The Nori-Hilbert scheme is not smooth for 2-Calabi Yau algebras

Let $k$ be an algebraically closed field of characteristic zero and let $A$ be a finitely generated $k-$algebra. The Nori - Hilbert scheme of $A$, parameterizes left ideals of codimension $n$ in $A,$ and it is well known to be smooth when $A$ is formally smooth. In this paper we will study the Nori - Hilbert scheme for $2-$Calabi Yau algebras. The main examples of these are surface group algebras and preprojective algebras. For the former we show that the Nori-Hilbert scheme is smooth for $n=1$ only, while for the latter we show that the smooth components that contain simple representations are precisely those that only contain simple representation. Under certain conditions we can generalize this last statement to arbitrary $2-$Calabi Yau algebras.Comment: 30 pages, research paper. Accepted for publication in Journal of Noncommutative Geometr

A new family of algebras whose representation schemes are smooth

We give a necessary and sufficient smoothness condition for the scheme parameterizing the n-dimensional representations of a finitely generated associative algebra over an algebraically closed field of characteristic zero. In particular, our result implies that the points M of the above scheme, satisfying Ext^2_A(M,M)=0, are regular. This generalizes well-known results on finite-dimensional algebras to finitely generated algebras

Independência do auditor em Portugal: o estudo teórico e empírico do remotness gap

La independencia en la auditoría es un concepto difícil de definir, se debe insertar en la participación y, por lo tanto, es un concepto históricamente cambiante. La objetividad y la neutralidad en el concepto de independencia en la auditoría y, por tanto, el joint supply audit, aunque validado por la teoría económica pura tiene costos significativos para el auditor y para el mercado, además de representar una amenaza a todos los stakeholders. Por tratarse de un concepto multidimensional, está constantemente en el blanco de los reguladores por su importancia en el eficiente funcionamiento de los mercados financieros. La sociedad exige la independencia, para convertirse en una norma fundamental en la práctica de auditoría

Immune Thrombocytopenia in Antiphospholipid Syndrome: Is It Primary or Secondary?

Antiphospholipid syndrome (APS) is frequently associated with thrombocytopenia, in most cases mild and in the absence of major bleedings. In some patients with a confirmed APS diagnosis, secondary immune thrombocytopenia (ITP) may lead to severe thrombocytopenia with consequent major bleeding. At the same time, the presence of antiphospholipid antibodies (aPL) in patients with a diagnosis of primary ITP has been reported in several studies, although with some specific characteristics especially related to the variety of antigenic targets. Even though it does not enter the APS defining criteria, thrombocytopenia should be regarded as a warning sign of a “high risk” APS and thus thoroughly evaluated. The presence of aPL in patients with ITP should be assessed as well to stratify the risk of paradoxical thrombosis. In detail, besides the high hemorrhagic risk in secondary thrombocytopenia, patients with a co-diagnosis of APS or only antibodies are also at risk of arterial and venous thrombosis. In this narrative review, we discuss the correlation between APS and ITP, the mechanisms behind the above-reported entities, in order to support clinicians to define the most appropriate treatment strategy in these patients, especially when anticoagulant or antiplatelet agents may be needed

Irreversible Electroporation (IRE) for Prostate Cancer (PCa) Treatment: The State of the Art

We evaluated the most recent research from 2000 to 2023 in order to deeply investigate the applications of PCa IRE, first exploring its usage with primary intent and then salvage intent. Finally, we discuss the differences with other focal PCa treatments. In the case of primary-intent IRE, the in-field recurrence is quite low (ranges from 0% to 33%). Urinary continence after the treatment remains high (>86%). Due to several different patients in the studies, the preserved potency varied quite a lot (59–100%). Regarding complications, the highest occurrence rates are for those of Grades I and II (20–77% and 0–29%, respectively). Grade III complications represent less than 7%. Regarding the specific oncological outcomes, both PCa-specific survival and overall survival are 100%. Metastasis-free survival is 99.6%. In a long-term study, the Kaplan–Meier FFS rates reported are 91% at 3 years, 84% at 5 years, and 69% at 8 years. In the single study with salvage-intent IRE, the in-field recurrence was 7%. Urinary continence was still high (93%), but preserved potency was significantly lower than primary-intent IRE patients (23%). In addition, Grade III complications were slightly higher (10.8%). In conclusion, in males with localized low–intermediate-risk prostate cancer, IRE had an excellent safety profile and might have positive results for sexual and urinary function

Overview of the Current Knowledge and Conventional MRI Characteristics of Peri- and Para-Vascular Spaces

Brain spaces around (perivascular spaces) and alongside (paravascular or Virchow–Robin spaces) vessels have gained significant attention in recent years due to the advancements of in vivo imaging tools and to their crucial role in maintaining brain health, contributing to the anatomic foundation of the glymphatic system. In fact, it is widely accepted that peri- and para-vascular spaces function as waste clearance pathways for the brain for materials such as ß-amyloid by allowing exchange between cerebrospinal fluid and interstitial fluid. Visible brain spaces on magnetic resonance imaging are often a normal finding, but they have also been associated with a wide range of neurological and systemic conditions, suggesting their potential as early indicators of intracranial pressure and neurofluid imbalance. Nonetheless, several aspects of these spaces are still controversial. This article offers an overview of the current knowledge and magnetic resonance imaging characteristics of peri- and para-vascular spaces, which can help in daily clinical practice image description and interpretation. This paper is organized into different sections, including the microscopic anatomy of peri- and para-vascular spaces, their associations with pathological and physiological events, and their differential diagnosis