Limit Theorems for Height Fluctuations in a Class of Discrete Space and Time Growth Models

We introduce a class of one-dimensional discrete space-discrete time stochastic growth models described by a height function h_t(x) with corner initialization. We prove, with one exception, that the limiting distribution function of h_t(x) (suitably centered and normalized) equals a Fredholm determinant previously encountered in random matrix theory. In particular, in the universal regime of large x and large t the limiting distribution is the Fredholm determinant with Airy kernel. In the exceptional case, called the critical regime, the limiting distribution seems not to have previously occurred. The proofs use the dual RSK algorithm, Gessel's theorem, the Borodin–Okounkov identity and a novel, rigorous saddle point analysis. In the fixed x, large t regime, we find a Brownian motion representation. This model is equilvalent to the Seppäläinen–Johansson model. Hence some of our results are not new, but the proofs are.     

The behavior of poly(amino acids) containing l‐cysteine and their block copolymers with poly(ethylene glycol) on gold surfaces

Poly(ethylene glycol) (PEG) is often used to biocompatibilize surfaces of implantable biomedical devices. Here, block copolymers consisting of PEG and l ‐cysteine‐containing poly(amino acid)s (PAA's) were synthesized as polymeric multianchor systems for the covalent attachment to gold surfaces or surfaces decorated with gold nanoparticles. Amino‐terminated PEG was used as macroinitiator in the ring‐opening polymerization, (ROP), of respective amino acid N‐carboxyanhydrides (NCA's) of l ‐cysteine (l ‐Cys), l ‐glutamate (l ‐Glu), and l ‐lysine (l ‐Lys). The resulting block copolymers formed either diblock copolymers, PEG‐b‐p(l ‐Glu_x‐co‐l ‐Cys_y) or triblock copolymers, PEG‐b‐p(l ‐Glu)_x‐b‐p(l ‐Cys)_y. The monomer feed ratio matches the actual copolymer composition, which, together with high yields and a low polydispersity, indicates that the NCA ROP follows a living mechanism. The l ‐Cys repeat units act as anchors to the gold surface or the gold nanoparticles and the l ‐Glu repeat units act as spacers for the reactive l ‐Cys units. Surface analysis by atomic force microscopy revealed that all block copolymers formed homogenous and pin‐hole free surface coatings and the phase separation of mutually immiscible PEG and PAA blocks was observed. A different concept for the biocompatibilization of surfaces was followed when thiol‐terminated p(l ‐Lys) homopolymer was first grafted to the surface and then covalently decorated with HOOC‐CH₂‐PEG‐b‐p(Bz‐l ‐Glu) polymeric micelles. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 248–257     

Simultaneous Determination of Carvedilol,Enalaprilat, and Perindoprilat in Human Plasma Using LC–MS/MS and Its Application to a Pharmacokinetic Pilot Study

Chromatographia - A method for the extraction and quantification of carvedilol, enalaprilat, and perindoprilat in 50 µL human plasma, using high-performance liquid chromatography with...     

Sponge-like nanostructured conducting polymers for electrically controlled drug release

An electrically controlled drug release (ECDR) system based on sponge-like nanostructured conducting polymer (CP) polypyrrole (PPy) film was developed. The nanostructured PPy film was composed of template-synthesized nanoporous PPy covered with a thin protective PPy layer. The proposed controlled release system can load drug molecules in the polymer backbones and inside the nanoholes respectively. Electrical stimulation can release drugs from both the polymer backbones and the nanoholes, which significantly improves the drug load and release efficiency. Furthermore, with one drug incorporated in the polymer backbone during electrochemical polymerization, the nanoholes inside the polymer can act as containers to store a different drug, and simultaneous electrically triggered release of different drugs can be realized with this system.     

Arylthiolate-protected silver quantum dots

This paper describes a new, organic-soluble 4-tert-butylbenzyl mercaptan (BBT) monolayer-protected silver cluster (AgBBT MPC) as the first example of a dissolved silver nanoparticle that exhibits quantized one-electron double layer charging (QDL) voltammetry. Polydisperse AgBBT MPCs made by two different synthetic protocols, but with similar average core diameters (2.1 nm), exhibit sharply differing electrochemistry and optical absorbance spectra. A two-phase procedure (organic/aqueous, termed Prep A-AgBBT) produced MPCs exhibiting a 475 nm surface plasmon absorbance and QDL voltammetry. Neither property was seen for MPCs made by a single-phase procedure, termed Prep B-AgBBT. The difference is thought to reflect poor passivation to oxide formation in the latter Prep B procedure, which is supported by X-ray photoelectron spectroscopy results. Thermogravimetry, mass spectra, and electrochemistry results suggest an average stoichiometric formula of Ag140BBT53, but transmission electron microscopy shows that the products are also polydisperse and include polycrystalline aggregates. Dry, cast films of both Ag MPC preparations on interdigitated array electrodes exhibit low electron hopping conductivity, compared to Au MPCs.     

A threaded loop conformation adopted by a family of peptoid nonamers

Non-natural polymers with well-defined three-dimensional folds offer considerable potential for engineering novel functions that are outside the scope of biological polymers. Here we describe a family of N-substituted glycine or "peptoid" nonamers that folds into an unusual "threaded loop" structure of exceptional thermal stability and conformational homogeneity in acetonitrile. The structure is chain-length-specific and relies on bulky, chiral side chains and chain-terminating functional groups for stability. Notable elements of the structure include the engagement of the positively charged amino terminus by carbonyl groups of the backbone through hydrogen bonding interactions and shielding of polar groups from and near-complete exposure of hydrophobic groups to solvent, in a manner resembling a folded polypeptide globular domain turned inside-out. The structure is stable in a variety of organic solvents but is readily denatured in any solvent/cosolvent milieu with hydrogen bonding potential. The structure could serve as a scaffold for the elaboration of novel functions and could be used to test methodologies for predicting solvent-dependent polymer folding.     

Potential energy surfaces for small alcohol dimers I: methanol and ethanol

Potential energy landscapes for homogeneous dimers of methanol and ethanol were calculated using counterpoise (CP) corrected energies at the MP26-311+G(2df,2pd) level. The landscapes were sampled at approximately 15 dimer separation distances for different relative monomer geometries, or routes, given in terms of a relative monomer yaw, pitch, and roll and the spherical angles between the monomer centers (taken as the C atom attached to the O). The 19 different routes studied for methanol and the 22 routes examined for ethanol include 607 CP corrected energies. Both landscapes can be adequately represented by site-site, pairwise-additive models, suitable for use in molecular simulations. A modified Morse potential is used for the individual pair interactions either with or without point charges to represent the monomer charge distribution. A slightly better representation of the methanol landscape is obtained using point charges, while the potential energy landscape of ethanol is slightly better without point charges. This latter representation may be computationally advantageous for molecular simulations because it avoids difficulties associated with long-range effects of point-charge-type models.     

Single-index quantile regression

Nonparametric quantile regression with multivariate covariates is a difficult estimation problem due to the “curse of dimensionality”. To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a single-index function , where a univariate link function g₀(⋅) is applied to a linear combination of covariates , often called the single-index. We introduce a practical algorithm where the unknown link function g₀(⋅) is estimated by local linear quantile regression and the parametric index is estimated through linear quantile regression. Large sample properties of estimators are studied, which facilitate further inference. Both the modeling and estimation approaches are demonstrated by simulation studies and real data applications.