CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C

A brief overview is given of recent developments and fresh ideas at the intersection of PT and/or CPT-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). We study the consequences of the assumption that the "charge" operator C is represented in a differential-operator form. Besides the freedom allowed by the Hermiticity constraint for the operator CP, encouraging results are obtained in the second-order case. The integrability of intertwining relations proves to match the closure of nonlinear SUSY algebra. In an illustration, our CPT-symmetric SUSY QM leads to non-Hermitian polynomial oscillators with real spectrum which turn out to be PT-asymmetric.Comment: 25 page

Monitoring Endothelin-A Receptor Expression during the Progression of Atherosclerosis

Cardiovascular disease remains the most frequent cause of death worldwide. Atherosclerosis, an underlying cause of cardiovascular disease, is an inflammatory disorder associated with endothelial dysfunction. The endothelin system plays a crucial role in the pathogenesis of endothelial dysfunction and is involved in the development of atherosclerosis. We aimed to reveal the expression levels of the endothelin-A receptor (ETAR) in the course of atherogenesis to reveal possible time frames for targeted imaging and interventions. We used the ApoE−/− mice model and human specimens and evaluated ETAR expression by quantitative rtPCR (qPCR), histology and fluorescence molecular imaging. We found a significant upregulation of ETAR after 22 weeks of high-fat diet in the aortae of ApoE−/− mice. With regard to translation to human disease, we applied the fluorescent probe to fresh explants of human carotid and femoral artery specimens. The findings were correlated with qPCR and histology. While ETAR is upregulated during the progression of early atherosclerosis in the ApoE−/− mouse model, we found that ETAR expression is substantially reduced in advanced human atherosclerotic plaques. Moreover, those expression changes were clearly depicted by fluorescence imaging using our in-house designed ETAR-Cy 5.5 probe confirming its specificity and potential use in future studies