Quiver e loro rappresentazioni: il Teorema di Gabriel

Un quiver è costituito da un insieme di vertici e un insieme di frecce fra di essi.Verrà introdotta la nozione di rappresentazione per un quiver che abbia un numero finito di vertici e frecce. La categoria delle rappresentazioni e loro morfismi è equivalente a quella degli A-moduli destri dove A è l'algebra dei cammini del quiver, ovvero l' algebra che ha come base tutti i cammini ottenibili percorrendo le frecce e come prodotto quello indotto dalla composizione di cammini. Dal punto di vista della teoria delle rappresentazioni lo studio delle algebre finito dimensionali si riduce allo studio di quozienti dell'algebra dei cammini. Lo scopo di questa tesi è arrivare a una classificazione dei quiver che hanno solamente un numero finito di rappresentazioni indecomponibili (ovvero che non si possono scrivere come somma diretta di altre rappresentazioni non banali) a meno di isomorfismo. Il risultato è abbastanza recente ed è stato provato da Gabriel nel 1972. Vi è un numero finito di classi di isomorfismo di rappresentazioni solamente nei casi in cui il grafo associato al quiver è un particolare diagramma di Dynkin. Questo è sorprendente poiché questi diagrammi sono in corrispondenza biunivoca con le algebre di Lie semisemplici su un campo algebricamente chiuso

Automorphisms of irreducible holomorphic symplectic manifolds and related problems

We study automorphisms and the mapping class group of irreducible holomorphic symplectic (IHS) manifolds. We produce two examples of manifolds of K3[2] type with a symplectic action of the alternating group A7. Our examples are realized as double EPW-sextics, the large cardinality of the group allows us to prove the irrationality of the associated families of Gushel-Mukai threefolds. We describe the group of automorphisms of double EPW-cubes. We give an answer to the Nielsen realization problem for IHS manifolds in analogy to the case of K3 surfaces, determining when a finite group of mapping classes fixes an Einstein (or Kähler-Einstein) metric. We describe, for some deformation classes, the mapping class group and its representation in second cohomology. We classify non-symplectic involutions of manifolds of OG10 type determining the possible invariant and coinvariant lattices. We study non-symplectic involutions on LSV manifolds that are geometrically induced from non-symplectic involutions on cubic fourfolds

Robertsite: un nuovo fosfato di grotta scoperto nella Tagusan Cave(Palawan – Filippine)

La Tagusan Cave è una cavità di attraversamento che si apre nel massiccio calcareo che ospita la famosa grotta Porto Pricesa Undergroud River nell’isola di Palawan (Filippine). Al suo interno sono state rivenute alcune pisoliti di colore nero che sono state campionate e quindi analizzate dal punto di vista tessiturale e mineralogico. Le analisi al microscopio ottico hanno evidenziato come queste pisoliti non siano omogenee ma siano costituite da un nucleo spesso costituito da una aggregazione di ooliti giallastre su cui si è depositata un’alternanza di sottili strati picei e rossastri. L’analisi mineralogica delle bande di accrescimento ha evidenziato la presenza, oltre a fosfati di calcio praticamente amorfi, di robertsite [Ca2Mn3(PO4)3O2•3H2O], un fosfato che non era mai stato segnalato prima in grotta. Sempre in queste bande, sulla base degli esami röntgenografici e delle analisi EDAX, si è ipotizzata la presenza anche di janggunite [Mn5-x(Mn,Fe)1-xO8(OH)6], di cui però non si è raggiunta la certezza. Nel nucleo invece è stato possibile identificare la presenza di strengite-Al [(Fe,Al) (PO4) •2H2O]. La genesi di queste particolari pisoliti è da mettere in relazione con i processi di digestione biologica del guano che all’inizio della loro evoluzione doveva essere abbondante nelle acque che fluivano nella grotta, mentre ora, l’apporto idrico è molto più scarso e proviene da stillicidi che hanno scarsa relazione con il guano medesimo.The Tagusan cave is a hydrologic tunnel in the karst massif hosting the famous Porto Pricesa Underground River in the Palawan Island (Philippines). It hosts some speleothems among which are worth to be cited some black pearls. A few of them have been sampled to be analyzed from the textural and mineralogical point of view. The optical microscope analyses put in evidence that the inner structure of these pearls is un-homogeneous, consisting of a nucleus often made by aggregates of yellowish oolites covered by alternated pitch-dark and reddish layers. The mineralogical analyses find out that the growing layers consist of amorphous phosphates and robertsite [Ca6Mn9(PO4)9O6(H2O)6•3(H2O)], which is here recognized, for the first time, as cave mineral. The x-ray patterns and the EDAX analyses suggest also the presence of janggunite [Mn5-x(Mn,Fe)1-xO8(OH)6], but no definitive proof of it has been yet achieved. Strengite-Al, [(Fe,Al)PO4•2H2O)] is the main component of the yellowish oolites in the pearl’s nucleus. The genesis of these peculiar cave pearls is strictly related to the biological digestion processes of the guano deposits. In fact at the beginning of their evolution the feeding water directly crossed guano deposits, while now the few still active dripping practically has no contact with it

