Human mandibular premolars have earned the reputation for having an extremely complex root and root canal morphology. The incidence of multiple roots and canals in mandibular second premolars is lower than those in mandibular first premolars. Mandibular second premolars with three root canals and separate foramina are very rare. In this case report, endodontic management of a three-rooted mandi...

The vast majority of mandibular second molars have two roots with three root canals; however, variations in molar root canal anatomy are not uncommon. To the best of our knowledge, four rooted mandibular second molar with three mesial roots and one distal root has never been reported. Herein, we present the endodontic management of a four rooted mandibular second molar tooth, diagnosed with the...

The aim of this paper is to give a complete picture of approximability for two tree consensus problems which are of particular interest in computational biology: Maximum Agreement SubTree (MAST) and Maximum Compatible Tree (MCT). Both problems take as input a label set and a collection of trees whose leaf sets are each bijectively labeled with the label set. Define the size of a tree as the num...

A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary trees on four leaves. We give exact algorithms constructing rooted and unrooted maximum consistent supertrees in time O(2nm log m) for a set of m triplets (qua...

In this paper, we develop a method to find Chung-Feller extensions for three kinds of different rooted lattice paths and prove Chung-Feller theorems for such lattice paths. In particular, we compute a generating function S(z) of a sequence formed by rooted lattice paths. We give combinatorial interpretations to the function of Chung-Feller type S(z)−yS(yz) 1−y for the generating function S(z). ...

Given a set R of rooted phylogenetic trees on overlapping taxa, it takes polynomial time to decide whether or not there exists a rooted phylogenetic tree that is compatible with R. Since not all evolutionary histories for a set of species can be explained by a single tree, it is natural to ask for the minimum number of rooted phylogenetic trees needed such that each tree in R is compatible with...

Dentigerous cyst is a benign odontogenic cyst associated with the crowns of permanent teeth. It is usually single in occurrence and located in the mandible of middle-aged persons. The teeth commonly affected are in order of frequency, the mandibular third molars, maxillary canines, maxillary third molars and, rarely central incisors. The present case report describes the surgical enucleation of...