Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra

It is shown that the radial part of the Hydrogen Hamiltonian factorizes as the product of two not mutually adjoint first order differential operators plus a complex constant epsilon. The 1-susy approach is used to construct non-hermitian Hamiltonians with hydrogen spectra. Other non-hermitian Hamiltonians are shown to admit an extra `complex energy' at epsilon. New self-adjoint hydrogen-like Hamiltonians are also derived by using a 2-susy transformation with complex conjugate pairs epsilon, (c.c) epsilon.Comment: LaTeX2e file, 13 pages, 6 EPS figures. New references added. The present is a reorganized and simplified versio

Genome-wide association analysis of dementia and its clinical endophenotypes reveal novel loci associated with Alzheimer's disease and three causality networks: The GR@ACE project

INTRODUCTION: Large variability among Alzheimer's disease (AD) cases might impact genetic discoveries and complicate dissection of underlying biological pathways. METHODS: Genome Research at Fundacio ACE (GR@ACE) is a genome-wide study of dementia and its clinical endophenotypes, defined based on AD's clinical certainty and vascular burden. We assessed the impact of known AD loci across endophenotypes to generate loci categories. We incorporated gene coexpression data and conducted pathway analysis per category. Finally, to evaluate the effect of heterogeneity in genetic studies, GR@ACE series were meta-analyzed with additional genome-wide association study data sets. RESULTS: We classified known AD loci into three categories, which might reflect the disease clinical heterogeneity. Vascular processes were only detected as a causal mechanism in probable AD. The meta-analysis strategy revealed the ANKRD31-rs4704171 and NDUFAF6-rs10098778 and confirmed SCIMP-rs7225151 and CD33-rs3865444. DISCUSSION: The regulation of vasculature is a prominent causal component of probable AD. GR@ACE meta-analysis revealed novel AD genetic signals, strongly driven by the presence of clinical heterogeneity in the AD series