Kan Chen

MODELLING COLLABORATION NETWORKS BASED ON NONLINEAR PREFERENTIAL ATTACHMENT

In this paper, we propose an alternative model for collaboration networks based on nonlinear preferential attachment. Depending on a single free parameter preferential exponent, this model interpolates between networks with a scale-free and an exponential degree distribution. The degree distribution in the present networks can be roughly classified into four patterns, all of which are observed in empirical data. And this model exhibits small-world effect, which means the corresponding networks are of very short average distance and highly large clustering coefficient. More interesting, we find a peak distribution of act-size from empirical data which has not been emphasized before. Our model can produce the peak act-size distribution naturally that agrees with the empirical data well.In this paper, we propose a general model for collaboration networks. Depending on a single free parameter{bf preferential exponent}, this model interpolates between networks with a scale-free and an exponential degree distribution. The degree distribution in the present networks can be roughly classified into four patterns, all of which are observed in empirical data. And this model exhibits small-world effect, which means the corresponding networks are of very short average distance and highly large clustering coefficient. More interesting, we find a peak distribution of act-size from empirical data which has not been emphasized before of some collaboration networks. Our model can produce the peak act-size distribution naturally that agrees with the empirical data well.

Dynamics of Dry Friction: A Numerical Investigation

We perform extended numerical simulation of the dynamics of dry friction, based on a model derived from the phenomenological description proposed by Baumberger et al. [Nature (London) 367, 544 (1994)] and Heslot et al. [Phys. Rev. E 49, 4973 (1994)]. Under a quasistationary approximation, the model is related to the Dieterich-Ruina aging (or slowness) law, which was introduced by Dieterich [Pure Appl. Geophys. 116, 790 (1978); J. Geophys. Res. 84, 2161 (1979); in Mechanical Behavior of Crustal Rocks, edited by N. L. Carter et al., Geophysics Monograph No. 24 (AGU, Washington, DC, 1981), p. 103] and Ruina [J. Geophys. Res. 88, 10 359 (1983)] on the basis of experiments on rocks. We obtain a dynamical phase diagram that agrees well with the experimental results on the paper-on-paper systems. In particular, the bifurcation between the stick-slip motion and steady sliding is shown to change from a direct (supercritical) Hopf type to an inverted (subcritical) one as the driving velocity increases, in agreement with the experiments.

The Emergence of Racial Segregation in an Agent-Based Model of Residential Location: The Role of Competing Preferences

Models of segregation dynamics have examined how individual preferences over neighborhood racial composition determine macroscopic patterns of segregation. Many fewer models have considered the role of household preferences over other location attributes, which may compete with preferences over racial composition. We hypothesize that household preferences over location characteristics other than racial composition affect segregation dynamics in nonlinear ways and that, for a critical range of parameter values, these competing preferences can qualitatively affect segregation outcomes. To test this hypothesis, we develop a dynamic agent-based model that examines macro-level patterns of segregation as the result of interdependent household location choices. The model incorporates household preferences over multiple neighborhood features, some of which are endogenous to residential location patterns, and allows for income heterogeneity across races and among households of the same race. Preliminary findings indicate that patterns of segregation can emerge even when individuals are wholly indifferent to neighborhood racial composition, due to competing preferences over neighborhood density. Further, the model shows a strong tendency to concentrate affluent families in a small number of suburbs, potentially mimicking recent empirical findings on favored quarters in metropolitan areas.

The Interaction of Segregation and Suburbanization in an Agent-Based Model of Residential Location

We present a model of the interaction of segregation and suburbanization in determining residential location. The model incorporates differential income between two classes of agents, a simplified market mechanism for the purchase of housing, and a simple geographic structure of one central city and four symmetrically arranged suburbs. Agents derive utility from neighborhood racial composition, the size of their lot, private amenities that are specific to neighborhoods, and public amenities that stretch across municipalities. We find that the public-amenities term leads to a positive-feedback loop in which migration to suburbs increases the public amenities in those municipalities while lowering amenities in the central city, thus sparking further migration. When the minority agents are uniformly less affluent than the majority agents, this dynamic produces discontinuity in segregation as measured by centralization. Such discontinuities are typical of first-order phase transitions. When minority and majority incomes overlap, significant regions appear over which there are multistable equilibria at high and low levels of segregation, along with considerable sensitivity to the initial distribution of minority agents. We discuss the implications of these findings.

