The environmental conditions experienced by hosts are known to affect their mean parasite transmission potential. How different conditions may affect the variance of transmission potential has received less attention, but is an important question for disease management, especially if specific ecological contexts are more likely to foster a few extremely infectious hosts. Using the obligate-kill...

 This paper proposes an analytical method to evaluate the delay violation probability of traffic flows with statistical Quality-of-Service (QoS) guarantees in an Earliest Deadline First (EDF) scheduler. The statistical QoS targets for each service class are expressed in terms of a delay threshold and delay violation probability. We study both cases isolated nodes and end-to-end paths comprisin...

The inherent variability or 'variance' of growth rate measurements is critical to the development of accurate predictive models in food microbiology. A large number of measurements are typically needed to estimate variance. To make these measurements requires a significant investment of time and effort. If a single growth rate determination is based on a series of independent measurements, then...

A commonly accepted traffic model for a large population of Internet users consists of a multiplex of Poisson-arriving heavy-tailed streams with the same constant rate (M/G/ ). We show that even though such regular model provides an accurate description of long-range dependence, the marginal distribution variance is underestimated, resulting in erroneous calculation of overflow probability in n...

Let K ⊂ R be a smooth convex set and let Pλ be a Poisson point process on R of intensity λ. The convex hull of Pλ ∩ K is a random convex polytope Kλ. As λ → ∞, we show that the variance of the number of k-dimensional faces of Kλ, when properly scaled, converges to a scalar multiple of the affine surface area of K. Similar asymptotics hold for the variance of the number of k-dimensional faces fo...

Many estimators in signal processing problems are defined implicitly as the maximum of some objective function. Examples of implicitly defined estimators include maximum likelihood, penalized likelihood, maximum a posteriori, and nonlinear least squares estimation. For such estimators, exact analytical expressions for the mean and variance are usually unavailable. Therefore, investigators usual...

Many estimators in signal processing problems are defined implicitly as the maximum of some objective function. Examples of implicitly defined estimators include maximum likelihood, penalized likelihood, maximum a posteriori, and nonlinear least squares estimation. For such estimators, exact analytical expressions for the mean and variance are usually unavailable. Therefore, investigators usual...

The Fourier Rebinning (FORE), which sorts 3D data into 2D data, requires that the 3D sinogram is previously corrected for non-quantitative physical effects. So, 2D sinograms are no longer Poisson distributed, an assumption behind OSEM (Ordered Subsets Expectation Maximization). This means that whenever data are corrected and OSEM is the reconstruction algorithm, the need to restore the Poisson ...

In this article we consider the Levy processes and the corresponding semi-group. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory of integral equations we investigate the properties of a wide class of Levy processes (potential, quasi-potential, the probability of the Levy process remaining within the given domain, long time b...