A protocol for the ranking of interpolation algorithms based on confidence levels

The choice of the best interpolation algorithm of data gathered at a finite number of locations has been a persistently relevant topic. Typical papers take a single data set, a single set of data points, and a handful of algorithms. The process considers a subset I of the data points as known, builds the interpolant with each algorithm, applies it to the points of another subset C, and evaluates the MAE (mean absolute error), the RMSE (root mean square error), or any other metric over such points. The less these statistics are, the better the algorithm is, so a deterministic ranking between methods (without confidence level) can be derived based upon it. Ties between methods are usually not considered. In this article a complete protocol is proposed in order to build, with a modest additional effort, a ranking with a confidence level. To illustrate this point, the results of two tests are shown. In the first one, a simple Monte Carlo experiment was devised using irregularly distributed points taken from a reference DEM (digital elevation model) in raster format. Different metrics led to different rankings, suggesting that the choice of the metric to define the ‘best interpolation algorithm’ would need a trade-off. The second experiment used mean daily radiation data from an international interpolation comparison exercise and RMSE as the metric of success. Only five simple interpolation methods were employed. The ranking using this protocol anticipated correctly the first and second place, afterwards confirmed employing independent control data.     

Learning vector quantization with training data selection

In this paper, we propose a method that selects a subset of the training data points to update LVQ prototypes. The main goal is to conduct the prototypes to converge at a more convenient location, diminishing misclassification errors. The method selects an update set composed by a subset of points considered to be at the risk of being captured by another class prototype. We associate the proposed methodology to a weighted norm, instead of the Euclidean, in order to establish different levels of relevance for the input attributes. The technique was implemented on a controlled experiment and on Web available data sets.     

Group weighted finite transducers

We consider weighted finite transducers over arbitrary groups, that is finite transducers having a counter in which, at any step, a value of the group is stored but no information regarding the content of this counter is available until the computation is finished. The computation is valid if the counter value is the neutral element of the group. We generalize here some results from [8] and [17]. Received: 28 January 2001 / 5 June 2001     

Second-Order Stiffness Matrix and Loading Vector of a Beam-Column with Semirigid Connections on an Elastic Foundation

The second-order stiffness matrix and corresponding loading vector of a prismatic beam–column subjected to a constant axial load and supported on a uniformly distributed elastic foundation (Winkler type) along its span with its ends connected to elastic supports are derived in a classical manner. The stiffness coefficients are expressed in terms of the ballast coefficient of the elastic foundation, applied axial load, support conditions, bending, and shear deformations. These individual parameters may be dropped when the appropriate effect is not considered; therefore, the proposed model captures all the different models of beams and beam–columns including those based on the theories of Bernoulli–Euler, Timoshenko, Rayleigh, and bending and shear.The expressions developed for the load vector are also general for any type or combinations of transverse loads including concentrated and partially nonuniform distributed loads. In addition, the transfer equations necessary to determine the transverse deflections, rotations, shear, and bending moments along the member are also developed and presented.     

Optical, electrical and structural characteristics of Al:ZnO thin films with various thicknesses deposited by DC sputtering at room temperature and annealed in air or vacuum

Transparent and conductive Al-doped ZnO (AZO) films have been grown with various thicknesses between 0.3 and 1.1 μm by magnetron sputtering at room temperature onto soda lime glass substrates. After deposition, the samples have been annealed at temperatures ranging from 150 to 450 °C in air or vacuum. The optical, electrical, and structural characteristics of the AZO coatings have been analyzed as a function of the film thickness and the annealing parameters by spectrophotometry, Hall effect measurements, and X-ray diffraction. As-grown layers are found polycrystalline, with hexagonal structure that shows some elongation of the unit cells along the c-axis, having visible transmittance ∼85-90% and resistivity ∼1.6-2.0 mΩ cm, both parameters slightly decreasing when the film thickness increases. Heating in air or vacuum produces further elongation of the crystalline lattice together with some increase of the visible transmittance and a decrease of the electrical resistance that depends on the heating temperature and atmosphere. The best characteristics have been obtained after treatment in vacuum at 350 °C, where the highest carrier concentrations are achieved, giving visible transmittance ∼90-95% and resistivity ∼0.8-0.9 mΩ cm for the AZO layers with various thicknesses. Some relationships between the analyzed properties have been established, showing the dependence of the lattice distortion, the band gap energy and the mobility on the carrier concentration.     

Improvement of Glycaemia and Endothelial Function by a New Low-Dose Curcuminoid in an Animal Model of Type 2 Diabetes

Curcumin has been suggested as a promising treatment for metabolic diseases, but the high doses required limit its therapeutic use. In this study, a new curcuminoid is synthesised to increase curcumin anti-inflammatory and antioxidant potential and to achieve hypoglycaemic and protective vascular effects in type 2 diabetic rats in a lower dose. In vitro, the anti-inflammatory effect was determined through the Griess reaction, and the antioxidant activity through ABTS and TBARS assays. In vivo, Goto-Kakizaki rats were treated for 2 weeks with the equimolar dose of curcumin (40 mg/kg/day) or curcuminoid (52.4 mg/kg/day). Fasting glycaemia, insulin tolerance, plasma insulin, insulin signalling, serum FFA, endothelial function and several markers of oxidative stress were evaluated. Both compounds presented a significant anti-inflammatory effect. Moreover, the curcuminoid had a marked hypoglycaemic effect, accompanied by higher GLUT4 levels in adipose tissue. Both compounds increased NO-dependent vasorelaxation, but only the curcuminoid exacerbated the response to ascorbic acid, consistent with a higher decrease in vascular oxidative and nitrosative stress. SOD1 and GLO1 levels were increased in EAT and heart, respectively. Altogether, these data suggest that the curcuminoid developed here has more pronounced effects than curcumin in low doses, improving the oxidative stress, endothelial function and glycaemic profile in type 2 diabetes.     

Structural, chemical, and optical properties of tin sulfide thin films as controlled by the growth temperature during co-evaporation and subsequent annealing

Tin sulfide thin films on soda-lime glass substrate were prepared by co-evaporation. This technique uses a vapor phase procedure involving chemical reactions between the precursor species evaporated simultaneously. The influence of the substrate temperature in the crystal structure and chemical composition were determined by X-ray diffraction and energy dispersive analysis of X-rays, showing that thin films crystallized in SnS, SnS₂, and Sn₂S₃ phases. Scanning electron microscope shows thin films with homogenous and uniform surface. Some of the samples were annealed to study the variation of structural, chemical, and optical properties. The variation of refractive index (n), extinction coefficient (k), and dielectric constant (ε) with wavelength and photon energy are reported. The energy band gap was calculated from optical transmittance and reflectance measurements in the range 300–1500 nm. The calculated energy band gap values were between 1.75 and 2.3 eV, depending on the phase in which crystallized the different thin films.