The Marčenko‐Pastur law for sparse random bipartite biregular graphs

We prove that the empirical spectral distribution of a (d_L, d_R)‐biregular, bipartite random graph, under certain conditions, converges to a symmetrization of the Mar?enko‐Pastur distribution of random matrix theory. This convergence is not only global (on fixed‐length intervals) but also local (on intervals of increasingly smaller length). Our method parallels the one used previously by Dumitriu and Pal (2012). © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 313–340, 2016     

Strong Dunford-Pettis sets and spaces of operators (Monatsh. Math. 144, 275–284 (2005))

In a recent paper, Ghenciu and Lewis studied strong Dunford-Pettis sets and made the following two assertions:

Imaging of peptides in the rat brain using MALDI-FTICR mass spectrometry

Analytical methods are pursued to measure the identity and location of biomolecules down to the subcellular (microm) level. Available mass spectrometric imaging methods either compromise localization accuracy or identification accuracy in their analysis of surface biomolecules. In this study, imaging FTICR-MS is applied for the spatially resolved mass analysis of rat brain tissue with the aim to optimize protein identification by the high mass accuracy and online MS/MS capabilities of the technique. Mass accuracies up to 6 ppm were obtained in the direct MALDI-analysis of the tissue together with a spatial resolution of 200 microm. The spatial distributions of biomolecules differing in mass by less than 0.1 Da could be resolved, and are shown to differ significantly. Online MS/MS analysis of selected ions was demonstrated. A comparison of the FTICR-MS imaging results with stigmatic TOF imaging on the same sample is presented. To reduce the extended measuring times involved, it is recommended to restrict the FTICR-MS analyses to areas of interest as can be preselected by other, faster imaging methods.     

Gas sorption and barrier properties of polymeric membranes from molecular dynamics and Monte Carlo simulations

It is important for many industrial processes to design new materials with improved selective permeability properties. Besides diffusion, the molecule's solubility contributes largely to the overall permeation process. This study presents a method to calculate solubility coefficients of gases such as O2, H2O (vapor), N2, and CO2 in polymeric matrices from simulation methods (Molecular Dynamics and Monte Carlo) using first principle predictions. The generation and equilibration (annealing) of five polymer models (polypropylene, polyvinyl alcohol, polyvinyl dichloride, polyvinyl chloride-trifluoroethylene, and polyethylene terephtalate) are extensively described. For each polymer, the average density and Hansen solubilities over a set of ten samples compare well with experimental data. For polyethylene terephtalate, the average properties between a small (n = 10) and a large (n = 100) set are compared. Boltzmann averages and probability density distributions of binding and strain energies indicate that the smaller set is biased in sampling configurations with higher energies. However, the sample with the lowest cohesive energy density from the smaller set is representative of the average of the larger set. Density-wise, low molecular weight polymers tend to have on average lower densities. Infinite molecular weight samples do however provide a very good representation of the experimental density. Solubility constants calculated with two ensembles (grand canonical and Henry's constant) are equivalent within 20%. For each polymer sample, the solubility constant is then calculated using the faster (10x) Henry's constant ensemble (HCE) from 150 ps of NPT dynamics of the polymer matrix. The influence of various factors (bad contact fraction, number of iterations) on the accuracy of Henry's constant is discussed. To validate the calculations against experimental results, the solubilities of nitrogen and carbon dioxide in polypropylene are examined over a range of temperatures between 250 and 650 K. The magnitudes of the calculated solubilities agree well with experimental results, and the trends with temperature are predicted correctly. The HCE method is used to predict the solubility constants at 298 K of water vapor and oxygen. The water vapor solubilities follow more closely the experimental trend of permeabilities, both ranging over 4 orders of magnitude. For oxygen, the calculated values do not follow entirely the experimental trend of permeabilities, most probably because at this temperature some of the polymers are in the glassy regime and thus are diffusion dominated. Our study also concludes large confidence limits are associated with the calculated Henry's constants. By investigating several factors (terminal ends of the polymer chains, void distribution, etc.), we conclude that the large confidence limits are intimately related to the polymer's conformational changes caused by thermal fluctuations and have to be regarded--at least at microscale--as a characteristic of each polymer and the nature of its interaction with the solute. Reducing the mobility of the polymer matrix as well as controlling the distribution of the free (occupiable) volume would act as mechanisms toward lowering both the gas solubility and the diffusion coefficients.     

Constraining by a family of strictly nonexpansive idempotent functions with applications in image reconstruction

When solving an image reconstruction problem a previous knowledge concerning the original image may lead to various constraining strategies. A convergence result has been previously proved for a constrained version of the Kaczmarz projection algorithm with a single strictly nonexpansive idempotent function with a closed image. In this paper we consider a more general projection based iterative method and a family of such constraining functions with some additional hypotheses in order to better use the a priori information for every approximation calculated. We present a particular family of box-constraining functions which satisfies our assumptions and we design an adaptive algorithm that uses an iteration-dependent family of constraining functions for some numerical experiments of image reconstruction on Tomographic Particle Image Velocimetry.     

Synthesis of enantiomerically enriched (R)- and (S)-benzofuranyl- and benzo[b]thiophenyl-1,2-ethanediols via enantiopure cyanohydrins as intermediates

The chemoenzymatic synthesis of highly enantiopure (R)- and (S)-benzofuranyl- and benzo[b]thiophenyl-cyanohydrins and their chemical transformation into the corresponding heteroaryl-1,2-ethanediols is described.     

Analysis of underwater mammal vocalisations using time-frequency-phase tracker

One of the most challenging applications of time-frequency representations deals with the analysis of the signal issued from natural environment. Recently, the interest for passive underwater context increased, basically due to the rich information carried out by the natural signals. Taken into account the non-linear multi-component time-frequency behaviour of such signals, their analysis is a challenging problem.In this context, the analysis of underwater mammal’s whistles is aimed to extract, accurately and adaptively, their main time-frequency components. In this paper, we define a time-frequency-phase tracker which is composed of three steps. The first one consists of modelling the short-time segments of the vocalization by a set of third order polynomial phase modulations. The second step consists in the fusion of local polynomial phase modulations according to a local phase continuity criterion. Finally, in the third step, the detected time-frequency track is used to design the time-frequency filter, in charge of extracting the samples corresponding to the detected track. This procedure is then iterated until all component of interest are extracted.Tests provided for realistic scenarios and real data taken in Bay of Biscay at September 2009 containing whistles of common dolphin Delphinus delphis illustrate the potential and the benefits of the proposed approach.