Five image processing algorithms are proposed to measure the average orientation, eccentricity and size of cells in images of biological tissue. These properties, which can be embodied by an elliptical ‘composite cell’, are crucial for biomechanical tissue models. To automatically determine these properties is challenging due to the diverse nature of the image data, with tremendous and unpredic...

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...

A graph is a block if its blocks are all cliques. In this paper, we study the average eccentricity of graphs from perspective order sequences. An equivalence relation established under sequence and used to prove lower upper bounds on graphs. The result that 1 1n?34n2?12n?, respectively, where n graph. Finally, devise linear time algorithm calculate sequence.

PURPOSE To study the relationship between cone spacing and density and clinical measures of visual function near the fovea. METHODS High-resolution images of the photoreceptor mosaic were obtained with adaptive optics scanning laser ophthalmoscopy from 26 patients with inherited retinal degenerations. Cone spacing measures were made close to or at the foveal center (mean [SD] eccentricity, 0....

For a vertex v and a (k−1)-element subset P of vertices of a graph, one can define the distance from v to P in various ways, including the minimum, average, and maximum distance from v to P . Associated with each of these distances, one can define the keccentricity of the vertex v as the maximum distance over all P , and the k-eccentricity of the set P as the maximum distance over all v. If k =...

PURPOSE To determine the values in decibels of retinal sensitivity within the central 26 degrees of the visual field of normal subjects divided into homogenous age groups using the Octopus 1-2-3; to compare the values of retinal sensitivity we have found with those considered normal in the statistical package obtained by a multicenter study performed in 1994 with Octopus 201. METHODS 181 subj...

The eccentricity connectivity index of a molecular graph G is defined as (G) = aV(G) deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to other vertices of G and deg(a) is degree of vertex a. Here, we compute this topological index for some infinite classes of dendrimer graphs.

Studies have shown that spatial aftereffects increase with eccentricity. Here, we demonstrate that the shape-frequency and shape-amplitude aftereffects, which describe the perceived shifts in the shape of a sinusoidal-shaped contour following adaptation to a slightly different sinusoidal-shaped contour, also increase with eccentricity. Why does this happen? We first demonstrate that the percept...

The eccentricity of a vertex is the maximum distance from it to another vertex, and the average eccentricity of a graph is the mean eccentricity of a vertex. In this paper we introduce average edge and average vertex-edge mean eccentricities of a graph. Moreover, relations among these eccentricities for trees are provided as well as formulas for line graphs and cartesian product of graphs. In t...