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     

Absolutely indecomposable symmetric matrices

Let A be a symmetric matrix of size n×n with entries in some (commutative) field K. We study the possibility of decomposing A into two blocks by conjugation by an orthogonal matrix T∈Mat_n(K). We say that A is absolutely indecomposable if it is indecomposable over every extension of the base field. If K is formally real then every symmetric matrix A diagonalizes orthogonally over the real closure of K. Assume that K is a not formally real and of level s. We prove that in Mat_n(K) there exist symmetric, absolutely indecomposable matrices iff n is congruent to 0, 1 or −1 modulo 2s.     

Spinors and multivectors as a unified tool for spacetime geometry and for elementary particle physics

From the definition of spinors as the minimal left (right) modules of multivectors (that is, of vectors and their outer products), we can construct a unified mathematical approach for the study of matter and its interaction fields, which are either defined as fields in the geometrical spacetime or considered as generators of the physical spacetime. It is also shown how matter and interaction fields can be represented either by spinor fields or by multivector fields, both types of fields carrying the same information as the traditional corresponding spinors, vectors, or tensors. Geometry is more transparent in one representation (multivector form), and physics is more obvious in the spinor representation. Our theory provides a unified and totally self-consistent representation of quarks (barions), leptons, and all their known interactions.