Glioblastoma multiforme (GBM) is the most common primary malignant tumor of the brain with a dismal prognosis. Approximately 30.9% of these primary brain tumors are malignant, with GBM being the most commonly identified malignant histology with an annual-age adjusted incidence rate of 14.7%. The annual age-adjusted incidence for GBM among persons age above 40 years […]

Using spectral frequency analysis and visualization techniques on pediatric electroencephalogram recordings, we identify a method of detecting seizures thirty seconds before seizure onset by identifying significant preictal locations and their respective frequencies within the gamma band of 30 through 100 Hz. Using average log-power differences and visualization techniques to identify significant preictal patterns, intractable seizures […]

Classically, the heat equation on bounded domains, specifically on tori, yield theta functions as solutions. We study a finite analogue of the Poincare upper half-plane, namely, the finite upper half-plane introduced by Terras. Using this case, we investigate the periodicity inherent in the solutions of bounded domains. The solutions involve zonal spherical functions which come […]

Here, we analyze and compare properties of Cayley graphs of permutation graphs called transposition graphs as this family of graphs has better degree and diameter properties than the hypercube. First, the conjugacy class of the permutation group combined with its generators dictates the type of symmetry possessed by their respective Cayley graphs. In addition, the […]