In the glucose-insulin regulatory system, insulin secretion oscillates with a period of 50-150 minutes. Over the past decade, several mathematical models have been proposed to model these ultradian oscillations as well as the metabolic system producing them. However these existing models yield profiles deviant from a normal physiological range. We introduce a DDE (delay differential equation) model with two discrete delays for better understanding and more accurately modeling the glucose-insulin dynamics and the insulin secretory oscillations. With the same set of experimental data used to test other existing models, the simulation profiles obtained from this two time delay model fall within a normal physiological range.

We consider the edge Hall conductance and show it is invariant under perturbations located in a strip along the edge. This enables us to prove for the edge conductances a general sum rule relating currents due to the presence of two different media located respectively on the left and on the right half plane. As a particular interesting case we put forward a general quantization formula for the difference of edge Hall conductances in semi-infinite samples with and without a confining wall. Applications to disordered Hall systems with and without a confining potential are discussed.

Experimental measurements of transdermal vapor alcohol concentration are used to estimate alcohol concentration in the body using an inverse problem approach. First we propose a model for the transport of alcohol from blood compartments to the skin surface and use the transdermal measurements to estimate the signal obtained by a breathalyzer which is the standard for blood alcohol concentration. Later we couple our skin model to a body model of the human body. The human body is divided in several compartments to facilitate the description of the transport of alcohol in the human body from ingestion to elimination. The adjoint method is used for the computation of the least squares functional gradient. Parameters of the model are estimated using real breathalyzer and a transdermal alcohol skin device data applied to individuals in a hospital. The parameter values obtained are used to predict the evolution of alcohol concentration for patients in the field. Kalman filtering techniques can be used to correct predictions in real time.