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

Evaluating the Urban Heat Mitigation Potential of a Living Wall in Milan: One Year of Microclimate Monitoring

Urban heat island (UHI) mitigation and adaptation are urgent needs in a built environment, which requires us to search for sustainable solutions to limit the urban heat island effect and improve the energy efficiency of building envelopes. Among these solutions, vertical green structures (VGSs) have recently attracted significant attention for their potential to mitigate adverse effects, especially in densely built areas. This study presents a comprehensive data analysis of the microclimate of a living wall in Milan, Italy. Our aim was to evaluate this VGS's performance in mitigating temperature increases caused by the UHI effect. In the literature, similar studies are limited to shorter monitoring periods (mostly in cooling seasons) and specific orientations (mostly facing south). However, the VGS presented in this case study here faces northwest and was continuously monitored for one calendar year. During this continuous in situ monitoring campaign, air temperature data from sensors either embedded in vegetation or exposed on a bare wall were collected and analysed over a whole calendar year, which is a novelty compared to the existing literature focused on VGSs due to the long duration. The findings indicate that the studied VGS has the ability to influence the outdoor microclimate depending on the season, the precipitation events, the wall exposure, the type of vegetation, and the vegetation's phenological attributes. The analysis showed that the VGS consistently maintained cooler temperatures than the bare wall, with mean temperature differences ranging from 2.8 degrees C in autumn to 0.8 degrees C in spring through the winter. The vegetation acted as a natural insulator by reducing the air temperature during the hot summer and in early autumn, corresponding to the growing period of the vegetation. Thus, VGSs show potential to mitigate the global warming effect. These findings provide valuable insights on vegetation's capability to act as a thermal regulator for sustainable urban planning and energy-efficient building design and retrofitting

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