conclusions we explain embryologic origin, differential diagnosis, other associated anomalies and its treatment by reviewing literature. introduction midline cleft of mandible, classified as tessier 30 clefts is extremely rare, with less than 100 reported cases in the latest studies. variations in severity and associated malformations have been reported before. case presentation in this report,...

in this paper we study finding the $(k,l)$-core problem on a tree which the vertices have positive or negative weights. let $t=(v,e)$ be a tree. the $(k,l)$-core of $t$ is a subtree with at most $k$ leaves and with a diameter of at most $l$ which the sum of the weighted distances from all vertices to this subtree is minimized. we show that, when the sum of the weights of vertices is negative, t...

In this paper, we introduce a new mesh filtering method: a mesh median filter. This is an application of the median filter to smoothen 3-D noisy shapes given by triangle meshes. An algorithm of the mesh median filter is realized by applying the median filter to face normals on triangle meshes and updating mesh vertex positions to make them fit to the filtered normals. As an advanced modificatio...

Ensemble clustering is a recently evolving research direction in cluster analysis and has found several different application domains. In this work the complex ensemble clustering problem is reduced to the well-known Euclidean median problem by clustering embedding in vector spaces. The Euclidean median problem is solved by the Weiszfeld algorithm and an inverse transformation maps the Euclidea...

A profile π = (x1, ..., xk), of length k, in a finite connected graph G is a sequence of vertices of G, with repetitions allowed. A median x of π is a vertex for which the sum of the distances from x to the vertices in the profile is minimum. The median function finds the set of all medians of a profile. Medians are important in location theory and consensus theory. A median graph is a graph fo...

The median problem seeks a permutation whose total distance to a given set of permutations (the base set) is minimal. This is an important problem in comparative genomics and has been studied for several distance measures such as reversals. The transposition distance is less relevant biologically, but it has been shown that it behaves similarly to the most important biological distances, and ca...

Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of G × P3 is median if and only if G is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form G ×K2 are proved, and it is shown that the only nonb...