In this study, we analyze how vitamin D (VD) serum levels flow with latitude and throughout seasons of the year within a population sample over three years, taking into account that VD is mainly photosynthesized in the skin from sun exposure. Vitamin D levels have been measured in 80,763 patients during 2013, 2014, and 2015. To accomplish the objectives, we first perform some inference tests like two-way Analysis of Variance (ANOVA) followed by post-hoc tests. Secondly, we develop time series techniques including cross correlation calculations. Least than 10% of the sample had healthy VD levels, which should be a fact of public health major concern. The effect of the interaction between the two factors, zones and seasons, was proved by ANOVA. The mean values which are significantly different were determined by post hoc test. Furthermore, we find that mean serum VD levels, measured as 25-hydroxy-VD, follow a seasonal lag pattern of 9 weeks, a delay for minimum and maximum values after the respective equinoxes and daily sunlight duration. Reliable estimates of the population are provided in the present study, since one of the strengths is its huge sample size. We have quantitatively characterized the seasonality of serum vitamin D levels in the Argentine and the seasonal lag pattern has been determined for the study region.

The Generalized Markov Fluid Model (GMFM), introduced in [1], is assumed for modeling sources in the network because it is versatile to describe the traffic fluctuations. In order to estimate resources allocations or in other words the channel occupation of each source, the concept of effective bandwidth proposed by Kelly [2] is used. In this paper, we present a formula for calculating the effective bandwidth, developed for the Generalized Markovian Flow model, which is of particular interest because it allows expressing said magnitude depending on the parameters of the model. We present unbiased estimators for these parameters that can be obtained from real data. The convergence and the consistency of the estimation are studied, and confidence bands are found. Illustrative calculation and performance of the proposed estimators were tested with simulated data and ideal results were obtained.

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The purpose of this work is to apply techniques to estimate the Effective Bandwidth, from traffic traces, for the Generalized Markov Fluid Model in data networks. This model is assumed because it is versatile in describing traffic fluctuations. The concept of Effective Bandwidth proposed by Kelly is used to measure the channel occupancy of each source. Since the estimation techniques we will use require prior knowledge of the number of clustering clusters, the Silhouette algorithm is used as a first step to determine the number of classes of the modulating chain involved in the model. Using that optimal number of clusters, the Kernel Estimation and Gaussian Mixture Models techniques are used to estimate the model parameters. After that, the performance of the proposed methods is analyzed using simulated traffic traces generated by Markov Chain Monte Carlo algorithms.

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