Strong Connections on Quantum Principal Bundles

A gauge invariant notion of a strong connection is presented and characterized. It is then used to justify the way in which a global curvature form is defined. Strong connections are interpreted as those that are induced from the base space of a quantum bundle. Examples of both strong and non-strong connections are provided. In particular, such connections are constructed on a quantum deformation of the fibration $S^2 -> RP^2$. A certain class of strong $U_q(2)$-connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with the q-dependent hermitian metric. A particular form of the Yang-Mills action on a trivial U\sb q(2)-bundle is investigated. It is proved to coincide with the Yang-Mills action constructed by A.Connes and M.Rieffel. Furthermore, it is shown that the moduli space of critical points of this action functional is independent of q.Comment: AMS-LaTeX, 40 pages, major revision including examples of connections over a quantum real projective spac

Host and microbiome features of secondary infections in lethal covid-19

Secondary infections contribute significantly to covid-19 mortality but driving factors remain poorly understood. Autopsies of 20 covid-19 cases and 14 controls from the first pandemic wave complemented with microbial cultivation and RNA-seq from lung tissues enabled description of major organ pathologies and specification of secondary infections. Lethal covid-19 segregated into two main death causes with either dominant diffuse alveolar damage (DAD) or secondary pneumonias. The lung microbiome in covid-19 showed a reduced biodiversity and increased prototypical bacterial and fungal pathogens in cases of secondary pneumonias. RNA-seq distinctly mirrored death causes and stratified DAD cases into subgroups with differing cellular compositions identifying myeloid cells, macrophages and complement C1q as strong separating factors suggesting a pathophysiological link. Together with a prominent induction of inhibitory immune-checkpoints our study highlights profound alterations of the lung immunity in covid-19 wherein a reduced antimicrobial defense likely drives development of secondary infections on top of SARS-CoV-2 infection