Showing papers in "Physica A-statistical Mechanics and Its Applications in 2006"
TL;DR: The authors show that the absence of any clue of assortativity differentiates urban street networks from other non-geographic systems and that most of the considered networks have a broad degree distribution typical of scale-free networks and exhibit small-world properties as well.
Abstract: The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation between measures of the structure of the network and measures of the dynamics on the network, what are the possible contributions from the GIS community. In this paper, the author considers six cases of urban street networks characterized by different patterns and historical roots. The authors propose a representation of the street networks based firstly on a primal graph, where intersections are turned into nodes and streets into edges. In a second step, a dual graph, where streets are nodes and intersections are edges, is constructed by means of a generalization model named Intersection Continuity Negotiation, which allows to acknowledge the continuity of streets over a plurality of edges. Finally, the authors address a comparative study of some structural properties of the dual graphs, seeking significant similarities among clusters of cases. A wide set of network analysis techniques are implemented over the dual graph: in particular the authors show that the absence of any clue of assortativity differentiates urban street networks from other non-geographic systems and that most of the considered networks have a broad degree distribution typical of scale-free networks and exhibit small-world properties as well.
726 citations
TL;DR: A wide class of time-continuous microscopic traffic models is generalized to include essential aspects of driver behaviour not captured by these models, including finite reaction times, estimation errors, and looking several vehicles ahead (spatial anticipation), and temporal anticipation.
Abstract: We generalize a wide class of time-continuous microscopic traffic models to include essential aspects of driver behaviour not captured by these models. Specifically, we consider (i) finite reaction times, (ii) estimation errors, (iii) looking several vehicles ahead (spatial anticipation), and (iv) temporal anticipation. The estimation errors are modelled as stochastic Wiener processes and lead to time-correlated fluctuations of the acceleration. We show that the destabilizing effects of reaction times and estimation errors can essentially be compensated for by spatial and temporal anticipation, that is, the combination of stabilizing and destabilizing effects results in the same qualitative macroscopic dynamics as that of the, respectively, underlying simple car-following model. In many cases, this justifies the use of simplified, physics-oriented models with a few parameters only. Although the qualitative dynamics is unchanged, multi-anticipation increase both spatial and temporal scales of stop-and-go waves and other complex patterns of congested traffic in agreement with real traffic data. Remarkably, the anticipation allows accident-free smooth driving in complex traffic situations even if reaction times exceed typical time headways.
508 citations
TL;DR: In this paper, the authors apply several paradigmatic models of epidemics to empirical data on the advent and spread of Feynman diagrams through the theoretical physics communities of the USA, Japan, and the USSR in the period immediately after World War II.
Abstract: The population dynamics underlying the diffusion of ideas hold many qualitative similarities to those involved in the spread of infections. In spite of much suggestive evidence this analogy is hardly ever quantified in useful ways. The standard benefit of modeling epidemics is the ability to estimate quantitatively population average parameters, such as interpersonal contact rates, incubation times, duration of infectious periods, etc. In most cases such quantities generalize naturally to the spread of ideas and provide a simple means of quantifying sociological and behavioral patterns. Here we apply several paradigmatic models of epidemics to empirical data on the advent and spread of Feynman diagrams through the theoretical physics communities of the USA, Japan, and the USSR in the period immediately after World War II. This test case has the advantage of having been studied historically in great detail, which allows validation of our results. We estimate the effectiveness of adoption of the idea in the three communities and find values for parameters reflecting both intentional social organization and long lifetimes for the idea. These features are probably general characteristics of the spread of ideas, but not of common epidemics.
432 citations
TL;DR: The detailed dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation, and Poincare mapping.
Abstract: This paper constructs a new hyperchaotic system based on Lu system by using a state feedback controller. The detailed dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation, and Poincare mapping. Moreover, a novel circuit diagram is designed for verifying the hyperchaotic behaviors and some experimental observations are also given.
