A note on correlations in randomly oriented graphs

Given a graph $G$, we consider the model where $G$ is given a random orientation by giving each edge a random direction. It is proven that for $a,b,s\in V(G)$, the events $\{s\to a\}$ and $\{s\to b\}$ are positively correlated. This correlation persists, perhaps unexpectedly, also if we first condition on \{s\nto t\} for any vertex $t\neq s$. With this conditioning it is also true that $\{s\to b\}$ and $\{a\to t\}$ are negatively correlated. A concept of increasing events in random orientations is defined and a general inequality corresponding to Harris inequality is given. The results are obtained by combining a very useful lemma by Colin McDiarmid which relates random orientations with edge percolation, with results by van den Berg, H\"aggstr\"om, Kahn on correlation inequalities for edge percolation. The results are true also for another model of randomly directed graphs.Comment: 7 pages. The main lemma was first published by Colin McDiarmid. Relevant reference added and text rewritten to reflect this fac

The process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions

We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random walker in a higher-dimensional space. The spatial distribution of nucleation events is shown to differ markedly from the mean-field estimate except in the limit of very weak step-edge barriers. The nucleation rate is computed exactly, including numerical prefactors.Comment: 22 pages, 10 figures. To appear in Phys. Rev.

A search for edge-on galaxy lenses in the CFHT Legacy Survey

[ABRIDGED] The new generation of wide field optical imaging like the Canada France Hawaii Telescope Legacy Survey (CFHTLS) enables discoveries of all types of gravitational lenses present in the sky. The Strong Lensing Legacy Survey (SL2S) project has started an inventory, respectively for clusters or groups of galaxies lenses, and for Einstein rings around distant massive ellipticals. Here we attempt to extend this inventory by finding lensing events produced by massive edge-on disk galaxies which remains a poorly documented class of lenses. We implement and test an automated search procedure of edge-on galaxy lenses in the CFHTLS Wide fields with magnitude 18Comment: several major edits, 8 pages, A&A accepte

Observations of shallow convective clouds generated by solar heating of dark smoke plumes

The SEVIRI instrument on the Meteosat Second Generation satellite with both fine spatial and temporal resolution allows to detect and follow the dynamics of fast developing meteorological events like spreading smoke plumes and the lifecycles of convective clouds. Smoke plumes have the ability to change the atmospheric heat content due to absorption and reduced reflection of solar radiation. By these means they can trigger formation of shallow convective clouds at their edge. A heavy smoke plume emerging from burning Lebanese oil tanks and spreading over adjacent deserts on 17 July 2006 has been observed as an example of such an effect. This study suggests a physical explanation of the observed convection along the edge of the smoke plume, namely the strong thermal contrast resulting from solar heating of the smoke layer

Activity clocks: spreading dynamics on temporal networks of human contact

Dynamical processes on time-varying complex networks are key to understanding and modeling a broad variety of processes in socio-technical systems. Here we focus on empirical temporal networks of human proximity and we aim at understanding the factors that, in simulation, shape the arrival time distribution of simple spreading processes. Abandoning the notion of wall-clock time in favour of node-specific clocks based on activity exposes robust statistical patterns in the arrival times across different social contexts. Using randomization strategies and generative models constrained by data, we show that these patterns can be understood in terms of heterogeneous inter-event time distributions coupled with heterogeneous numbers of events per edge. We also show, both empirically and by using a synthetic dataset, that significant deviations from the above behavior can be caused by the presence of edge classes with strong activity correlations