Phylogenetic networks are leaf-labeled directed acyclic graphs that are used to describe nontreelike evolutionary histories and are thus a generalization of phylogenetic trees. The hybridization number of a phylogenetic network is the sum of all in-degrees minus the number of nodes plus one. The hybridization number problem takes as input a collection of rooted binary phylogenetic trees and ask...

Complex root canal system with atypical variations is a common finding among mandibular premolars. Endodontic treatment in these teeth may not be successful due to the failure to recognise and treat multiple canals. This paper presents endodontic treatment of a mandibular second premolar with three roots and three canals.

To compare the fracture resistance of immature teeth subjected to apexification with three different bioactive materials. Sixty non-carious, single-rooted premolar straight canals were decoronated at cementoenamel junction, standardizing 13 mm length. After access preparation, accessed #10 K-file followed by biomechanical preparation using Ni-Ti ProTaper Gold rotary files upto F3 and irrigation...

This case report presents treatment of a distally impacted mandibular 2nd premolar having a 90° tilt to the long axis of the tooth. In this 16 year old girl radiological finding described that horizontally impacted mandibular second premolar was positioned below the roots of the mandibular first molar. Due to the abnormal position of impacted premolar, it was planned to be removed surgically. F...

When G is a rooted graph where each edge may independently succeed with probability p, we consider the expected number of vertices in the operational component of G containing the root. This expected value EV (G;p) is a polynomial in p. We present several distinct equivalent formulations of EV (G;p), unifying prior treatments of this topic. We use results on network resilience (introduced by Co...

A mandibular second premolar with four canals is an interesting example of anatomic variations. This report describes a case of a mandibular second premolar with three roots and four canals (one mesiobuccal, two distobuccal and one lingual). The canals were prepared using K-files and irrigated with NaOCl (5.25%) and normal saline as the final irrigant. The canals were filled laterally with gutt...