402 citations
TL;DR: In this paper, a robust algorithm for analyzing the geometry and connectivity of the pore space of sedimentary rock is proposed based on fundamental concepts of mathematical morphology, where the information about the skeleton is stored through the maximal inscribed balls or spheres associated with each voxel.
Abstract: A new robust algorithm analyzing the geometry and connectivity of the pore space of sedimentary rock is based on fundamental concepts of mathematical morphology. The algorithm distinguishes between the “pore bodies” and “pore throats,” and establishes their respective volumes and connectivity. The proposed algorithm also produces a stick-and-ball diagram of the rock pore space. The tests on a pack of equal spheres, for which the results are verifiable, confirm its stability. The impact of image resolution on the algorithm output is investigated on the images of computer-generated pore space. One of distinctive features of our approach is that no image thinning is applied. Instead, the information about the skeleton is stored through the maximal inscribed balls or spheres (MIS) associated with each voxel. These maximal balls retain information about the entire pore space. Comparison with the results obtained by a thinning procedure preserving some topological properties of the pore space shows that our method produces more realistic estimates of the number and shapes of pore bodies and pore throats, and the pore coordination numbers. The distribution of maximal inscribed spheres makes possible simulation of mercury injection and computation of the corresponding dimensionless capillary pressure curve. It turns out that the calculated capillary pressure curve is a robust descriptor of the pore space geometry and, in particular, can be used to determine the quality of computer-based rock reconstruction.
393 citations
TL;DR: The urban road networks of the 20 largest German cities have been analysed, based on a detailed database providing the geographical positions as well as the travel-times for network sizes up to 37,000 nodes and 87,000 links, finding that traffic strongly concentrates on only a small fraction of the roads.
Abstract: The urban road networks of the 20 largest German cities have been analysed, based on a detailed database providing the geographical positions as well as the travel-times for network sizes up to 37,000 nodes and 87,000 links. As the human driver recognises travel-times rather than distances, faster roads appear to be ‘shorter’ than slower ones. The resulting metric space has an effective dimension δ>2, which is a significant measure of the heterogeneity of road speeds. We found that traffic strongly concentrates on only a small fraction of the roads. The distribution of vehicular flows over the roads obeys a power law, indicating a clear hierarchical order of the roads. Studying the cellular structure of the areas enclosed by the roads, the distribution of cell sizes is scale invariant as well.
375 citations
TL;DR: In this article, the authors provide a pedagogical introduction to the abelian sandpile model of self-organized criticality, and its related models, including the ABELIAN group, the algebra of particle addition operators, the burning test for recurrent states, equivalence to the spanning trees problem, and the exact solution of the directed version of the model in any dimension.
Abstract: These notes are intended to provide a pedagogical introduction to the abelian sandpile model of self-organized criticality, and its related models. The abelian group, the algebra of particle addition operators, the burning test for recurrent states, equivalence to the spanning trees problem are described. The exact solution of the directed version of the model in any dimension is explained. The model's equivalence to Scheidegger's model of river basins, Takayasu's aggregation model and the voter model is discussed. For the undirected case, the solution for one-dimensional lattices and the Bethe lattice is briefly described. Known results about the two dimensional case are summarized. Generalization to the abelian distributed processors model is discussed. Time-dependent properties and the universality of critical behavior in sandpiles are briefly discussed. I conclude by listing some still-unsolved problems.
337 citations
TL;DR: In this paper, the authors discuss bounds on the values adopted by the generalized statistical complexity measures introduced by Lopez Ruiz et al. and Shiner et al., and prove new theorems with reference to the celebrated logistic map.
Abstract: We discuss bounds on the values adopted by the generalized statistical complexity measures [M.T. Martin et al., Phys. Lett. A 311 (2003) 126; P.W. Lamberti et al., Physica A 334 (2004) 119] introduced by Lopez Ruiz et al. [Phys. Lett. A 209 (1995) 321] and Shiner et al. [Phys. Rev. E 59 (1999) 1459]. Several new theorems are proved and illustrated with reference to the celebrated logistic map.
