Corrector-predictor methods for sufficient linear complementarity problems

We present a new corrector-predictor method for solving sufficient linear complementarity problems for which a sufficiently centered feasible starting point is available. In contrast with its predictor-corrector counterpart proposed by Miao, the method does not depend on the handicap κ of the problem. The method has \(O((1+\kappa)\sqrt{n}L)\)-iteration complexity, the same as Miao’s method, but our error estimates are sightly better. The algorithm is quadratically convergent for problems having a strictly complementary solution. We also present a family of infeasible higher order corrector-predictor methods that are superlinearly convergent even in the absence of strict complementarity. The algorithms of this class are globally convergent for general positive starting points. They have \(O((1+\kappa)\sqrt{n}L)\)-iteration complexity for feasible, or “almost feasible”, starting points and O((1+κ)² nL)-iteration complexity for “sufficiently large” infeasible starting points.     

Thin film assembly of spider silk-like block copolymers

We report the self-assembly of monolayers of spider silk-like block copolymers. Langmuir isotherms were obtained for a series of bioengineered variants of the spider silks, and stable monolayers were generated. Langmuir-Blodgett films were prepared by transferring the monolayers onto silica substrates and were subsequently analyzed by atomic force microscopy (AFM). Static contact angle measurements were performed to characterize interactions across the interface (thin film, water, air), and molecular modeling was used to predict 3D conformation of spider silk-like block copolymers. The influence of molecular architecture and volume fraction of the proteins on the self-assembly process was assessed. At high surface pressure, spider silk-like block copolymers with minimal hydrophobic block (f(A) = 12%) formed oblate structures, whereas block copolymer with a 6-fold larger hydrophobic domain (f(A) = 46%) formed prolate structures. The varied morphologies obtained with increased hydrophobicity offer new options for biomaterials for coatings and related options. The design and use of bioengineered protein block copolymers assembled at air-water interfaces provides a promising approach to compare 2D microstructures and molecular architectures of these amphiphiles, leading to more rationale designs for a range of nanoengineered biomaterial needs as well as providing a basis of comparison to more traditional synthetic block copolymer systems.     

Universal Objects in Some Classes of Clifford Topological Inverse Semigroups

We construct universal objects in various classes of Clifford topological inverse semigroups. In particular, we show that each compact Abelian topological inverse semigroup with Lawson maximal semilattice embeds into a power of the cone over the circle.     

Sampling Bias Correction in the Model of Mixtures with Varying Concentrations

Model of mixture with varying concentrations is a generalization of the classical finite mixture model in which the mixing probabilities (concentrations) vary from observation to observation. We consider the case when the concentrations of the mixture components are known, but no assumptions on the distributions of the observed variable are made. The problem is to estimate the moments of the components’ distributions. We propose a modification of the Horvitz-Thompson weighting for moments estimation by observations from mixture with varying concentrations in presence of sampling bias. Consistency of obtained estimators is demonstrated. Results of simulations are presented.     

Fermi Arcs and DC Transport in Nanowires of Dirac and Weyl Semimetals

The transport properties and electron states in cylinder nanowires of Dirac and Weyl semimetals are studied paying special attention to the structure and properties of the surface Fermi arcs. The latter make the electric charge and current density distributions in nanowires strongly nonuniform as the majority of the charge density is accumulated at the surface. It is found that a Weyl semimetal wire also supports a magnetization current localized mainly at the surface because of the Fermi arcs contribution. By using the Kubo linear response approach, the direct current (DC) conductivity is calculated and it is found that its spatial profile is nontrivial. By explicitly separating the contributions of the surface and bulk states, it is shown that when the electric chemical potential and/or the radius of the wire is small, the electron transport is determined primarily by the Fermi arcs and the electrical conductivity is much higher at the surface than in the bulk. Due to the rise of the surface-bulk transition rate, the relative contribution of the surface states to the total conductivity gradually diminishes as the chemical potential increases. In addition, the DC conductivity at the surface demonstrates noticeable peaks when the Fermi level crosses energies of the surface states.     

Microwave-Assisted Synthesis of Modified Glycidyl Methacrylate–Ethyl Methacrylate Oligomers,Their Physico-Chemical and Biological Characteristics

In this study, well-known oligomers containing ethyl methacrylate (EMA) and glycidyl methacrylate (GMA) components for the synthesis of the oligomeric network [P(EMA)-co-(GMA)] were used. In order to change the hydrophobic character of the [P(EMA)-co-(GMA)] to a more hydrophilic one, the oligomeric chain was functionalized with ethanolamine, xylitol (Xyl), and L-ornithine. The oligomeric materials were characterized by nuclear magnetic resonance and Fourier transform infrared spectroscopy, scanning electron microscopy, and differential thermogravimetric analysis. In the final stage, thanks to the large amount of -OH groups, it was possible to obtain a three-dimensional hydrogel (HG) network. The HGs were used as a matrix for the immobilization of methylene blue, which was chosen as a model compound of active substances, the release of which from the matrix was examined using spectrophotometric detection. The cytotoxic test was performed using fluid extracts of the HGs and human skin fibroblasts. The cell culture experiment showed that only [P(EMA)-co-(GMA)] and [P(EMA)-co-(GMA)]-Xyl have the potential to be used in biomedical applications. The studies revealed that the obtained HGs were porous and non-cytotoxic, which gives them the opportunity to possess great potential for use as an oligomeric network for drug reservoirs in in vitro application.     

A transition state analogue for an RNA-editing reaction

Deamination at C6 of adenosine in RNA catalyzed by the ADAR enzymes generates inosine at the corresponding position. Because inosine is decoded as guanosine during translation, this modification can lead to codon changes in messenger RNA. Hydration of 8-azanebularine across the C6-N1 double bond generates an excellent mimic of the transition state proposed for the hydrolytic deamination reaction catalyzed by ADARs. Here, we report the synthesis of a phosphoramidite of 8-azanebularine and its use in the preparation of RNAs mimicking the secondary structure found at a known editing site in the glutamate receptor B subunit pre-mRNA. The binding properties of analogue-containing RNAs indicate that a tight binding ligand for an ADAR can be generated by incorporation of 8-azanebularine. The observed high-affinity binding is dependent on a functional active site, the presence of one, but not the other, of ADAR2's two double-stranded RNA-binding motifs (dsRBMs), and the correct placement of the nucleoside analogue into the sequence/structural context of a known editing site. These results advance our understanding of substrate recognition during ADAR-catalyzed RNA editing and are important for structural studies of ADAR.RNA complexes.