Calculating the Malliavin derivative of some stochastic mechanics problems.

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method.

Alterations in cerebrospinal fluid glycerophospholipids and phospholipase A2 activity in Alzheimer's disease.

Our aim is to study selected cerebrospinal fluid (CSF) glycerophospholipids (GP) that are important in brain pathophysiology. We recruited cognitively healthy (CH), minimally cognitively impaired (MCI), and late onset Alzheimer's disease (LOAD) study participants and collected their CSF. After fractionation into nanometer particles (NP) and supernatant fluids (SF), we studied the lipid composition of these compartments.