Uncertainty quantification for kinetic models in socio-economic and life sciences

Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronization phenomena in biological systems and lane formation in pedestrian traffic. The construction of kinetic models describing the above processes, however, has to face the difficulty of the lack of fundamental principles since physical forces are replaced by empirical social forces. These empirical forces are typically constructed with the aim to reproduce qualitatively the observed system behaviors, like the emergence of social structures, and are at best known in terms of statistical information of the modeling parameters. For this reason the presence of random inputs characterizing the parameters uncertainty should be considered as an essential feature in the modeling process. In this survey we introduce several examples of such kinetic models, that are mathematically described by nonlinear Vlasov and Fokker--Planck equations, and present different numerical approaches for uncertainty quantification which preserve the main features of the kinetic solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic Equations

A comparative scanning electron microscopy evaluation of smear layer removal with apple vinegar and sodium hypochlorite associated with EDTA

OBJECTIVE: The purpose of this study was to evaluate by scanning electron microscopy (SEM) the removal of smear layer from the middle and apical root thirds after use of different irrigating solutions. MATERIAL AND METHODS: Forty roots of permanent human teeth had their canals instrumented and were randomly assigned to 4 groups (n=10), according to the irrigating solution: apple vinegar (group A), apple vinegar finished with 17% ethylenediaminetetraacetic acid (EDTA) (group B), 1% sodium hypochlorite (NaOCl) finished with 17% EDTA (group C) and saline (group D - control). After chemomechanical preparation, the roots were cleaved longitudinally and their middle and apical thirds were examined by SEM at ×1,000 magnification. Two calibrated examiners (kappa=0.92) analyzed the SEM micrographs qualitatively attributing scores that indicated the efficacy of the solutions in removing the smear layer from the surface of the dentin tubules (1 - poor, 2 - good and 3 - excellent). Data from the control and experimental groups were analyzed by the Kruskal-Wallis and Dunn's test, while the Wilcoxon test was used to compare the middle and apical thirds of the canals within the same group (a=0.05). RESULTS: The middle third presented less amount of smear layer than the apical third, regardless of the irrigant. There was statistically significant difference (p=0.0402) among the groups in the middle third. In the apical third, the apple vinegar/EDTA group showed the greatest removal of smear layer (p=0.0373). CONCLUSION: Apple vinegar associated or not with EDTA was effective in removing smear layer when used as an endodontic irrigant