Optimal linear interpolation of multiple missing values

Statistical Inference for Stochastic Processes - The problem of linear interpolation in the context of a multivariate time series having multiple (possibly non-consecutive) missing values is...     

Unconventional Secondary Structure Mimics: Ladder-Rungs

Secondary structures tend to be recognizable because they have repeating structural motifs, but mimicry of these does not have to follow such well-defined patterns. Bioinformatics studies to match side-chain orientations of a novel hydantoin triazole chemotype ( 1 ) to protein-protein interfaces revealed it tends to align well across parallel and antiparallel sheets, like rungs on a ladder. One set of these overlays was observed for the protein-protein interaction uPA⋅uPAR. Consequently, chemotype 1 was made with appropriate side-chains to mimic uPA at this interface. Biophysical assays indicate these compounds did in fact bind uPAR, and elicit cellular responses that affected invasion, migration, and wound healing.     

Facile non‐lithographic route to highly aligned silica nanopatterns using unidirectionally aligned polystyrene‐block‐polydimethylsiloxane films

Thin films (monolayer and bilayer) of cylinder forming polystyrene‐block‐polydimethylsiloxane (PS‐b‐PDMS) were shear aligned by the swelling and deswelling of a crosslinked PDMS pad that was physically adhered to the film during solvent vapor annealing. The nanostructures formed by self‐assembly were exposed to ultraviolet‐ozone to partially oxidize the PDMS, followed by calcination in air at 500 °C. In this process, the PS segments were fully decomposed, while the PDMS yielded silica nanostructures. The highly aligned PDMS cylinders were thus deposited as silica nanolines on the silicon substrate. Using a bilayer film, the center‐to‐center distance of these features were effectively halved from 38 to 19 nm. Similarly, by sequential shear‐alignment of two distinct layers, a rhombic array of silica nanolines was fabricated. This methodology provides a facile route to fabricating complex topographically patterned nanostructures. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1058–1064     

Black and white local invariants of mappings from surfaces into three-space

Goryunov proved that the space of local invariants of Vassiliev type for generic maps from surfaces to three-space is three-dimensional. The basic invariants were the number of pinch points, the number of triple points and one linked to a Rokhlin type invariant. In this paper we show that, by colouring the complement of the image of the map with a chess board pattern, we can produce a six-dimensional space of local invariants. These are essentially black and white versions of the above. Simple examples show how these are more effective. This revised version was published online in August 2006 with corrections to the Cover Date.