We consider extended binary trees and study the common right and left depth of leaf j, where the leaves are labelled from left to right by 0, 1, . . . , n, and the common right and left external pathlength of binary trees of size n. Under the random tree model, i.e., the Catalan model, we characterize the common limiting distribution of the suitably scaled left depth and the difference between ...

We deene a model for heuristic tree search which assumes that the quality of the heuristic used for ordering the successors of a node improves as depth increases. We show that a usual value ordering heuristic for solving constraint satisfaction problems ts to this model. Our model deenes a partial order on the leaf nodes of the search tree, according to their probability to be a solution. We ch...

Aims: Sphenoid sinus is one of the most inaccessible paranasal sinus, and is closely correlated to many vascular and neural structures. Anatomic variation of the sphenoid sinus can complicate surgery in this area. The aim of the present investigation was to define the sphenoid sinus variations and the relevant structures using cone-beam computed tomography (CBCT). Methods: This cross-sectiona...

Introduction: Ectopic tooth eruption may result owing to one of 3 processes: developmentalDisturbance, iatrogenic activity, or pathologic process, such as a tumor or a cyst. In rare cases, occlusion of the sinus ostia may predispose a patient to develop a maxillary sinus mucocele. When the maxillary sinus is invaded, symptoms usually occur late in the process.   Case report: A 17 years old boy...

Introduction: Maxillary sinuses are among the largest paranasal sinuses with various shapes and volumes. The dimensions and volumes of maxillary sinuses play an important role in the surgical treatment plan. The higher levels of pneumatization of alveolar bone lead to the increase of odontogenic sinusitis which cause problems in dental implantation. Therefore, this study aimed to evaluate...

The sensitivity of the near-infrared spectroscopy signal to the brain activation depends on the thickness and structure of the superficial tissues. The influence of the frontal sinus, which is void region in the skull, on the sensitivity to the brain activation is investigated by the time-resolved experiments and the theoretical modelling of the light propagation in the head. In the time-resolv...

CUP-SHAPED COTYLEDON1 (CUC1), CUC2, and CUC3 define the boundary domain around organs in the Arabidopsis thaliana meristem. CUC1 and CUC2 transcripts are targeted by a microRNA (miRNA), miR164, encoded by MIR164A, B, and C. We show that each MIR164 is transcribed to generate a large population of primary miRNAs of variable size with a locally conserved secondary structure around the pre-miRNA. ...

Digital searching is a well-known technique for storing and retrieving information using lexicographical (digital) structure of words. A radix trie (in short: trie) is such a digital search tree that edges are labelled by elements from aa alphabet (e.g., binary alphabet consisting of O’s and l’s) and leaves (external nodes) contain keys [ 1,4,9]. More precisely, in a binary case a key is a (pos...