 1995 to 2003. Some interesting agreements are found.
TL;DR: In this article, a probabilistic theory of highway capacity is presented which is based on the three-phase traffic theory and a critical discussion of model results about congested pattern features which have been derived within the fundamental diagram approach to traffic flow theory and modeling is made.
Abstract: Hypotheses and some results of the three-phase traffic theory by the author are compared with results of the fundamental diagram approach to traffic flow theory. A critical discussion of model results about congested pattern features which have been derived within the fundamental diagram approach to traffic flow theory and modeling is made. The empirical basis of the three-phase traffic theory is discussed and some new spatial–temporal features of the traffic phase “synchronized flow” are considered. A probabilistic theory of highway capacity is presented which is based on the three-phase traffic theory. In the frame of this theory, the probabilistic nature of highway capacity in free flow is linked to an occurrence of the first order local phase transition from the traffic phase “free flow” to the traffic phase “synchronized flow”. A numerical study of congested pattern highway capacity based on simulations of a KKW cellular automata model within the three-phase traffic theory is presented. A congested pattern highway capacity which depends on features of congested spatial–temporal patterns upstream of a bottleneck is studied.
TL;DR: The influence of the social networks on the presence of such a dynamical behavior is studied using small-world networks with variable connectivity and randomness of the connections, which finds that the drift to a single extreme appears only beyond a critical level of connectivity, which decreases when the randomness increases.
Abstract: In Deffuant et al (J Artif Soc Soc Simulation 5 (2002) 4), we proposed a simple model of opinion dynamics, which we used to simulate the influence of extremists in a population Simulations were run without any specific interaction structure and varying the simulation parameters, we observed different attractors such as predominance of centrism or of extremism We even observed in certain conditions, that the whole population drifts to one extreme of the opinion, even if initially there are an equal number of extremists at each extreme of the opinion axis In the present paper, we study the influence of the social networks on the presence of such a dynamical behavior In particular, we use small-world networks with variable connectivity and randomness of the connections We find that the drift to a single extreme appears only beyond a critical level of connectivity, which decreases when the randomness increases
TL;DR: An information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels is proposed, providing new derivations of the advantage afforded by closed-loop control and proposing an information-based optimality criterion for control systems.
Abstract: We propose an information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels. A communication channel takes an input state and transforms it into an output state. A controller, similarly, takes the initial state of a system to be controlled and transforms it into a target state. In this sense, a controller can be thought of as an actuation channel that acts on inputs to produce desired outputs. In this transformation process, two different control strategies can be adopted: (i) the controller applies an actuation dynamics that is independent of the state of the system to be controlled (open-loop control); or (ii) the controller enacts an actuation dynamics that is based on some information about the state of the controlled system (closed-loop control). Using this communication channel model of control, we provide necessary and sufficient conditions for a system to be perfectly controllable and perfectly observable in terms of information and entropy. In addition, we derive a quantitative trade-off between the amount of information gathered by a closed-loop controller and its relative performance advantage over an open-loop controller in stabilizing a system. This work supplements earlier results (Phys. Rev. Lett. 84 (2000) 1156) by providing new derivations of the advantage afforded by closed-loop control and by proposing an information-based optimality criterion for control systems. New applications of this approach pertaining to proportional controllers, and the control of chaotic maps are also presented.
TL;DR: In this paper, the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and in this region the growth rate of each firm is independent of the firm's size.
Abstract: By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto–Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find that detailed balance holds in the large-size region for periods we investigated; the empirical probability for a firm to change its size from a value to another is statistically the same as that for its reverse process. We prove several relationships among Pareto–Zipf's law, Gibrat's law and the condition of detailed balance. As a consequence, we show that the distribution of growth rate possesses a non-trivial relation between the positive side of the distribution and the negative side, through the value of Pareto index, as is confirmed empirically.
TL;DR: The clustering coefficient, path length and average vertex degree of two urban train line networks have been calculated and the results are compared with theoretical predictions for appropriate random bipartite graphs to investigate the effect of architecture on the small-world properties.
