Accuracy of radial basis function interpolation and derivative approximations on 1-D infinite grids

Radial basis function (RBF) interpolation can be very effective for scattered data in any number of dimensions. As one of their many applications, RBFs can provide highly accurate collocation-type numerical solutions to several classes of PDEs. To better understand the accuracy that can be obtained, we survey here derivative approximations based on RBFs using a similar Fourier analysis approach that has become the standard way for assessing the accuracy of finite difference schemes. We find that the accuracy is directly linked to the decay rate, at large arguments, of the (generalized) Fourier transform of the radial function. Three different types of convergence rates can be distinguished as the node density increases – polynomial, spectral, and superspectral, as exemplified, for example, by thin plate splines, multiquadrics, and Gaussians respectively. Bengt Fornberg: The work was supported by NSF grants DMS-9810751 (VIGRE), DMS-0073048 and DMS-0309803.Natasha Flyer: The work was supported by the NSF grant DMS-9810751 (VIGRE).     

Distribution analysis of ultra-high molecular mass poly(ethylene oxide) containing silica particles by size-exclusion chromatography with dual light-scattering and refractometric detection

Two different size-exclusion chromatography (SEC) systems, connected in-line either to a low-angle light scattering (LALS) or to a multiangle light scattering (MALS) detector, are employed for determination of molecular mass distributions (MMD) of poly(ethylene oxide) (PEO) samples having a weight average molecular mass up to eight millions. The detrimental effect of the presence of strongly scattering silica particles in the samples on the light scattering signal can be eliminated using a suitable sample dissolution procedure utilizing silica solubility in aqueous mobile phase. The selection of flow-rate and sample concentration have a large impact on the obtained results. Hydrodynamic retardation phenomena and nonlinearity effects are shown to introduce severe errors in the molecular mass distributions unless flow-rate and sample concentration are kept at sufficiently low levels. Self-compensating ability of the dual detection in flow-rate effects is shown to be the main advantage here. A good agreement between the results obtained using LALS and MALS detection is found provided that a carefully selected angular extrapolation procedure is used in the case of MALS data. Thus, using carefully selected experimental conditions, SEC with light-scattering (LS) and refractometric detection proved to be an efficient technique for MMD characterisation also of ultra-high molecular mass (UHM) PEO polymers.     

Simulation of proliferation of neural stem cells on a surface with emphasis on spatial constraints on cell division

We present Monte Carlo lattice simulations of proliferation of cells on a surface in the situation when the cell-cell adhesion is relatively strong and the cells may form islands and/or flattened hemispheres. The model parameters were chosen to mimic proliferation of adult rat neural stem cells (or, more specifically, adult hippocampal progenitor cells) deposited on polyornithine and laminin coated polystyrene. The results obtained show that the spatial constraints on cell division may result in slowdown of the exponential growth. Depending on the rules used for cell division, this effect may be either nearly negligible or appreciable. In the latter case, the scale of the deviations from the exponential growth is comparable with that observed in our experiments. In the simulations, the slowdown of the growth starts however somewhat earlier and occurs in a less abrupt manner. This seems to indicate that the spatial constraints on division of cells are not the main factor behind the experimentally observed termination of the growth.     

On the structure of the ethylene chlorine complex

An ethylene chlorine complex has been prepared in a nitrogen matrix at 20 K. Its ultraviolet and infrared spectra have been recorded. The results are compared with CNDO/2 calculations of structure. Both infrared data and CNDO calculations favor a C_2v symmetric complex. The CNDO calculations predict that the ClCl bond is orthogonal to the ethylene plane. The infrared data give no evidence for or against this prediction. Photolysis of the complex leads to the formation of 1,2-dichloroethane.     

Enzyme thermistors for process monitoring and control

In today’s biotechnology there is an increasing demand for appropriate analytical systems for process control. At present the most widely used control systems are based on measurements of pH, pO₂, and pCO₂. Such systems do not allow the direct measurement of substrates and products. To overcome this drawback sensors such as enzyme thermistors and enzyme electrodes have been designed and their development into industrial useful sensors for monitoring and controlling is the subject of active research.     

Synthesis of [11C]/(13C)amines via carbonylation followed by reductive amination

Twelve 11C-labelled amines were prepared via 11C-carbonylation followed by reductive amination. The 11C-carbonylation was performed in the presence of tetrakis(triphenylphosphine)palladium using aryl iodides or aryl triflates, [11C]carbon monoxide and phenyl-/methylboronic acid. The [11C]ketones formed in this step were then transformed directly into amines by reductive amination using different amines in the presence of TiCl4 and NaBH3CN. The 11C-labelled amines were obtained with decay-corrected radiochemical yields in the range 2-78%. The radiochemical purity of the isolated products exceeded 98%. (13C)Benzhydryl-phenyl-amine was synthesised and analysed by NMR spectroscopy for confirmation of the labelling position. Specific radioactivity was determined for the same compound. The reference compounds were prepared by reductive amination of ketones using conventional reaction conditions and three of the compounds were novel. The presented approach is a new method for the synthesis of [11C]/(13C)amines.     

Rapid Fluorometric Screening of Antibiotics in Seafood

Simple and rapid fluorometric screening methods have been developed based on the competitive binding between the target and an intercalating fluorophore dye to double-stranded-DNA (dsDNA). In this study, the long-wavelength fluorescente dye TOTO-3 was employed as the indicator. Compounds that interact with dsDNA will affect the binding of TOTO-3 to the nucleic acid thereby changing the fluorescence intensity. The analyte concentration is indirectly determined by the decrease in fluorescence intensity. A fiber optic fluorescence screening system was developed for rapid and convenient sample processing. Lambda DNA (48.5 kb) was chosen as a suitable sensing nucleic acid material. Detection of sulfathiazole and chloramphenicol in shrimps using this method was studied in the range of 0.5–25 ng mL⁻¹ of sulfathiazole and of 1–50 ng mL⁻¹ of chloramphenicol. Detection limits of 0.5 ng mL⁻¹ of sulfathiazole and 1 ng mL⁻¹ of chloramphenicol were achieved. This approach is useful as a routine test in the monitoring of antibiotics in the environment or aquaculture products. The easy operation and the rapid and sensitive detection make this a potential high-throughput screening method.