Stochastic Order and Generalized Weighted Mean Invariance.

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov-Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

Green Synthesis of Ag Nanoparticles Using Grape Stalk Waste Extract for the Modification of Screen-Printed Electrodes.

The chemical synthesis of silver nanoparticles (Ag-NPs) by using an environmentally friendly methodology for their preparation is presented. Thus, considering that plants possess components that can act as reducing agents and stabilizers in nanoparticles' production, the synthesis of Ag-NPs by using an extract aqueous solution of grape stalk waste as a reducing and capping agent is studied. First, the total polyphenols and reducing sugars contained in the produced extracts at different conditions are characterized. After that, Ag-NPs are synthesized regarding the interaction of Ag ions (from silver nitrate) and the grape stalk extract. The effect of temperature, contact time, extract/metal solution volume ratio and pH solution in the synthesis of metal nanoparticles are also studied. Different sets of nanoparticle samples are characterized by means of Electron Microscopy coupled with Energy Dispersive X-Ray for qualitative chemical identification. Ag-NPs with an average diameter of 27.7 ± 0.6 nm are selected to proof their suitability for sensing purposes. Finally, screen-printed electrodes modified with Ag-NPs are tested for the simultaneous stripping voltammetric determination of Pb(II) and Cd(II). Results indicate good reproducibility, sensitivity and limits of detection around 2.7 µg L-1 for both metal ions.

Some Order Preserving Inequalities for Cross Entropy and Kullback-Leibler Divergence.

Cross entropy and Kullback-Leibler (K-L) divergence are fundamental quantities of information theory, and they are widely used in many fields. Since cross entropy is the negated logarithm of likelihood, minimizing cross entropy is equivalent to maximizing likelihood, and thus, cross entropy is applied for optimization in machine learning. K-L divergence also stands independently as a commonly used metric for measuring the difference between two distributions. In this paper, we introduce new inequalities regarding cross entropy and K-L divergence by using the fact that cross entropy is the negated logarithm of the weighted geometric mean. We first apply the well-known rearrangement inequality, followed by a recent theorem on weighted Kolmogorov means, and, finally, we introduce a new theorem that directly applies to inequalities between K-L divergences. To illustrate our results, we show numerical examples of distributions.

New approach in modeling Cr(VI) sorption onto biomass from metal binary mixtures solutions.

In the last decades Cr(VI) sorption equilibrium and kinetic studies have been carried out using several types of biomasses. However there are few researchers that consider all the simultaneous processes that take place during Cr(VI) sorption (i.e., sorption/reduction of Cr(VI) and simultaneous formation and binding of reduced Cr(III)) when formulating a model that describes the overall sorption process. On the other hand Cr(VI) scarcely exists alone in wastewaters, it is usually found in mixtures with divalent metals. Therefore, the simultaneous removal of Cr(VI) and divalent metals in binary mixtures and the interactive mechanism governing Cr(VI) elimination have gained more and more attention. In the present work, kinetics of Cr(VI) sorption onto exhausted coffee from Cr(VI)-Cu(II) binary mixtures has been studied in a stirred batch reactor. A model including Cr(VI) sorption and reduction, Cr(III) sorption and the effect of the presence of Cu(II) in these processes has been developed and validated. This study constitutes an important advance in modeling Cr(VI) sorption kinetics especially when chromium sorption is in part based on the sorbent capacity of reducing hexavalent chromium and a metal cation is present in the binary mixture.

Biosorbent encapsulation in calcium alginate: Effects of process variables on Cr(VI) removal from solutions.

Selected biosorbents, brewers draff and grape waste, have been encapsulated in calcium alginate beads and used for the removal of Cr(VI) from aqueous solutions. The effects of encapsulation variables, including the type of waste, the percentage of waste in the beads and the curing time of the beads in CaCl2, on the diameters of the beads and Cr(VI) sorption kinetics have been evaluated. In total, 21 different types of beads were produced. The diameters of the beads increased with increasing amounts of encapsulated biomaterial. Beads that contained grape waste were larger than those containing brewers draff. The most efficient beads for Cr(VI) removal were beads that contained 4% (w/w) of grape waste. No significant differences in the kinetics of Cr(VI) sorption were found with respect to the curing time variable in the case of grape waste calcium alginate beads. Statistical analysis confirmed that the type and percentage of waste are the critical parameters influencing the diameters of the beads and Cr(VI) removal. It was proven that the sorption efficiencies of the beads containing draff and grape waste encapsulated under the optimum conditions were much higher than the efficiencies obtained when using both wastes in their native states.

Overestimation and Underestimation Biases in Photon Mapping with Non-Constant Kernels.

This paper presents an analysis of the overestimation bias in common used filtering kernels in the context of photon mapping density estimation. We use the joint distribution of order statistics to calculate the expected value of the estimators of irradiance, and show that the estimator provided by the cone filter is not consistent unless the slope is one (yielding the triangular kernel), and that the Epanechnikov and Silverman kernels are consistent. The Gaussian filter has two different estimation biases: the original normalization constant α underestimates radiance by 46.9 percent, and the use of the kth nearest photon reduces this underestimation slightly. We also show that a new normalization constant for the Gaussian filter together with discarding the contribution of the kth nearest photon in the Gaussian and cone filter estimators produces new, consistent estimators. The specialized differential filter also benefits from the new estimate.

