Constructing fixed rank optimal estimators with method of best recurrent approximations

We propose a new approach which generalizes and improves principal component analysis (PCA) and its recent advances. The approach is based on the following underlying ideas. PCA can be reformulated as a technique which provides the best linear estimator of the fixed rank for random vectors. By the proposed method, the vector estimate is presented in a special quadratic form aimed to improve the error of estimation compared with customary linear estimates. The vector is first pre-estimated from the special iterative procedure such that each iterative loop consists of a solution of the unconstrained nonlinear best approximation problem. Then, the final vector estimate is obtained from a solution of the constrained best approximation problem with the quadratic approximant. We show that the combination of these techniques allows us to provide a new nonlinear estimator with a significantly better performance compared with that of PCA and its known modifications.     

Polar nanoregions in Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> (PMN): insights from a supercell approach

We report construction of a model of polar nanoregions in the PMN relaxor ferroelectric based on first-principles lattice dynamics for chemically ordered supercells [S.A. Prosandeev et al., Phys. Rev. B 70, 134110 (2004)], combined with invariance under permutations and dipole-dipole interaction as a source supporting randomly oriented residual polarization. Representative analytical estimates of polar nanore-gion — supercell mapping reproduce both nonzero local and zero macroscopic polarization of the structure, as well as the temperature change of the supercell anisotropy at cooling and field cooling.     

UV resonance Raman spectroscopy probes the localization of tryptophan‐containing antimicrobial peptides in lipid vesicles

In this work we employed UV resonance Raman spectroscopy with 229 nm excitation to study two tryptophan‐containing antimicrobial peptides with a broad‐spectrum activity against Gram‐positive and Gram‐negative bacteria: lactoferricin B (LfB, RRWQWRMKKLG) and pEM‐2 (KKWRWWLKALAKK). UV resonance Raman spectra of both peptides are dominated by tryptophan bands. Raman spectra of LfB and pEM‐2 in D₂O and 2,2,2‐trifluoro ethanol (TFE) have been measured and used to identify the hydrogen‐bond strength marker bands W6 and W17. The tryptophan doublet, W7, at 1340 and 1360 cm⁻¹ was used to detect an increase in the hydrophobicity of Trp environment in TFE. The spectra of LfB in complex with model cell membranes composed of zwitterionic dipalmitoylglycero‐phosphocholine (DPPC) or anionic dipalmitoyglycero‐phosphoglycerol (DPPG) lipid vesicles revealed a more hydrophobic Trp environment in DPPG, suggesting stronger interactions between the cationic peptide and anionic model cell membrane. Copyright © 2008 John Wiley & Sons, Ltd.     

On the Interaction of Turbulent Shear Layers with Harmonic Perturbations

The problem of coherent perturbations in a turbulent shear layer is considered for the purpose of developing a mathematical model based on a triple decomposition that extracts the coherent components of random fluctuations. The governing equations for the mean and the coherent parts of flow are derived, assuming the eddy-viscosity equivalence for the random part of flow, and solved by iterations to provide a coupled solution of the problem as a whole. Calculations agree well with experimental data in the upstream part of the layer where the mean–coherent flow interaction is the most important. In this region, the interaction changes the mean flow velocity distribution in such a manner that the neutral stability curve is shifted upstream relative to its position in the undisturbed layer and the perturbation intensity decreases further downstream. Experiments show that the coherent waves suppress the turbulent Reynolds stress production downstream of this region, but the model fails to predict the layer spreading correctly probably due to an inadequate turbulence closure of the mean flow. For the case of a turbulent mixing layer, we suggest a new closure relation that takes into account this coherent-random interaction.     

Light backscattering by hexagonal ice crystals

Backscattering of light by hexagonal ice columns and plates has been calculated by means of a ray-tracing code. It is shown that backscattering by the hexagonal ice cylinders at their arbitrary orientations is caused by a peculiar corner-reflector effect. A gigantic peak of backscattering is found at the angle of about 32.5° between the principal axis of a particle and the incidence direction for both hexagonal ice columns and plates. This peak is explained by multiple total internal reflections inside the crystals that take place for a part of incident rays. The obtained results on backscattering efficiency allow one to calculate backscattering by an ensemble of the hexagonal ice cylinders of various sizes, shapes and orientations. Slant lidar remote sensing of cirrus clouds for discrimination between aligned columns and plates is suggested as an application of the results obtained.     

Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators

The majority of first-order methods for large-scale convex–concave saddle point problems and variational inequalities with monotone operators are proximal algorithms. To make such an algorithm practical, the problem’s domain should be proximal-friendly—admit a strongly convex function with easy to minimize linear perturbations. As a by-product, this domain admits a computationally cheap linear minimization oracle (LMO) capable to minimize linear forms. There are, however, important situations where a cheap LMO indeed is available, but the problem domain is not proximal-friendly, which motivates search for algorithms based solely on LMO. For smooth convex minimization, there exists a classical algorithm using LMO—conditional gradient. In contrast, known to us similar techniques for other problems with convex structure (nonsmooth convex minimization, convex–concave saddle point problems, even as simple as bilinear ones, and variational inequalities with monotone operators, even as simple as affine) are quite recent and utilize common approach based on Fenchel-type representations of the associated objectives/vector fields. The goal of this paper was to develop alternative (and seemingly much simpler) decomposition techniques based on LMO for bilinear saddle point problems and for variational inequalities with affine monotone operators.     

Ganglioside partitioning and aggregation in phase-separated monolayers characterized by bodipy GM1 monomer/dimer emission

The distribution of Bodipy GM1 in monolayers of binary and ternary lipid mixtures with coexisting fluid and ordered phases has been examined using a combination of atomic force microscopy and near-field scanning optical microscopy. Monolayers deposited at high (30 mN/m) and low (5 or 10 mN/m) surface pressures were examined and compared to those containing the same concentration of unlabeled ganglioside. Measurements of monomer and dimer Bodipy emission were used to distinguish aggregated from dilute ganglioside levels. For binary DPPC/DOPC monolayers, Bodipy GM1 is distributed throughout both the fluid and ordered phases at low surface pressures, and both labeled and unlabeled gangliosides result in a reduction in the size of ordered DPPC domains at 0.4% and the appearance of small aligned ganglioside-rich domains at 4%. In agreement with earlier studies, GM1 is heterogeneously distributed in small islands in the condensed DPPC domains at high surface pressure. By contrast, Bodipy GM1 causes the disappearance of large DPPC domains at 0.4% and the formation of a new GM1-rich phase at 4%. The addition of both gangliosides leads to a comparable loss of large ordered domains at low surface pressure and the appearance of a new GM1-rich phase at 30 mN/m for ternary lipid mixtures containing cholesterol. The results demonstrate the complexity of GM1 partitioning and illustrate the utility of complementary AFM and high spatial resolution two-color fluorescence experiments for understanding Bodipy GM1 aggregation and distribution.     

Surface patterning of silica nanostructures using bio-inspired templates and directed synthesis

Natural systems excel in directing the synthesis of inorganic materials for various functional purposes. One of the best-studied systems is silica synthesis, as occurs in diatoms and marine sponges. Various biological and synthetic polymers have been shown to template and catalyze silica formation from silicic acid precursors. Here, we describe the use of poly-L-lysine to promote the synthesis of silica in neutral, aqueous solution and when immobilized onto a silicon support structure under similar conditions. Either reagent jetting or conventional photolithography techniques can be used to pattern the templating polymer. Spots created by reagent jetting led to the creation of silica structures in the shape of a ring that may be a result of the spotting process. Photolithographically defined poly-L-lysine spots led to thin laminate structures after exposure to a dilute aqueous silicic acid solution. The laminate structures were nanostructured and highly interconnected. Photolithographic patterning of (3-aminopropyl)trimethoxysilane, a reagent that mimics the lysine functional group, led to similar silica coatings even though low-molecular-weight materials do not rapidly promote silica synthesis in solution. This result highlights the importance of functional-group arrangement for templating and promoting the synthesis of inorganic materials. The described surface-patterning techniques offer a route to integrate conventional silicon-patterning technologies with biologically based material synthesis. Such combined fabrication techniques enable controlled assembly over multiple length scales and an approach to understanding interfacial silica synthesis, as occurs in natural systems.     

Polymerization of propylene by metallocene and Ziegler–Natta mixed catalytic systems. Study of polypropylene properties

Propylene was polymerized with metallocene and Ziegler–Natta mixed-catalytic systems to obtain reactor blends of metallocene and Ziegler–Natta-derived propylene homopolymers. The two catalytic systems are able to act jointly, providing individual polymers with different melting and crystallization temperatures. Compatibility between the components of the mixed-catalytic systems and the influence of the components on the polymerization process and on the properties of the reactor blends were studied. Thermal, mechanical, viscoelastic, rheological, and optical properties of the blends were tested and compared with those of conventional polypropylene grades. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 3063–3072, 1998