Sums of random symmetric matrices and quadratic optimization under orthogonality constraints

Let B _i be deterministic real symmetric m × m matrices, and ξ _i be independent random scalars with zero mean and “of order of one” (e.g., ). We are interested to know under what conditions “typical norm” of the random matrix is of order of 1. An evident necessary condition is , which, essentially, translates to ; a natural conjecture is that the latter condition is sufficient as well. In the paper, we prove a relaxed version of this conjecture, specifically, that under the above condition the typical norm of S _N is : for all Ω > 0 We outline some applications of this result, primarily in investigating the quality of semidefinite relaxations of a general quadratic optimization problem with orthogonality constraints , where F is quadratic in X = (X ₁,... ,X _k ). We show that when F is convex in every one of X _j , a natural semidefinite relaxation of the problem is tight within a factor slowly growing with the size m of the matrices . Research was partly supported by the Binational Science Foundation grant #2002038.     

Characterization of water distribution in bread during storage using magnetic resonance imaging

A soy bread of fully acceptable quality and containing 49% soy ingredients (with or without 5% almond powder) has been recently developed in our laboratory.

An investigation on water distribution and mobility, as probed by proton signal intensity and T₂ magnetic resonance images, during storage was designed to examine possible relations between water states and hindered staling rate upon soy or soy–almond addition.

Water proton distribution throughout soy-containing loaves was found to be very homogeneous in fresh breads with and without almond, with minimal water migration occurring during prolonged storage. In contrast, traditional wheat bread displayed an inhomogeneous water proton population that tended to change (with higher moisture migration towards the outer perimeter of the slice) during storage. Similar results were found for water mobility throughout the loaves, as depicted in T₂ images. On intensity images of all considered bread varieties, the outer perimeter corresponding to the crust exhibited lower signal intensity due to decreased water content. Higher T₂ values were found in the crust of soy breads with and without almond, which were attributed to lipids.

The results indicated that the addition of soy to bread improved the homogeneous distribution of water molecules, which may hinder the staling rate of soy-containing breads. However, incorporation of almond had little effect on the water proton distribution or mobility of soy breads.     

Triggered release of aqueous content from liposome-derived sol-gel nanocapsules

Liposomes prepared from a mixture of L-alpha-dipalmitoylphosphatidylcholine and the PEGilated phospholipid N-(carbonylmethoxypoly(ethylene glycol 2000))-1,2-distearoyl-sn-glycero-3-phosphoethanolamine were used as templates for the production of silica and alkylated silica approximately 100 nm capsules, "liposils", entrapping aqueous solutions of anionic dyes. Triggered release of this content was successfully affected by either low-frequency ultrasound or by microwave treatments. Cryo-TEM was used to follow the formation process of these particles, which are aggregated in a chain-like manner. A mechanism explaining this phenomenon is suggested.     

Anion-binding properties of the tripyrrolemethane group: a combined experimental and theoretical study

Tripyrrolemethane- and bistripyrrolemethane-containing systems were recently reported to be efficient and selective hosts for anions. Nevertheless, the basic intrinsic properties of tripyrrolemethane as a ligand for anions have not yet been explored. Here we report the study of the anion-binding properties of the tripyrrolemethane group. We applied a combined experimental and theoretical approach to determine the affinity of the tripyrrolemethane system for different anions in the gas phase, in solution and in the crystalline state. In the crystal, the tripyrrolemethane group forms a number of different complexes with the bromide ion, some involving the participation of more than one ligand species. Despite the very similar basicity of fluoride and dihydrogen phosphate, the tripyrrolemethane ligand exhibits a clear preference for the fluoride anion in solution, which indicates an anion-binding system and not merely deprotonation. Although the affinity of the tripyrrolemethane ligand for other ions was negligible in solution, gas-phase studies show that complexation with larger halide ions is favoured over complexation with fluoride.     

Latex interpenetrating polymer networks: From structure to properties

Latex interpenetrating and semi-interpenetrating polymer networks (LIPNs and semi-LIPNs) combine the morphological characteristics of bulk-polymerized IPNs with the characteristics of polymers produced by emulsion polymerization; there are IPN structures within the latex particles. These LIPNs can be injection-molded using standard thermoplastic methods and machinery. A dual thermoset—thermoplastic nature characterizing the LIPN manifests itself in the mechanical and rheological behavior reflecting unique morphologies. These morphologies result from a sequential two-stage latex (TSL) polymerization and include core—shell, domain, interpenetrating polymer networks and various other combinations. Elastomeric TSL with crosslinked polyacrylates (xPA) as the first stage and crosslinked polystyrene (xPS) as the second, each stage lightly crosslinked, yield IPN-nano-domain structural particles. Upon molding, the particles become interconnected by joint PS nanodomains, introducing a particle—particle strength-forming mechanism. The intraparticle glassy PS nanodomains reinforce the soft elastomeric particles enhancing their modulus. Glassy “all-styrene” semi-LIPNs made of PS and xPS show improved mechanical performance compared to PS, while exhibiting good transparency. Volumetric crazing in these PS/xPS materials develops in tension-improving elongation and strength. The presence of xPS particles, denser and thus stiffer than the PS matrix, renders a higher modulus. Essentially xPS highly filled blends are achieved along with significant particle—matrix interactions. The ability to generate a controlled plethora of morphologies offers a wealth of potential applications, from reinforced elastomers to high impact plastics. Poly(acrylonitrile—butadiene—styrene), a semi-LIPN, is a commodity plastic, clearly demonstrating the utilization potential of the TSL procedure for generating very fine multiphase materials of scientific and technological merits.     

