Cellular Probabilistic Automata - A Novel Method for Uncertainty Propagation

We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve the latter. The translation is achieved by state discretization as in set oriented numerics and the use of the locality concept from cellular automata theory. We develop the method at the example of initial value uncertainties under deterministic dynamics and prove a consistency result. As an application we discuss arsenate transportation and adsorption in drinking water pipes and compare our results to Monte Carlo computations

Scalable Mining of Common Routes in Mobile Communication Network Traffic Data

A probabilistic method for inferring common routes from mobile communication network traffic data is presented. Besides providing mobility information, valuable in a multitude of application areas, the method has the dual purpose of enabling efficient coarse-graining as well as anonymisation by mapping individual sequences onto common routes. The approach is to represent spatial trajectories by Cell ID sequences that are grouped into routes using locality-sensitive hashing and graph clustering. The method is demonstrated to be scalable, and to accurately group sequences using an evaluation set of GPS tagged data

EPR Paradox,Locality and Completeness of Quantum Theory

The quantum theory (QT) and new stochastic approaches have no deterministic prediction for a single measurement or for a single time -series of events observed for a trapped ion, electron or any other individual physical system. The predictions of QT being of probabilistic character apply to the statistical distribution of the results obtained in various experiments. The probability distribution is not an attribute of a dice but it is a characteristic of a whole random experiment : '' rolling a dice''. and statistical long range correlations between two random variables X and Y are not a proof of any causal relation between these variable. Moreover any probabilistic model used to describe a random experiment is consistent only with a specific protocol telling how the random experiment has to be performed.In this sense the quantum theory is a statistical and contextual theory of phenomena. In this paper we discuss these important topics in some detail. Besides we discuss in historical perspective various prerequisites used in the proofs of Bell and CHSH inequalities concluding that the violation of these inequalities in spin polarization correlation experiments is neither a proof of the completeness of QT nor of its nonlocality. The question whether QT is predictably complete is still open and it should be answered by a careful and unconventional analysis of the experimental data. It is sufficient to analyze more in detail the existing experimental data by using various non-parametric purity tests and other specific statistical tools invented to study the fine structure of the time-series. The correct understanding of statistical and contextual character of QT has far reaching consequences for the quantum information and quantum computing.Comment: 16 pages, 59 references,the contribution to the conference QTRF-4 held in Vaxjo, Sweden, 11-16 june 2007. To be published in the Proceeding