Condensate statistics in one-dimensional interacting Bose gases: exact results

Recently, a quantum Monte Carlo method alternative to the path integral Monte Carlo method was developed for solving the N-boson problem; it is based on the stochastic evolution of classical fields. Here we apply it to obtain exact results for the occupation statistics of the condensate mode in a weakly interacting trapped one-dimensional Bose gas. The temperature is varied across the critical region down to temperatures lower than the trap level spacing. We also derive the condensate statistics in the Bogoliubov theory: this reproduces the exact results at low temperature and explains the suppression of odd numbers of noncondensed particles at T approximately 0.     

Evaluation of different warping methods for the analysis of CE profiles of urinary nucleosides

Nowadays, numerous metabolite concentrations can readily be determined in a given biological sample by high-throughput analytical methods. However, such raw analytical data comprise noninformative components due to many disturbances normally occurring in the analyses of biological material. To eliminate those unwanted original analytical data components, advanced chemometric data preprocessing methods might be of help. Here, such methods are applied to electrophoretic nucleoside profiles in urine samples of cancer patients and healthy volunteers. In this study, three warping methods: dynamic time warping (DTW), correlation optimized warping (COW), and parametric time warping (PTW) were examined on two sets of electrophoretic data by means of quality of peaks alignment, time of preprocessing, and way of customization. The application of warping methods helped to limit shifting of peaks and enabled differentiation between whole electropherograms of healthy and cancer patients objectively by a principal component analysis (PCA). The evaluation of preprocessed data and raw data by PC analysis confirms differences between the applied warping tools and proves their suitability in metabonomic data interpretation.     

Algebraic analysis of aggregation‐based multigrid

A convergence analysis of two‐grid methods based on coarsening by (unsmoothed) aggregation is presented. For diagonally dominant symmetric (M‐)matrices, it is shown that the analysis can be conducted locally; that is, the convergence factor can be bounded above by computing separately for each aggregate a parameter, which in some sense measures its quality. The procedure is purely algebraic and can be used to control a posteriori the quality of automatic coarsening algorithms. Assuming the aggregation pattern is sufficiently regular, it is further shown that the resulting bound is asymptotically sharp for a large class of elliptic boundary value problems, including problems with variable and discontinuous coefficients. In particular, the analysis of typical examples shows that the convergence rate is insensitive to discontinuities under some reasonable assumptions on the aggregation scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

Predictive-property-ranked variable reduction in partial least squares modelling with final complexity adapted models: Comparison of properties for ranking

The calibration performance of partial least squares regression for one response (PLS1) can be improved by eliminating uninformative variables. Many variable-reduction methods are based on so-called predictor-variable properties or predictive properties, which are functions of various PLS-model parameters, and which may change during the steps of the variable-reduction process. Recently, a new predictive-property-ranked variable reduction method with final complexity adapted models, denoted as PPRVR-FCAM or simply FCAM, was introduced. It is a backward variable elimination method applied on the predictive-property-ranked variables. The variable number is first reduced, with constant PLS1 model complexity A, until A variables remain, followed by a further decrease in PLS complexity, allowing the final selection of small numbers of variables.     

Similarity analyses of chromatographic herbal fingerprints: A review

Herbal medicines are becoming again more popular in the developed countries because being “natural” and people thus often assume that they are inherently safe. Herbs have also been used worldwide for many centuries in the traditional medicines. The concern of their safety and efficacy has grown since increasing western interest. Herbal materials and their extracts are very complex, often including hundreds of compounds. A thorough understanding of their chemical composition is essential for conducting a safety risk assessment. However, herbal material can show considerable variability. The chemical constituents and their amounts in a herb can be different, due to growing conditions, such as climate and soil, the drying process, the harvest season, etc. Among the analytical methods, chromatographic fingerprinting has been recommended as a potential and reliable methodology for the identification and quality control of herbal medicines. Identification is needed to avoid fraud and adulteration. Currently, analyzing chromatographic herbal fingerprint data sets has become one of the most applied tools in quality assessment of herbal materials. Mostly, the entire chromatographic profiles are used to identify or to evaluate the quality of the herbs investigated. Occasionally only a limited number of compounds are considered. One approach to the safety risk assessment is to determine whether the herbal material is substantially equivalent to that which is either readily consumed in the diet, has a history of application or has earlier been commercialized i.e. to what is considered as reference material. In order to help determining substantial equivalence using fingerprint approaches, a quantitative measurement of similarity is required. In this paper, different (dis)similarity approaches, such as (dis)similarity metrics or exploratory analysis approaches applied on herbal medicinal fingerprints, are discussed and illustrated with several case studies.     

Carboxyl terminated polyamide 12 chain extension using a dioxazoline coupling agent

High molar mass Polyester Amide was obtained by coupling reaction of Carboxyl-Terminated Polyamide 12 (CTPA) with a dioxazoline (OO). The analysis of the experimental condition effects on the reaction conversion and the structure of the polymer obtained did not show any particular side reaction. A kinetic study comparing the reactivity of the dioxazoline used with CTPA and decanoic acid (DA) as model reactants showed the equireactivity of the two oxazoline functions and of the acid functions of the CTPA and DA. A kinetic model was proposed. The reaction rate at different temperatures and the activation energy were calculated. The evolution of the different reactant concentrations were modeled and compared with experimental data. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3697–3705, 1997     

Novel styrene-butadiene block copolymers by sequential and statistical copolymerization of corresponding macromonomers

This paper concerns the synthesis of two different structures of styrene-butadiene block copolymers that were respectively obtained via sequential and statistical ring-opening metathesis copolymerization of norbornene-terminated polystyrene (PS) and polybutadiene (PB) macromonomers. The stimulus for preparing such styrene-butadiene copolymers originates from the observation that phase-separated morphologies in block copolymers not only depend on the respective size of the blocks and the interaction parameter (χ), but also on the topological constraints introduced in the copolymer structure. From the differential scanning calorimetry study that was carried, it can be inferred that the two types of copolymers -prepared by sequential and statistical copolymerization of PS and PB macromonomers respectively- exhibit quite different phase separation behaviors, indicating that they develop distinct equilibrium domain morphologies.     

An all-at-once algebraic multigrid method for finite element discretizations of Stokes problem

We consider numerical solution of finite element discretizations of the Stokes problem. We focus on the transform-then-solve approach, which amounts to first apply a specific algebraic transformation to the linear system of equations arising from the discretization, and then solve the transformed system with an algebraic multigrid method. The approach has recently been applied to finite difference discretizations of the Stokes problem with constant viscosity, and has recommended itself as a robust and competitive solution method. In this work, we examine the extension of the approach to standard finite element discretizations of the Stokes problem, including problems with variable viscosity. The extension relies, on one hand, on the use of the successive over-relaxation method as a multigrid smoother for some finite element schemes. On the other hand, we present strategies that allow us to limit the complexity increase induced by the transformation. Numerical experiments show that for stationary problems our method is competitive compared to a reference solver based on a block diagonal preconditioner and MINRES, and suggest that the transform-then-solve approach is also more robust. In particular, for problems with variable viscosity, the transform-then-solve approach demonstrates significant speed-up with respect to the block diagonal preconditioner. The method is also particularly robust for time-dependent problems whatever the time step size.