Distributional Borel Summability of Odd Anharmonic Oscillators

It is proved that the divergent Rayleigh-Schrodinger perturbation expansions for the eigenvalues of any odd anharmonic oscillator are Borel summable in the distributional sense to the resonances naturally associated with the system

Faraday effect revisited: sum rules and convergence issues

This is the third paper of a series revisiting the Faraday effect. The question of the absolute convergence of the sums over the band indices entering the Verdet constant is considered. In general, sum rules and traces per unit volume play an important role in solid state physics, and they give rise to certain convergence problems widely ignored by physicists. We give a complete answer in the case of smooth potentials and formulate an open problem related to less regular perturbations.Comment: Dedicated to the memory of our late friend Pierre Duclos. Accepted for publication in Journal of Physics A: Mathematical and Theoretical

DNA hypermethylation markers of poor outcome in laryngeal cancer

This study examined molecular (DNA hypermethylation), clinical, histopathological, demographical, smoking, and alcohol variables to assess diagnosis (early versus late stage) and prognosis (survival) outcomes in a retrospective primary laryngeal squamous cell carcinoma (LSCC) cohort. The study cohort of 79 primary LSCC was drawn from a multi-ethnic (37% African American), primary care patient population, diagnosed by surgical biopsies in the Henry Ford Health System from 1991 to 2004 and followed from 5 to 18 years (through 2009). Of the 41 variables, univariate risk factors of p < 0.10 were tested in multivariate models (logistic regression (diagnosis) and Cox (survival) models (p < 0.05)). Aberrant methylation of estrogen receptor 1 (ESR1; p = 0.01), race as African American (p = 0.04), and tumor necrosis (extensive; p = 0.02) were independent predictors of late stage LSCC. Independent predictors of poor survival included presence of vascular invasion (p = 0.0009), late stage disease (p = 0.03), and methylation of the hypermethylated in cancer 1 (HIC1) gene (p = 0.0002). Aberrant methylation of ESR1 and HIC1 signified independent markers of poorer outcome. In this multi-ethnic, primary LSCC cohort, race remained a predictor of late stage disease supporting disparate diagnosis outcomes for African American patients with LSCC