Isotropic covariance functions on graphs and their edges

We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, i.e., graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a new metric called the resistance metric (which extends the classical resistance metric developed in electrical network theory on the vertices of a graph to the continuum of edge points). We discuss the advantages of using the resistance metric in comparison with the geodesic metric as well as the restrictions these metrics impose on the investigated covariance functions. In particular, many of the commonly used isotropic covariance functions in the spatial statistics literature (the power exponential, Mat{\'e}rn, generalized Cauchy, and Dagum classes) are shown to be valid with respect to the resistance metric for any graph with Euclidean edges, whilst they are only valid with respect to the geodesic metric in more special cases.Comment: 6 figures, 1 tabl

Measuring degradation of transgenic DNA and screening for horizontal gene transfer from GMO-plant material during composting

The experiments show that composting of GM plant residues greatly increases the rate of degradation of transgenic DNA compared to the rate for plant residues left in the soil. If the persistence of transgenic DNA in the environments is considered as the only risk factor, composting is a 'DNA-safe' method to treat GM plant residues. However, even though transgenic plant DNA was not detected in bacterial isolates in our experiments, we cannot conclude that horizontal gene transfer can not take place. The 300 isolates tested proved to be too low a number to be conclusive. The numbers of isolates tested were based on the screenings indicating high transfer, but the screenings were biased apparently because some Bacillus species gave PCR products matching the transgenic DNA. Thus, it is still an open question if composting constitutes a safe way of disposing of GM plant residues. Furthermore, these experiments give rise to other interesting questions, e.g., the behavior of GM plant materials decomposing in waste piles or manure yards under composting-like conditions and the possibility of horizontal gene transfer to indigenous bacteria at the comparably lower temperatures presentat these environments.These questions need to be assessed if the risk associated with the use of GM plants is to be thoroughly investigated

Stochastic Analysis of Synchronization in a Supermarket Refrigeration System

Display cases in supermarket systems often exhibit synchronization, in which the expansion valves in the display cases turn on and off at exactly the same time. The study of the influence of switching noise on synchronization in supermarket refrigeration systems is the subject matter of this work. For this purpose, we model it as a hybrid system, for which synchronization corresponds to a periodic trajectory. Subsequently, we investigate the influence of switching noise. We develop a statistical method for computing an intensity function, which measures how often the refrigeration system stays synchronized. By analyzing the intensity, we conclude that the increase in measurement uncertainty yields the decrease at the prevalence of synchronization.Comment: In Proceedings HAS 2014, arXiv:1501.0540