A hyperbolic 4-manifold with a perfect circle-valued Morse function

We exhibit a finite-volume cusped hyperbolic four-manifold $W$ with a perfect circle-valued Morse function, that is a circle-valued Morse smooth function $f\colon W \to S^1$ with $\chi(W)$ critical points, all of index 2. The map $f$ is built by extending and smoothening a combinatorial Morse function defined by Jankiewicz - Norin - Wise via Bestvina - Brady theory. By elaborating on this construction we also prove the following facts: There are infinitely many finite-volume hyperbolic 4-manifolds $M$ having a handle decomposition with bounded numbers of 1- and 3-handles, so with bounded Betti numbers $b_1(M)$ and $b_3(M)$. The kernel of $f_*\colon \pi_1(W) \to \pi_1(S^1) = \mathbb Z$ determines a geometrically infinite hyperbolic four-manifold $\widetilde W$ obtained by adding infinitely many 2-handles to a product $N \times [0,1]$, for some cusped hyperbolic 3-manifold $N$. The manifold $\widetilde W$ is infinitesimally (and hence locally) rigid. There are type-preserving representations of the fundamental groups of ${\tt m036}$ and of the surface $\Sigma$ with genus 2 and one puncture in ${\rm Isom}^+(\mathbb H^4)$ whose image is a discrete subgroup with limit set $S^3$. These representations are not faithful. We do not know if they are rigid.Comment: 50 pages, 22 figure

Adiabatic response and quantum thermoelectrics for ac driven quantum systems

We generalize the theory of thermoelectrics to include coherent electron systems under adiabatic ac driving, accounting for quantum pumping of charge and heat as well as the associated work exchange between electron system and driving potentials. We derive the relevant response coefficients in the adiabatic regime and show that they obey Onsager reciprocity relations. We analyze the consequences of our generalized thermoelectric framework for quantum motors, generators, heat engines, and heat pumps, characterizing them in terms of efficiencies and figures of merit.Comment: Published versio

Mosè typus papae nel decreto Moyses vir Dei (1439). II parte: Le radici nella dottrina teocratica

Il presente saggio si propone di prendere in esame la trattatistica filo-papale di Pietro del Monte e Juan de Torquemada, per evidenziare come l’applicazione tipologica al papa del modello di Mosè testimoni una lenta ma significativa trasformazione ideologica del suo potere, che lo ha portato a modificare la propria proiezione universalistica adattandola al nuovo contesto delle potenze europee, e a sdoppiarsi in due nature: una sempre spirituale e sacerdotale, l’altra apertamente temporale e principesca, con la nascita di un vero e proprio principato ecclesiastico. Per comprendere le specificità di questa evoluzione ideologica, il paper ne rileva tuttavia anche gli elementi di continuità con la trattatistica teocratica precedente, che la resero possibile e la fecero sviluppare a partire dalle tradizionali istanze universalistiche. In questo senso, dimostrando come i passi sull’interpretazione tipologica di Mosè come figura papale fossero in larga parte dipendenti da autori come Egidio Romano, Giacomo da Viterbo e Agostino d’Ancona, ci si propone di evidenziare su quali basi ideologiche si innestasse quest’evoluzione e su quali aspetti essa facesse perno. Ne emerge così una nuova immagine dei motivi teorici e delle condizioni di possibilità della trasformazione della sovranità papale sul modello di Mosè, ruotante in particolare attorno alla straordinaria elaborazione teologico-politica di Egidio Romano, che aveva tematizzato la supremazia assoluta del pontefice come riserva di potere d’eccezione rispetto alla legge e all’ordine che egli pone, quindi la legittimità dell’utilizzo straordinario della spada temporale al fine di difendere il bene spirituale.This essay aims to examine the pro-papal treatises of Pietro del Monte and Juan de Torquemada, to highlight how the typological application to the pope of the Moses’ model testifies to a slow ideological transformation of his power: the papacy revised his own universalistic projection by adapting it to the new context of European powers, and the figure of the Pontiff split into two natures: one spiritual and priestly, the other temporal and princely, with the construction of an ecclesiastical principality. In order to understand the specifics of this ideological evolution, the paper focuses however on its elements of continuity with earlier theocratic treatises. By emphasizing the fact that the typological interpretations of Moses as a papal figure are largely dependent on authors such as Aegidius Romanus, James of Viterbo and Augustine of Ancona, the paper aims to highlight on what ideological basis this development was grafted and on what aspects it pivoted. Thus, a new picture emerges of the theoretical conditions of possibility of the transformation of papal sovereignty on the model of Moses, based on the theological-political elaboration of Aegidius Romanus, who had thematized the absolute supremacy of the pontiff as a reserve of power of exception to every law and order he posits; thus who had stated the legitimacy of the extraordinary use of the material sword in order to defend the spiritual good

