Henar Urmeneta

On Complete Convergence for Arrays of Random Elements

Abstract A complete convergence theorem for arrays of rowwise independent random variables was obtained by Kruglov, Volodin, and Hu (Statistics and Probability Letters 2006, 76:1631–1640). In this article, we extend the result to a Banach space without any additional conditions. No assumptions are made concerning the geometry of the underlying Banach space.

On Complete Convergence for Arrays of Random Elements and Variables

Abstract We obtain complete convergence results for arrays of row-wise independent Banach space valued random elements. The main result deals with two cases that usually are considered separately: when no assumptions are made concerning the geometry of the underlying Banach space and when the Banach space is of Rademacher type p.

Effects of reduced levels of sulfite in wine production using mixtures with lysozyme and dimethyl dicarbonate on levels of volatile and biogenic amines

ABSTRACT Sulphur dioxide (SO2) is an important preservative for wine, but its presence in foods can cause allergies and this has given impetus to the research for alternatives. The aim of this study was to reduce levels of sulfite in wine production using mixtures with lysozyme and dimethyl dicarbonate and examine the influence on levels of volatile and biogenic amines. To do so, vinifications were carried out using lysozyme, dimethyl dicarbonate (DMDC) and mixtures of these with SO2 in different concentrations (25 and 50 mg l−1). Results were compared with a control vinification with only SO2 (50 mg l−1). Mixing low concentrations of SO2 with lysozyme and DMDC reduced the concentration of biogenic amines (histamine, tyramine, putrescine, cadaverine, phenylethylamine + spermidine and spermine). In general, the total concentration of volatile amines (dimethylamine, isopropylamine, isobutylamine, pyrrolidine, ethylamine, diethylamine, amylamine and hexylamine) was higher in the sample fermented only with SO2. The concentrations of amines with secondary amino groups (dimethylamine, diethylamine, pyrrolidine) were higher in the sample only fermented with SO2 than those fermented with DMDC and lysozyme or with a mixture of preservatives. When SO2 was the only preservative in wine, total amine concentration (biogenic and volatile amines) was higher than for the rest of the treatments. Lysozyme by itself, and lysozyme mixed with SO2, both reduced the formation of biogenic amines but given the antioxidant activity of SO2 the use of the preservative mixture seems more advisable.

A Note on Complete Convergence for Arrays of Rowwise Independent Banach Space Valued Random Elements

We obtain complete convergence results for arrays of rowwise independent Banach space valued random elements. Compared with similar results presented in the probabilistic literature our conditions are weaker.

Random Riemann Sum estimator versus Monte Carlo

Two estimators of the expectation of a function, the classical based in Monte Carlo sampling method and one based in Random Riemann Sums, are compared. It presents the differences on bias, variance, convergence and mainly convergence rates. Two ways of sampling to obtain a Random Riemann Sum estimator are given. The first one provides a sequence of estimations whose terms are independent, this fact produces a loss of order one in the convergence rate for the strong law compared with Monte Carlo sampling method. The second one is considered in order to improve these results.

Oak wood extracts applied to the grapevine. An alternative to obtain quality Garnacha wines

Stomata in leaves regulate gas interchange and transpiration in the grapevine and through these pores both the penetration of aqueous solutions with nutrients as well as the excretion of products take place. The aim of this work was to study the influence of spraying the vineyard with toasted and untoasted oak extracts on the volatile composition and on the organoleptic quality of wine made from Garnacha grapes. The results were compared with a Garnacha control wine obtained with grapes sprayed with distilled water. The absorption of the compounds from the oak wood extracts was irregular and some of these compounds were modified by the yeast during fermentation so as to prevent fermentation problems. This was observed particularly in the case of furfural which were transformed into furfuryl alcohol by yeast in order to avoid irreversible cellular damage. On applying a discriminant analysis to the concentration of volatile compounds in the wines, the three treatments (control, toasted and untoasted oak extracts) were differentiate. The wine obtained from grapes treated with toasted oak extract showed a more intense wood aroma after 18months of bottle aging than the other wines. Likewise, spicy aromas were found to be more intense in the samples treated with some type of oak wood extracts.

Simulation of household electricity consumption by using Functional Data Analysis

Obtaining patterns for electricity consumption in a particular household is a key issue to simulate and dimension the electricity supply needed in an isolated house. The electricity consumption profile (load curve) of a user is a function that indicates the electrical consumption in a dwelling over a period of time, usually one day. When this function is considered as a datum and several days are observed, a sample of functions is obtained. Functional Data Analysis (FDA) provides procedures and techniques to analyze this kind of data. Specifically, functional linear regression is used to estimate the average daily consumption of electricity for a given household type. Classification of households is carried out by using characteristics of the dwellings and their inhabitants. Nevertheless, the electricity consumption is very variable among different households, even those belonging to the same type. Inhabitant behavior strongly influences energy consumption patterns and is an important factor that accounts for a major share of the observed variability in the household consumption. The error term of the regression model captures this specific variability. In this paper we propose a method for its modeling based on a functional principal component analysis, which captures the homoscedasticity and main variability patterns, followed by fitting a sinusoidal function series to the error remainder. This statistical modeling facilitates the simulation of new individual load curves for any household, depending on the profile of the dwelling and its inhabitants. We illustrate this methodology with a real data set of household consumptions.