Absence of increased genomic variants in the cyanobacterium Chroococcidiopsis exposed to Mars-like conditions outside the space station

Despite the increasing interest in using microbial‑based technologies to support human space exploration, many unknowns remain not only on bioprocesses but also on microbial survivability and genetic stability under non‑Earth conditions. Here the desert cyanobacterium Chroococcidiopsis sp. CCMEE 029 was investigated for robustness of the repair capability of DNA lesions accumulated under Mars‑like conditions (UV radiation and atmosphere) simulated in low Earth orbit using the EXPOSE‑R2 facility installed outside the International Space Station. Genomic alterations were determined in a space‑derivate of Chroococcidiopsis sp. CCMEE 029 obtained upon reactivation on Earth of the space‑exposed cells. Comparative analysis of whole‑genome sequences showed no increased variant numbers in the space‑derivate compared to triplicates of the reference strain maintained on the ground. This result advanced cyanobacteria‑based technologies to support human space exploratio

The role of immune suppression in COVID-19 hospitalization: clinical and epidemiological trends over three years of SARS-CoV-2 epidemic

Specific immune suppression types have been associated with a greater risk of severe COVID-19 disease and death. We analyzed data from patients >17 years that were hospitalized for COVID-19 at the “Fondazione IRCCS Ca′ Granda Ospedale Maggiore Policlinico” in Milan (Lombardy, Northern Italy). The study included 1727 SARS-CoV-2-positive patients (1,131 males, median age of 65 years) hospitalized between February 2020 and November 2022. Of these, 321 (18.6%, CI: 16.8–20.4%) had at least one condition defining immune suppression. Immune suppressed subjects were more likely to have other co-morbidities (80.4% vs. 69.8%, p < 0.001) and be vaccinated (37% vs. 12.7%, p < 0.001). We evaluated the contribution of immune suppression to hospitalization during the various stages of the epidemic and investigated whether immune suppression contributed to severe outcomes and death, also considering the vaccination status of the patients. The proportion of immune suppressed patients among all hospitalizations (initially stable at <20%) started to increase around December 2021, and remained high (30–50%). This change coincided with an increase in the proportions of older patients and patients with co-morbidities and with a decrease in the proportion of patients with severe outcomes. Vaccinated patients showed a lower proportion of severe outcomes; among non-vaccinated patients, severe outcomes were more common in immune suppressed individuals. Immune suppression was a significant predictor of severe outcomes, after adjusting for age, sex, co-morbidities, period of hospitalization, and vaccination status (OR: 1.64; 95% CI: 1.23–2.19), while vaccination was a protective factor (OR: 0.31; 95% IC: 0.20–0.47). However, after November 2021, differences in disease outcomes between vaccinated and non-vaccinated groups (for both immune suppressed and immune competent subjects) disappeared. Since December 2021, the spread of the less virulent Omicron variant and an overall higher level of induced and/or natural immunity likely contributed to the observed shift in hospitalized patient characteristics. Nonetheless, vaccination against SARS-CoV-2, likely in combination with naturally acquired immunity, effectively reduced severe outcomes in both immune competent (73.9% vs. 48.2%, p < 0.001) and immune suppressed (66.4% vs. 35.2%, p < 0.001) patients, confirming previous observations about the value of the vaccine in preventing serious disease

COVID-19 and Re-Globalization: What Can We Foresee?

The coronavirus outbreak has shown how interdependent and interconnected the world is. A virus that originated in Wuhan, China continues to spread to nearly every country. Two weeks after the detection of the first coronavirus case in Wuhan, coronavirus cases appeared across multiple continents, depicting the rapid spread of the virus due to the rise of globalization. In less than three weeks, the virus spread across multiple continents, traveling to Europe, Thailand, Japan, South Korea, the United States, and Canada. G20 leaders, in a virtual meeting, noted in their statement, “The virus respects no borders. Combatting this pandemic calls for a transparent, robust, coordinated, large-scale, and science-based global response in the spirit of solidarity.” Which is right. Addressing and mitigating the outbreak requires a comprehensive international response

How hydrocarbons move along faults. Evidence from microstructural observations of hydrocarbon-bearing carbonate fault rocks

