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In this paper, we apply statistical methods for functional data to explore the heterogeneity in the registered number of deaths of COVID-19, over time. The cumulative daily number of deaths in regions across Brazil is treated as continuous curves (functional data). The first stage of the analysis applies clustering methods for functional data to identify and describe potential heterogeneity in the curves and their functional derivatives. The estimated clusters are labeled with different "levels of alert" to identify cities in a possible critical situation. In the second stage of the analysis, we apply a functional quantile regression model for the death curves to explore the associations with functional rates of vaccination and stringency and also with several scalar geographical, socioeconomic and demographic covariates. The proposed model gave a better curve fit at different levels of the cumulative number of deaths when compared to a functional regression model based on ordinary least squares. Our results add to the understanding of the development of COVID-19 death counts.

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Type 1 diabetes mellitus is a disease that affects millions of people around the world. Recent progress in embedded devices has allowed the development of artificial pancreas that can pump insulin subcutaneously to automatically regulate blood glucose levels in diabetic patients. In this work, a Lyapunov-based intelligent controller using artificial neural networks is proposed for application in automated insulin delivery systems. The adoption of an adaptive radial basis function network within the control scheme allows regulation of blood glucose levels without the need for a dynamic model of the system. The proposed model-free approach does not require the patient to inform when they are going to have a meal and is able to deal with inter- and intrapatient variability. To ensure safe operating conditions, the stability of the control law is rigorously addressed through a Lyapunov-like analysis. In silico analysis using virtual patients are provided to demonstrate the effectiveness of the proposed control scheme, showing its ability to maintain normoglycemia in patients with type 1 diabetes mellitus. Three different scenarios were considered: one long- and two short-term simulation studies. In the short-term analyses, 20 virtual patients were simulated for a period of 7 days, with and without prior basal therapy, while in the long-term simulation, 1 virtual patient was assessed over 63 days. The results show that the proposed approach was able to guarantee a time in the range above 95% for the target glycemia in all scenarios studied, which is in fact well above the desirable 70%. Even in the long-term analysis, the intelligent control scheme was able to keep blood glucose metrics within clinical care standards: mean blood glucose of 119.59 mg/dL with standard deviation of 32.02 mg/dL and coefficient of variation of 26.78%, all below the respective reference values.

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The determination of The Radial Basis Function Network centers is an open problem. This work determines the cluster centers by a proposed gradient algorithm, using the information forces acting on each data point. These centers are applied to a Radial Basis Function Network for data classification. A threshold is established based on Information Potential to classify the outliers. The proposed algorithms are analysed based on databases considering the number of clusters, overlap of clusters, noise, and unbalance of cluster sizes. Combined, the threshold, and the centers determined by information forces, show good results in comparison to a similar Network with a k-means clustering algorithm.

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The transition temperatures of nanoscale polymeric films are measured from a leveling experiment where a designed nanostructure is heated from below. Surface tension forces drive the relaxation of the polymeric features, allowing direct measurement of the critical temperature of collapse, Tflow, and indirect measurement of the glass transition temperature, TG. Small-angle X-ray scattering and atomic force microscopy are used to follow the leveling dynamics, whereas a mathematical model for the momentum balance is implemented to extract the viscosity of the polymer film as a function of temperature. Our methodology is illustrated in the context of films of poly(methyl methacrylate) that are patterned via nanoimprint lithography into dense gratings. We study how the glass transition temperature and the critical temperature of collapse vary as a function of the film size and the inclusion of the antiplasticizer, tris(2-chloropropyl) phosphate. The grating periods are varied consistently between 80 and 240 nm, whereas the antiplasticizer concentrations are 1, 3, 5, and 10 wt %. The solution of the momentum balance allows the detailed correlation between stresses, curvature, heating, and shear rates during leveling. We found that both temperatures, TG and Tflow, decrease as the film size decreases or as the concentration of the antiplasticizer increases. In addition, antiplasticizer concentrations between 3 and 5 wt % stabilize the size dependence of Tflow. We show that the nature of the antiplasticizer is effectively to increase the low-temperature viscosity of the film. However, during leveling, the antiplasticized film sustains its curvature, thereby driving a sudden relaxation, once TG is reached, and increasing the possibilities of defects.

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The lack of accurate time-spatial temperature estimators/predictors conditions the safe application of thermal therapies, such as hyperthermia. In this paper, a comparison between a linear and a non-linear class of models for non-invasive temperature prediction in a homogeneous medium, subjected to ultrasound at physiotherapeutic levels is presented. The linear models used were autoregressive with exogenous inputs (ARX) and the non-linear models were radial basis functions neural networks (RBFNN). In order to create and validate the models, an experiment was build to extract in vitro ultrasound RF-lines, as well as its correspondent temperature values. Then, features were extracted from the measured RF-lines and the models were trained and validated. For both the models, the best-fitted structures were selected using the multi-objective genetic algorithm (MOGA), given the enormous number of possible structures. The best RBFNN model presented a maximum absolute predictive error in the validation set five times less than the value presented by the best ARX model. In this work, the best RBFNN reached a maximum absolute error of 0.42 ºC, which is bellow the value pointed as a borderline between an appropriate and an undesired temperature estimator, which is 0.5 ºC. The average error was one order of magnitude less in the RBFNN case, and a less biased estimation was met. In addition, the best RBFNN needed less environmental information(inputs), given the capacity to non-linearly relate the information. The results obtained are encouraging, considering that coherent results should be obtained in a time-spatial modelling schema using RBFNN models.

A falta de estimadores de temperatura espaço-temporais que sejam precisos impede a aplicação segura das terapias térmicas, como por exemplo a hipertermia. Neste artigo é apresentada uma comparação entre uma classe de modelos lineares e uma classe de modelos não lineares, na predição não invasiva de temperatura num meio homogêneo, quando o mesmo é aquecido por ultra-som em níveis usados em fisioterapia. Os modelos lineares considerados foram do tipo auto-regressivo com entradas exógenas (ARX); a nível não-linear foram considerados redes neuronais RBF (RBFNN). Para treinar e validar os modelos foram recolhidas os ecos provenientes do meio, bem como os correspondentes valores de temperatura. Após a colheita de informação, foram extraídas características dos ecos medidos e posteriormente os modelos foram treinados e validados. Para ambas as classes de modelos, as melhores estruturas foram seleccionadas usando um algoritmo genético multi-objectivo (MOGA), devido ao número elevado de estruturas possíveis. O melhor modelo RBFNN apresentou um erro máximo absoluto cinco vezes inferior ao erro máximo absoluto apresentado pelo melhor modelo ARX. Neste trabalho, o melhor modelo RBFNN apresentou um erro máximo absolutode 0,42 ºC, valor este que é inferior ao limite (0,5 ºC) apresentado como sendo a fronteira entre um estimador desejado e um estimador indesejado. O erro médio cometido pelo melhor modelo neuronal é uma ordem de grandeza inferior ao erro médio apresentado pelo melhor modelo linear, obtendo-se deste modo uma estimação menos enviesada no caso das redes neuronais, com menos informação do ambiente (menos entradas) devido ao processamento não-linear dos dados de entrada. Os resultados obtidos são encorajadores, apontando no sentido de se obter bons resultados numa estimação espaço-temporal.

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