Showing papers in "Physica A-statistical Mechanics and Its Applications in 2007"
TL;DR: A leader-following consensus problem of a group of autonomous agents with time-varying coupling delays with a necessary and sufficient condition in the case when the interconnection topology is fixed and directed.
Abstract: In this paper, we consider a leader-following consensus problem of a group of autonomous agents with time-varying coupling delays. Two different cases of coupling topologies are investigated. At first, a necessary and sufficient condition is proved in the case when the interconnection topology is fixed and directed. Then a sufficient condition is proposed in the case when the coupling topology is switched and balanced. Numerical examples are also given to illustrate our results.
900 citations
TL;DR: This work introduces a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet).
Abstract: We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet.
709 citations
TL;DR: The network topology of the interbank payments transferred between commercial banks over the Fedwire® Funds Service is explored and it is found that the network has both a low average path length and low connectivity.
Abstract: We explore the network topology of the interbank payments transferred between commercial banks over the Fedwire ® Funds Service. We find that the network has both a low average path length and low connectivity. The network includes a tightly connected core of banks to which most other banks connect. The degree distribution is scale free over a substantial range. We find that the properties of the network changed considerably in the immediate aftermath of the events of September 11, 2001.
666 citations
TL;DR: A novel algorithm to identify overlapping communities in complex networks by the combination of a new modularity function based on generalizing NG's Q function, an approximation mapping of network nodes into Euclidean space and fuzzy c-means clustering is devised.
Abstract: Identification of (overlapping) communities/clusters in a complex network is a general problem in data mining of network data sets. In this paper, we devise a novel algorithm to identify overlapping communities in complex networks by the combination of a new modularity function based on generalizing NG's Q function, an approximation mapping of network nodes into Euclidean space and fuzzy c-means clustering. Experimental results indicate that the new algorithm is efficient at detecting both good clusterings and the appropriate number of clusters.
544 citations
TL;DR: In this article, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size-distribution function in the practically important 2D and 3D cases as well Denoting the dimensionality of the space by d ( d = 1, 2, 3 ) the f ( y ) = Const * y ( 3 d - 1 ) / 2 exp ( - ( 3d + 1 ) y / 2 ) compact form is suggested for the normalized cell-size distribution function.
Abstract: Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices Although this particular space tessellation is intensively studied by mathematicians, in two- and three-dimensional (3D) spaces there is no exact result known for the size distribution of Voronoi cells Motivated by the simple form of the distribution function in the 1D case, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size-distribution function in the practically important 2D and 3D cases as well Denoting the dimensionality of the space by d ( d = 1 , 2 , 3 ) the f ( y ) = Const * y ( 3 d - 1 ) / 2 exp ( - ( 3 d + 1 ) y / 2 ) compact form is suggested for the normalized cell-size distribution function By using large-scale computer simulations the viability of the proposed distribution function is studied and critically discussed
517 citations
TL;DR: A bidimensional cellular automaton model is used to simulate the process of evacuation of pedestrians in a room with fixed obstacles and fails when obstacles are present, as their presence introduces local bottlenecks whose effect outweighs the benefits of increasing door width beyond a certain threshold.
Abstract: A bidimensional cellular automaton model is used to simulate the process of evacuation of pedestrians in a room with fixed obstacles. A floor field is defined so that moving to a cell with lower floor field means approaching an exit door. The model becomes non-deterministic by introducing a “panic” parameter, given by a probability of not moving, and by a random choice to resolve conflicts in the update of pedestrian positions. Two types of exit doors are considered: single (where only one person can pass) and double (two persons can pass simultaneously). For a double door, the longest evacuation time turns out to occur for a very traditional location of the door. The optimum door position is determined. Replacing the double door by two single doors does not improve evacuation times noticeably. On the other hand, for a room without obstacles, a simple scaling law is proposed to model the dependence of evacuation time with the number of persons and exit width. This model fails when obstacles are present, as their presence introduces local bottlenecks whose effect outweighs the benefits of increasing door width beyond a certain threshold.
366 citations
TL;DR: It is shown that when the propagation requires simultaneous exposure to multiple sources of activation, called complex propagation, the effect of random links can be just the opposite; it can make the propagation more difficult to achieve.
Abstract: Random links between otherwise distant nodes can greatly facilitate the propagation of disease or information, provided contagion can be transmitted by a single active node. However, we show that when the propagation requires simultaneous exposure to multiple sources of activation, called complex propagation , the effect of random links can be just the opposite; it can make the propagation more difficult to achieve. We numerically calculate critical points for a threshold model using several classes of complex networks, including an empirical social network. We also provide an estimation of the critical values in terms of vulnerable nodes.
