Pei-Ling Zhou

Scaling and memory in recurrence intervals of Internet traffic

By studying the statistics of recurrence intervals, τ, between volatilities of Internet traffic rate changes exceeding a certain threshold q, we find that the probability distribution functions, Pq(τ), for both byte and packet flows, show scaling property as . The scaling functions for both byte and packet flows obey the same stretching exponential form, f(x)=Aexp (-Bxβ), with β≈0.45. In addition, we detect a strong memory effect that a short (or long) recurrence interval tends to be followed by another short (or long) one. The detrended fluctuation analysis further demonstrates the presence of long-term correlation in recurrence intervals.

HIERARCHICAL ORGANIZATION AND DISASSORTATIVE MIXING OF CORRELATION-BASED WEIGHTED FINANCIAL NETWORKS

Correlation-based weighted financial networks are analyzed to present cumulative distribution of strength with a power-law tail, which suggests that a small number of hub-like stocks have greater influence on the whole fluctuation of financial market than others. The relationship between clustering and connectivity of vertices emphasizes hierarchical organization, which has been depicted by minimal span tree in previous work. These results urge us to further study the mixing patter of financial network to understand the tendency for vertices to be connected to vertices that are like (or unlike) them in some way. The measurement of average nearest-neighbor degree running over classes of vertices with degree k shows a descending trend when k increases. This interesting result is first uncovered in our work, and suggests the disassortative mixing of financial network which refers to a bias in favor of connections between dissimilar vertices. All the results in weighted complex network aspect may provide some insights to deeper understand the underlying mechanism of financial market and model the evolution of financial market.

Diffusion entropy analysis on the scaling behavior of financial markets

In this paper the diffusion entropy technique is applied to investigate the scaling behavior of financial markets. The scaling behaviors of four representative stock markets, Dow Jones Industrial Average, StandardP with the scale-invariance exponents all in the interval [0.92,0.95]. We also estimate the local scaling exponents which indicate the financial time series is homogenous perfectly. In addition, a parsimonious percolation model for stock markets is proposed, of which the scaling behavior agrees with the real-life markets well.

Scale invariance of human electroencephalogram signals in sleep

In this paper, we investigate the dynamical properties of electroencephalogram (EEG) signals of humans in sleep. By using a modified random walk method, we demonstrate that scale-invariance is embedded in EEG signals after a detrending procedure is applied. Furthermore, we study the dynamical evolution of the probability density function (PDF) of the detrended EEG signals by nonextensive statistical modeling. It displays a scale-independent property, which is markedly different from the usual scale-dependent PDF evolution and cannot be described by the Fokker-Planck equation.

Scaling behavior of an artificial traffic model on scale-free networks

In this Letter, we investigate an artificial traffic model on scale-free networks. Instead of using the routing strategy of the shortest path, a generalized routing algorithm is introduced to improve the transportation throughput, which is measured by the value of the critical point disjoining the free-flow phase and the congested phase. By using the detrended fluctuation analysis, we found that the traffic rate fluctuation near the critical point exhibits the 1/f-type scaling in the power spectrum. The simulation results agree very well with the empirical data, thus the present model may contribute to the understanding of the underlying mechanism of network traffics.

Diffusion entropy analysis on the stride interval fluctuation of human gait

In this paper, the diffusion entropy technique is applied to investigate the scaling behavior of stride interval fluctuations of human gait. The scaling behaviors of the stride interval of human walking at norm, slow, and fast rate are similar; with the scale-invariance exponents in the interval [0.663,0.955], of which the mean value is 0.821±0.011. Dynamical analysis of these stride interval fluctuations reveals a self-similar pattern: fluctuation at one time scale are statistically similar to those at multiple other time scales, at least over hundreds of steps, while the healthy subjects walk at their norm rate. The long-range correlations are observed during the spontaneous walking by removal of the trend in the time series with Fourier filter. These findings uncover that the fractal dynamics of stride interval fluctuation of human gait are normally intrinsic to the locomotor systems.

Synchronization-based approach for detecting functional activation of brain

In this paper, we investigate a synchronization-based, data-driven clustering approach for the analysis of functional magnetic resonance imaging (fMRI) data, and specifically for detecting functional activation from fMRI data. We first define a new measure of similarity between all pairs of data points (i.e., time series of voxels) integrating both complete phase synchronization and amplitude correlation. These pairwise similarities are taken as the coupling between a set of Kuramoto oscillators, which in turn evolve according to a nearest-neighbor rule. As the network evolves, similar data points naturally synchronize with each other, and distinct clusters will emerge. The clustering behavior of the interaction network of the coupled oscillators, therefore, mirrors the clustering property of the original multiple time series. The clustered regions whose cross-correlation coefficients are much greater than other regions are considered as the functionally activated brain regions. The analysis of fMRI data in auditory and visual areas shows that the recognized brain functional activations are in complete correspondence with those from the general linear model of statistical parametric mapping, but with a significantly lower time complexity. We further compare our results with those from traditional K-means approach, and find that our new clustering approach can distinguish between different response patterns more accurately and efficiently than the K-means approach, and therefore more suitable in detecting functional activation from event-related experimental fMRI data.

Boolean game on scale-free networks

Inspired by the local minority game, we propose a network Boolean game and investigate its dynamical properties on scale-free networks. The system can self-organize to a stable state with better performance than the random choice game, although only the local information is available to each agent. By introducing the heterogeneity of local interactions, we find that the system will achieve the best performance when each agents interaction frequency is linearly correlated with its information capacity. Generally, the agents with more information gain more than those with less information, while in the optimal case, each agent almost has the same average profit. In addition, we investigate the role of irrational factor and find an interesting symmetrical behavior.

Community Identification of Financial Market Based on Affinity Propagation

Community identification in complex financial system is an important task in the exploratory analysis of stock time series. In this paper, a recently proposed message-passing-based algorithm called affinity propagation is introduced to identify stock groups. First, the similarities computed between all pairs of stocks of portfolio by considering the synchronous time evolution of their logarithm return are mapped into spatial distances. Then, the spatial distances are used to cluster the stocks into different communities of financial network via choosing appropriate preference according to affinity propagation. The results suggest that the approach is demonstrably effective in identifying multiple stock groups without any extra knowledge of stocks, and provide a meaningful economic taxonomy.

Note on two phase phenomena in financial markets

The two phase behavior in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. In this paper, the bifurcation phenomenon in Hang-Seng index is carefully investigated. It is observed that the bifurcation phenomenon in financial index is not universal, but specific under certain conditions. The phenomenon just emerges when the power-law exponent of absolute increment distribution is between 1 and 2 with appropriate period. Simulations on a randomly generated time series suggest the bifurcation phenomenon itself is subject to the statistics of absolute increment, thus it may not be able to reflect the essential financial behaviors. However, even under the same distribution of absolute increment, the range where bifurcation phenomenon occurs is far different from real market to artificial data, which may reflect certain market information.