Random Assignment Problems on 2d Manifolds

We consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold Ω of unit area. It is known that the average cost scales as EΩ(N) ∼ 1 / 2 πln N with a correction that is at most of order lnNlnlnN. In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first Ω -dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on Ω. We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics

Antimicrobial activity of aztreonam in combination with old and new β-lactamase inhibitors against mbl and esbl co-producing gram-negative clinical isolates: Possible options for the treatment of complicated infections

none14noMetallo-β-lactamases (MBLs) are among the most challenging bacterial enzymes to over-come. Aztreonam (ATM) is the only β-lactam not hydrolyzed by MBLs but is often inactivated by co-produced extended-spectrum β-lactamases (ESBL). We assessed the activity of the combination of ATM with old and new β-lactamases inhibitors (BLIs) against MBL and ESBL co-producing Gram-negative clinical isolates. Six Enterobacterales and three non-fermenting bacilli co-producing MBL and ESBL determinants were selected as difficult-to-treat pathogens. ESBLs and MBLs genes were characterized by PCR and sequencing. The activity of ATM in combination with seven different BLIs (clavulanate, sulbactam, tazobactam, vaborbactam, avibactam, relebactam, zidebactam) was assessed by microdilution assay and time–kill curve. ATM plus avibactam was the most effective combination, able to restore ATM susceptibility in four out of nine tested isolates, reaching in some cases a 128-fold reduction of the MIC of ATM. In addition, relebactam and zidebactam showed to be effective, but with lesser reduction of the MIC of ATM. E. meningoseptica and C. indologenes were not inhibited by any ATM–BLI combination. ATM–BLI combinations demonstrated to be promising against MBL and ESBL co-producers, hence providing multiple options for treatment of related infections. However, no effective combination was found for some non-fermentative bacilli, suggesting the presence of additional resistance mechanisms that complicate the choice of an active therapy.openMorroni G.; Bressan R.; Fioriti S.; D'Achille G.; Mingoia M.; Cirioni O.; Di Bella S.; Piazza A.; Comandatore F.; Mauri C.; Migliavacca R.; Luzzaro F.; Principe L.; Lagatolla C.Morroni, G.; Bressan, R.; Fioriti, S.; D'Achille, G.; Mingoia, M.; Cirioni, O.; Di Bella, S.; Piazza, A.; Comandatore, F.; Mauri, C.; Migliavacca, R.; Luzzaro, F.; Principe, L.; Lagatolla, C

Un problema di iconografia trinitaria tra Oriente e Occidente: l'affresco di Vallepietra e le immagini di Faras (Nubia). Convergenze poligenetiche o emergenze corradicali?

Argomento di questo studio è la rappresentazione della Trinità isomorfa: si tratta di un’iconografia assai rara il cui primo esempio in ambito occidentale è costituito dall’affresco del Santuario sul Monte Autore a Vallepietra nel Lazio. L’autrice, dopo aver discusso e ribadito la datazione dell’opera al XII secolo, analizza l’origine del tema individuando in Nubia un consistente numero di testimonianze di tale iconografia, che qui si moltiplica in modo quasi esponenziale a partire dall’XI secolo. Si avanzano, infine, alcune ipotesi sia sui modelli di riferimento (forse provenienti dal mondo bizantino), sia sui possibili tramiti che hanno veicolato il tema dall’Oriente all’Occidente. This study focuses on the depiction of isomorph Trinity: that is a very rare iconography whose first occurance in Western Europe is a fresco in the Sanctuary on Mount Autore in Vallepietra (Latium). The authoress, after discussing and confirming the dating of the work of art to the 12th century, reviews the origin of that theme, picking out a considerable number of such an iconography examples in Nubia, where it increased in an exponantial way since the 11th century. Finally, some hypotheses about both the reference models (perhaps coming from the Byzantine world) and the possible ways through which the theme passed from the East to the West, are put forth