349 citations
TL;DR: A fractional order model for nonlocal epidemics is given and stability of fractional orders equations is studied to be relevant to foot-and-mouth disease, SARS and avian flu.
Abstract: A fractional order model for nonlocal epidemics is given. Stability of fractional order equations is studied. The results are expected to be relevant to foot-and-mouth disease, SARS and avian flu.
331 citations
TL;DR: In this article, the effect of inflexible agents on two state opinion dynamics is studied and the model operates via repeated local updates of random grouping of agents, where floater agents do eventually flip their opinion to follow the local majority, inflexibly agents keep their opinion always unchanged, and an incompressible minority around the inflexibles, one of the pure attractors becoming a mixed phase attractor.
Abstract: We study the effect of inflexible agents on two state opinion dynamics. The model operates via repeated local updates of random grouping of agents. While floater agents do eventually flip their opinion to follow the local majority, inflexible agents keep their opinion always unchanged. It is a quenched individual opinion. In the bare model (no inflexibles), a separator at 50 % drives the dynamics towards either one of two pure attractors, each associated with a full polarization along one of the opinions. The initial majority wins. The existence of inflexibles for only one of the two opinions is found to shift the separator at a lower value than 50 % in favor of that side. Moreover it creates an incompressible minority around the inflexibles, one of the pure attractors becoming a mixed phase attractor. In addition above a threshold of 17 % inflexibles make their side sure of winning whatever the initial conditions are. The inflexible minority wins. An equal presence of inflexibles on both sides restores the balanced dynamics with again a separator at 50 % and now two mixed phase attractors on each side. Nevertheless, beyond 25 % the dynamics is reversed with a unique attractor at a 50–50 stable equilibrium. But a very small advantage in inflexibles results in a decisive lowering of the separator at the advantage of the corresponding opinion. A few percent advantage does guarantee to become majority with one single attractor. The model is solved exhaustedly for groups of size 3.
299 citations
TL;DR: A large sample of 40 US cities and a few more from elsewhere of different sizes is derived, finding that all the topologies of urban street networks based on street–street intersection demonstrate a small world structure, and a scale-free property for both street length and connectivity degree.
Abstract: In this paper, we derive a topological pattern of urban street networks using a large sample (the largest so far to the best of our knowledge) of 40 US cities and a few more from elsewhere of different sizes. It is found that all the topologies of urban street networks based on street–street intersection demonstrate a small world structure, and a scale-free property for both street length and connectivity degree. More specifically, for any street network, about 80% of its streets have length or degrees less than its average value, while 20% of streets have length or degrees greater than the average. Out of the 20%, there are less than 1% of streets which can form a backbone of the street network. Based on the finding, we conjecture that the 20% streets account for 80% of traffic flow, and the 1% streets constitute a cognitive map of the urban street network. We illustrate further a peculiarity about the scale-free property.
296 citations
TL;DR: An evolutionary algorithm is used to evolve complex networks that are resilient to cascading failure and analyzes these networks for topological regularities that explain the source of such resilience.
Abstract: Our modern society has come to depend on large-scale infrastructure networks to deliver resources to our homes and businesses in an efficient manner Over the past 10 years there have been numerous examples where a local disturbance has lead to the global failure of systems In this paper, we use an evolutionary algorithm to evolve complex networks that are resilient to such cascading failure We then analyze these networks for topological regularities that explain the source of such resilience The analysis reveals that clustering, modularity and long path lengths all play an important part in the design of robust large-scale infrastructure
TL;DR: In this paper, the synchronization problem in an array of linearly stochastically coupled identical networks with time delays is investigated, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly.
Abstract: In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.
TL;DR: In this article, the authors show that the prices of European-style options satisfy a fractional partial differential equation (FPDE) and use numerical techniques to price exotic options by solving the corresponding FPDEs derived.
Abstract: Most of the recent literature dealing with the modeling of financial assets assumes that the underlying dynamics of equity prices follow a jump process or a Levy process. This is done to incorporate rare or extreme events not captured by Gaussian models. Of those financial models proposed, the most interesting include the CGMY, KoBoL and FMLS. All of these capture some of the most important characteristics of the dynamics of stock prices. In this article we show that for these particular Levy processes, the prices of financial derivatives, such as European-style options, satisfy a fractional partial differential equation (FPDE). As an application, we use numerical techniques to price exotic options, in particular barrier options, by solving the corresponding FPDEs derived.
