On level crossings for a general class of piecewise-deterministic Markov processes

We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. We study the point process of upcrossings of a level $b$ by the Markov process. Our main result shows that, under a suitable scaling $\nu(b)$, the point process converges, as $b$ tends to infinity, weakly to a geometrically compound Poisson process. We also prove a version of Rice's formula relating the stationary density of the process to level crossing intensities. This formula provides an interpretation of the scaling factor $\nu(b)$. While our proof of the limit theorem requires additional assumptions, Rice's formula holds whenever the (stationary) overall intensity of jumps is finite.Comment: 25 page

A family of Schr\"odinger operators whose spectrum is an interval

By approximation, I show that the spectrum of the Schr\"odinger operator with potential $V(n) = f(n\rho \pmod 1)$ for f continuous and $\rho > 0$, $\rho \notin \N$ is an interval.Comment: Comm. Math. Phys. (to appear

Palm pairs and the general mass-transport principle

We consider a lcsc group G acting properly on a Borel space S and measurably on an underlying sigma-finite measure space. Our first main result is a transport formula connecting the Palm pairs of jointly stationary random measures on S. A key (and new) technical result is a measurable disintegration of the Haar measure on G along the orbits. The second main result is an intrinsic characterization of the Palm pairs of a G-invariant random measure. We then proceed with deriving a general version of the mass-transport principle for possibly non-transitive and non-unimodular group operations first in a deterministic and then in its full probabilistic form.Comment: 26 page

Normal Approximation of Kabanov–Skorohod Integrals on Poisson Spaces

We consider the normal approximation of Kabanov–Skorohod integrals on a general Poisson space. Our bounds are for the Wasserstein and the Kolmogorov distance and involve only difference operators of the integrand of the Kabanov–Skorohod integral. The proofs rely on the Malliavin–Stein method and, in particular, on multiple applications of integration by parts formulae. As examples, we study some linear statistics of point processes that can be constructed by Poisson embeddings and functionals related to Pareto optimal points of a Poisson process

Hemotropic mycoplasmas in little brown bats (Myotis lucifugus).

BackgroundHemotropic mycoplasmas are epicellular erythrocytic bacteria that can cause infectious anemia in some mammalian species. Worldwide, hemotropic mycoplasmas are emerging or re-emerging zoonotic pathogens potentially causing serious and significant health problems in wildlife. The objective of this study was to determine the molecular prevalence of hemotropic Mycoplasma species in little brown bats (Myotis lucifugus) with and without Pseudogymnoascus (Geomyces) destrucans, the causative agent of white nose syndrome (WNS) that causes significant mortality events in bats.MethodsIn order to establish the prevalence of hemotropic Mycoplasma species in a population of 68 little brown bats (Myotis lucifugus) with (n = 53) and without (n = 15) white-nose syndrome (WNS), PCR was performed targeting the 16S rRNA gene.ResultsThe overall prevalence of hemotropic Mycoplasmas in bats was 47%, with similar (p = 0.5725) prevalence between bats with WNS (49%) and without WNS (40%). 16S rDNA sequence analysis (~1,200 bp) supports the presence of a novel hemotropic Mycoplasma species with 91.75% sequence homology with Mycoplasma haemomuris. No differences were found in gene sequences generated from WNS and non-WNS animals.ConclusionsGene sequences generated from WNS and non-WNS animals suggest that little brown bats could serve as a natural reservoir for this potentially novel Mycoplasma species. Currently, there is minimal information about the prevalence, host-specificity, or the route of transmission of hemotropic Mycoplasma spp. among bats. Finally, the potential role of hemotropic Mycoplasma spp. as co-factors in the development of disease manifestations in bats, including WNS in Myotis lucifugus, remains to be elucidated

X-Ray Pinhole Camera Spatial Resolution Using High Aspect Ratio LIGA Pinhole Apertures

X ray pinhole cameras are employed to provide the transverse profile of the electron beam from which the emittance, coupling and energy spread are calculated in the storage ring of Diamond Light Source. Tungsten blades separated by shims are commonly used to form the pinhole aperture. However, this approach introduces uncertainties regarding the aperture size. X ray lithography, electroplating and moulding, known as LIGA, has been used to provide thin screens with well defined and high aspect ratio pinhole apertures. Thus, the optimal aperture size given the beam spectrum can be used to improve the spatial resolution of the pinhole camera. Experimental results using a LIGA screen of different aperture sizes have been compared to SRW Python simulations over the 15 35 keV photon energy range. Good agreement has been demonstrated between the experimental and the simulation data. Challenges and considerations for this method are also presente

Bloch electron in a magnetic field and the Ising model

The spectral determinant det(H-\epsilon I) of the Azbel-Hofstadter Hamiltonian H is related to Onsager's partition function of the 2D Ising model for any value of magnetic flux \Phi=2\pi P/Q through an elementary cell, where P and Q are coprime integers. The band edges of H correspond to the critical temperature of the Ising model; the spectral determinant at these (and other points defined in a certain similar way) is independent of P. A connection of the mean of Lyapunov exponents to the asymptotic (large Q) bandwidth is indicated.Comment: 4 pages, 1 figure, REVTE

Second order analysis of geometric functionals of Boolean models

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.

Double butterfly spectrum for two interacting particles in the Harper model

We study the effect of interparticle interaction $U$ on the spectrum of the Harper model and show that it leads to a pure-point component arising from the multifractal spectrum of non interacting problem. Our numerical studies allow to understand the global structure of the spectrum. Analytical approach developed permits to understand the origin of localized states in the limit of strong interaction $U$ and fine spectral structure for small $U$.Comment: revtex, 4 pages, 5 figure