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 quiver Grassmannians and orbit closures for representation-finite algebras

We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective-injective; its endomorphism ring is called the projective quotient algebra. For any representation- nite algebra, we use the projective quotient algebra to construct desingularizations of quiver Grassmannians, orbit closures in representation varieties, and their desingularizations. This generalizes results of Cerulli Irelli, Feigin and Reineke

The potential impact of enhanced hygienic measures during the COVID-19 outbreak on hospital-acquired infections: A pragmatic study in neurological units

Objective: Hospital-acquired infections (HAIs) are frequent complications among acute patients hospitalized in neurological units, especially among those hospitalized for stroke. This study aimed to investigate if enhanced hygienic measures, including the systematic use of personal protective equipment (PPE), determined a decrease in HAI during the recent COVID-19 outbreak in “COVID-free” neurological units. Methods: Patients hospitalized in neurology and stroke units of Policlinico Umberto I Hospital in Rome from March 8, 2020 and discharged prior to May 31, 2020 were included in the study and compared with patients hospitalized during the same period in 2019. Results: A total of 319 patients were included in the study (n = 103 in 2020, n = 216 in 2019). Among patients hospitalized in 2019, the incidence of HAIs was 31.5% (95% confidence interval (CI): 0.25–0.38), compared with 23.3% (95% CI: 0.15–0.32) in 2020 (p = 0.12). Multivariable logistic regression showed that hospitalization during 2020 was independently associated with a lower risk of HAIs (odds ratio: 0.34, 95% CI:0.16–0.71, p = 0.004). Poisson regression models showed that hospitalization during 2020 was also independently associated with both a lower number of HAIs (relative risk [RR]: 0.56, 95% CI:0.38–0.81, p = 0.01) and a lower number of prescribed antibiotics per patient (RR: 0.66, 95% CI: 0.49–0.87, p = 0.02). Conclusion: Our study design provides evidence regarding the impact of stricter hygienic measures, such as increased PPE use, on HAIs. Larger studies are needed to support the extension of preventive measures even after the COVID-19 outbreak in order to limit the occurrence of HAIs

Cluster algebras of type A2(1)A_2^{(1)}

In this paper we study cluster algebras \myAA of type $A_2^{(1)}$. We solve the recurrence relations among the cluster variables (which form a T--system of type $A_2^{(1)}$). We solve the recurrence relations among the coefficients of \myAA (which form a Y--system of type $A_2^{(1)}$). In \myAA there is a natural notion of positivity. We find linear bases \BB of \myAA such that positive linear combinations of elements of \BB coincide with the cone of positive elements. We call these bases \emph{atomic bases} of \myAA. These are the analogue of the "canonical bases" found by Sherman and Zelevinsky in type $A_{1}^{(1)}$. Every atomic basis consists of cluster monomials together with extra elements. We provide explicit expressions for the elements of such bases in every cluster. We prove that the elements of \BB are parameterized by \ZZ^3 via their $\mathbf{g}$--vectors in every cluster. We prove that the denominator vector map in every acyclic seed of \myAA restricts to a bijection between \BB and \ZZ^3. In particular this gives an explicit algorithm to determine the "virtual" canonical decomposition of every element of the root lattice of type $A_2^{(1)}$. We find explicit recurrence relations to express every element of \myAA as linear combinations of elements of \BB.Comment: Latex, 40 pages; Published online in Algebras and Representation Theory, springer, 201

Low energy high angular resolution neutral atom detection by means of micro-shuttering techniques: the BepiColombo SERENA/ELENA sensor

The neutral sensor ELENA (Emitted Low-Energy Neutral Atoms) for the ESA cornerstone BepiColombo mission to Mercury (in the SERENA instrument package) is a new kind of low energetic neutral atoms instrument, mostly devoted to sputtering emission from planetary surfaces, from E ~20 eV up to E~5 keV, within 1-D (2x76 deg). ELENA is a Time-of-Flight (TOF) system, based on oscillating shutter (operated at frequencies up to a 100 kHz) and mechanical gratings: the incoming neutral particles directly impinge upon the entrance with a definite timing (START) and arrive to a STOP detector after a flight path. After a brief dissertation on the achievable scientific objectives, this paper describes the instrument, with the new design techniques approached for the neutral particles identification and the nano-techniques used for designing and manufacturing the nano-structure shuttering core of the ELENA sensor. The expected count-rates, based on the Hermean environment features, are shortly presented and discussed. Such design technologies could be fruitfully exported to different applications for planetary exploration.Comment: 11 page

Sustained seizure freedom with adjunctive brivaracetam in patients with focal onset seizures

The maintenance of seizure control over time is a clinical priority in patients with epilepsy. The aim of this study was to assess the sustained seizure frequency reduction with adjunctive brivaracetam (BRV) in real-world practice. Patients with focal epilepsy prescribed add-on BRV were identified. Study outcomes included sustained seizure freedom and sustained seizure response, defined as a 100% and a ≥50% reduction in baseline seizure frequency that continued without interruption and without BRV withdrawal through the 12-month follow-up. Nine hundred ninety-four patients with a median age of 45 (interquartile range = 32–56) years were included. During the 1-year study period, sustained seizure freedom was achieved by 142 (14.3%) patients, of whom 72 (50.7%) were seizure-free from Day 1 of BRV treatment. Sustained seizure freedom was maintained for ≥6, ≥9, and 12 months by 14.3%, 11.9%, and 7.2% of patients from the study cohort. Sustained seizure response was reached by 383 (38.5%) patients; 236 of 383 (61.6%) achieved sustained ≥50% reduction in seizure frequency by Day 1, 94 of 383 (24.5%) by Month 4, and 53 of 383 (13.8%) by Month 7 up to Month 12. Adjunctive BRV was associated with sustained seizure frequency reduction from the first day of treatment in a subset of patients with uncontrolled focal epilepsy

Principio di legalità e poteri straordinari dell’amministrazione.

Il saggio ha ad oggetto 1’esame dei poteri amministrativi, ordinari e straordinari. In particolare, analizza la specie dei poteri di ordinanza: poteri di ordinanza secondo il diritto amministrativo “comune” e poteri di ordinanza del c.d. diritto dell’emergenza (protezione civile e dintorni), evidenziandone problemi di inquadramento sistematico e di legittimità costituzional