Higher-dimensional study of extensions via torsors

Let S be a site. First we define the 3-category of torsors under a Picard S-2-stack and we compute its homotopy groups. Using calculus of fractions we define also a pure algebraic analogue of the 3-category of torsors under a Picard S-2-stack. Then we describe extensions of Picard S-2-stacks as torsors endowed with a group law on the fibers. As a consequence of such a description, we show that any Picard S-2-stack admits a canonical free partial left resolution that we compute explicitly. Moreover we get an explicit right resolution of the 3-category of extensions of Picard S-2-stacks in terms of 3-categories of torsors. Using the homological interpretation of Picard S-2-stacks, we rewrite this three categorical dimensions higher right resolution in the derived category of abelian sheaves on S.Comment: We change the title and we add new result

Uniqueness properties for discrete equations and Carleman estimates

Using Carleman estimates, we give a lower bound for solutions to the discrete Schrödinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions

ON (GLOBAL) UNIQUE CONTINUATION PROPERTIES OF THE FRACTIONAL DISCRETE LAPLACIAN

We study various qualitative and quantitative (global) unique continuation prop- erties for the fractional discrete Laplacian. We show that while the fractional Laplacian enjoys striking rigidity properties in the form of (global) unique continuation properties, the fractional discrete Laplacian does not enjoy these in general. While discretization thus counteracts the strong rigidity properties of the continuum fractional Laplacian, by discussing quantitative forms of unique continuation, we illustrate that these properties can be recovered if exponen- tially small (in the lattice size) correction terms are added. In particular, this allows us to deduce stability properties for a discrete, linear inverse problem for the fractional Laplacian. We complement these observations with a transference principle and the discussion of these properties on the discrete torus

Feeding habits of three seal species at the Danco Coast, Antarctica: A re-assessment

The analysis of prey overlap among Weddell, Antarctic fur and leopard seals was conducted using fecal samples collected at the Danco Coast, Antarctic Peninsula, in 1998 and 2000. The re-occurrence of prey species was moderate in samples collected in 1998, and low in 2000, and reflects resource partitioning among seal species. Prey species that mostly co-occurred in seals' diet were the Antarctic krill Euphausia superba, bivalves, and the myctophids Gymnoscopelus nicholsi and Electrona antarctica. A dietary similarity index of prey overlap has been calculated and demonstrates evident fluctuations in pairwise comparisons between the seal species. The highest and lowest values of prey overlap were observed between Antarctic fur seals and leopard seals, and between Weddell seals and leopard seals, respectively. Prey overlap between Antarctic fur seals and Weddell seals was moderate in both seasons.Fil: Casaux, Ricardo Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Bertolin, María Lila. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Carlini, A.. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; Argentin

Preliminary evaluation of the climate-induced fatigue in wood: A physical and computational approach

Wood is the organic hygroscopic material for excellence. Due to its extremely easy handling, it has always been used in many applications, especially as building material for artefacts and works of art. However, it is highly climate-susceptible as it swells or shrinks by exchanging moisture with the surrounding environment when natural or artificial microclimatic fluctuations occur. The shrinkage/swelling of wood, if repeated over time, may cause the arising of deformations or damage that may lead to catastrophic failures. For this reason, in this work, a preliminary study about the effect that repeated microclimatic loads have on wooden samples is carried out. To do so, well-established fatigue approaches have been implemented, with few simplifying considerations. The case study is a slice of Scots pine which is assumed to be stored inside Ringebu stave church (Norway). Ringebu indoor microclimate is reconstructed, through a proper transfer function, starting from outdoor temperature data downloaded from web platforms. The reconstructed indoor temperature timeseries cover three periods: far past (1948–1977), recent past (1981–2010) and far future (2071–2100). The results obtained for the three periods made it possible to gain insights about the climate-induced fatigue of wood and to preliminary assess the impact of climate change. It has been observed that successive similar temperature fluctuations can be potentially treated as a block of constant amplitude and constant frequency fatigue-like load. Finally, introducing few simplifying considerations, it has been assessed that the simulated behavior is coherent with the theoretical one coming from exploiting well-established thermo-based methods

Unimpaired Neuropsychological Performance and Enhanced Memory Recall in Patients with Sbma: A Large Sample Comparative Study.

Peculiar cognitive profile of patients with SBMA has been described by fragmented literature. Our retrospective study reports the neuropsychological evaluations of a large cohort of patients in order to contribute towards the understanding of this field. We consider 64 neuropsychological evaluations assessing mnesic, linguistic and executive functions collected from 2013 to 2015 in patients attending at Motor Neuron Disease Centre of University of Padova. The battery consisted in: Digit Span forwards and backwards, Prose Memory test, Phonemic Verbal fluency and Trail making tests. ANCOVA statistics were employed to compare tests scores results with those obtained from a sample of healthy control subjects. Multiple linear regressions were used to study the effect on cognitive performance of CAG-repeat expansion, the degree of androgen insensitivity and their interaction to cognitive performance. Statistical analyses did not reveal altered scores in any neuropsychological tests among those adopted. Interestingly, patients performed significantly better in the Prose Memory test's score. No relevant associations were found with genetic, hormonal or clinical patients' profile. Results inconsistent with previous studies have been interpreted according to the phenomenon of somatic mosaicism. We suggest a testosterone-related and the mood state-dependant perspectives as two possible interpretations of the enhanced performances in the Prose Memory test. Further studies employing more datailed tests batteries are encouraged

Mechanical properties of the most common european woods: A literature review

Wood is an orthotropic material used since ancient time. A literature research about the mechanical properties of density, fracture toughness, modulus of elasticity, and Poisson’s ratio has been done to have a broader view on the subject. The publications relating to the topic were found through the two search engines Scopus and Google Scholar that have yielded several papers, including articles and book sections. In general, there is no standardization on the method of analysis carried out on wood, underlining the great difficulty in studying this complex material. The parameter of density has a great variability and needs a deeper investigation; fracture toughness is not always available in literature, not even in the different directions of the wood sample. Interesting is the modulus of elasticity, which provides a correlation with density, especially in longitudinal section but, again, it needs to be studied in detail. The parameter of Poisson’s ratio is provided as single values in three different directions, but mainly for softwood. All the parameters require a more in-depth study for both softwood and hardwood. Furthermore, the type of analysis, whether experimental or modelling, needs to be standardized to have more comparable results