Introduction Since the release of anthrax in October of 2001, there has been increased interest in developing efficient prospective disease surveillance schemes. Poisson CUSUM is a control chart-based method that has been widely used to detect aberrations in disease counts in a single region collected over fixed time intervals. Over the past few years, different methods have been proposed to ex...

We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. The classical theory claims that the solution can be approximated by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer derived from Milne problem. In this paper, we construct counterexamples to disprove such formulation in...

This paper extends Kontsevich’s ideas on quantizing Poisson manifolds. A new differential is added to the Hodge decomposition of the Hochschild complex, so that it becomes a bicomplex, even more similar to the classical Hodge theory for complex manifolds. These notes grew out of the author’s attempt to understand Kontsevich’s ideas [Kon95a] on quantizing Poisson manifolds. We introduce a new di...

Given a compact oriented surface, we classify log Poisson bivectors whose degeneracy loci are locally modeled by a finite set of lines in the plane intersecting at a point. Further, we compute the Poisson cohomology of such structures and discuss the relationship between our classification and the second Poisson cohomology.

Using exact results from the theory of completely integrable systems of the Painlevé/Toda type, we examine the consequences for the theory of polyelectrolytes in the (nonlinear) Poisson-Boltzmann approximation.

Noncommutatively deformed geometries, such as the noncommutative torus, do not exist generically. I showed in a previous paper that the existence of such a deformation implies compatibility conditions between the classical metric and the Poisson bivector (which characterizes the noncommutativity). Here I present another necessary condition: the vanishing of a certain rank 5 tensor. In the case ...

Since interference is the main performance-limiting factor in most wireless networks, it is crucial to characterize the interference statistics. The two main determinants of the interference are the network geometry (spatial distribution of concurrently transmitting nodes) and the path loss law (signal attenuation with distance). For certain classes of node distributions, most notably Poisson p...

A recent light scattering cuvette has been successful in differentiating the type of microemboli in flowing whole blood. However, since the technique was designed assuming the microemboli are concentrated near the center of the scattering medium, it is necessary to investigate the effect of off-center locations on discrimination. The scattering intensities from 5 off-center locations were inves...

In previous works ([11, 12]) we have introduced a new method called the lent particle method which is an efficient tool to establish existence of densities for Poisson functionals. We now go further and iterate this method in order to prove smoothness of densities. More precisely, we construct Sobolev spaces of any order and prove a Malliavin-type criterion of existence of smooth density. We ap...