Quantum Principal Bundles and Corresponding Gauge Theories

A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge transformations, are introduced and investigated. A natural differential calculus on quantum gauge bundles is constructed and analyzed. Kinematical and dynamical properties of corresponding gauge theories are discussed.Comment: 28 pages, AMS-LaTe

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

Microscale Temperature Shaping Using Spatial Light Modulation on Gold Nanoparticles

Abstract Heating on the microscale using focused lasers gave rise to recent applications, e.g., in biomedicine, biology and microfluidics, especially using gold nanoparticles as efficient nanoabsorbers of light. However, such an approach naturally leads to nonuniform, Gaussian-like temperature distributions due to the diffusive nature of heat. Here, we report on an experimental means to generate arbitrary distributions of temperature profiles on the micrometric scale (e.g. uniform, linear, parabolic, etc) consisting in illuminating a uniform gold nanoparticle distribution on a planar substrate using spatially contrasted laser beams, shaped using a spatial light modulator (SLM). We explain how to compute the light pattern and the SLM interferogram to achieve the desired temperature distribution, and demonstrate the approach by carrying out temperature measurements using quantitative wavefront sensing