Hans Blumenberg e la “Selbstdestruktion” del cristianesimo. La prima fase del suo pensiero (1946-1966): da Agostino a Nietzsche

La tesi propone una ricostruzione biografica e filosofica della genesi e dello sviluppo della riflessione di Hans Blumenberg, a partire dal tema di fondo del confronto con la storia del cristianesimo. L'originalità del lavoro consiste nel far emergere un intero versante giovanile della sua produzione in cui si profila una prospettiva in netta discontinuità, per non dire antitetica, rispetto alla successiva posizione matura. Il primo Blumenberg, la cui impostazione risente fortemente della riflessione heideggeriana prima che di quella husserliana, individua nella parabola della teologia cristiana la chiave di lettura per interpretare e per correggere la crisi di sensatezza della filosofia contemporanea, derivante dall’imporsi della “tecnica” come nichilistico orizzonte ultimo della realtà umana. Blumenberg parte dall’individuazione fenomenologica di un orizzonte “cristiano” di storicizzazione e metaforizzazione delle categorie ermeneutiche della razionalità, una modalità teologica agostiniana di apertura di un orizzonte “originario” (in senso heideggeriano) dell’ontologia. L’approfondimento in chiave storico-filosofica e storico-teologica di questa prima fase costituisce, quindi, un’inedita e straordinaria opportunità di rileggere in una prospettiva originale la proposta filosofica blumenberghiana, confermando la possibilità di individuare nel corpo a corpo con il cristianesimo e con la storia delle dottrine teologiche un aspetto fondamentale della sua ricerca, attraverso il quale essa si orienta nella progressiva ridefinizione del proprio statuto critico-metodologico. L’evoluzione della sua prospettiva filosofica, infatti, ruota evidentemente intorno alle risorse di razionalità e alle aporie derivanti dall’individuazione di tali dispositivi teologici di radicalizzazione dell’esperienza della finitezza e della contingenza; aporie che, però, lo porteranno infine a ritrattare interamente tale iniziale intuizione, identificando un orizzonte antropologico e radicalmente anti-teologico per la propria teoria metaforologica. In ogni caso, grazie a un rigoroso attraversamento critico di tale evoluzione e delle ragioni che soggiacciono alla riformulazione della posizione blumenberghiana, emergono le interlocuzioni fondamentali, le condizioni preliminari e le motivazioni più profonde della tesi matura, quindi le considerazioni sul significato complessivo della sua ridefinizione tendenzialmente anti-cristiana della razionalità moderna. Il saggio si presenta dunque come una ricognizione di alcuni dei primi testi e delle prime riflessioni giovanili di Blumenberg, alla ricerca del percorso che lo ha poi portato alla formulazione della tesi della Legittimità dell’età moderna. Esso si articola in cinque capitoli: i primi due sono dedicati alla descrizione del ruolo di due figure fondamentali per la comprensione del primissimo svolgimento della riflessione fenomenologica blumenberghiana: Pascal e Agostino; il terzo ed il quarto, impegnandosi invece nello studio degli scritti degli anni ’50 e ‘60, si concentreranno sul progressivo emergere di una prospettiva sempre più critica nei confronti delle strutture di significazione cristiane, quindi sulla centralità del tutto strutturale che acquisisce la radicale messa in questione del paradigma della secolarizzazione. Ciò avverrà, dapprima, seguendo l’evoluzione dell’interrogazione blumenberghiana della genesi della modernità tecnologica, originariamente inscritta in una “rivoluzione” ontologica di cui è confessato essere responsabile il cristianesimo; poi, seguendo le riflessioni contemporanee intorno al problema della grazia, che chiariranno ulteriormente i motivi dello slittamento dell’orizzonte della prima indagine verso una tesi del necessario superamento moderno del dualismo apocalittico ed escatologico gnostico-cristiano. L’ultimo capitolo sarà infine dedicato a interrogare i motivi e la dinamica concettuale che si nascondono dietro la formulazione definitiva della tesi sul moderno, a partire dal recupero fondamentale della riflessione nietzschiana come prospettiva immunizzante rispetto al pericolo delle tesi sulla secolarizzazione, in quanto disattivante qualsiasi residuo teologico-conservatore. Esso sarà quindi preliminare alle osservazioni conclusive, che identificheranno in Nietzsche la figura chiave per intendere il peculiare rovesciamento della tesi blumenberghiana, vera e propria Aufhebung della posizione precedente, che conserva la validità delle intuizioni originarie sul rapporto tra storicità e cristianesimo, pur rispondendo al bisogno, divenuto consapevole, di uno scarto in senso antropologico e anti-teologico del problema dell’inconcettualità

