We consider the macroscopic, second order model of Kerner–Konhäuser for traffic flow given by a system of PDE. Assuming conservation of cars, traveling waves solution of the PDE are reduced to a dynamical system in the plane. We prove that under generic conditions on the so called fundamental diagram, the surface of critical points has a fold or cusp catastrophe and each fold point gives rise t...

A new method for analysing nonlinear and non-stationary data has recently been developed, namely the partial-differential-equation (PDE) transform. The PDE transform is based on the use of coupled arbitrarily high order PDEs to decompose signals and images into various functional frequency modes, which allow perfect reconstruction of the original signals and images. The PDE transform is compare...

In order to develop novel and orally active phosphodiesterase (PDE) 4 inhibitors, random screening was performed using our chemical library to find YM-10335 possessing the 1,8-naphthyridin-2(1H)-one skeleton which is a completely different structure from rolipram. In this report, the syntheses and structure-activity relationships of the YM-10335 derivatives were described. Some compounds showed...

Driven by diverse applications, several recent models impose randomly switching boundary conditions on either a PDE or SDE. The purpose of this paper is to provide tools for calculating statistics of these models and establish a connection between these two perspectives on diffusion in a random environment. Under general conditions, we prove that the moments of a solution to a randomly switchin...

The G protein cascade of vision depends on two peripheral membrane proteins: the G protein, transducin (Gt), and cGMP phosphodiesterase (PDE). Each has covalently attached lipids, and interacts with transduction components on the membrane surface. We have found that their surface interactions are critically dependent on the nature of the lipid. Membranes enhance their protein-protein interactio...

The promyelocytic HL60 cell can be differentiated with dimethyl sulphoxide or dibutyryl cyclic AMP leading to the appearance of fMetLeuPhe receptors on the cell surface. G-protein-stimulated polyphosphoinositide phosphodiesterase (PPI-pde) activity was assessed in membranes prepared from both differentiated and non-differentiated HL60 cells. Both the extent of the response and the rank order of...

LAser Detection And Ranging (LADAR) is a promising tool for precise 3D-imaging, which enables field surveillance and target identification under low-light-level conditions in many military applications. For the time resolution and sensitivity requirements of LADAR applications, InGaAsP/InP Geiger-mode (GM) avalanche photodiodes (APDs) excel in the spectrum band between 1.0~1.6 μm. Previously MI...

When a time-dependent partial differential equation (PDE) is discretized in space with a spectral approximation, the result is a coupled system of ordinary differential equations (ODEs) in time. This is the notion of the method of lines (MOL), and the resulting set of ODEs is stiff; the stiffness may be even exacerbated sometimes. The linear terms are the primarily responsible for the stiffness...