305 citations
TL;DR: This study applies a backpropagation neural network because of its nonlinear structures to forecast fuzzy time series, and proposes two models: a basic model using a neural network approach to forecast all of the observations, and a hybrid model consisting of a Neural Network Approach to forecast the known patterns.
Abstract: Fuzzy time series models have been applied to handle nonlinear problems. To forecast fuzzy time series, this study applies a backpropagation neural network because of its nonlinear structures. We propose two models: a basic model using a neural network approach to forecast all of the observations, and a hybrid model consisting of a neural network approach to forecast the known patterns as well as a simple method to forecast the unknown patterns. The stock index in Taiwan for the years 1991–2003 is chosen as the forecasting target. The empirical results show that the hybrid model outperforms both the basic and a conventional fuzzy time series models.
290 citations
TL;DR: The concepts of subgraph centrality and clustering for complex networks represented by hypergraphs: complex hyper-networks are extended and another measure characterizing the formation of triples of mutually adjacent groups in the hyper-network is introduced.
Abstract: The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited information about the structure of the system. Consequently, we extend the concepts of subgraph centrality and clustering for complex networks represented by hypergraphs: complex hyper-networks . The first parameter characterizes the node participation in different sub-hypergraphs and the second one characterizes the transitivity in the hyper-network through the proportion of hyper-triangles to paths of length two. Another measure characterizing the formation of triples of mutually adjacent groups in the hyper-network is also introduced. All of these characteristics are studied in three different hyper-networks: a scientific collaboration hyper-network, an ecological competition hyper-network and the hyper-network formed by the American corporate elite in 1999.
266 citations
TL;DR: In this article, a simplified version of the well-scaled transition of CTRW to the diffusive or hydrodynamic limit is presented, and applications of CTRWs to the ruin theory of insurance companies, to growth and inequality processes and to the dynamics of prices in financial markets are outlined and briefly discussed.
Abstract: This paper reviews some applications of continuous time random walks (CTRWs) to Finance and Economics. It is divided into two parts. The first part deals with the connection between CTRWs and anomalous diffusion. In particular, a simplified version of the well-scaled transition of CTRWs to the diffusive or hydrodynamic limit is presented. In the second part, applications of CTRWs to the ruin theory of insurance companies, to growth and inequality processes and to the dynamics of prices in financial markets are outlined and briefly discussed.
TL;DR: In this paper, a basic introduction to the physics of phase transitions under non-equilibrium conditions is given, followed by a general introduction to nonequilibrium statistical mechanics followed by four parts.
Abstract: These lecture notes give a basic introduction to the physics of phase transitions under non-equilibrium conditions. The notes start with a general introduction to non-equilibrium statistical mechanics followed by four parts. The first one discusses the universality class of directed percolation, which plays a similar role as the Ising model in equilibrium statistical physics. The second one gives an overview about other universality classes which have been of interest in recent years. The third part extends the scope to models with long-range interactions, including memory effects and the so-called Levy flights. Finally, the fourth part is concerned with deposition–evaporation phenomena leading to wetting transitions out of equilibrium.
TL;DR: It is shown that any complex network may be viewed as a bipartite graph with some specific characteristics, and that its main properties may be views as consequences of this underlying structure.
Abstract: It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model which achieves the following challenges: it produces graphs which have the three main wanted properties (clustering, degree distribution, average distance), it is based on some real-world observations, and it is sufficiently simple to make it possible to prove its main properties. This model consists in sampling a random bipartite graph with prescribed degree distribution. Indeed, we show that any complex network may be viewed as a bipartite graph with some specific characteristics, and that its main properties may be viewed as consequences of this underlying structure. We also propose a growing model based on this observation.
TL;DR: Analysis of the world's largest subway systems reveals two related classes of complex network that can be approximated by an evolutionary network with an associated exponential degree distribution.
Abstract: Analysis of the world's largest subway systems reveals two related classes of complex network that can be approximated by an evolutionary network with an associated exponential degree distribution. The characteristic high connectivity but low maximum vertex degree of these networks provides robustness to random attack, although one of the two classes is noticeably more vulnerable to targeted attack.