Dodecahedral L-spaces and hyperbolic 4-manifolds

We prove that exactly 6 out of the 29 rational homology 3-spheres tessellated by four or less right-angled hyperbolic dodecahedra are L-spaces. The algorithm used is based on the L-space census provided by Dunfield in arXiv:1904.04628, and relies on a result by Rasmussen-Rasmussen arXiv:1508.05900. We use the existence of these manifolds together with a result of Martelli arXiv:1510.06325 to construct explicit examples of hyperbolic 4-manifolds containing separating L-spaces, and therefore having vanishing Seiberg-Witten invariants. This answers a question asked by Agol and Lin in arXiv:1812.06536.Comment: 39 pages, 10 figures, 6 tables. Comments are welcome

Bounded Cohomology Classes of Exact Forms

On negatively curved compact manifolds, it is possible to associate to every closed form a bounded cocycle - hence a bounded cohomology class - via integration over straight simplices. The kernel of this map is contained in the space of exact forms. We show that in degree 2 this kernel is trivial, in contrast with higher degree. In other words, exact non-zero $2$-forms define non-trivial bounded cohomology classes. This result is the higher dimensional version of a classical theorem by Barge and Ghys for surfaces. As a consequence, one gets that the second bounded cohomology of negatively curved manifolds contains an infinite dimensional space, whose classes are explicitly described by integration of forms. This also showcases that some recent results by Marasco (arXiv:2202.04419, arXiv:2209.00560) can be applied in higher dimension to obtain new non-trivial results on the vanishing of certain cup products and Massey products. Some other applications are discussed.Comment: 11 pages. Some minor changes made upon referee's suggestions. Final version to appear in PAM

Serum Albumin Is Inversely Associated With Portal Vein Thrombosis in Cirrhosis

We analyzed whether serum albumin is independently associated with portal vein thrombosis (PVT) in liver cirrhosis (LC) and if a biologic plausibility exists. This study was divided into three parts. In part 1 (retrospective analysis), 753 consecutive patients with LC with ultrasound-detected PVT were retrospectively analyzed. In part 2, 112 patients with LC and 56 matched controls were entered in the cross-sectional study. In part 3, 5 patients with cirrhosis were entered in the in vivo study and 4 healthy subjects (HSs) were entered in the in vitro study to explore if albumin may affect platelet activation by modulating oxidative stress. In the 753 patients with LC, the prevalence of PVT was 16.7%; logistic analysis showed that only age (odds ratio [OR], 1.024; P = 0.012) and serum albumin (OR, -0.422; P = 0.0001) significantly predicted patients with PVT. Analyzing the 112 patients with LC and controls, soluble clusters of differentiation (CD)40-ligand (P = 0.0238), soluble Nox2-derived peptide (sNox2-dp; P < 0.0001), and urinary excretion of isoprostanes (P = 0.0078) were higher in patients with LC. In LC, albumin was correlated with sCD4OL (Spearman's rank correlation coefficient [r(s)], -0.33; P < 0.001), sNox2-dp (r(s), -0.57; P < 0.0001), and urinary excretion of isoprostanes (r(s), -0.48; P < 0.0001) levels. The in vivo study showed a progressive decrease in platelet aggregation, sNox2-dp, and urinary 8-iso prostaglandin F2 alpha-III formation 2 hours and 3 days after albumin infusion. Finally, platelet aggregation, sNox2-dp, and isoprostane formation significantly decreased in platelets from HSs incubated with scalar concentrations of albumin. Conclusion: Low serum albumin in LC is associated with PVT, suggesting that albumin could be a modulator of the hemostatic system through interference with mechanisms regulating platelet activation

Risk factors associated with adverse fetal outcomes in pregnancies affected by Coronavirus disease 2019 (COVID-19): a secondary analysis of the WAPM study on COVID-19.

