Two repelling random walks on Z\mathbb Z

We consider two interacting random walks on $\mathbb{Z}$ such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter $\beta \geq 0$. When $\beta = 0$ both processes are independent symmetric random walks on $\mathbb{Z}$, and hence recurrent. We show that both random walks are further recurrent if $\beta \in (0,1]$. We also show that these processes are transient and diverge in opposite directions if $\beta > 2$. The case $\beta \in (1,2]$ remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations.Comment: 17 pages. Added references and corrected typos. Revised the argument for the convergence to equilibria of the vector field. Improved the proof for the recurrence when beta belongs to (0,1); leading to the removal of a previous conjectur

Quasi-free Standing Epitaxial Graphene on SiC by Hydrogen Intercalation

Quasi-free standing epitaxial graphene is obtained on SiC(0001) by hydrogen intercalation. The hydrogen moves between the 6root3 reconstructed initial carbon layer and the SiC substrate. The topmost Si atoms which for epitaxial graphene are covalently bound to this buffer layer, are now saturated by hydrogen bonds. The buffer layer is turned into a quasi-free standing graphene monolayer with its typical linear pi-bands. Similarly, epitaxial monolayer graphene turns into a decoupled bilayer. The intercalation is stable in air and can be reversed by annealing to around 900 degrees Celsius.Comment: Accepted for publication in Physical Review Letter

Correlating sea otter density and behavior to habitat attributes in Prince William Sound, Alaska: A model for prediction

As a benthic foraging marine mammal, sea otters ( Enhydra lutris) present a unique opportunity for conducting a quantitative assessment of behavior based on habitat use as well as developing a habitat based density model using GIS because of the sea otter\u27s well defined habitat requirements. Several studies have documented sea otter behavior but none have calculated the probability of occurrence of a particular behavior based on habitat attributes. Previous predictive models of sea otter density have been constructed, however these models have excluded offshore habitat. Seven aerial surveys, that included offshore habitats, were conducted between 1995 and 2005 in western Prince William Sound to estimate distribution and abundance of sea otters (Enhydra lutris). The location and densities of sea otters that resulted from these surveys were used to explore relationships between sea otters and habitat attributes, both nearshore and offshore. These relationships described in western Prince William Sound were then used to construct habitat based models to predict sea otter carrying capacity and total abundance at different spatial scales. The data from the aerial surveys were also used to quantify the relationship between a sea otter\u27s behavior and the habitat attributes associated with the location of the animals when the behavior occurred. Stepwise logistic regression was used to describe relationships between behavior, diving or not diving (assumed resting) and habitat attributes. Three subsets of the data were examined; all animals, all single animals without pups and all single animals with pups. Bathymetry was consistently significant (alpha = 0.05) in determining the probability of a behavior being diving or not diving, regardless of size of group or reproductive status. Group size was the first variable to enter the stepwise regression analysis of all available sightings, regardless of reproductive status, with bathymetry as the second and final variable. Among single animals with pups bathymetry was the first variable and distance to shore was the second and final variable to enter the model. Bathymetry was the only significant variable in the analysis of single animals without pups. The aerial survey data from western Prince William Sound, AK, was used to create a predictive density model based on five habitat attributes; bathymetry, distance to the closest shoreline, distance to the closest protected shoreline, distance to the closest tidewater glacier and distance to the closest anadromous stream. The mean predictive density estimate was 2.0316/km2 with a total corrected population estimate within the survey boundaries of 16,441, with a range of 14,468 to 18,803 (alpha = 0.05). Special attention was given to northern Knight Island, an area heavily impacted by the Exxon Valdez oil spill in 1989. Predicted densities within that area were 1.5792/km2 with an estimated abundance of 384. The actual mean abundance estimate at northern Knight Island between 1995 and 2005 was 68 with a range of 34 to 102 (alpha = 0.05), illustrating a discrepancy between predicted estimates and of actual survey abundance estimates. The analysis and results presented in this work give insight into the density and distribution variation of sea otters in Prince William Sound as well as contribute to the understanding of the sea otter\u27s use of its nearshore habitat

Testing Closed String Field Theory with Marginal Fields

We study the feasibility of level expansion and test the quartic vertex of closed string field theory by checking the flatness of the potential in marginal directions. The tests, which work out correctly, require the cancellation of two contributions: one from an infinite-level computation with the cubic vertex and the other from a finite-level computation with the quartic vertex. The numerical results suggest that the quartic vertex contributions are comparable or smaller than those of level four fields.Comment: 14 pages, LaTeX. v2: New references to work of Beccaria and Rampino, and Taylor. Improved numerical analysis at the end of section

Analysis of the seismic site effects along the ancient Via Laurentina (Rome)

This paper presents an evaluation of the Local Seismic Response (LSR) along the route of the ancient Roman road Via Laurentina, which has been exposed in several areas of southwest Rome over the last decade during the construction of new buildings and infrastructures. It is an example of LSR analysis applied to ancient and archaeological sites located in alluvial valleys with some methodological inferences for the design of infrastructure and urban planning. Since the ancient road does not cross the alluvial valley (namely the Fosso di Vallerano Valley) normal to its sides, it was not possible to directly perform 2D numerical modelling to evaluate the LSR along the road route. Therefore, outputs of 2D numerical models, obtained along three cross sections that were normal oriented respect to the valley, were projected along the route of the Via Laurentina within a reliable buffer attributed according to an available high-resolution geological model of the local subsoil. The modelled amplification functions consider physical effects due to both the 2D shape of the valley and the heterogeneities of the alluvial deposits. The 1D and 2D amplification functions were compared to output that non-negligible effects are related to the narrow shape of the fluvial valley and the lateral contacts between the lithotecnical units composing the alluvial fill. The here experienced methodology is suitable for applications to the numerical modelling of seismic response in case of linear infrastructures (i.e., roads, bridges, railways) that do not cross the natural system along physically characteristic directions (i.e. longitudinally or transversally)