Quantitative isoperimetric inequalities in H^n

In the Heisenberg group H^n, we prove quantitative isoperimetric inequalities for Pansu's spheres, that are known to be isoperimetric under various assumptions. The inequalities are shown for suitably restricted classes of competing sets and the proof relies on the construction of sub-calibrations

Il problema isoperimetrico in spazi di Carnot-Carathéodory

We present some recent results obtained on the isoperimetric problem in a class of Carnot-Carathéodory spaces, related to the Heisenberg group. This is the framework of Pansu’s conjecture about the shape of isoperimetric sets. Two different approaches are considered. On one hand we describe the isoperimetric problem in Grushin spaces, under a symmetry assumption that depends on the dimension and we provide a classification of isoperimetric sets for special dimensions. On the other hand, we present some results about the isoperimetric problem in a family of Riemannian manifolds approximating the Heisenberg group. In this context we study constant mean curvature surfaces. Inspired by Abresch and Rosenberg techniques on holomorphic quadratic differentials, we classify isoperimetric sets under a topological assumption.Presentiamo risultati recenti ottenuti sul problema isoperimetrico in spazi di Carnot-Carathéodory legati al gruppo di Heisenberg. Questo è il contesto della congettura di Pansu sulla forma degli insiemi isoperimetrici. Presentiamo due diversi approcci. Da un lato, descriviamo il problema isoperimetrico negli spazi di Grushin, sotto un’ipotesi di simmetria che dipende dalla dimensione. In questo contesto, forniamo una classificazione degli insiemi isoperimetrici, valida per specifiche dimensioni. Dall’altro lato, presentiamo alcuni risultati sul problema isoperimetrico in una famiglia di varietà Riemanniane che approssimano il gruppo di Heisenberg. In questo contesto, studiamo superfici a curvatura media costante. Ispirati dalle tecniche di Abresch and Rosenberg sui differenziali quadratici olomorfi, classifichiamo gli insiemi isoperimetrici sotto un’ipotesi topologica

Bovine herpesvirus 4 Immediate Early II gene is essential and can be duplicated

Bovine herpesvirus 4 (BoHV-4) is a virus with a worldwide distribution in cattle population that has been isolated from a lot of different tissues and samples from animal with various clinical manifestations, ranging from conjunctivitis, ocular discharge and genital diseases as post-partum metritis or abortion, but even in apparently healthy animal. Even if a clear correlation between BoHV-4 and any pathologies has never been demonstrated; BoHV-4 is most consistently associated with metritis, a very common postpartum disease of the uterus, in which the role of BoHV-4 as a secondary pathogen is well documented. BoHV-4 has a well known tropism for endometrial stromal and epithelial cells, in which causes non-apoptotic cell death and de novo virus production associated with an increased prostaglandin-endoperoxide synthase 2 protein, cyclo-ossigenase 2 (COX2) and prostaglandin E2 production and secretion from stromal cell. BoHV-4 activation and replication in the bovine endometrium is associated with the early transactivation of the BoHV-4 IE2 gene promoter from endometrial cells. BoHV-4 IE2 gene promoter transactivation and viral replication were associated also with extracellular stimuli belonging to the intrauterine microenvironment such as E. coli LPS and PGE. A model that fits well endometrial BoHV-4 disease is described in literature, involving a vicious circle comprising of bacterial endometritis leading to secretion of PGE, then PGE and LPS stimulating virus replication, which causes further endometrial tissue damage and inflammation. The existence of a virus patho-biotype causing uterine disease appears possible; virus strain adaptation to an organ, tissue or cell type is infact a very important issue for the study of pathology, even because the function of most of the viral genes remains still unknown. In this study a BoHV-4 strain was isolated from the uterus of a persistently infected cow affected with non-responsive post-partum metritis and designated BoHV-4-U. After the characterization this uterine strain was cloned as a bacterial artificial chromosome (BAC) to easily manipulate and study the viral genome. The feasibility of using BoHV-4-U for mutagenesis was demonstrated using the BAC recombineering system, that allows to study single or multiple gene disruptions, opening the way to the clarification of the interactions between BoHV-4 infection and the host endometrial cells. After the generation of the BAC-BoHV-4-U the first gene we decided to investigate was the ORF50/Rta gene, that has been shown to be an essential gene for DNA replication and latency reactivation in many gammaherpesviruses. Although the BoHV-4 ORF50/Rta homolog, immediate early gene 2 (IE2), has been shown to activate several BoHV-4 early and late promoters in co-transfection assays, there is no direct proof of its real indispensability for progression of the virus to the lytic replication cycle in the context of the viral genome. Through different strategies the ORF50 gene was interrupted generating before some mutants, replication defective BoHV-4-V.test /IE2 mutants, as a control viruses, and then some BoHV-4-U/IE2 mutants. The BoHV-4-V.test/IE2 mutants was efficiently rescued, with respect to the production of infectious virus and DNA replication, upon the expression of the BoHV-4 ORF50/Rta protein in trans by different complementing cell lines; the BoHV-4-U/IE2 mutants surprisingly were all able to growth, even in non-complementing cell lines. The generation of a suitable probe led to discover that the IE2 gene is duplicated in the genome of BoHV-4-U. These data demonstrated that in BoHV-4, too, ORF50/Rta is the master replication switch gene and, that can be duplicated in some strains, as in our uterine strain. The deletion of the second gene copy of BoHV-4-U Rta unable the virus the capacity to replicate, and this inability was completely complemented by the in trans expression of ORF50/Rta. The generation of this completely replication un-competent virus maybe will provide a new powerful tool for recombinant vaccine production, even in respect to the rescue of the virus through the expression, under a strictly inducible promoter, of the Rta protein

