Informational entropy : a failure tolerance and reliability surrogate for water distribution networks

Evolutionary algorithms are used widely in optimization studies on water distribution networks. The optimization algorithms use simulation models that analyse the networks under various operating conditions. The solution process typically involves cost minimization along with reliability constraints that ensure reasonably satisfactory performance under abnormal operating conditions also. Flow entropy has been employed previously as a surrogate reliability measure. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. This paper describes a multi-objective genetic algorithm that maximizes the flow entropy under multiple operating conditions for any given network. The new methodology proposed is consistent with the maximum entropy formalism that requires active consideration of all the relevant information. Furthermore, an alternative but equivalent flow entropy model that emphasizes the relative uniformity of the nodal demands is described. The flow entropy of water distribution networks under multiple operating conditions is discussed with reference to the joint entropy of multiple probability spaces, which provides the theoretical foundation for the optimization methodology proposed. Besides the rationale, results are included that show that the most robust or failure-tolerant solutions are achieved by maximizing the sum of the entropies

Frequency of root fenestration in a Greek subpopulation: A cone beam computed tomography clinical study

This cone beam computed tomography (CBCT) study aimed to assess the root fenestration (RF) frequency in healthy, intact teeth and analyse their features in a Greek subpopulation. 432 CBCT scans were examined. 5486 teeth were evaluated for RF prevalence. RF prevalence and distribution were recorded for each jaw, tooth group, as well as patient age and sex. RF symmetry, distribution to the affected root surface and the effects of age and sex were evaluated. The prevalence of RF ranged from 0.57% (central incisors) to 7.18% (first premolars) and from 0.48% (second premolars) to 10.79% (lateral incisors) for the maxilla and the mandible, respectively. No symmetrical occurrence of RF was detected. Most RF patients presented one or two defects in both jaws. Types I and IV were the most prevalent in the maxilla, while Types III, II and V were the most prevalent in the mandible. No statistical difference was detected between different sexes and age groups (P > 0.05). © 2021 Australian Society of Endodontology In

Computerized 3-D reconstruction of two “double teeth”

"Double teeth" is a root malformation in the dentition and the purpose of this study was to reconstruct three-dimensionally the external and internal morphology of two "double teeth". The first set of "double teeth" was formed by the conjunction of a mandibular molar and a premolar, and the second by a conjunction of a maxillary molar and a supernumerary tooth. The process of 3-D reconstruction included serial cross-sectioning, photographs of the sections, digitization of the photographs, extraction of the boundaries of interest for each section, surface representation using triangulation and, finally, surface rendering using photorealistic effects. The resulting three-dimensional representations of the two teeth helped us visualize their external and internal anatomy. The results showed: a) in the first case, fusion of the radical and coronal dentin, as well as fusion of the pulp chambers; and b) in the second case, fusion only of the radical dentin and the pulp chambers