TL;DR: A general model of complex delayed dynamical networks withImpulsive effects is formulated, which can well describe practical architectures of more realistic complex networks related to impulsive effects.
Abstract: The present paper is mainly concerned with the issues of synchronization dynamics of complex delayed dynamical networks with impulsive effects. A general model of complex delayed dynamical networks with impulsive effects is formulated, which can well describe practical architectures of more realistic complex networks related to impulsive effects. Based on impulsive stability theory on delayed dynamical systems, some simple but less conservative criterion are derived for global synchronization of such dynamical network. It is shown that synchronization of the networks is heavily dependent on impulsive effects of connecting configuration in the networks. Furthermore, the theoretical results are applied to a typical SF network composing of impulsive coupled chaotic delayed Hopfield neural network nodes, and are also illustrated by numerical simulations.
TL;DR: By utilizing the stability theory for impulsive functional differential equations, several new criteria are obtained to ensure the robust synchronization of coupled networks via impulsive control via Impulsive control with time delays.
Abstract: This paper investigates the synchronization scheme of coupled neural networks with time delays. The coupling function, which can be linear or nonlinear, is subject to uncertainties in the network. By utilizing the stability theory for impulsive functional differential equations, several new criteria are obtained to ensure the robust synchronization of coupled networks via impulsive control. Furthermore, an estimation of the predicted stable region is derived to facilitate the design of the control gain. Finally, numerical simulations are presented to demonstrate the effectiveness of our results.
TL;DR: In this article, synchronization control of stochastic neural networks with time-varying delays has been considered and a novel control method is given using the Lyapunov functional method and linear matrix inequality (LMI) approach.
Abstract: In this paper, synchronization control of stochastic neural networks with time-varying delays has been considered. A novel control method is given using the Lyapunov functional method and linear matrix inequality (LMI) approach. Several sufficient conditions have been derived to ensure the global asymptotical stability in mean square for the error system, and thus the drive system synchronize with the response system. Also, the estimation gains can be obtained. With these new and effective methods, synchronization can be achieved. Simulation results are given to verify the theoretical analysis in this paper.
TL;DR: It is shown that the movement of pedestrians in an oblique direction to the grid is successfully simulated by RCA, which was not taken into account in the previous CA models.
Abstract: In this paper, we propose a new approach for pedestrian dynamics. We call it a real-coded cellular automata (RCA). The scheme is based on the real-coded lattice gas (RLG), which has been developed for fluid simulation. Similar to RLG, the position and velocity can be freely given, independent of grid points. Our strategy including the procedure for updating the position of each pedestrian is explained. It is shown that the movement of pedestrians in an oblique direction to the grid is successfully simulated by RCA, which was not taken into account in the previous CA models. Moreover, from simulations of evacuation from a room with an exit of various widths, we obtain the critical number of people beyond which the clogging appears at the exit.
TL;DR: It is argued that crowd forces (and associated injuries) are an essential characteristic of crowds, and that their omission will negatively affect the model's ability to make predictions (e.g. time for a crowd to pass through an exit).
Abstract: Crowd scenarios have attracted attention from computer modellers, perhaps because of the impracticality of studying the phenomenon by traditional experimental methods. For example, Kirchner has proposed an agent-based crowd model inspired by fields of elementary particles [A. Kirchner, A. Schadschneider, Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics, Physica A 312 (2002) 260–276.], but chose not to incorporate crowd forces. We argue that crowd forces (and associated injuries) are an essential characteristic of crowds, and that their omission will negatively affect the model's ability to make predictions (e.g. time for a crowd to pass through an exit). To support this position we describe an evolution of Kirchner's model that includes a vector-based particle field to represent forces. We show qualitative and quantitative differences compared to Kirchner's model when force is included. The Swarm Force model demonstrates—by showing non-linear effects of force—the necessity of force in crowd models.
TL;DR: In this paper, the adaptive synchronization and lag synchronization are considered for uncertain dynamical system with time delay based on parameter identification and a novel control method is then further given using the Lyapunov functional method.
Abstract: In this paper, the adaptive synchronization and lag synchronization are considered for uncertain dynamical system with time delay based on parameter identification and a novel control method is then further given using the Lyapunov functional method. With this new and effective method, parameter identification and lag synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper.
