Borel Degenerations of Arithmetically Cohen-Macaulay curves in P^3

We investigate Borel ideals on the Hilbert scheme components of arithmetically Cohen-Macaulay (ACM) codimension two schemes in P^n. We give a basic necessary criterion for a Borel ideal to be on such a component. Then considering ACM curves in P^3 on a quadric we compute in several examples all the Borel ideals on their Hilbert scheme component. Based on this we conjecture which Borel ideals are on such a component, and for a range of Borel ideals we prove that they are on the component.Comment: 20 pages, shorter and more effective versio

Evaluation of the impact of heat-wave on distribution system resilience

This paper addresses the impact of heat waves on a real urban distribution system. A data-driven methodology is proposed to simulate the portion of faults that can be associated to normal conditions (and hence to reliability) and the portion correlated to the heat wave occurrence. Based on real data collected in the years 2012-2017, the fault rates associated to reliability and resilience have been calculated and then used to feed a Monte Carlo simulation aiming to manage the uncertainty in the fault occurrence. Finally, based on the Italian legislation, the avoided costs deriving by the substitution of the faulted portion of the system have been calculated. The results show the different nature of reliability and resilience in terms of empirical cumulative curve, suggesting the necessity of using a stochastic-based methodology within regulatory frameworks, especially in case of output-based regulation

Unusual Presentation of Localized Gastric Mucosa-Associated Lymphoid Tissue Lymphoma Mimicking Poorly Differentiated Gastric Adenocarcinoma

The risk of misdiagnosing neoplastic cells typically infiltrating an epithelium forming a lymphoepithelial lesion as poorly differentiated gastric cancer in endoscopic biopsies, particularly in low-grade mucosa-associated lymphoid tissue (MALT) lymphomas, is described. A 76-year-old woman was referred for management of a poorly differentiated gastric adenocarcinoma. Diagnostic endoscopy in our unit showed a 2 cm raised, submucosal lesion with central erosion in the upper body of the stomach, but repeat biopsies of the lesion were interpreted as inflamed gastric mucosa and negative for malignancy. Systematic gastric biopsies to rule out any foci of MALT lymphoma changes were also negative. Therefore, endoscopic submucosal dissection was performed to obtain an accurate specimen. Histology revealed centrocyte-like cells and a lymphoepithelial lesion invading into the mucosa with obliteration of the gastric glands, which was initially interpreted as poorly differentiated adenocarcinoma

Congruences of lines in P5\mathbb{P}^5, quadratic normality, and completely exceptional Monge-Amp\`ere equations

The existence is proved of two new families of locally Cohen-Macaulay sextic threefolds in $\mathbb{P}^5$, which are not quadratically normal. These threefolds arise naturally in the realm of first order congruences of lines as focal loci and in the study of the completely exceptional Monge-Amp\`ere equations. One of these families comes from a smooth congruence of multidegree $(1,3,3)$ which is a smooth Fano fourfold of index two and genus 9.Comment: 16 page