A homological interpretation of the transverse quiver Grassmannians

In recent articles, the investigation of atomic bases in cluster algebras associated to affine quivers led the second-named author to introduce a variety called transverse quiver Grassmannian and the first-named and third-named authors to consider the smooth loci of quiver Grassmannians. In this paper, we prove that, for any affine quiver Q, the transverse quiver Grassmannian of an indecomposable representation M is the set of points N in the quiver Grassmannian of M such that Ext^1(N,M/N)=0. As a corollary we prove that the transverse quiver Grassmannian coincides with the smooth locus of the irreducible components of minimal dimension in the quiver Grassmannian.Comment: final version, 7 pages, corollary 1.2 has been modifie

Linear degenerations of flag varieties: partial flags, defining equations, and group actions

We continue, generalize and expand our study of linear degenerations of flag varieties from Cerulli Irelli et al. (Math Z 287(1–2):615–654, 2017). We realize partial flag varieties as quiver Grassmannians for equi-oriented type A quivers and construct linear degenerations by varying the corresponding quiver representation. We prove that there exists the deepest flat degeneration and the deepest flat irreducible degeneration: the former is the partial analogue of the mf-degenerate flag variety and the latter coincides with the partial PBW-degenerate flag variety. We compute the generating function of the number of orbits in the flat irreducible locus and study the natural family of line bundles on the degenerations from the flat irreducible locus. We also describe explicitly the reduced scheme structure on these degenerations and conjecture that similar results hold for the whole flat locus. Finally, we prove an analogue of the Borel–Weil theorem for the flat irreducible locus

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

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

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

Quadratic differentials as stability conditions

We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using quivers with potential associated to triangulated surfaces. We relate the finite-length trajectories of such quadratic differentials to the stable objects of the corresponding stability condition.Comment: 123 pages; 38 figures. Version 2: hypotheses in the main results mildly weakened, to reflect improved results of Labardini-Fragoso and coauthors. Version 3: minor changes to incorporate referees' suggestions. This version to appear in Publ. Math. de l'IHE

Seizures in autoimmune encephalitis: Findings from an EEG pooled analysis

Purpose: Seizures are common in autoimmune encephalitis (AE), and an extensive work-up is required to exclude alternative etiologies. The aim of our study was to identify possible clinical/EEG peculiarities suggesting the immune-mediated origin of late-onset seizures. Methods: Thirty patients diagnosed with AE (19 men, median age 68 years, 18 seronegative) were included. Overall 212 video-electroencephalographic (EEG) and 31 24-h ambulatory EEG (AEEG) recordings were retrospectively reviewed. Posterior dominant rhythm, interictal epileptiform discharges (IEDs), clinical (CSs) and subclinical seizures (SCSs) were analyzed. Results: Six-hundred-nineteen ictal events were recorded in 19/30 subjects, mostly (568/619) during AE acute stage. Among ten patients with CSs other than faciobrachial dystonic seizures, 7 showed prominent autonomic and emotional manifestations. SCSs were detected in 11 subjects, mainly via AEEG (260/287 SCSs vs 150/332 CSs, p < 0.001). Eight patients presented seizures during hyperventilation. IEDs, documented in 21 cases, were bilateral in 14 and focal temporal in 13. Multiple ictal EEG patterns were detected in 9/19 patients, 6 of whom had both CSs and SCSs, bilateral asynchronous seizures and ictal activities arising from temporal and extra-temporal regions. No correlation was found between the lateralization of MRI alterations and that of EEG findings. Conclusion: Our study confirms that adult-onset, high frequency focal seizures with prominent autonomic and emotional manifestations should be investigated for AE. Multiple ictal EEG patterns could represent a ‘red flag’, reflecting a widespread neuronal excitability related to the underlying immune-mediated process. Finally, our work enhances the crucial role of long-lasting EEG monitoring in revealing subclinical and relapsing seizures

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

factors underlying the development of chronic temporal lobe epilepsy in autoimmune encephalitis

Abstract Purpose Limbic encephalitis (LE) is an autoimmune condition characterized by amnestic syndrome, psychiatric features and seizures. Early diagnosis and prompt treatment are crucial to avoid long-term sequelae, including psycho-cognitive deficits and persisting seizures. The aim of our study was to analyze the characteristics of 33 LE patients in order to identify possible prognostic factors associated with the development of chronic epilepsy. Methods This is a retrospective cohort study including adult patients diagnosed with LE in the period 2010–2017 and followed up for ≥12 months. Demographics, seizure semiology, EEG pattern, MRI features, CSF/serum findings were reviewed. Results All 33 LE patients (19 M/14F, mean age 61.2 years) presented seizures. Thirty subjects had memory deficits; 22 presented behavioural/mood disorders. Serum and/or CSF auto-antibodies were detected in 12 patients. In 31 subjects brain MRI at onset showed typical alterations involving temporal lobes. All patients received immunotherapy. At follow-up, 13/33 had developed chronic epilepsy; predisposing factors included delay in diagnosis (p = .009), low seizure frequency at onset (p = .02), absence of amnestic syndrome (p = .02) and absence/rarity of inter-ictal epileptic discharges on EEG (p = .06). Conclusions LE with paucisymptomatic electro-clinical presentation seemed to be associated to chronic epilepsy more than LE presenting with definite and severe "limbic syndrome"

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