Adiabatic theory for the population distribution in the evolutionary minority game

We discover the mechanism for the phase transition from self-segregation (into opposing groups) to clustering (towards cautious behaviors) in the evolutionary minority game (EMG). The mechanism is illustrated with an analytical solution of a simplified EMG with three groups: two groups of opposing agents and one group of cautious agents. Two key factors affect the population distribution of the agents. One is the market impact (the selfinteraction), which has been identified previously. The other is the market inefficiency due to the short-time imbalance in the number of agents using opposite strategies. Large market impact favors “extreme” players who choose fixed strategies, while large market inefficiency favors cautious players. The phase transition depends on the number of agents (N), the reward-to-fine ratio (R), as well as the wealth reduction threshold (d) for switching strategy. When the rate for switching strategy is large we have strong clustering of cautious agents. On the other hand, when N is small, the market impact is large, and the extreme behavior is favored.

Scale-dependent dimension in the forest fire model

The forest fire model is a reaction-diffusion model where energy, in the form of trees, is injected uniformly, and burned (dissipated) locally. We show that the spatial distribution of fires forms a geometric structure where the fractal dimension varies continuously with the length scale. In the three-dimensional model, the dimensions vary from zero to three, proportional with ln(l), as the length scale increases from l approximately 1 to a correlation length l=xi. Beyond the correlation length, which diverges with the growth rate p as xi approximately p(-2/3), the distribution becomes homogeneous. We suggest that this picture applies to the intermediate range of turbulence where it provides a natural interpretation of the extended scaling that has been observed at small length scales. Unexpectedly, it might also be applicable to the spatial distribution of luminous matter in the universe. In the two-dimensional version, the dimension increases to D=1 at a length scale l approximately 1/p, where there is a crossover to homogeneity, i.e., a jump from D=1 to D=2.

Conditional Probability as a Measure of Volatility Clustering in Financial Time Series

In the past few decades considerable effort has been expended in characterizing and modeling financial time series. A number of stylized facts have been identified, and volatility clustering or the tendency toward persistence has emerged as the central feature. In this paper we propose an appropriately defined conditional probability as a new measure of volatility clustering. We test this measure by applying it to different stock market data, and we uncover a rich temporal structure in volatility fluctuations described very well by a scaling relation. The scale factor used in the scaling provides a direct measure of volatility clustering; such a measure may be used for developing techniques for option pricing, risk management, and economic forecasting. In addition, we present a stochastic volatility model that can display many of the salient features exhibited by volatilities of empirical financial time series, including the behavior of conditional probabilities that we have deduced.

Evolutionary dynamics and the phase structure of the minority game

We show that a simple evolutionary scheme, when applied to the minority game (MG), changes the phase structure of the game. In this scheme each agent evolves individually whenever his wealth reaches the specified bankruptcy level, in contrast to the evolutionary schemes used in the previous works. We show that evolution greatly suppresses herding behavior, and it leads to better overall performance of the agents. Similar to the standard nonevolutionary MG, the dependence of the standard deviation sigma on the number of agents N and the memory length m can be characterized by a universal curve. We suggest a crowd-anticrowd theory for understanding the effect of evolution in the MG.

Emergence of complex dissipative structures in the Bak–Chen–Tang forest fire model

The Bak–Chen–Tang forest fire model (Phys. Lett. A 147 (1999) 297) was proposed as a toy model of turbulent systems, where energy (in the form of trees) is injected uniformly and globally, but is dissipated (burns) locally. We review the existing results on the spatial and temporal distribution of fires and present our recent results on scaling in the higher-order moments. We show that the spatial distribution of fires (dissipation) can also be characterized by extended self-similarity used to describe the moments of energy dissipation in turbulence.

Forest fires and the structure of the universe

The forest fire model (Phys. Lett. A 147 (1990) 297) was proposed as a toy model of turbulent systems, where energy (in the form of trees) is injected uniformly and globally, but is dissipated (burns) locally. We found a novel scaling form for the spatial distribution of dissipation (fires) in the forest fire model. The fractal dimension describing the fire distribution gradually increases from zero to three as the length scale increases from the smallest scale to a correlation length. We suggest that this picture might applies to “intermediate dissipative range” of turbulence. A study of galaxy catalogues indicates that the distribution of luminous matter in the universe follows a similar pattern. At small distances, the universe is zero-dimensional and point-like; at distances of the order of 1Mpc the dimension is unity, indicating perhaps a filamentary, string-like structure. When viewed at larger scales it gradually becomes two dimensional; finally, at the correlation length, 300Mpc, it becomes uniform.