Corner effects on the perturbation of an electric potential

We consider the perturbation of an electric potential due to an insulating inclusion with corners. This perturbation is known to admit a multipole expansion whose coefficients are linear combinations of generalized polarization tensors. We define new geometric factors of a simple planar domain in terms of a conformal mapping associated with the domain. The geometric factors share properties of the generalized polarization tensors and are the Fourier series coefficients of a kind of generalized external angle of the inclusion boundary. Since the generalized external angle contains the Dirac delta singularity at corner points, we can determine the criterion for the existence of corner points on the inclusion boundary in terms of the geometric factors. We illustrate and validate our results with numerical examples computed to a high degree of precision using integral equation techniques, Nystr\"om discretization, and recursively compressed inverse preconditioning.Comment: 25 pages, 6 figure

Protein Kinase C-Regulated Aβ Production and Clearance

Alzheimer's disease (AD) is the most common form of dementia among the elderly population. AD, which is characterized as a disease of cognitive deficits, is mainly associated with an increase of amyloid β-peptide (Aβ) in the brain. A growing body of recent studies suggests that protein kinase C (PKC) promotes the production of the secretory form of amyloid precursor protein (sAPPα) via the activation of α-secretase activity, which reduces the accumulation of pathogenic Aβ levels in the brain. Moreover, activation of PKCα and mitogen-activated protein kinase (MAPK) is known to increase sAPPα. A novel type of PKC, PKCε, activates the Aβ degrading activity of endothelin converting enzyme type 1 (ECE-1), which might be mediated via the MAPK pathway as well. Furthermore, dysregulation of PKC-MAPK signaling is known to increase Aβ levels in the brain, which results in AD phenotypes. Here, we discuss roles of PKC in Aβ production and clearance and its implication in AD

The Determinants of Adult Education and Training Participation in the US: A Machine Learning Approach

This study aims to explore the determinants of adult education and training (AET) participation of working adults. Through random forest analysis, we discovered important factors contributing to AET participation