TL;DR: In this article, a minimum spanning tree is used to study the process of market integration for a large group of national stock market indices, and the authors show how the asset tree evolves over time and describe the dynamics of its normalized length, mean occupation layer, and single and multiple-step linkage survival rates.
Abstract: The concept of a minimum spanning tree is used to study the process of market integration for a large group of national stock market indices. We show how the asset tree evolves over time and describe the dynamics of its normalized length, mean occupation layer, and single- and multiple-step linkage survival rates. Over the period studied, 1997–2006, the tree shows a tendency to become more compact. This implies that global equity markets are increasingly interrelated. The consequence for global investors is a potential reduction of the benefits of international portfolio diversification.
TL;DR: An adaptive procedure to the problem of synchronization and parameters identification for chaotic neural networks with time-varying delay is introduced by combining the adaptive control and linear feedback with appropriate update law based on the invariance principle of functional differential equations.
Abstract: In this paper, an adaptive procedure to the problem of synchronization and parameters identification for chaotic neural networks with time-varying delay is introduced by combining the adaptive control and linear feedback with appropriate update law. Based on the invariance principle of functional differential equations, all the connection weight matrices can be efficiently estimated according to a simple, rigorous, and systematic technique. This approach is also able to track the changes in the operating parameters of the experimental neural networks rapidly. The speed of synchronization and parameters estimation can be adjusted under the adaptive gain properly chosen. In addition, the method is simple to implement in practice, and it is quite robust against the effect of slight noise in the given time series and the estimated value of a parameter fluctuates around the correct value.
TL;DR: Some generic stability criteria based on master stability function (MSF) are derived for such a general controlled network, which guarantee that the whole network can be pinned to its equilibrium by placing feedback control only on a small fraction of nodes.
Abstract: Recently, the researches on pinning control of complex dynamical networks have mainly focused on such networks with very specific coupling schemes (e.g., symmetric coupling, uniform coupling and linear coupling). However, most real networks often consist of local units, which interact with each other via asymmetric and heterogeneous connections. In this paper, pinning control of a continuous-time complex dynamical network with general coupling topologies is studied. Some generic stability criteria based on master stability function (MSF) are derived for such a general controlled network, which guarantee that the whole network can be pinned to its equilibrium by placing feedback control only on a small fraction of nodes. Then, these results are extended to discrete-time case. Previous results about symmetric, uniform or linear coupled networks in this area are included as special cases of the present work. Numerical simulations of directed networks with weighted coupling pinned by specifically selective pinning scheme are given for illustration and verification.
TL;DR: A large number of network properties can now be described through a set of simple scaling exponents, in analogy with traditional fractal theory, which has an important effect in understanding of the evolution and behavior of such systems.
Abstract: We review recent findings of self-similarity in complex networks. Using the box-covering technique, it was shown that many networks present a fractal behavior, which is seemingly in contrast to their small-world property. Moreover, even non-fractal networks have been shown to present a self-similar picture under renormalization of the length scale. These results have an important effect in our understanding of the evolution and behavior of such systems. A large number of network properties can now be described through a set of simple scaling exponents, in analogy with traditional fractal theory.
TL;DR: In this paper, the effects of variable thermal conductivity and radiation on the flow and heat transfer of an electrically conducting micropolar fluid over a continuously stretching surface with varying temperature in the presence of a magnetic field are considered.
Abstract: In this paper, the effects of variable thermal conductivity and radiation on the flow and heat transfer of an electrically conducting micropolar fluid over a continuously stretching surface with varying temperature in the presence of a magnetic field are considered. The surface temperature is assumed to vary as a power-law temperature. The governing conservation equations of mass, momentum, angular momentum and energy are converted into a system of non-linear ordinary differential equations by means of similarity transformation. The resulting system of coupled non-linear ordinary differential equations is solved numerically. The numerical results show that the thermal boundary thickness increases as the thermal conductivity parameter S increases, while it decreases as the radiation parameter F increases. Also, it was found that the Nusselt number increases as F increases and decreases as S increases.
TL;DR: In this article, the authors investigate course registration data of 18 semesters at a Korean University to portray the time evolution of students' positions in the network of fellow students. And they find that the students' ties to the classmates of the first semester will, on average, become stronger as time progresses.
