Self-concordant barriers for hyperbolic means

The geometric mean and the function (det(·)) ^1/m (on the m-by-m positive definite matrices) are examples of “hyperbolic means”: functions of the form p ^1/m , where p is a hyperbolic polynomial of degree m. (A homogeneous polynomial p is “hyperbolic” with respect to a vector d if the polynomial t↦p(x+td) has only real roots for every vector x.) Any hyperbolic mean is positively homogeneous and concave (on a suitable domain): we present a self-concordant barrier for its hypograph, with barrier parameter O(m ²). Our approach is direct, and shows, for example, that the function −mlog(det(·)−1) is an m ²-self-concordant barrier on a natural domain. Such barriers suggest novel interior point approaches to convex programs involving hyperbolic means. Received: December 2, 1999 / Accepted: February 2001?Published online September 3, 2001     

New model potentials for sulfur-copper(I) and sulfur-mercury(II) interactions in proteins: from ab initio to molecular dynamics

We have developed new force field and parameters for copper(I) and mercury(II) to be used in molecular dynamics simulations of metalloproteins. Parameters have been derived from fitting of ab initio interaction potentials calculated at the MP2 level of theory, and results compared to experimental data when available. Nonbonded parameters for the metals have been calculated from ab initio interaction potentials with TIP3P water. Due to high charge transfer between Cu(I) or Hg(II) and their ligands, the model is restricted to a linear coordination of the metal bonded to two sulfur atoms. The experimentally observed asymmetric distribution of metal ligand bond lengths (r) is accounted for by the addition of an anharmonic (r3) term in the potential. Finally, the new parameters and potential, introduced into the CHARMM force field, are tested in short molecular dynamics simulations of two metal thiolates fragments in water. (Brooks BR et al. J Comput Chem 1983, 4, 1987.1).     

Antibacterial mono- and sesquiterpene esters of benzoic acids from Iranian propolis

Background  

Propolis (bee glue) has been used as a remedy since ancient times. Propolis from unexplored regions attracts the attention of scientists in the search for new bioactive molecules.     

Algorithms for Approximate Shortest Path Queries on Weighted Polyhedral Surfaces

We consider the well-known geometric problem of determining shortest paths between pairs of points on a polyhedral surface P, where P consists of triangular faces with positive weights assigned to them. The cost of a path in P is defined to be the weighted sum of Euclidean lengths of the sub-paths within each face of P.     

Improvement of the Antimicrobial Activity of Oregano Oil by Encapsulation in Chitosan—Alginate Nanoparticles

Oregano oil (OrO) possesses well-pronounced antimicrobial properties but its application is limited due to low water solubility and possible instability. The aim of this study was to evaluate the possibility to incorporate OrO in an aqueous dispersion of chitosan—alginate nanoparticles and how this will affect its antimicrobial activity. The encapsulation of OrO was performed by emulsification and consequent electrostatic gelation of both polysaccharides. OrO-loaded nanoparticles (OrO-NP) have small size (320 nm) and negative charge (−25 mV). The data from FTIR spectroscopy and XRD analyses reveal successful encapsulation of the oil into the nanoparticles. The results of thermogravimetry suggest improved thermal stability of the encapsulated oil. The minimal inhibitory concentrations of OrO-NP determined on a panel of Gram-positive and Gram-negative pathogens (ISO 20776-1:2006) are 4–32-fold lower than those of OrO. OrO-NP inhibit the respiratory activity of the bacteria (MTT assay) to a lower extent than OrO; however, the minimal bactericidal concentrations still remain significantly lower. OrO-NP exhibit significantly lower in vitro cytotoxicity than pure OrO on the HaCaT cell line as determined by ISO 10993-5:2009. The irritation test (ISO 10993-10) shows no signs of irritation or edema on the application site. In conclusion, the nanodelivery system of oregano oil possesses strong antimicrobial activity and is promising for development of food additives.     

The Shape of the Borwein–Affleck–Girgensohn Function Generated by Completely Monotone and Bernstein Functions

Fifteen years ago, J. Borwein, I. Affleck, and R. Girgensohn posed a problem concerning the shape (convexity, log-convexity, reciprocal concavity) of a certain function of several arguments that had manifested in a number of contexts concerned with optimization problems. In this paper we further explore the shape of the Borwein–Affleck–Girgensohn function as well as of its extensions generated by completely monotone and Bernstein functions.     

The ω-Turing degrees

In this paper we initiate the study of the ω-Turing reducibility between sequences of sets of natural numbers. We shall prove that the induced degree structure is an extension of the structure of the Turing degrees and that the two structures are closely connected, but different enough. Further we shall prove some definability results for the local theory of the newly defined structure.     

Ultrafast geminate recombination after photodetachment of aqueous hydroxide

The photodetachment of aqueous hydroxide (OH(?)(aq) and OD(?)(aq)) is studied using femtosecond pump?probe and pump?repump?probe spectroscopy. The electron is detached after excitation of the hydroxide ion to a charge-transfer-to-solvent (CTTS) state at 202 nm. An early intermediate is observed that builds up within 160 fs and is assigned to nonequilibrated OH?electron pairs. The subsequent dynamics are governed by thermalization, partial recombination, and dissociation of the pairs, yielding the final hydrated electrons and hydroxyl radicals. An additional pulse at 810 nm is used for secondary excitation of the intermediate species so that more insight is gained into the recombination process(es). Using this technique we observe a novel geminate recombination channel of OH with adjacent hydrated electrons. This channel leads to ultrafast quenching (700 fs) of almost half the initial number of radicals. The fast mechanism displays an isotope effect of 1.4 (for OD(?)(aq) quantum yield 35%, time constant 1.0 ps). This process was not observed in similar experiments on aqueous bromide and seems to be related to the special properties of the hydroxide ion and its local H-bonding environment. Our findings underline the high reactivity of the prehydrated electron.