The tamed unadjusted Langevin algorithm

In this article, we consider the problem of sampling from a probability measure $\pi$ having a density on ${\mathbb{R}}^d$ proportional to $x?{\mathrm{e}}^{?U\left(x\right)}$. The Euler discretization of the Langevin stochastic differential equation (SDE) is known to be unstable, when the potential $U$ is superlinear. Based on previous works on the taming of superlinear drift coefficients for SDEs, we introduce the Tamed Unadjusted Langevin Algorithm (TULA) and obtain non-asymptotic bounds in $V$-total variation norm and Wasserstein distance of order 2 between the iterates of TULA and $\pi$, as well as weak error bounds. Numerical experiments are presented which support our findings.     

Designer peptide surfactants stabilize diverse functional membrane proteins

Multi-spanning integral membrane proteins, including G-protein coupled receptors (GPCR), ion channels, and ion transporters, comprise a major class of drug targets. However, despite their vital importance, most molecular structures of membrane proteins remain elusive. This is largely due to lack of effective materials and methods to stabilize their functional conformation for sufficient time. Thus finding optimal surfactants and developing new approaches to study fundamental properties of unstable membrane proteins is urgently needed. In this tutorial review we summarize designer peptides with surfactant properties and their usefulness to stabilize membrane proteins. These peptide surfactants present new opportunities for the stabilization and characterization of diverse membrane proteins. Previous studies on the interaction between surfactant peptides and membrane proteins revealed strategies to design new peptides tailor-made for the stabilization of specific proteins. We review examples of solubilization, purification, long-term stabilization of membrane proteins, and the design principles of peptide sequences. We discuss future trends for exploiting spatial features, thermodynamic parameters, and self-assembling properties to create peptide surfactant structures to facilitate the characterization of diverse membrane proteins.     

Comparison of ISO-GUM and Monte Carlo methods for the evaluation of measurement uncertainty: application to direct cadmium measurement in water by GFAAS

The propagation stage of uncertainty evaluation, known as the propagation of distributions, is in most cases approached by the GUM (Guide to the Expression of Uncertainty in Measurement) uncertainty framework which is based on the law of propagation of uncertainty assigned to various input quantities and the characterization of the measurand (output quantity) by a Gaussian or a t-distribution. Recently, a Supplement to the ISO-GUM was prepared by the JCGM (Joint Committee for Guides in Metrology). This Guide gives guidance on propagating probability distributions assigned to various input quantities through a numerical simulation (Monte Carlo Method) and determining a probability distribution for the measurand.In the present work the two approaches were used to estimate the uncertainty of the direct determination of cadmium in water by graphite furnace atomic absorption spectrometry (GFAAS). The expanded uncertainty results (at 95% confidence levels) obtained with the GUM Uncertainty Framework and the Monte Carlo Method at the concentration level of 3.01 μg/L were ±0.20 μg/L and ±0.18 μg/L, respectively. Thus, the GUM Uncertainty Framework slightly overestimates the overall uncertainty by 10%. Even after taking into account additional sources of uncertainty that the GUM Uncertainty Framework considers as negligible, the Monte Carlo gives again the same uncertainty result (±0.18 μg/L). The main source of this difference is the approximation used by the GUM Uncertainty Framework in estimating the standard uncertainty of the calibration curve produced by least squares regression. Although the GUM Uncertainty Framework proves to be adequate in this particular case, generally the Monte Carlo Method has features that avoid the assumptions and the limitations of the GUM Uncertainty Framework.     

Improving the Performance of the Chi-square Control Chart via Runs Rules

The most popular multivariate process monitoring and control procedure used in the industry is the chi-square control chart. As with most Shewhart-type control charts, the major disadvantage of the chi-square control chart, is that it only uses the information contained in the most recently inspected sample; as a consequence, it is not very efficient in detecting gradual or small shifts in the process mean vector. During the last decades, the performance improvement of the chi-square control chart has attracted continuous research interest. In this paper we introduce a simple modification of the chi-square control chart which makes use of the notion of runs to improve the sensitivity of the chart in the case of small and moderate process mean vector shifts.      

The Decomposition of 2,2-Bis(tert-Butylperoxy)-butane under High Pressure

The thermal decomposition of the bifunctional peroxide 2,2-bis(tertbuty1 peroxy)butane was investigated in a flow reactor at temperatures of 135 to 212°C and pressures of up to 2000 bar. The concentration of the peroxide in isododecane was varied between 1 and 22% by weight. The rate of decomposition measured was used to determine the energy of activation (E_A = 151.1 ± 3 kJ/mol) and the activation volume (Δv” = 22.3 mL/mol). Up to a peroxide concentration of 5% by weight, the decomposition takes place according to a firat-order rate equation. Above this concentration, induced decomposition takes effect. Gas chromatographic analysis showed that the liquid decomposition products consisted mainly of acetone and tert-butyl alcohol apart from methyl ethyl ketone, propionic acid methyl ester, acetic acid ethyl ester, tert-butyl methyl ether, and oligomers of the solvent. The gaseous decomposition products consisted of methane and carbon dioxide as well as small quantities of ethane, propane, and ethylene. A theoretical explanation of the mechanism of decomposition is postulated which explains the spectrum of these components and its changes as a function of the peroxide concentration, the residence time, the temperature, and the pressure.     

Optimized 90° Polarization Shift Step Twists for Ku, K and Ka Bands

Optimized models for 90° polarization shift step twists for Ku, K and Ka bands are presented. The cross-section of the waveguide employed is similar to that of a rectangular one, with the difference that the walls of the shorter side are part of a circular one with the proper diameter. The optimized models have been found using the CST Microwave Studio simulation tool and in all cases the return loss is kept below -20 dB for a wide range of frequency spectrum. Two examples are given, one for Ku band and the other for K and Ka ones.     

On the student evaluation of university courses and faculty members’ teaching performance

Trying to determine higher education quality, one gets quickly to one of its significant dimensions, namely the quality of faculty members’ teaching. The latter and, overall, the quality of any university course should be certainly evaluated by their recipients, namely students. In this paper we develop a statistical framework based on Statistical Quality Control mainly, which can be used in order to exploit student evaluations as much as possible. More specifically we present two directions of data monitoring and analysis; the one uses control charts and the other hypotheses testing. The results that can be raised through both directions are crucial for any decision maker.