Extensions of Picard 2-Stacks and the cohomology groups Ext^i of length 3 complexes

The aim of this paper is to define and study the 3-category of extensions of Picard 2-stacks over a site S and to furnish a geometrical description of the cohomology groups Ext^i of length 3 complexes of abelian sheaves. More precisely, our main Theorem furnishes (1) a parametrization of the equivalence classes of objects, 1-arrows, 2-arrows, and 3-arrows of the 3-category of extensions of Picard 2-stacks by the cohomology groups Ext^i, and (2) a geometrical description of the cohomology groups Ext^i of length 3 complexes of abelian sheaves via extensions of Picard 2-stacks. To this end, we use the triequivalence between the 3-category of Picard 2-stacks and the tricategory T^[-2,0](S) of length 3 complexes of abelian sheaves over S introduced by the second author in arXiv:0906.2393, and we define the notion of extension in this tricategory T^[-2,0](S), getting a pure algebraic analogue of the 3-category of extensions of Picard 2-stacks. The calculus of fractions that we use to define extensions in the tricategory T^[-2,0](S) plays a central role in the proof of our Main Theorem.Comment: 2 New Appendix: in the first Appendix we compute a long exact sequence involving the homotopy groups of an extension of Picard 2-stacks, and in the second Appendix we sketch the proof that the fibered sum of Picard 2-stacks satisfies the universal propert

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

Reply to the ‘Critical review on the paper: The earliest datable noctilucent cloud observation (Parma, Italy AD 1840)’

In this reply, the aim of the authors is to correct the calculation errors on solar depression angle and azimuth angle as recognized by Dr. Dalin in his critical review. However, these updated and corrected calculations do not affect the possibility for Antonio Colla of having observed the Noctilucent Cloud (NLC) plausible both in the direction and for the duration he described in his observations. In this reply, the authors offer two different interpretations in this regard

Western Mediterranean precipitation over the last 300 years from instrumental observations

The paper reports the results of the analysis of the 14 longest precipitation instrumental series, covering the last 300 years, that have been recovered in six subareas of the Western Mediterranean basin, i.e., Portugal, Northern and Southern Spain, Southern France, Northern and Southern Italy. This study extends back by one century our knowledge about the instrumental precipitation over theWestern Mediterranean, and by two centuries in some specific subareas. All the time series show repeated swings. No specific trends have been found over the whole period, except in a few cases, but with modest time changes and sometimes having opposite tendency. The same can be said for the most recent decades although with some more marked departures from the average. The correlation between the various Mediterranean subareas is generally not significant, or almost uncorrelated. The Wavelet Spectral Analysis applied to the precipitation identifies only a minor 56-year cycle in autumn, i.e., the same return period that has been found in literature for the Sea Surface Temperature over North Atlantic. A comparison with a gridded dataset reconstruction based on mixed multiproxy and instrumental observations, shows that the grid reconstruction is in good agreement with the observed data for the period after 1900, less for the previous period

Multi-year total ozone column variability at three Norwegian sites and the influence of Northern Hemisphere Climatic indices

Total ozone column (TOC) measurements are retrieved from the Ozone Monitoring Instrument (OMI) onboard the NASA Earth Observing System (EOS) Aura satellite at the three Norwegian sites: Oslo (59.9 degrees N 10.7 degrees E, 1 m a.s. l.), Trondheim (63.4 degrees N 10.4 degrees E, 3 m a.s.l.) and Andoya (69.1 degrees N 15.7 degrees E, 32 m a.s.l.). TOC data have been analysed from 2005 to 2021, in order to detect annual and multi-years total ozone variability. The relationship between geopotential height (GPH) at 250 hPa and total ozone column has been evaluated after showing that monthly anomalies in GPH and TOC are correlated amongst the three sites. The influence of the three Northern Hemisphere Tele Connection (TC) indices (North Atlantic Oscillation, Arctic Oscillation and Scandinavia) on TOC variability has been investigated. It is found that Scandinavia index plays a prominent role for the northernmost latitudes of Andoya and Trondheim while North Atlantic Oscillation and Arctic Oscillation indices are weakly correlated (negatively) to TOC and (positively) to GPH at Oslo. The response of TOC variability to the solar activity at the three sites is also explored and it is noticed that in the period of increasing variation of solar activity, significant TOC anomaly events are only observed in Andoya and Trondheim

An early mid-latitude aurora observed by Rozier (Béziers, 1780)

Aurora observations are an uncommon phenomenon at low and mid latitudes that, at the end of the 18th century, were not well known and understood. Low and mid geomagnetic latitude aurora observations provide information about episodes of intense solar storms associated with flares and outstanding coronal mass ejection (CME) and about the variation of the geomagnetic field. However, for many observers at mid and low latitudes, the features of a northern light were unknown, so they could easily report it as a phenomenon without explanation. In this work, we found that an earlier mid geomagnetic latitude aurora was observed in Beaus jour, close to B ziers (43°190 N, 3°130 E), France, by the abbot Fran ois Rozier. He was a meticulous botanist, doctor and agronomist with a special interest in atmospheric phenomena. On 15 August 1780, from 19:55 to 20:07 (Universal Time), Fran ois Rozier observed a phosphoric cloud . A careful analysis of the report indicates that he was reporting an auroral event. The recovery of auroral events at low and mid latitude during the 1780s is very useful for shedding light on solar activity during this period because there are few records of sunspot observations

Biextensions and 1-motives

The notion of biextension of two abelian groups by another abelian group is a classical one coming from [SGA7, VII], later extended by Deligne in [D, 10.2] to the case where K0 and K1 are two complexes of abelian sheaves and H is another abelian sheaf. His result Biext1 (K1 , K2 ; H) 3c Ext1 (K1 97L K2 , H) suggests that the biextension of two 1-motives is related to their tensor product, which is outside the category of 1-motives for trivial reasons

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

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