Steiner transitive-closure spanners of low-dimensional posets

Given a directed graph G=(V, E) and an integer k ≥ 1, a k-transitive-closure spanner (k-TC-spanner) of G is a directed graph H=(V, E _H ) that has (1) the same transitive closure as G and (2) diameter at most k. In some applications, the shortcut paths added to the graph in order to obtain small diameter can use Steiner vertices, that is, vertices not in the original graph G. The resulting spanner is called a Steiner transitive-closure spanner (Steiner TC-spanner). Motivated by applications to property reconstruction and access control hierarchies, we concentrate on Steiner TC-spanners of directed acyclic graphs or, equivalently, partially ordered sets. In these applications, the goal is to find a sparsest Steiner k-TC-spanner of a poset G for a given k and G. The focus of this paper is the relationship between the dimension of a poset and the size of its sparsest Steiner TC-spanner. The dimension of a poset G is the smallest d such that G can be embedded into a d-dimensional directed hypergrid via an order-preserving embedding. We present a nearly tight lower bound on the size of Steiner 2-TC-spanners of d- dimensional directed hypergrids. It implies better lower bounds on the complexity of local reconstructors of monotone functions and functions with small Lipschitz constant. The lower bound is derived from an explicit dual solution to a linear programming relaxation of the Steiner 2-TC-spanner problem. We also give an efficient construction of Steiner 2-TC-spanners, of size matching the lower bound, for all low-dimensional posets. Finally, we present a lower bound on the size of Steiner k-TC-spanners of d-dimensional posets. It shows that the best-known construction, due to De Santis et al., cannot be improved significantly.     

Translocation of DNA molecules through nanopores with salt gradients: the role of osmotic flow

Recent experiments of translocation of double-stranded DNA through nanopores [M. Wanunu et al., Nature Nanotech. 5, 160 (2009)] reveal that the DNA capture rate can be significantly influenced by a salt gradient across the pore. We show that osmotic flow combined with electrophoretic effects can quantitatively explain the experimental data on the salt-gradient dependence of the capture rate.     

Initial growth at the F16CoPc/Ag(111) interface

An extended, combined (STM/STS)–(UPS/XPS) study was carried out towards a comprehensive understanding of the mechanism responsible for the F₁₆CoPc/Ag(111) interface formation. The evolution of the morphology and the electronic properties at the organic/metal interface is investigated for the early-stage growth of the ultrathin molecular film. Template-guided molecular structures are formed via a strong molecule–substrate interaction which leads to the formation of a new adsorption-induced interface state close to the Fermi energy (E_F). With increasing the thickness the molecular coupling to the metal surface states becomes less important while the more dominant molecule–molecule interaction governs the second layer formation. The quenching of the interface state upon increasing the molecular thickness, together with the changes observed in the Co 2p and F 1s core levels, is explained based on a charge transfer at the interface and a corresponding charge redistribution within the molecular ligand. A detailed “picture” of the energy level alignment close to E_F is achieved by correlating the high resolution UPS and highly localized STS data.     

Generalized complex structures and Lie brackets

We remark that the equations underlying the notion of generalized complex structure have simple geometric meaning when passing to Lie algebroids/groupoids.     

Palladium-catalyzed C-S coupling: access to thioethers, benzo[b]thiophenes, and thieno[3,2-b]thiophenes

The first C-S bond formation/cross-coupling/cyclization domino reaction using thiourea as a cheap and easy to handle dihydrosulfide surrogate has been developed. Structurally important biarylthioether, benzo[b]thiophenes, and thieno[3,2-b]thiophene scaffolds are provided in high yield.     

Polymer-and Glass-based Fluorescence Standards for the Near Infrared (NIR) Spectral Region

The widespread use and acceptance of fluorescence techniques especially in regulated areas like medical diagnostics is closely linked to standardization concepts that guarantee and improve the comparability and reliability of fluorescence measurements. At the core of such concepts are dependable fluorescence standards that are preferably certified. The ever rising interest in fluorescence measurements in the near-infrared (NIR) spectral region renders the availability of spectral and intensity standards for this wavelength region increasingly important. This encouraged us to develop approaches to solid NIR standards based upon dye-doped polymers and assess their application-relevant properties in comparison to metal ion-doped glasses. The overall goal is here to provide inexpensive, easily fabricated, and robust internal and external calibration tools for a broad variety of fluorescence instruments ranging e.g. from spectrofluorometers over fluorescence microscopes to miniaturized fluorescence sensors.     

Global strong solutions to 3-D Navier-Stokes system with strong dissipation in one direction

Science China Mathematics - We consider three-dimensional incompressible Navier-Stokes equations (NS) with different viscous coefficients in the vertical and horizontal variables. In particular,...