Anticipative LQG Control

The continuous-time LQG problem with complete state observationis solved in the ‘clairvoyant’ case when controlis based on knowledge of the complete past and future of thenoise. This allows us to compute explicitly the expected valueof perfect information, i.e. the reduction in average cost thatis possible if the usual nonanticipativity constraint on thecontrols is waived.     

The role of water in the design of glycosidic linkage flexibility

In this paper we show how a variety of computational methods are used to understand the role that water plays in the solution conformational dynamics of carbohydrates. A comparison is made between maltose and a designed disaccharide (α-D-Glc-NAc-(1→4)-β-D-Glc-3-NH₂) in which the cross glycosidic linkage hydrogen bonds have been significantly strengthened. However, despite the stronger intramolecular hydrogen bonds in the maltose derivative, the correlation times for glycosidic dihedral angle fluctuations are approximately the same for the two sugars. Upon investigation of the water in the first hydration shells for the two disaccharides, high water probability densities were found between the functional groups straddling the glycosidic linkage that bonds the two monosaccharides together. This probability density corresponds to single water molecules forming bridging hydrogen bonds between the functional groups on either side of the linkage for periods of 3.66 ps in the case of maltose and 8.36 ps in the case of the amine derivative. Ab initio studies of saccharide structure interaction with single water molecules reveal that these intermolecular (sugar-solvent) hydrogen bonds are of similar strength to the intramolecular (sugar-sugar) hydrogen bonds. This combination of molecular dynamics and ab initio computational methods demonstrates that increasing the internal hydrogen bond strength in oligosaccharides does not lead to significantly slower internal molecular motion of these sugars in solution. The intermolecular hydrogen bonds formed with water compete equally with the intramolecular hydrogen bonds in the sugar. This result has important implications when considering hydrophobic versus hydrophilic effects in glycoproteins.     

A Moving Boundary Problem for the Sphere

A new technique is employed to solve a moving boundary problemin a sphere. A transformation is given which considerably simplifiesthe non-linearities associated with the moving boundary andenables an iterative analytic series solution to be found. Threeterms of the series expansion are obtained analytically andnumerically evaluated for comparison with results of previousauthors. Graphs of the motion of the reaction (freezing) frontand concentration (temperature) profiles behind the front aregiven. Also tabulated are the times to complete reaction (freezing)of the particle (that is the time for the moving boundary toreach the centre of the sphere).