Degenerate flag varieties: moment graphs and Schr\"oder numbers

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is given by a natural statistics counting the number of diagonal steps in a Schr\"oder path. As an application we obtain a new combinatorial description of the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page

An amphitropic cAMP-binding protein in yeast mitochondria

ABSTRACT: We describe the first example of a mitochondrial protein with a covalently attached phos-phatidylinositol moiety acting as a membrane anchor. The protein can be metabolically labeled with both stearic acid and inositol. The stearic acid label is removed by phospholipase D whereupon the protein with the retained inositol label is released from the membrane. This protein is a cAMP receptor of the yeast Saccharomyces cereuisiae and tightly associated with the inner mitochondrial membrane. However, it is converted into a soluble form during incubation of isolated mitochondria with Ca2+ and phospholipid (or lipid derivatives). This transition requires the action of a proteinaceous, N-ethylmaleimide-sensitive component of the intermembrane space and is accompanied by a decrease in the lipophilicity of the cAMP receptor. We propose that the component of the intermembrane space triggers the amphitropic behavior of the mitochondrial lipid-modified CAMP-binding protein through a phospholipase activity. Only in recent years specific fatty acids have been recog-nized to play important roles in the association of proteins with membranes. Both noncovalent and covalent interactions be-tween fatty acids and proteins have been reported. Among the latter are GTP-binding proteins (Molenaar et al., 1988)

Prevalence and prognostic value of neurological affections in hospitalized patients with moderate to severe COVID-19 based on objective assessments.

Neurological manifestations of coronavirus disease 2019 (COVID-19) have been frequently described. In this prospective study of hospitalized COVID-19 patients without a history of neurological conditions, we aimed to analyze their prevalence and prognostic value based on established, standardized and objective methods. Patients were investigated using a multimodal electrophysiological approach, accompanied by neuropsychological and neurological examinations. Prevalence rates of central (CNS) and peripheral (PNS) nervous system affections were calculated and the relationship between neurological affections and mortality was analyzed using Firth logistic regression models. 184 patients without a history of neurological diseases could be enrolled. High rates of PNS affections were observed (66% of 138 patients receiving electrophysiological PNS examination). CNS affections were less common but still highly prevalent (33% of 139 examined patients). 63% of patients who underwent neuropsychological testing (n = 155) presented cognitive impairment. Logistic regression models revealed pathology in somatosensory evoked potentials as an independent risk factor of mortality (Odds Ratio: 6.10 [1.01-65.13], p = 0.049). We conclude that hospitalized patients with moderate to severe COVID-19 display high rates of PNS and CNS affection, which can be objectively assessed by electrophysiological examination. Electrophysiological assessment may have a prognostic value and could thus be helpful to identify patients at risk for deterioration