Fully asynchronous stochastic coordinate descent: a tight lower bound on the parallelism achieving linear speedup

Mathematical Programming - We seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent that achieves linear speedup. We focus on asynchronous coordinate...     

Preliminary studies on a variable energy positron annihilation lifetime spectroscopy system

There are many advantages in being able to perform positron annihilation lifetime spectroscopy (PALS) using a variable energy positron beam, the most obvious being the easy identification of different defect types at different depths. The difficulty in conducting variable energy (VE) PALS studies lies in the fact that a “start” signal is required to signal the entry of the positron into the target. Two methods have been used to overcome this problem, namely the bunching technique, which employs radio frequency (RF) cavities and choppers, and secondly the use of secondary electrons emitted from the target. The latter technique is in terms of experimental complexity much simpler, but has in the past suffered from poor time resolution (typically ∼500 ps). In this work, we present a series of computer simulations of a design based on the secondary electron emission from thin C-foils in transmission mode which shows that significant improvements in time resolution can be made with resolutions ∼200 ps being in principle possible.     

Probabilistic Analysis of Condition Numbers for Linear Programming

In this paper, we provide bounds for the expected value of the log of the condition number C(A) of a linear feasibility problem given by a n × m matrix A (Ref. 1). We show that this expected value is O(min{n, m log n}) if n > m and is O(log n) otherwise. A similar bound applies for the log of the condition number C _R(A) introduced by Renegar (Ref. 2).     

Fixed-sign solutions for a system of singular focal boundary value problems

We consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments. Using Schauder fixed point theorem, we establish criteria such that the system of boundary value problems has at least one fixed-sign solution.     

Some new nonlinear inequalities and applications to boundary value problems

In this paper, we establish some new nonlinear integral inequalities of the Gronwall–Bellman–Ou-Iang-type in two variables. These on the one hand generalizes and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of differential equations. We illustrate this by applying our new results to certain boundary value problem.     

O− and OH− chemical ionization of some fatty acid methyl esters and triacylglycerols

O^? and OH^? react with fatty acid methyl esters (FAMES) under chemical ionization conditions both as Bronsted bases to form [M - H]^? and as nucleophiles to form the carboxylate ion RCOO^?. O^? shows a much greater tendency to react as a nucleophile than does OH^?. The [M - H]^? ions fragment by elimination of CH³OH, with unsaturation in certain positions in the fatty acid hydrocarbon chain promoting this elimination for unknown reasons. The reaction of O^? and OH^? with triacylglycerols leads to [M - H]^?, characteristic of the molecular mass, and to carboxylate ions characteristic of the fatty acid(s) present in the lipid. The presence of the three ester functions in the lipids greatly enhances the formation of carboxylate ions compared to the FAMES.     

Multilayers as defect barriers

A multilayer structure consisting of undoped GaAs and AlAs layers was incorporated into a buffer layer on GaAs substrates. This reduces the spreading of impurities from the substrate (e.g. tellurium) into layers deposited on top of the multilayer system as observed by SIMS and C/V profiling. Incorporation coefficients for tellurium in GaAs, AlAs and multilayers were calculated.     

Improved estimation of a covariance matrix in an elliptically contoured matrix distribution

In this paper, the problem of estimating the covariance matrix of the elliptically contoured distribution (ECD) is considered. A new class of estimators which shrink the eigenvalues towards their arithmetic mean is proposed. It is shown that this new estimator dominates the unbiased estimator under the squared error loss function. Two special classes of ECD, namely, the multivariate-elliptical t distribution and the ε-contaminated normal distribution are considered. A simulation study is carried out and indicates that this new shrinkage estimator provides a substantial improvement in risk under most situations.