TL;DR: This work presents a model for an undirected growing network which reproduces characteristics of a social network, with the aim of producing efficiently very large networks to be used as platforms for studying sociodynamic phenomena.
Abstract: Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e., highly connected vertices tend to connect to other highly connected vertices, and have broad degree distributions. We present a model for an undirected growing network which reproduces these characteristics, with the aim of producing efficiently very large networks to be used as platforms for studying sociodynamic phenomena. The communities arise from a mixture of random attachment and implicit preferential attachment. The structural properties of the model are studied analytically and numerically, using the k-clique method for quantifying the communities. r 2006 Elsevier B.V. All rights reserved.
TL;DR: A mathematical model for the adaptive dynamics of the transport network in an amoeba-like organism, the true slime mold Physarum polycephalum, is proposed, based on physiological observations of this species and the results of simulations of some complicated networks are described.
Abstract: We have proposed a mathematical model for the adaptive dynamics of the transport network in an amoeba-like organism, the true slime mold Physarum polycephalum. The model is based on physiological observations of this species, but can also be used for path-finding in the complicated networks of mazes and road maps. In this paper, we describe the physiological basis and the formulation of the model, as well as the results of simulations of some complicated networks. The path-finding method used by Physarum is a good example of cellular computation.
TL;DR: A new LG-based discrete model entitled “multi-grid model” is composed; in the new model, finer lattice is used; thus each pedestrian occupies multiple grids instead of one, and the rules of interactions among pedestrians or pedestrians and constructions are built.
Abstract: Introducing the force concept of a social force model into the lattice gas (LG) model, a new LG-based discrete model entitled “multi-grid model” is composed. In the new model, finer lattice is used; thus each pedestrian occupies multiple grids instead of one, and the rules of interactions among pedestrians or pedestrians and constructions are built. The interaction forces including extrusion, repulsion and friction are considered as passive factors for evacuation. The strength of the drift, or the intensity of the pedestrians to move toward the exit rapidly, is considered an active factor. A simple situation is studied in which pedestrians try to evacuate from a large room with only one door. The influences of interaction forces and drift on evacuation time are analyzed. The mutual restriction relation of the two factors in the course of evacuating is found.
TL;DR: Econophysics has already made a number of important empirical contributions to our understanding of the social and economic world as mentioned in this paper, and econophysicists have attempted to apply the theoretical approach of statistical physics to try to understand empirical findings.
Abstract: Econophysics has already made a number of important empirical contributions to our understanding of the social and economic world. These fall mainly into the areas of finance and industrial economics, where in each case there is a large amount of reasonably well-defined data. More recently, Econophysics has also begun to tackle other areas of economics where data is much more sparse and much less reliable. In addition, econophysicists have attempted to apply the theoretical approach of statistical physics to try to understand empirical findings. Our concerns are fourfold. First, a lack of awareness of work that has been done within economics itself. Second, resistance to more rigorous and robust statistical methodology. Third, the belief that universal empirical regularities can be found in many areas of economic activity. Fourth, the theoretical models which are being used to explain empirical phenomena. The latter point is of particular concern. Essentially, the models are based upon models of statistical physics in which energy is conserved in exchange processes. There are examples in economics where the principle of conservation may be a reasonable approximation to reality, such as primitive hunter–gatherer societies. But in the industrialised capitalist economies, income is most definitely not conserved. The process of production and not exchange is responsible for this. Models which focus purely on exchange and not on production cannot by definition offer a realistic description of the generation of income in the capitalist, industrialised economies.
TL;DR: In this paper, a modified social force model was used to analyze the influence of various approaches for the interaction between the pedestrians on the resulting velocity-density relation, and the role of the required space and remote force was investigated.