Abstract: The clustering coefficient, path length and average vertex degree of two urban train line networks have been calculated. The results are compared with theoretical predictions for appropriate random bipartite graphs. They have also been compared with one another to investigate the effect of architecture on the small-world properties.
TL;DR: In this paper, two types of walkers, going to the right and to the left, are taken into account, and the video recordings and measurements of individual arrival times are evaluated.
Abstract: Pedestrian counter flow is investigated by experiment and simulation. The experiment is performed for the channel with open boundaries. Two types of walkers, going to the right and to the left, are taken into account. The video recordings and measurements of individual arrival times are evaluated. The pattern formation and jamming transition are discussed. The experiment is mimicked by the lattice gas simulation where each person is simulated by a biased random walker taking into account following the front persons with the same direction. The experimental result is compared with the simulation result. It is shown that the arrival time obtained from experiment is consistent with that of the simulation. Also, the jamming transition does not occur in the experiment because of the finite size effect.
TL;DR: A simple model of deterministic walk in a random environment reproduces the observed angular correlations between successive steps, and in some cases, the emergence of Levy distributions for the length of the steps.
Abstract: We discuss various features of the trajectories of spider monkeys lookingfor food in a tropical forest, as observed recently in an extensive in situ study. Some of the features observed can be interpreted as the result of social interactions. In addition, a simple model of deterministic walk in a random environment reproduces the observed angular correlations between successive steps, and in some cases, the emergence of L, evy distributions for the length of the steps. c
TL;DR: The main goal of the paper is to show how mutual information can be used as a measure of dependence in financial time series with no need to specify a theoretical probability distribution or use of a mean-variance model.
Abstract: The main goal of the paper is to show how mutual information can be used as a measure of dependence in financial time series. One major advantage of this approach resides precisely in its ability to account for nonlinear dependencies with no need to specify a theoretical probability distribution or use of a mean-variance model.
TL;DR: In this article, the efficient market hypothesis is tested for China, Hong Kong and Singapore by means of the long memory dependence approach, and evidence suggests that Hong Kong is the most efficient market followed by Chinese A type shares and Singapore and finally by Chinese B type shares, which suggests that liquidity and capital restrictions may play a role in explaining results of market efficiency tests.
Abstract: In this paper, the efficient market hypothesis is tested for China, Hong Kong and Singapore by means of the long memory dependence approach. We find evidence suggesting that Hong Kong is the most efficient market followed by Chinese A type shares and Singapore and finally by Chinese B type shares, which suggests that liquidity and capital restrictions may play a role in explaining results of market efficiency tests.
TL;DR: In this article, the authors derived the solution of further generalized fractional kinetic equations in a compact form in terms of generalized Mittag-Leffler functions and a number of representations of these functions were compiled for the first time.
Abstract: In a recent paper, Saxena et al. (Astro Phys. Space Sci. 282 (2002) 281) developed solutions of generalized fractional kinetic equations in terms of Mittag–Leffler functions. The object of the present paper is to derive the solution of further generalized fractional kinetic equations. Their relation to fundamental laws of physics is briefly discussed. Results are obtained in a compact form in terms of generalized Mittag–Leffler functions and a number of representations of these functions, which are widely distributed in the literature, are compiled for the first time.
TL;DR: In this article, the authors investigated possible extensions of the susceptible-infective-removed (SIR) epidemic model and showed that there exists a large class of functions representing interaction between the susceptible and infective populations for which the model has a realistic behaviour and preserves the essential features of the classical SIR model.
Abstract: We investigate possible extensions of the susceptible–infective-removed (SIR) epidemic model We show that there exists a large class of functions representing interaction between the susceptible and infective populations for which the model has a realistic behaviour and preserves the essential features of the classical SIR model We also present a new discretisation of the SIR model which has the advantage of possessing a conserved quantity, thus making possible the estimation of the non-infected population at the end of the epidemic A cellular automaton SIR is also constructed on the basis of the discrete-time system