Poisson-Furstenberg boundary and growth of groups

We study the Poisson-Furstenberg boundary of random walks on permutational wreath products. We give a sufficient condition for a group to admit a symmetric measure of finite first moment with non-trivial boundary, and show that this criterion is useful to establish exponential word growth of groups. We construct groups of exponential growth such that all finitely supported (not necessarily symmetric, possibly degenerate) random walks on these groups have trivial boundary. This gives a negative answer to a question of Kaimanovich and Vershik.Comment: 24 page

Chronic lung diseases are associated with gene expression programs favoring SARS-CoV-2 entry and severity

AbstractPatients with chronic lung disease (CLD) have an increased risk for severe coronavirus disease-19 (COVID-19) and poor outcomes. Here, we analyze the transcriptomes of 611,398 single cells isolated from healthy and CLD lungs to identify molecular characteristics of lung cells that may account for worse COVID-19 outcomes in patients with chronic lung diseases. We observe a similar cellular distribution and relative expression of SARS-CoV-2 entry factors in control and CLD lungs. CLD AT2 cells express higher levels of genes linked directly to the efficiency of viral replication and the innate immune response. Additionally, we identify basal differences in inflammatory gene expression programs that highlight how CLD alters the inflammatory microenvironment encountered upon viral exposure to the peripheral lung. Our study indicates that CLD is accompanied by changes in cell-type-specific gene expression programs that prime the lung epithelium for and influence the innate and adaptive immune responses to SARS-CoV-2 infection.</jats:p