The microscale mechanisms of hydrocarbons movement along faults and fault zones, the potential carriers of hydrocarbons toward the productive geological traps, remain largely unknown. The majority of previous studies inferred the hydraulic behavior of faults with respect to hydrocarbon movements without providing meso and microstructural observations from faults permeated by hydrocarbons. To fill this gap, we document meso-structures together with the first fossil microstructural portraits of hydrocarbon flow and pathways along two hydrocarbon-bearing carbonate-hosted normal faults exposed in the central Apennines, Italy. In particular, we show that hydrocarbons cyclically move within tectonically active carbonate normal faults possibly during interseismic and coseismic phases of the seismic cycle. Channelized structures, injection features, and clast-cortex grains suggest the occurrence of transient and localized pulses of pressurized hydrocarbons during coseismic slip. In particular, clast-cortex grains are very similar to microstructures that develop along fault planes for slip velocities between 0.0001 and 1 m/s. Patches of hydrocarbon-bearing breccias/cataclasites with lobate and irregular boundaries, crackle breccias filled by hydrocarbons, and hydrocarbons arrested against hydrocarbon-free discrete fault planes suggest hydrocarbon flow during the interseismic phases with hydrocarbon (over)pressure dissipation after coseismic phases. Fault permeability is created during the coseismic phase and hydrocarbons penetrate the most permeable and uncemented uncohesive fault rocks within the damage zone and arrest against and/or within low-permeability and cemented fault cores. Results are consistent with previous numerical simulations on hydrocarbon movements along faults and time-lapse seismic-reflection imaging, suggesting that the movement of hydrocarbon occurs during interseismic periods within tectonically active faults and along permeable zones cyclically created by seismic activity. Results from this paper are crucial for modelling the hydraulic behavior of carbonate fault damage zone, which have progressively gained popularity as targets of hydrocarbon exploration and production and for CO2 or H storage.(C) 2022 Elsevier B.V. All rights reserved

Cenozoic massive carbonate breccia in the External Dinarides of Croatia: the largest outcrop on the island of Krk

The Cenozoic carbonate breccias in the External Dinarides, known as Jelar deposits or Velebit breccia, have been puzzling geologists for decades. The timing and formation mechanisms of this interesting lithological unit is still debatable. The largest breccia outcrop on the Adriatic islands is located on the southeasternmost part of the island of Krk, on the karstic plateau between Stara Baška and Draga Bašćanska. Approximately 11.5 km long and 350 to 1300 m wide outcrop of a typical Dinaric strike (NW–SE) was studied by detailed geological mapping, structural measurements and sampled along the profile normal to the structure. The breccia outcrops are massive, mostly clast-supported, mostly lacking sedimentary structures. Clasts are unsorted and typically angular, ranging in size from sand to gravel, with rare cobbles and boulders. Clasts are mainly derived from adjacent lithostratigraphic units, many showing calcite-filled fissures, indicating intense tectonics prior to deposition. Clast contacts are commonly characterized by pressure solution, while grey, whitish, yellowish to reddish matrix mostly consists of finely crushed limestone particles or coarse-crystalline calcite grains. Rare small-sized sedimentary bodies rich in matrix with numerous rounded clasts indicate local fluvial transport prior to deposition. Most of the breccia outcrops are located in the hinge zone of the NE-verging overturned anticline (a tectonic transport not common in the Dinarides but typical for all Cenozoic carbonate breccia zones). Along the studied profile, the contacts between breccia and the surrounding rocks are steep but gradual. In most places transition zones from (i) limestones to (ii) tectonized limestones to (iii) cataclastic limestones to (iv) monomict and/ or polymict breccia can be several meters wide. Results of studied breccia outcrop suggest that breccia formation probably onset during the late stage of the principal Late Eocene–Oligocene Dinaric compressional phase by disintegration of source rocks into smallsized clasts. Subsequent localized extension in the hinge of the overturned large-scale anticline created a series of deep canyon-like fractures filled by a large quantity of clasts lithified by mosaic calcite cement

Cenozoic massive carbonate breccia in the External Dinarides of Croatia: the largest outcrop on the island of Krk

The Cenozoic carbonate breccias in the External Dinarides, known as Jelar deposits or Velebit breccia, have been puzzling geologists for decades. The timing and formation mechanisms of this interesting lithological unit is still debatable. The largest breccia outcrop on the Adriatic islands is located on the southeasternmost part of the island of Krk, on the karstic plateau between Stara Baška and Draga Bašćanska. Approximately 11.5 km long and 350 to 1300 m wide outcrop of a typical Dinaric strike (NW–SE) was studied by detailed geological mapping, structural measurements and sampled along the profile normal to the structure. The breccia outcrops are massive, mostly clast-supported, mostly lacking sedimentary structures. Clasts are unsorted and typically angular, ranging in size from sand to gravel, with rare cobbles and boulders. Clasts are mainly derived from adjacent lithostratigraphic units, many showing calcite-filled fissures, indicating intense tectonics prior to deposition. Clast contacts are commonly characterized by pressure solution, while grey, whitish, yellowish to reddish matrix mostly consists of finely crushed limestone particles or coarse-crystalline calcite grains. Rare small-sized sedimentary bodies rich in matrix with numerous rounded clasts indicate local fluvial transport prior to deposition. Most of the breccia outcrops are located in the hinge zone of the NE-verging overturned anticline (a tectonic transport not common in the Dinarides but typical for all Cenozoic carbonate breccia zones). Along the studied profile, the contacts between breccia and the surrounding rocks are steep but gradual. In most places transition zones from (i) limestones to (ii) tectonized limestones to (iii) cataclastic limestones to (iv) monomict and/ or polymict breccia can be several meters wide. Results of studied breccia outcrop suggest that breccia formation probably onset during the late stage of the principal Late Eocene–Oligocene Dinaric compressional phase by disintegration of source rocks into smallsized clasts. Subsequent localized extension in the hinge of the overturned large-scale anticline created a series of deep canyon-like fractures filled by a large quantity of clasts lithified by mosaic calcite cement