La competencia: El trabajo colaborativo: una oportunidad para incorporar las TIC en la didáctica universitaria. Descripción de la experiencia...

Material que hace referencia a la importancia de las nuevas tecnologías en la transición de las transformaciones que se han operado en el aprendizaje: la web 2.0 y, más recientemente, la web 3.0, que han modificado los conceptos de información y de comunicación y un buen aporte que analiza el concepto de competencias educativas.

A model to describe Cr(VI) kinetics biosorption.

In this work, the effect of pH control on kinetics of Cr(VI) sorption onto grape stalks has been studied. A set of experiments were performed at a constant pH 3+/-0.1 which was assured by means of a Programmable Logic Controller (PLC). In a second set of experiments the initial pH was adjusted to pH 3 and then pH was allowed to freely evolve during the sorption process. Both sets of experiments were carried out at different temperatures within the range 5-50 degrees C. Constant temperature was assured by water recirculation from a thermostatic bath. Results demonstrated that pH has high influence on kinetics only at the lowest temperatures studied. A model based on a complex reaction sequence which takes into account Cr(VI) sorption, reduction of Cr(VI) to Cr(III), sorption of the formed Cr(III) which includes the pH variation during the sorption process has been proposed to model Cr(VI) kinetics sorption onto grape stalk waste. Furthermore, the robustness of the model has been tested.

Modeling of kinetics of Cr(VI) sorption onto grape stalk waste in a stirred batch reactor.

Recently, Cr(VI) removal by grape stalks has been postulated to follow two mechanisms, adsorption and reduction to trivalent chromium. Nevertheless, the rate at which both processes take place and the possible simultaneity of both processes has not been investigated. In this work, kinetics of Cr(VI) sorption onto grape stalk waste has been studied. Experiments were carried out at different temperatures but at a constant pH (3+/-0.1) in a stirred batch reactor. Results showed that three steps take place in the process of Cr(VI) sorption onto grape stalk waste: Cr(VI) sorption, Cr(VI) reduction to Cr(III) and the adsorption of the formed Cr(III). Taking into account the evidences above mentioned, a model has been developed to predict Cr(VI) sorption on grape stalks on the basis of (i) irreversible reduction of Cr(VI) to Cr(III) reaction, whose reaction rate is assumed to be proportional to the Cr(VI) concentration in solution and (ii) adsorption and desorption of Cr(VI) and formed Cr(III) assuming that all the processes follow Langmuir type kinetics. The proposed model fits successfully the kinetic data obtained at different temperatures and describes the kinetics profile of total, hexavalent and trivalent chromium. The proposed model would be helpful for researchers in the field of Cr(VI) biosorption to design and predict the performance of sorption processes.

Removal of lead(II) and cadmium(II) from aqueous solutions using grape stalk waste.

The sorption of lead and cadmium from aqueous solutions by grape stalk waste (a by-product of wine production) was investigated. The effects of the contact time, pH of the solution, ionic medium, initial metal concentration, other metal ions present and ligands were studied in batch experiments at 20 degrees C. Maximum sorption for both metals was found to occur at an initial pH of around 5.5. The equilibrium process was described well by the Langmuir isotherm model, with maximum grape stalk sorption capacities of 0.241 and 0.248 mmol g(-1) for Pb(II) and Cd(II), respectively, at pH around 5.5. Kinetic studies showed good correlation coefficients for a pseudo-second-order kinetic model. The presence of NaCl and NaClO(4) in the solution caused a reduction in Pb and Cd sorption, the latter being more strongly suppressed. The presence of other metals in the uptake process did not affect the removal of Pb, while the Cd uptake was much reduced. HCl or EDTA solutions were able to desorb lead from the grape stalks completely, while an approximately 65% desorption yield was obtained for cadmium. From the results obtained it seems that other mechanisms, such as surface complexation and electrostatic interactions, must be involved in the metal sorption in addition to ion exchange.

Removal of copper and nickel ions from aqueous solutions by grape stalks wastes.

In the present work, the usefulness of grape stalks wastes generated in the wine production process has been investigated for the removal of copper and nickel ions from aqueous solutions. The sorption process was relatively fast and equilibrium was reached after about 60 min of contact. The influence of pH, sodium chloride and metal concentration on metal removal has been studied. Uptake showed a pH-dependent profile. Maximum sorption for both metals was found to occur at around pH 5.5-6.0. An increase of sodium chloride concentration caused a decrease in metal removal. Langmuir isotherms, at pH 6.0, for each metal were used to describe sorption equilibrium data. Maximum uptake obtained was 1.59x10(-4) mol of copper and 1.81x10(-4) mol of nickel per gram of dry sorbent. Sorption of copper and nickel on grape stalks released an equivalent amount of alkaline and alkaline earth metals (K+, Mg2+, Ca2+) and protons, indicating that ionic exchange is predominantly responsible for metal ion uptake. Fourier transform infrared (FTIR) spectrometry analysis indicated that lignin C-O bond might be involved in metal uptake. Equilibrium batch sorption studies were also performed using a two metal system containing (Cu(II)+Ni(II)). In the evaluation of the two metal sorption system performance, single isotherm curves had to be replaced by three-dimensional sorption isotherm surface. In order to describe the isotherm surface mathematically, the extended-Langmuir model was used. Nickel was found to be much more sensitive to the presence of copper than copper is to the presence of nickel.