Abstract: We investigate course registration data of 18 semesters at a Korean University to portray the time evolution of students’ positions in the network of fellow students Apart from being a study of the social positions of students, the present work is also an example of how large-scale, time resolved, affiliation networks can be analyzed For example, we discuss the proper definitions of weights, and propose a redefined weighted clustering coefficient Among other things, we find that the students enter the network at the center and are gradually diffusing towards the periphery On the other hand, the ties to the classmates of the first semester will, on average, become stronger as time progresses
TL;DR: The pathway model of Mathai is shown to be inferable from the maximization of a certain generalized entropy measure, which can be given probabilistic interpretations in terms of inaccuracy measure, expected value, and information content in a scheme.
Abstract: The pathway model of Mathai [A pathway to matrix-variate gamma and normal densities, Linear Algebra Appl. 396 (2005) 317–328] is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order α , considered in Mathai and Rathie [Basic Concepts in Information Theory and Statistics: Axiomatic Foundations and Applications, Wiley Halsted, New York and Wiley Eastern, New Delhi, 1975], and it is also associated with Shannon, Boltzmann–Gibbs, Renyi, Tsallis, and Havrda–Charvat entropies. The generalized entropy measure introduced here is also shown to have interesting statistical properties and it can be given probabilistic interpretations in terms of inaccuracy measure , expected value , and information content in a scheme. Particular cases of the pathway model are shown to be Tsallis statistics [C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52 (1988) 479–487] and superstatistics introduced by Beck and Cohen [Superstatistics, Physica A 322 (2003) 267–275]. The pathway model's connection to fractional calculus is illustrated by considering a fractional reaction equation.
TL;DR: In this article, the authors used two physics derived hierarchical techniques, a minimal spanning tree and an ultrametric hierarchical tree, to extract a topological influence map for major currencies.
Abstract: This paper uses two physics derived hierarchical techniques, a minimal spanning tree and an ultrametric hierarchical tree, to extract a topological influence map for major currencies from the ultrametric distance matrix for 1995–2001. We find that these two techniques generate a defined and robust scale free network with meaningful taxonomy. The topology is shown to be robust with respect to method, to time horizon and is stable during market crises. This topology, appropriately used, gives a useful guide to determining the underlying economic or regional causal relationships for individual currencies and to understanding the dynamics of exchange rate price determination as part of a complex network.
TL;DR: Using Lyapunov theory, an adaptive feedback controlling method is proposed to identify the exact topology of a rather general weighted complex dynamical network model.
Abstract: Recently, various papers investigated the geometry features, synchronization and control of complex network provided with certain topology. While, the exact topology of a network is sometimes unknown or uncertain. Using Lyapunov theory, we propose an adaptive feedback controlling method to identify the exact topology of a rather general weighted complex dynamical network model. By receiving the network nodes evolution, the topology of such kind of network with identical or different nodes, or even with switching topology can be monitored. Experiments show that the methods presented in this paper are of high accuracy with good performance.
TL;DR: In this article, the authors study the evacuation of a set of 200 pedestrians from a room under a state of panic using the Social Force Model, where the degree of panic is controlled by a parameter v d which represents the velocity at which pedestrians wish to move.
Abstract: We study the evacuation of a set of 200 pedestrians from a room under a state of panic. The dynamics of the pedestrians is given by the Social Force Model. The degree of panic is controlled by a parameter v d which represents the velocity at which pedestrians wish to move. We show that the “faster is slower effect” can be understood in terms of the works performed by the different forces present in the system and the role played by dissipative terms in the model. Beyond the maximum flow rate the “granular cluster” mass distribution displays a transition from exponentially decaying to “U-shaped” as this value of v d evacuation efficiency begins to decrease rapidly.
TL;DR: In this paper, a detailed investigation on the nature of the phase transition in the scalar noise model (SNM) of collective motion is presented, and the results confirm the original findings of Vicsek et al. [Phys. Rev. Lett. 75 (1995) 1226].
Abstract: In this paper we present our detailed investigations on the nature of the phase transition in the scalar noise model (SNM) of collective motion. Our results confirm the original findings of Vicsek et al. [Phys. Rev. Lett. 75 (1995) 1226] that the disorder–order transition in the SNM is a continuous, second order phase transition for small particle velocities ( v ⩽ 0.1 ) . However, for large velocities ( v ⩾ 0.3 ) we find a strong anisotropy in the particle diffusion in contrast with the isotropic diffusion for small velocities. The interplay between the anisotropic diffusion and the periodic boundary conditions leads to an artificial symmetry breaking of the solutions (directionally quantized density waves) and a consequent first order transition like behavior. Thus, it is not possible to draw any conclusion about the physical behavior in the large particle velocity regime of the SNM.