The local adjacency polynomials can be thought of as a generalization, for all graphs, of (the sums of ) the distance polynomials of distance-regular graphs. The term ``local'' here means that we ``see'' the graph from a given vertex, and it is the price we must pay for speaking of a kind of distance-regularity when the graph is not regular. It is shown that when the value at * (the maximum eig...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

We prove two results for directed strongly regular graphs that have an eigenvalue of multiplicity less than k, the common out-degree of each vertex. The first bounds the size of an independent set, and the second determines an eigenvalue of the subgraph on the out-neighborhood of a vertex. Both lead to new nonexistence results for parameter sets.

PURPOSE To study the variation of cone photoreceptor packing density across the retina in healthy subjects of different ages. METHODS High-resolution adaptive optics scanning laser ophthalmoscope (AOSLO) systems were used to systematically image the retinas of two groups of subjects of different ages. Ten younger subjects (age range, 22-35 years) and 10 older subjects (age range, 50-65 years)...

The targets for saccadic eye movements in natural visual scenes are spatially extended objects, yet saccades land at a single position within them. To characterize the spatial transformation that determines the saccadic goal position within attended objects, we studied saccadic localization of large patterns of random dots. Saccades landed with a high degree of precision near the center-of-grav...

We study a deterministic scale-free network recently proposed by Barabási, Ravasz, and Vicsek. We find that there are two types of nodes: the hub and rim nodes, which form a bipartite structure of the network. We first derive the exact numbers P (k) of nodes with degree k for the hub and rim nodes in each generation of the network, respectively. Using this, we obtain the exact exponents of the ...

The nearly circular (mean eccentricity [Formula: see text]) and coplanar (mean mutual inclination [Formula: see text]) orbits of the solar system planets motivated Kant and Laplace to hypothesize that planets are formed in disks, which has developed into the widely accepted theory of planet formation. The first several hundred extrasolar planets (mostly Jovian) discovered using the radial veloc...

We first establish the relationship between the largest eigenvalue of the Laplacian matrix of a graph and its bipartite density. Then we present lower and upper bounds for the largest Laplacian eigenvalue of a graph in terms of its largest degree and diameter.

To examine the distribution of ERG-activity in the central visual field after local bleaching of the fovea, multifocal electroretinograms were recorded in eight normal volunteers before, during and after recurrent light exposure. During bleaching (90% bleached pigment), the response density (scalar product) of the foveal area (0-2 degrees eccentricity) decreased from 10.7 +/- 3.5 to 4.1 +/- 1.9...