Objectives To evaluate the strength of association between maternal and pregnancy characteristics and the risk of adverse perinatal outcomes in pregnancies with laboratory confirmed COVID-19. Methods Secondary analysis of a multinational, cohort study on all consecutive pregnant women with laboratory-confirmed COVID-19 from February 1, 2020 to April 30, 2020 from 73 centers from 22 different countries. A confirmed case of COVID-19 was defined as a positive result on real-time reverse-transcriptase-polymerase-chain-reaction (RT-PCR) assay of nasal and pharyngeal swab specimens. The primary outcome was a composite adverse fetal outcome, defined as the presence of either abortion (pregnancy loss before 22 weeks of gestations), stillbirth (intrauterine fetal death after 22 weeks of gestation), neonatal death (death of a live-born infant within the first 28 days of life), and perinatal death (either stillbirth or neonatal death). Logistic regression analysis was performed to evaluate parameters independently associated with the primary outcome. Logistic regression was reported as odds ratio (OR) with 95% confidence interval (CI). Results Mean gestational age at diagnosis was 30.6+/-9.5 weeks, with 8.0% of women being diagnosed in the first, 22.2% in the second and 69.8% in the third trimester of pregnancy. There were six miscarriage (2.3%), six intrauterine device (IUD) (2.3) and 5 (2.0%) neonatal deaths, with an overall rate of perinatal death of 4.2% (11/265), thus resulting into 17 cases experiencing and 226 not experiencing composite adverse fetal outcome. Neither stillbirths nor neonatal deaths had congenital anomalies found at antenatal or postnatal evaluation. Furthermore, none of the cases experiencing IUD had signs of impending demise at arterial or venous Doppler. Neonatal deaths were all considered as prematurity-related adverse events. Of the 250 live-born neonates, one (0.4%) was found positive at RT-PCR pharyngeal swabs performed after delivery. The mother was tested positive during the third trimester of pregnancy. The newborn was asymptomatic and had negative RT-PCR test after 14 days of life. At logistic regression analysis, gestational age at diagnosis (OR: 0.85, 95% CI 0.8-0.9 per week increase; pPeer reviewe

Maternal and perinatal outcomes of pregnant women with SARS-CoV-2 infection

Objectives To evaluate the maternal and perinatal outcomes of pregnancies affected by SARS-CoV-2 infection. Methods This was a multinational retrospective cohort study including women with a singleton pregnancy and laboratory-confirmed SARS-CoV-2 infection, conducted in 72 centers in 22 different countries in Europe, the USA, South America, Asia and Australia, between 1 February 2020 and 30 April 2020. Confirmed SARS-CoV-2 infection was defined as a positive result on real-time reverse-transcription polymerase chain reaction (RT-PCR) assay of nasopharyngeal swab specimens. The primary outcome was a composite measure of maternal mortality and morbidity, including admission to the intensive care unit (ICU), use of mechanical ventilation and death. Results In total, 388 women with a singleton pregnancy tested positive for SARS-CoV-2 on RT-PCR of a nasopharyngeal swab and were included in the study. Composite adverse maternal outcome was observed in 47/388 (12.1%) women; 43 (11.1%) women were admitted to the ICU, 36 (9.3%) required mechanical ventilation and three (0.8%) died. Of the 388 women included in the study, 122 (31.4%) were still pregnant at the time of data analysis. Among the other 266 women, six (19.4% of the 31 women with first-trimester infection) had miscarriage, three (1.1%) had termination of pregnancy, six (2.3%) had stillbirth and 251 (94.4%) delivered a liveborn infant. The rate of preterm birth before 37 weeks' gestation was 26.3% (70/266). Of the 251 liveborn infants, 69/251(27.5%) were admitted to the neonatal ICU, and there were five (2.0%) neonatal deaths. The overall rate of perinatal death was 4.1% (11/266). Only one (1/251, 0.4%) infant, born to a mother who tested positive during the third trimester, was found to be positive for SARS-CoV-2 on RT-PCR. Conclusions SARS-CoV-2 infection in pregnant women is associated with a 0.8% rate of maternal mortality, but an 11.1% rate of admission to the ICU. The risk of vertical transmission seems to be negligible. (C) 2020 International Society of Ultrasound in Obstetrics and Gynecology.Peer reviewe