Simultaneous optimization of shape parameters and weight factors in ensemble of radial basis functions

Radial basis functions (RBFs) are approximate mathematical models that can mimic the behavior of fast changing responses. Different formulations of RBFs can be combined in the form of an ensemble model to improve prediction accuracy. The conventional approach in constructing an RBF ensemble is based on a two-step procedure. In the first step, the optimal values of the shape parameters of each stand-alone RBF model are determined. In the second step, the shape parameters are fixed to these optimal values and the weight factors of each stand-alone RBF model in the ensemble are optimized. In this paper, simultaneous optimization of shape parameters and weight factors is proposed as an alternative to this two-step procedure for further improvement of prediction accuracy. Gaussian, multiquadric and inverse multiquadric RBF formulations are combined in the ensemble model. The efficiency of the proposed method is evaluated through example problems of varying dimensions from two to twelve. It is found that the proposed method improves the prediction accuracy of the ensemble compared to the conventional two-step procedure for the example problems considered.The author gratefully acknowledges the funding provided by The Scientific and Technological Research Council of Turkey (TUBITAK), under award 109M537

In situ Effect of Nanohydroxyapatite Paste in Enamel Teeth Bleaching

Federal University of Para. Department of Restorative Dentistry. Belem, PA, Brazil.Federal University of Para. Department of Restorative Dentistry. Belem, PA, Brazil.Federal University of Para. Department of Restorative Dentistry. Belem, PA, Brazil.Federal University of Para. Department of Restorative Dentistry. Belem, PA, Brazil.Ministério da Saúde. Secretaria de Vigilância em Saúde. Instituto Evandro Chagas. Departamento de Toxicologia. Ananindeua, PA, Brasil.Federal University of Para. Department of Restorative Dentistry. Belem, PA, Brazil.AIM: Evaluate in situ the effect of nanohydroxyapatite paste (nano-HAP) before bleaching with hydrogen peroxide 35% (HP35%) by ion chromatography (IC) Knoop hardness number (KHN) and tristimulus colorimetry (TC). MATERIALS AND METHODS: A total of 60 fragments were obtained from third molars included (3 mm × 3 mm × 3 mm) and the specimens were divided into three groups (n = 20): Gas chromatography (CG) (negative control group) = no bleaching; HP35% (positive control group) = HP35% whitening (whiteness HP35%); nano-HAP = application for 10 minutes before bleaching treatment + HP35%. The specimens were fixed to the volunteers' molars. The KHN and TC were measured before and after bleaching. For IC, the dentin layer was removed, leaving the enamel that was crushed, and autoclaved for chemical quantification (calcium, fluorine, and phosphorus). The results of KHN and TC were analyzed statistically by analysis of variance (ANOVA) followed by Tukey test (p < 0.05). RESULTS: The HP35% group showed reduction of the Ca, F, and P ions. The initial and final KHN mean of the CG and nano-HAP did not differ statistically; however, the group of HP35% did differ statistically. The mean ΔE of the HP35% and nano-HAP groups did not differ statistically from each other. However, they differed from the CG. CONCLUSION: The nano-HAP paste preserved the KHN, promoted the lower loss of Ca and P ions and an increase of F ions when compared with the CG, but did not influence the effectiveness of the bleaching treatment. CLINICAL SIGNIFICANCE: Nano-HA is a biomaterial that has shown positive results in the prevention of deleterious effects on the enamel by the action of the office bleaching treatment