Abstract: For the modelling of pedestrian dynamics we treat persons as self-driven objects moving in a continuous space. On the basis of a modified social force model we qualitatively analyze the influence of various approaches for the interaction between the pedestrians on the resulting velocity–density relation. To focus on the role of the required space and remote force we choose a one-dimensional model for this investigation. For those densities, where in two dimensions also passing is no longer possible and the mean value of the velocity depends primarily on the interaction, we obtain the following result: If the model increases the required space of a person with increasing current velocity, the reproduction of the typical form of the fundamental diagram is possible. Furthermore, we demonstrate the influence of the remote force on the velocity–density relation.
TL;DR: In this article, the Laplace transformation theory was used to derive the sufficient conditions for synchronization between two identical Chua systems with the same fractional order, and the necessary conditions for achieving synchronization between these two systems were derived via Laplace transform theory.
Abstract: Chaos synchronization of two identical Chua systems with the same fractional order is studied by utilizing the Pecora–Carroll (PC) method, the active–passive decomposition (PAD) method, the one-way coupling method and the bidirectional coupling one. The sufficient conditions for achieving synchronization between these two systems are derived via the Laplace transformation theory. Numerical simulations show the effectiveness of the theoretical analyses.
TL;DR: The theoretical arguments for the advantage of the technique, termed phase-rectified signal averaging (PRSA), over conventional spectral analysis are given and it is shown in a numerical test that the threshold intensity for the detection of additional quasi-periodic components is approximately 75% lower with PRSA.
Abstract: We present an efficient technique for the study of quasi-periodic oscillations in noisy, non-stationary signals, which allows the assessment of system dynamics despite phase resetting and noise. It is based on the definition of anchor points in the signal (in the simplest case increases or decreases of the signal) which are used to align (i.e., phase-rectify) the oscillatory fluctuations followed by an averaging of the surroundings of the anchor points. We give theoretical arguments for the advantage of the technique, termed phase-rectified signal averaging (PRSA), over conventional spectral analysis and show in a numerical test using surrogate heartbeat data that the threshold intensity for the detection of additional quasi-periodic components is approximately 75% lower with PRSA. With the use of different anchor point criteria PRSA is capable of separately analysing quasi-periodicities that occur during increasing or decreasing parts of the signal. We point to a variety of applications in the analysis of medical, biological, and geophysical data containing quasi-periodicities besides non-stationarities and 1 / f noise.
TL;DR: In this paper, a hierarchical taxonomy of currencies constructing minimal-spanning trees is derived by analyzing the foreign exchange market data of various currencies, and the key currencies in each cluster are found.
Abstract: By analyzing the foreign exchange market data of various currencies, we derive a hierarchical taxonomy of currencies constructing minimal-spanning trees. Clustered structure of the currencies and the key currency in each cluster are found. The clusters match nicely with the geographical regions of corresponding countries in the world such as Asia or East Europe, the key currencies are generally given by major economic countries as expected.
TL;DR: In this paper, the authors analyzed the quarterly average sale prices of new houses sold in the USA as a whole, in the Northeast, Midwest, South, and West of the USA, in each of the 50 states and the District of Columbia of USA, to determine whether they have grown at a faster-than-exponential rate which they took as the diagnostic of a bubble.
Abstract: Using a methodology developed in previous papers, we analyze the quarterly average sale prices of new houses sold in the USA as a whole, in the Northeast, Midwest, South, and West of the USA, in each of the 50 states and the District of Columbia of the USA, to determine whether they have grown at a faster-than-exponential rate which we take as the diagnostic of a bubble. We find that 22 states (mostly Northeast and West) exhibit clear-cut signatures of a fast-growing bubble. From the analysis of the S&P 500 Home Index, we conclude that the turning point of the bubble will probably occur around mid-2006.
TL;DR: A new characteristic (residual closeness) which can measure the network resistance is presented, which is more sensitive than the well-known measures of vulnerability and captures the result of actions even if they are small enough not to disconnect the graph.
Abstract: A new characteristic (residual closeness) which can measure the network resistance is presented. It evaluates closeness after removal of vertices or links, hence two types are considered—vertices and links residual closeness. This characteristic is more sensitive than the well-known measures of vulnerability—it captures the result of actions even if they are small enough not to disconnect the graph. A definition for closeness is modified so it still can be used for unconnected graphs but the calculations are easier.
