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

On some classes of Lindel\"of Sigma-spaces

We consider special subclasses of the class of Lindel\"of Sigma-spaces obtained by imposing restrictions on the weight of the elements of compact covers that admit countable networks: A space $X$ is in the class $L\Sigma(\leq\kappa)$ if it admits a cover by compact subspaces of weight $\kappa$ and a countable network for the cover. We restrict our attention to $\kappa\leq\omega$. In the case $\kappa=\omega$, the class includes the class of metrizably fibered spaces considered by Tkachuk, and the $P$-approximable spaces considered by Tkacenko. The case $\kappa=1$ corresponds to the spaces of countable network weight, but even the case $\kappa=2$ gives rise to a nontrivial class of spaces. The relation of known classes of compact spaces to these classes is considered. It is shown that not every Corson compact of weight $\aleph_1$ is in the class $L\Sigma(\leq \omega)$, answering a question of Tkachuk. As well, we study whether certain compact spaces in $L\Sigma(\leq\omega)$ have dense metrizable subspaces, partially answering a question of Tkacenko. Other interesting results and examples are obtained, and we conclude the paper with a number of open questions.Comment: 21 pages. to appear in Topology and its Application

Rettungsdienststrukturen neu denken – Ergebnisse der Expertenworkshops „Logistik in der präklinischen Notfallversorgung“ [Rethinking emergency medical services (EMS)—results of an interdisciplinary expert panel on logistics in EMS]

Die rettungsdienstliche Struktur in Deutschland stellt eine Versorgung auf sehr hohem Niveau sicher. Dennoch ist es notwendig, die vorhandenen Strukturen zu überdenken und für die Zukunft zu härten. Nicht nur vor dem Hintergrund stetig steigender Einsatzzahlen, sondern auch wegen der Herausforderungen der Personalgewinnung und der Alterung der Bevölkerung sollten Reformen im Rettungsdienst dringend angegangen werden. Hier kann der Rettungsdienst viel von der Mathematik und gerade vom Bereich „operations research“ lernen. Dieser Fachbereich beschäftigt sich explizit mit der Verbesserung von logistischen Herausforderungen, die der Rettungsdienst ohne Frage ist. In der vorliegenden Arbeit berichten die Autorinnen und Autoren über die ersten Ergebnisse zweier Workshops zum Thema „Logistik in der präklinischen Versorgung“ und möchten damit die Diskussion im Rettungsdienst auf breiter Basis anregen sowie Verbesserungspotenziale und Herausforderungen für die verschiedenen Akteure in der präklinischen Behandlung herausarbeiten, aber auch erste Ideen zu Lösungsansätzen liefern

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

On the uniqueness of promotion operators on tensor products of type A crystals

The affine Dynkin diagram of type $A_n^{(1)}$ has a cyclic symmetry. The analogue of this Dynkin diagram automorphism on the level of crystals is called a promotion operator. In this paper we show that the only irreducible type $A_n$ crystals which admit a promotion operator are the highest weight crystals indexed by rectangles. In addition we prove that on the tensor product of two type $A_n$ crystals labeled by rectangles, there is a single connected promotion operator. We conjecture this to be true for an arbitrary number of tensor factors. Our results are in agreement with Kashiwara's conjecture that all `good' affine crystals are tensor products of Kirillov-Reshetikhin crystals.Comment: 31 pages; 8 figure