Banking risk as an epidemiological model: an optimal control approach

The process of contagiousness spread modelling is well-known in epidemiology. However, the application of spread modelling to banking market is quite recent. In this work, we present a system of ordinary differential equations, simulating data from the largest European banks. Then, an optimal control problem is formulated in order to study the impact of a possible measure of the Central Bank in the economy. The proposed approach enables qualitative specifications of contagion in banking obtainment and an adequate analysis and prognosis within the financial sector development and macroeconomy as a whole. We show that our model describes well the reality of the largest European banks. Simulations were done using MATLAB and BOCOP optimal control solver, and the main results are taken for three distinct scenarios.publishe

Influence of different methods of cervical flaring on establishment of working length Influência de diferentes métodos de ampliação cervical na determinação do comprimento de trabalho

OBJECTIVE: to investigate the influence of three different rotary systems for cervical flaring on establishment of the real working length. MATERIAL AND METHODS: Thirty mandibular first molars were submitted to conventional endodontic access and initial working length measurement, followed by irrigation/suction of the pulp chamber with 5% sodium hypochlorite. Teeth were randomly divided into 3 groups (n=10) and cervical flaring of the mesiobuccal canals were performed using one of the following instrument systems: Group 1 - Gates-Glidden burs; Group 2 - Orifice Openers; Group 3 - La Axxess system. Two subsequent numbers of instruments of each rotary system were used and the final working length was recorded. A digital calyper was used to record the working length, in millimeters, to investigate a possible discrepancy between initial and final measurements. RESULTS: Analysis of variance (Anova) na Tukey test revealed statistical difference between Group 1 and Groups 2 and 3 (p£ 0.05). CONCLUSIONS: all groups presented shorter working length after cervical flaring; groups prepared with instruments La Axxes and Orifice Opener presented the best results among the systems studied.<br>OBJETIVO: determinar a influência de três sistemas distintos de instrumentos rotatórios para alargamento cervical na determinação do comprimento real de trabalho. MATERIAL E MÉTODOS: Trinta primeiros molares inferiores foram submetidos ao acesso endodôntico convencional e odontometria inicial pelo método visual, utilizando-se para irrigação/aspiração da câmara pulpar o hipoclorito de sódio a 5%. Procedeu-se a ampliação cervical dos canais mésio-vestibulares empregando-se diferentes alargadores cervicais. De acordo com o sistema de ampliação cervical empregado, as 30 amostras foram divididas aleatoriamente em 3 grupos de 10 dentes cada. No Grupo 1 as brocas de Gates-Glidden foram utilizadas para a ampliação cervical; no Grupo 2, Orifice Openers foram empregados; e, no Grupo 3, foi usado o sistema La Axxess. Foram utilizadas em ordem crescente, duas numerações do sistema rotatório correspondente a cada grupo e, após, realizou-se a odontometria final. A leitura das duas tomadas odontométricas foi realizada com paquímetro digital, em milímetros, considerando-se duas casas decimais para averiguar a provável discrepância entre ambas as tomadas. RESULTADOS: a análise de variância (ANOVA) e o teste de Tukey (p£ 0,05) demonstraram diferença estatística entre o Grupo 1 e os Grupos 2 e 3. CONCLUSÕES: todos os grupos apresentaram encurtamento do comprimento de trabalho após alargamento cervical; os grupos preparados com instrumentos La Axxes e Orifice Opener apresentaram os melhores resultados