The isoperimetric problem for regular and crystalline norms in H1\mathbb H^1

We study the isoperimetric problem for anisotropic left-invariant perimeter measures on $\mathbb R^3$, endowed with the Heisenberg group structure. The perimeter is associated with a left-invariant norm $\phi$ on the horizontal distribution. We first prove a representation formula for the $\phi$-perimeter of regular sets and, assuming some regularity on $\phi$ and on its dual norm $\phi^*$, we deduce a foliation property by sub-Finsler geodesics of $\mathrm C^2$-smooth surfaces with constant $\phi$-curvature. We then prove that the characteristic set of $\mathrm C^2$-smooth surfaces that are locally extremal for the isoperimetric problem is made of isolated points and horizontal curves satisfying a suitable differential equation. Based on such a characterization, we characterize $\mathrm C^2$-smooth $\phi$-isoperimetric sets as the sub-Finsler analogue of Pansu's bubbles. We also show, under suitable regularity properties on $\phi$, that such sub-Finsler candidate isoperimetric sets are indeed $\mathrm C^2$-smooth. By an approximation procedure, we finally prove a conditional minimality property for the candidate solutions in the general case (including the case where $\phi$ is crystalline)

Learning Discrete Directed Acyclic Graphs via Backpropagation

Recently continuous relaxations have been proposed in order to learn Directed Acyclic Graphs (DAGs) from data by backpropagation, instead of using combinatorial optimization. However, a number of techniques for fully discrete backpropagation could instead be applied. In this paper, we explore that direction and propose DAG-DB, a framework for learning DAGs by Discrete Backpropagation. Based on the architecture of Implicit Maximum Likelihood Estimation [I-MLE, arXiv:2106.01798], DAG-DB adopts a probabilistic approach to the problem, sampling binary adjacency matrices from an implicit probability distribution. DAG-DB learns a parameter for the distribution from the loss incurred by each sample, performing competitively using either of two fully discrete backpropagation techniques, namely I-MLE and Straight-Through Estimation.Comment: 15 pages, 2 figures, 7 tables. Accepted for NeurIPS 2022 workshops on: Causal Machine Learning for Real-World Impact; and Neuro Causal and Symbolic A

Brain abscess and periodontal pathogens ( Fusobacterium Nucleatum ). Report of a case

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Parental Androids

About forty years ago, feminist scholars formulated several independent definitions of an ethics of care (Gilligan 1982; Ruddick 1989; Noddings 1984), suggesting the need to reframe human collective and personal interactions. However, care theory fails for the most part to consider the lived experiences and the needs of marginalized subjects (Gary 2022). This study observes care theory from a linguistic perspective in three audio-visual texts featuring examples of non-normative care. The sci-fi TV series Star Trek: The Next Generation, Battlestar Galactica, and Raised by Wolves will be considered, with a focus on androids acting as caregivers. The linguistic analysis, following a Discourse-Historical Approach (DHA), will focus on discursive strategies relating to the parties involved, their relational ties, care behaviors, and the androids’ adequacy as caretakers. The emerging perspectives may be mapped onto current discourse on minority groups’ access to fostering or adoption and their reproductive rights

Analytical evaluation of the new Seal Autoanalyzer 3 High Resolution for urinary iodine determination

Introduction: The aim of the study was to evaluate the analytical performance of the new colorimetric, automatic analyser, Seal AutoAnalyzer 3 High Resolution (Seal AA3 HR) (Seal Analytical, Wisconsin, USA) for urinary iodine measurement. Materials and methods: This study included testing of several analytical features of the method involving: imprecision (within-run %CVr, between- run %CVb and total laboratory precision %CVl), measurement uncertainty, carryover, linearity and method comparison, with 70 urine samples including the measuring range (20 - 700 μg/L). Results: Within-run, %CVb and %CVl of two control levels were 2.03% and 3.04%, 0.51% and 2.61%, and 2.09% and 4.01%, respectively. Carryover effect was less than 1%. The linearity was good in the range of urinary iodine values between 60 and 500 μg/L (R2 = 0.99). Good agreement of urinary iodine values was found between manual technique and Seal AA3 HR, using Passing-Bablok regression (y = 7.84 (- 3.00 to 15.29) + 0.95 (0.90 to 1.00) x) and Blant-Altman test. Cusum test for linearity indicates that there is no significant deviation from linearity (P > 0.1). Conclusions: The obtained results proved excellent precision, reproducibility and linearity, comparable to the already used, manual method. The New Seal AA3 HR automatic analyser is acceptable for urinary iodine measurement with very good analytical characteristics and can be used for urinary iodine epidemiological studies of the Croatian population