Johannes J. Schneider

GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model

The compute unified device architecture (CUDA) is a programming approach for performing scientific calculations on a graphics processing unit (GPU) as a data-parallel computing device. The programming interface allows to implement algorithms using extensions to standard C language. With continuously increased number of cores in combination with a high memory bandwidth, a recent GPU offers incredible resources for general purpose computing. First, we apply this new technology to Monte Carlo simulations of the two dimensional ferromagnetic square lattice Ising model. By implementing a variant of the checkerboard algorithm, results are obtained up to 60 times faster on the GPU than on a current CPU core. An implementation of the three dimensional ferromagnetic cubic lattice Ising model on a GPU is able to generate results up to 35 times faster than on a current CPU core. As proof of concept we calculate the critical temperature of the 2D and 3D Ising model using finite size scaling techniques. Theoretical results for the 2D Ising model and previous simulation results for the 3D Ising model can be reproduced.

Switching processes in financial markets

For an intriguing variety of switching processes in nature, the underlying complex system abruptly changes from one state to another in a highly discontinuous fashion. Financial market fluctuations are characterized by many abrupt switchings creating upward trends and downward trends, on time scales ranging from macroscopic trends persisting for hundreds of days to microscopic trends persisting for a few minutes. The question arises whether these ubiquitous switching processes have quantifiable features independent of the time horizon studied. We find striking scale-free behavior of the transaction volume after each switching. Our findings can be interpreted as being consistent with time-dependent collective behavior of financial market participants. We test the possible universality of our result by performing a parallel analysis of fluctuations in time intervals between transactions. We suggest that the well known catastrophic bubbles that occur on large time scales—such as the most recent financial crisis—may not be outliers but single dramatic representatives caused by the formation of increasing and decreasing trends on time scales varying over nine orders of magnitude from very large down to very small.

Accelerated Fluctuation Analysis by Graphic Cards and Complex Pattern Formation in Financial Markets

The compute unified device architecture is an almost conventional programming approach for managing computations on a graphics processing unit (GPU) as a data-parallel computing device. With a maximum number of 240 cores in combination with a high memory bandwidth, a recent GPU offers resources for computational physics. We apply this technology to methods of fluctuation analysis, which includes determination of the scaling behavior of a stochastic process and the equilibrium autocorrelation function. Additionally, the recently introduced pattern formation conformity (Preis T et al 2008 Europhys. Lett. 82 68005), which quantifies pattern-based complex short-time correlations of a time series, is calculated on a GPU and analyzed in detail. Results are obtained up to 84 times faster than on a current central processing unit core. When we apply this method to high-frequency time series of the German BUND future, we find significant pattern-based correlations on short time scales. Furthermore, an anti-persistent behavior can be found on short time scales. Additionally, we compare the recent GPU generation, which provides a theoretical peak performance of up to roughly 1012 floating point operations per second with the previous one.

Searching for backbones — an efficient parallel algorithm for the traveling salesman problem

The Traveling Salesman Problem (TSP) plays an important role in Operations Research, Applied Mathematics and Computational Physics. We investigated it using a stochastic approach. Studying several solutions of a special TSP we found that many parts of a good solution are the same in all other good solutions for this problem. In this paper we discuss an efficient parallel method to reduce the TSP to a smaller one by finding these backbones and eliminating them to get even better solutions in a very short time and a few observables of interest corresponding to this parallel approach.

Searching for Backbones—a high-performance parallel algorithm for solving combinatorial optimization problems

Abstract A highly efficient parallel algorithm called Searching for Backbones (SfB) is proposed: based on the finding, that many parts of a good configuration for a given optimization problem are the same in all other good solutions, SfB reduces the complexity of this problem by determining these “backbones” and eliminating them in order to get even better solutions in a very short time. Applications and results are presented for the Traveling Salesman Problem and the Vehicle Routing Problem.

The time-dependent traveling salesman problem

A problem often considered in Operations Research and Computational Physics is the traveling salesman problem, in which a traveling salesperson has to find the shortest closed tour between a given set of cities touching each city exactly once. The distances between the single nodes are known to the traveling salesperson. An extension of this problem is the time-dependent traveling salesman problem, in which these distances vary in time. I will show how this more complex problem is treated with physical optimization algorithms like simulated annealing. I will present results for the problem of the 127 beergardens in the area of Augsburg, in which I define a traffic zone in which traffic jams occur in the afternoon.

Fluctuation patterns in high-frequency financial asset returns

We introduce a new method for quantifying pattern-based complex short-time correlations of a time series. Our correlation measure is 1 for a perfectly correlated and 0 for a random walk time series. When we apply this method to high-frequency time series data of the German DAX future, we find clear correlations on short time scales. In order to subtract trivial autocorrelation parts from the pattern conformity, we introduce a simple model for reproducing the antipersistent regime and use alternatively level 1 quotes. When we remove the pattern conformity of this stochastic process from the original data, remaining pattern-based correlations can be observed.

THE IMPACT OF ELECTION RESULTS ON THE MEMBER NUMBERS OF THE LARGE PARTIES IN BAVARIA AND GERMANY

In this paper, we investigate the relations between the numbers of members of various parties and their results in the elections in Bavaria and in Germany. Deriving from the finding that there is a strong time-delayed correlation between these data-sets for the two largest parties in Bavaria, we show in a simulation based on the Sznajd model that such a correlation leads to very stable majorities, just as in Bavaria.

Search-space smoothing for combinatorial optimization problems

Commonly there are two types of local search approaches known to treat combinatorial optimization problems with very complex search-space structure: One is to introduce very complicated types of local move classes, allowing a bypass of high energetic barriers separating different minima. The second is introducing a control-parameter (i.e. temperature in physics terminology) dependent state space walker, which is — depending on this control parameter — more or less easily able to climb over barriers. A third, less well-known, but very obvious approach is to smooth the search space, i.e. to eliminate barriers between low-energy configurations and therefore to allow a fast and easy approach to the global optimum. This procedure will be discussed in depth in the following work.

ANTICIPATORY DRIVERS IN THE NAGEL SCHRECKENBERG-MODEL

This paper describes how the Nagel-Schreckenberg-model, which describes macroscopic features of traffic, is modified in order to characterize a single car drivers behavior more accurately.