Random walks on complex networks with inhomogeneous impact

In many complex systems, for the activity f(i) of the constituents or nodes i, a power-law relationship was discovered between the standard deviation sigma(i) and the average strength of the activity: sigma(i) ~ ^alpha; universal values alpha = 1/2 or 1 were found, however, with exceptions. With the help of an impact variable we introduce a random walk model where the activity is the product of the number of visitors at a node and their impact. If the impact depends strongly on the node connectivity and the properties of the carrying network are broadly distributed (like in a scale free network) we find both analytically and numerically non-universal alpha values. The exponent always crosses over to the universal value of 1 if the external drive dominates.Comment: 4 pages, 3 figures, revised tex

The contact dynamics method for granular media

In this paper we review the simulation method of the non-smooth contact dynamics. This technique was designed to solve the unilateral and frictional contact problem for a large number of rigid bodies and has proved to be especially valuable in research of dense granular materials during the last decade. We present here the basic principles compared to other methods and the detailed description of a 3D algorithm. We point out an artifact manifesting itself in spurious sound waves and discuss the applicability of the method.Comment: for the proceedings of the 7th Granada Seminar, 23 pages, 8 figure

The Epps effect revisited

We analyse the dependence of stock return cross-correlations on the sampling frequency of the data known as the Epps effect: For high resolution data the cross-correlations are significantly smaller than their asymptotic value as observed on daily data. The former description implies that changing trading frequency should alter the characteristic time of the phenomenon. This is not true for the empirical data: The Epps curves do not scale with market activity. The latter result indicates that the time scale of the phenomenon is connected to the reaction time of market participants (this we denote as human time scale), independent of market activity. In this paper we give a new description of the Epps effect through the decomposition of cross-correlations. After testing our method on a model of generated random walk price changes we justify our analytical results by fitting the Epps curves of real world data.Comment: 23 pages, 10 figures, 2 tables; added references, added figures and statistical details, extended overview on literatur

Size matters: some stylized facts of the stock market revisited

We reanalyze high resolution data from the New York Stock Exchange and find a monotonic (but not power law) variation of the mean value per trade, the mean number of trades per minute and the mean trading activity with company capitalization. We show that the second moment of the traded value distribution is finite. Consequently, the Hurst exponents for the corresponding time series can be calculated. These are, however, non-universal: The persistence grows with larger capitalization and this results in a logarithmically increasing Hurst exponent. A similar trend is displayed by intertrade time intervals. Finally, we demonstrate that the distribution of the intertrade times is better described by a multiscaling ansatz than by simple gap scaling.Comment: 10 pages, 13 figures, 2 tables, accepted to Eur. Phys. J. B, updated references, fixed some minor error