A rheological study of latex polystyrene-based model systems

Latex two-phased polystyrene blends have been produced by three different mixing routes. Polystyrene (PS) and lightly crosslinked polystyrene (XPS) latices were either mixed, or else used as seeds in two-stage polymerizations. This resulted in different microstructures by each of the procedures, leading to different rheological behaviors. Latex PS/XPS systems flow at every composition studied. Activation energies are independent of XPS content, and of the same order of magnitude as PS. Power-law relaxation has been observed for the physically blended system in the terminal region. This has been attributed to the formation of a “continuous” XPS network in the range 60–100% XPS.     

Photolysis of methyl-parathion thin films: Products,kinetics and quantum yields under different atmospheric conditions

The present study focuses on the photodegradation of methyl-parathion thin films, an organophosphate insecticide, under different atmospheric conditions. The latter include nitrogenated, oxygenated and ozonated atmospheres, under low and high relative humidity conditions. Addition of oxygen to the atmospheric mixture did not seem to affect the reaction rates and quantum yields. Relative humidity affect was minor, with a small enhancement in reaction rate under 254 nm radiation. The addition of ozone (to either dry or humid atmosphere), at all concentrations tested, largely enhanced degradation rates. In the absence of ozone, the obtained quantum yields for photolysis of methyl-parathion thin films under 254 and 313 nm were 0.024 ± 0.007 and 0.012 ± 0.005, respectively. These values are higher than the values previously reported for solutions of methanol and water. Although the presence of molecular oxygen and water vapors did not seem to affect much the reaction rates, it did have a certain effect on the resulted products. More polar products were obtained under oxygenated and ozonated atmospheres, as well as dimers under ozone conditions. The reaction on thin films has yielded more toxic products than usually found in solutions, adding alkylphosphate esters in addition to the oxons formed normally.     

Small molecule correctors of F508del-CFTR discovered by structure-based virtual screening

Folding correctors of F508del-CFTR were discovered by in silico structure-based screening utilizing homology models of CFTR. The intracellular segment of CFTR was modeled and three cavities were identified at inter-domain interfaces: (1) Interface between the two Nucleotide Binding Domains (NBDs); (2) Interface between NBD1 and Intracellular Loop (ICL) 4, in the region of the F508 deletion; (3) multi-domain interface between NBD1:2:ICL1:2:4. We hypothesized that compounds binding at these interfaces may improve the stability of the protein, potentially affecting the folding yield or surface stability. In silico structure-based screening was performed at the putative binding-sites and a total of 496 candidate compounds from all three sites were tested in functional assays. A total of 15 compounds, representing diverse chemotypes, were identified as F508del folding correctors. This corresponds to a 3% hit rate, ~tenfold higher than hit rates obtained in corresponding high-throughput screening campaigns. The same binding sites also yielded potentiators and, most notably, compounds with a dual corrector-potentiator activity (dual-acting). Compounds harboring both activity types may prove to be better leads for the development of CF therapeutics than either pure correctors or pure potentiators. To the best of our knowledge this is the first report of structure-based discovery of CFTR modulators.     

Sensitive and selective PET-based diimidazole luminophore for Zn(II) ions: a structure-activity correlation

3-(3-Ethoxymethyl-1H-imidazol-2-yl)-3-(1-ethoxymethyl-1H-imidazol-2-yl)-3H-benzo[de]isochromen-1-one, 4, is a novel photoinduced electron transfer (PET) chemosensor that becomes fluorescent upon binding metal ions and shows a strong preference toward Zn(II) ions. The new bisimidazol PET sensor and its zinc complex were prepared and characterized in terms of their crystal structures, absorption and emission spectra, and orbital energy diagrams. Free 4 is a weakly luminescent species. On the basis of detailed DFT calculations, we suggest that the poor luminescence yield of free 4 originates from its orbital structure in which two pi-orbitals of the two imidazole rings, HOMO and HOMO-1, are situated between two pi-orbitals of the isochromene-one system, HOMO-2 and LUMO. The absorption and emission processes occur between the two pi-orbitals of the isochromene-one system, HOMO-2 and LUMO, and the two pi-imidazole orbitals serve as quenchers for the excited state of the molecule through nonradiative processes. Upon binding Zn(II) ions, 4 becomes a highly luminescent species having a luminescence maximum peaking at 375 nm (lambda(ex) = 329 nm). The significant 900-fold enhancement in luminescence upon binding of the Zn(II) ions is attributed to the stabilization of the pi-orbitals of the imidazole rings upon their engagement in new bonds with the zinc ion. The affinity of 4 to zinc ions in acetonitrile is found to be very high, Ka > 3 x 10(6) M(-1), while with other metals ions, the association constants are considerably weaker.