309 research outputs found
Il problema isoperimetrico in spazi di Carnot-Carathéodory
We present some recent results obtained on the isoperimetric problem in a class of Carnot-CarathĂ©odory spaces, related to the Heisenberg group. This is the framework of Pansuâs 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-CarathĂ©odory legati al gruppo di Heisenberg. Questo Ăš 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 unâipotesi di simmetria che dipende dalla dimensione. In questo contesto, forniamo una classificazione degli insiemi isoperimetrici, valida per specifiche dimensioni. Dallâaltro lato, presentiamo alcuni risultati sul problema isoperimetrico in una famiglia di varietĂ 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 unâipotesi topologica
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
Mean value formulas on surfaces in Grushin spaces
We prove (sub)mean value formulas at the point for (sub)harmonic
functions a on a hypersurface where the
differentiable structure and the surface measure depend on the ambient Grushin
structure
Embedded trace operator for infinite metric trees
We consider a class of infinite weighted metric trees obtained as
perturbations of self-similar regular trees. Possible definitions of the
boundary traces of functions in the Sobolev space on such a structure are
discussed by using identifications of the tree boundary with a surface. Our
approach unifies some constructions proposed by Maury, Salort, Vannier (2009)
for dyadic discrete weighted trees (expansion in orthogonal bases of harmonic
functions on the graph and using Haar-type bases on the domain representing the
boundary), and by Nicaise, Semin (2018) and Joly, Kachanovska, Semin (2019) for
fractal metric trees (approximation by finite sections and identification of
the boundary with a interval): we show that both machineries give the same
trace map, and for a range of parameters we establish the precise Sobolev
regularity of the traces. In addition, we introduce new geometric ingredients
by proposing an identification with arbitrary Riemannian manifolds. It is shown
that any compact manifold admits a suitable multiscale decomposition and,
therefore, can be identified with a metric tree boundary in the context of
trace theorems.Comment: 67 pages. Several wrong citations were correcte
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
We study the isoperimetric problem for anisotropic left-invariant perimeter
measures on , endowed with the Heisenberg group structure. The
perimeter is associated with a left-invariant norm on the horizontal
distribution. We first prove a representation formula for the -perimeter
of regular sets and, assuming some regularity on and on its dual norm
, we deduce a foliation property by sub-Finsler geodesics of -smooth surfaces with constant -curvature. We then prove that the
characteristic set of -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 -smooth -isoperimetric sets as the
sub-Finsler analogue of Pansu's bubbles. We also show, under suitable
regularity properties on , that such sub-Finsler candidate isoperimetric
sets are indeed -smooth. By an approximation procedure, we finally
prove a conditional minimality property for the candidate solutions in the
general case (including the case where 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
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 androidsâ adequacy as caretakers. The emerging perspectives may be mapped onto current discourse on minority groupsâ access to fostering or adoption and their reproductive rights
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