TL;DR: The entropy of the degree distribution is an effective measure of network's resilience to random failures and is concluded that the optimal design of scale-free networks torandom failures is obtained.
Abstract: Many networks are characterized by highly heterogeneous distributions of links which are called scale-free networks, and the degree distributions follow p ( k ) ∼ ck - α . We study the robustness of scale-free networks to random failures from the character of their heterogeneity. Entropy of the degree distribution can be an average measure of a network's heterogeneity. Optimization of scale-free networks’ robustness to random failures with average connectivity constant is equivalent to maximizing the entropy of the degree distribution. By examining the relationship of the entropy of the degree distribution, scaling exponent and the minimal connectivity, we get the optimal design of scale-free networks to random failures. We conclude that the entropy of the degree distribution is an effective measure of network's resilience to random failures.
TL;DR: This paper improves a cellular automata model introduced recently, which quantifies evacuation process with three basic forces, and compares its performance with the social force model introduced by Helbing et al. in an 200-people evacuation of a single-exit square room.
Abstract: The problem of emergent evacuation is of obvious importance in common life. However, many existing evacuation models are either computationally inefficient, or are missing some crucial human behaviors in crowds. In this paper, we improve a cellular automata (CA) model introduced recently, which quantifies evacuation process with three basic forces, and compare its performance with the social force model introduced by Helbing et al. in an 200-people evacuation of a single-exit square room. The main characteristics compared include arching, clogging and faster-is-slower behaviors, as well as the evacuation time. The results show that the two models are comparable in all calculations, indicating that the three forces, i.e., repulsion, friction and attraction, are basic reasons for complex behaviors emerged from evacuation. Furthermore, because of its simple rules and fast calculation speed, the discussed CA model is easily analyzed and is very helpful to the applications.
TL;DR: In this paper, the authors present two applications with tick-by-tick stock and futures data, where the probability density functions for this limit process are solved to yield descriptions of long-term price changes, based on a high-resolution model of individual trades.
Abstract: Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typically not independent. For these coupled CTRW models, we can now compute the limiting stochastic process (just like Brownian motion is the limit of a simple random walk), even in the case of heavy tailed (power-law) price jumps and/or waiting times. The probability density functions for this limit process solve fractional partial differential equations. In some cases, these equations can be explicitly solved to yield descriptions of long-term price changes, based on a high-resolution model of individual trades that includes the statistical dependence between waiting times and the subsequent log-returns. In the heavy tailed case, this involves operator stable space-time random vectors that generalize the familiar stable models. In this paper, we will review the fundamental theory and present two applications with tick-by-tick stock and futures data.
TL;DR: In this paper, the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl were developed to provide a physical explanation for the fractional advectiondispersion equation for flow in heterogeneous porous media.
Abstract: We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection–dispersion equation for flow in heterogeneous porous media.
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TL;DR: The general properties of non-linear systems are reviewed and the basic techniques, used universally, to study the symmetry breaking and bifurcation properties are shown.
Abstract: We review the general properties of non-linear systems and show the basic techniques, used universally, to study the symmetry breaking and bifurcation properties. We exemplify these characteristics by using a Turing system that is general enough as to present many of the universal features of non-linear systems. We then show some interesting applications to various problems that we have treated in the past.
TL;DR: The evacuation process of students going on all fours is compared with that of walkers and it is shown that both experiment results are consistent with the simulation results.
Abstract: Evacuation processes of walkers (pedestrians) and crawlers are investigated by experiment and simulation. The experiments are performed for walkers and crawlers evacuating from the corridor (channel) with an exit. All students go on all fours in the evacuation experiment of crawlers. The video recordings and measurements of individual escape times are evaluated. The characteristics of evacuation processes are clarified experimentally. The evacuation process of students going on all fours is compared with that of walkers. Both experiments are mimicked by the lattice gas simulation, where each student is simulated by a biased random walker. The simulation results are compared with the experimental results. It is shown that both experiment results are consistent with the simulation results.