The synchronization of different brain regions is widely observed under both normal and pathological conditions, such as epilepsy. However, the relationship between dynamics these regions, connectivity them, ability to synchronize remains an open question. We investigate problem inter-region in networks Wilson--Cowan/neural field equations with homeostatic plasticity, each which acts a model fo...

This paper surveys the largest eigenvalue distributions appearing in random matrix theory and their application to multivariate statistical analysis.

After proper rescaling and under some technical assumptions, the smallest eigenvalue of a sample covariance matrix with aspect ratio bounded away from 1 converges to the Tracy–Widom distribution. This complements the results on the largest eigenvalue, due to Soshnikov and Péché. PRELIMINARY VERSION

The sharp lower bound of the kth largest positive eigenvalue of a tree T with n vertices, and the sharp lower bound of the positive eigenvalues of such a tree Tare worked out in this study. A conjecture on the sharp bound of the kth eigenvalue of such a T is proved.

Stability parameters for stabilized methods in uids are suggested. The computation of the largest eigenvalue of a generalized eigenvalue problem replaces controversial de nitions of element diameters and inverse estimate constants, used heretofore to compute these stability parameters. The design is employed in the advective-di usive model, incompressible Navier-Stokes equations and the Stokes ...

The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In this paper, we investigate Laplacian spread of graphs, and prove that there exist exactly five types of tricyclic graphs with maximum Laplacian spread among all tricyclic graphs of fixed order.

We calculate the Clarke and Michel-Penot subdifferentials of the function which maps a symmetric matrix to its mth largest eigenvalue. We show these two subdifferentials coincide, and are identical for all choices of index m corresponding to equal eigenvalues. Our approach is via the generalized directional derivatives of the eigenvalue function, thereby completing earlier studies on the classi...

We give several bounds on the second smallest eigenvalue of the weighted Laplacian matrix of a finite graph and on the second largest eigenvalue of its weighted adjacency matrix. We establish relations between the given Cheeger-type bounds here and the known bounds in the literature. We show that one of our bounds is the best Cheeger-type bound available.