A method for obtaining Laplace transforms of order statistics of Erlang random variables

We present a path-counting method for deriving Laplace transforms of order statistics of independent but not necessarily identically distributed Erlang random variables, based on a probabilistic interpretation of the Laplace transform. The method is applicable also to generalized Erlang variates having different parameters for the exponential stages. The idea is to provide an intuitive understanding of the Laplace transform, based on the Markovian properties of the stages of the Erlang random variable. Thus the derivation technique is applicable to many other Markovian stochastic models. Motivational examples for queues and reliability are mentioned. Computational considerations are discussed.

Drug disposition in obesity: toward evidence-based dosing

Obesity and morbid obesity are associated with many physiological changes affecting pharmacokinetics, such as increased blood volume, cardiac output, splanchnic blood flow, and hepatic blood flow. In obesity, drug absorption appears unaltered, although recent evidence suggests that this conclusion may be premature. Volume of distribution may vary largely, but the magnitude and direction of changes seem difficult to predict, with extrapolation on the basis of total body weight being the best approach to date. Changes in clearance may be smaller than in distribution, whereas there is growing evidence that the influence of obesity on clearance can be predicted on the basis of reported changes in the metabolic or elimination pathways involved. For obese children, we propose two methods to distinguish between developmental and obesity-related changes. Future research should focus on the characterization of physiological concepts to predict the optimal dose for each drug in the obese population.Pharmacolog

Non-cell-autonomous function of DR6 in Schwann cell proliferation.

Death receptor 6 (DR6) is an orphan member of the TNF receptor superfamily and controls cell death and differentiation in a cell-autonomous manner in different cell types. Here, we report an additional non-cell-autonomous function for DR6 in the peripheral nervous system (PNS). DR6-knockout (DR6 KO) mice showed precocious myelination in the PNS. Using an invitro myelination assay, we demonstrate that neuronal DR6 acts in trans on Schwann cells (SCs) and reduces SC proliferation and myelination independently of its cytoplasmic death domain. Mechanistically, DR6 was found to be cleaved in neurons by a disintegrin and metalloprotease 10 (ADAM10), releasing the soluble DR6 ectodomain (sDR6). Notably, in the invitro myelination assay, sDR6 was sufficient to rescue the DR6 KO phenotype. Thus, in addition to the cell-autonomous receptor function of full-length DR6, the proteolytically released sDR6 can unexpectedly also act as a paracrine signaling factor in the PNS in a non-cell-autonomous manner during SC proliferation and myelination. This new mode of DR6 signaling will be relevant in future attempts to target DR6 in disease settings

Queues with waiting time dependent service

Motivated by service levels in terms of the waiting-time distribution seen, for instance, in call centers, we consider two models for systems with a service discipline that depends on the waiting time. The first model deals with a single server that continuously adapts its service rate based on the waiting time of the first customer in line. In the second model, one queue is served by a primary server which is supplemented by a secondary server when the waiting of the first customer in line exceeds a threshold. Using level crossings for the waiting-time process of the first customer in line, we derive steady-state waiting-time distributions for both models. The results are illustrated with numerical examples. © 2011 The Author(s)