Non-Convex Global Minimization and False Discovery Rate Control for the TREX

The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a nonconvex optimization problem. This article shows a remarkable result: despite the nonconvexity of the TREX problem, there exists a polynomial-time algorithm that is guaranteed to find the global minimum. This result adds the TREX to a very short list of nonconvex optimization problems that can be globally optimized (principal components analysis being a famous example). After deriving and developing this new approach, we demonstrate that (i) the ability of the preexisting TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the new polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model. To achieve this last aim, we provide an extension of the results of Barber and Candes to establish that the knockoff filter framework can be applied to the TREX. This investigation thus provides both a rare case study of a heuristic for nonconvex optimization and a novel way of exploiting nonconvexity for statistical inference.     

Micellar nanocontainers based on cationic surfactants with a pyrrolidinium head group for increasing drug bioavailability

Russian Chemical Bulletin - A homologous series of cationic surfactants with a pyrrolidinium head group containing a hydroxyethyl moiety was studied for the solubilization of nonsteroidal...     

Micellar nanocontainers based on sterically hindered cationic phosphonium amphiphiles

Russian Chemical Bulletin - Self-aggregation processes in an H2O—DMF (10%) medium were studied for a homologous series of tri-tert-butyl(n-alkyl)phosphonium tetrafluoroborates (PIL-n, where n...     

Penalized Versus Constrained Generalized Eigenvalue Problems

We investigate the difference between using an ?₁ penalty versus an ?₁ constraint in generalized eigenvalue problems arising in multivariate analysis. Our main finding is that the ?₁ penalty may fail to provide very sparse solutions; a severe disadvantage for variable selection that can be remedied by using an ?₁ constraint. Our claims are supported both by empirical evidence and theoretical analysis. Finally, we illustrate the advantages of the ?₁ constraint in the context of discriminant analysis and principal component analysis. Supplementary materials for this article are available online.     

Structure and supramolecular organization of tri-n-butyl(octadecyl)phosphonium tetrafluoroborate and its influence on catalytic activity of stabilized palladium nanoparticles

Russian Chemical Bulletin - A crystal structure and aggregation properties of tri-n-butyl(octadecyl)phosphonium tetrafluoroborate were studied. Palladium nanoparticles stabilized by this...     

Self-Assembling Drug Formulations with Tunable Permeability and Biodegradability

This review focuses on key topics in the field of drug delivery related to the design of nanocarriers answering the biomedicine criteria, including biocompatibility, biodegradability, low toxicity, and the ability to overcome biological barriers. For these reasons, much attention is paid to the amphiphile-based carriers composed of natural building blocks, lipids, and their structural analogues and synthetic surfactants that are capable of self-assembly with the formation of a variety of supramolecular aggregates. The latter are dynamic structures that can be used as nanocontainers for hydrophobic drugs to increase their solubility and bioavailability. In this section, biodegradable cationic surfactants bearing cleavable fragments are discussed, with ester- and carbamate-containing analogs, as well as amino acid derivatives received special attention. Drug delivery through the biological barriers is a challenging task, which is highlighted by the example of transdermal method of drug administration. In this paper, nonionic surfactants are primarily discussed, including their application for the fabrication of nanocarriers, their surfactant-skin interactions, the mechanisms of modulating their permeability, and the factors controlling drug encapsulation, release, and targeted delivery. Different types of nanocarriers are covered, including niosomes, transfersomes, invasomes and chitosomes, with their morphological specificity, beneficial characteristics and limitations discussed.     

Encapsulation of quantum dots in supramolecular systems based on amphiphilic compounds and polyelectrolytes

Supramolecular nanocontainers based on monocationic and gemini surfactants and oppositely charged polyelectrolytes (polyacrylic acid, polyethyleneimine) for the stabilization and enhancement of solubility of hydrophobic quantum dots CdSe/ZnS were formed. The size (from 2 to 70 nm depending on the type of nanocontainers) and shape of aggregates containing quantum dots were determined by transmission electron microscopy. It was shown that the nature of the stabilizing agent influences the morphology of aggregates. The increase in photostability of quantum dots in micellar solutions of gemini surfactants and the possibility of their preservation in the polyelectrolyte capsules are identified.     

Effect of ATP and amino acids on the properties of cationic amphiphiles in solution and on the surface

Russian Chemical Bulletin - The interaction between a number of cationic surfactants bearing the head group with different structures (triallyl, morpholinium, including hydroxyethyl-substituted)...     

Supramolecular Tools to Improve Wound Healing and Antioxidant Properties of Abietic Acid: Biocompatible Microemulsions and Emulgels

Abietic acid, a naturally occurring fir resin compound, that exhibits anti-inflammatory and wound-healing properties, was formulated into biocompatible emulgels based on stable microemulsions with the addition of a carbamate-containing surfactant and Carbopol^® 940 gel. Various microemulsion and emulgel formulations were tested for antioxidant and wound-healing properties. The chemiluminescence method has shown that all compositions containing abietic acid have a high antioxidant activity. Using Strat-M^® skin-modelling membrane, it was found out that emulgels significantly prolong the release of abietic acid. On Wistar rats, it was shown that microemulsions and emulgels containing 0.5% wt. of abietic acid promote the rapid healing of an incised wound and twofold tissue reinforcement compared to the untreated group, as documented by tensiometric wound suture-rupture assay. The high healing-efficiency is associated with a combination of antibacterial activity of the formulation components and the anti-inflammatory action of abietic acid.     

Aggregation behavior of the surfactant bearing pyrrolidinium head group in the presence of polyacrylic acid

Russian Chemical Bulletin - The aggregation characteristics of binary systems based on a novel pyrrolidinium surfactant with the hexadecyl hydrocarbon tail and hydroxyethyl fragment at the nitrogen...