Cyclotomic valuation of qq-Pochhammer symbols and qq-integrality of basic hypergeometric series

We give a formula for the cyclotomic valuation of $q$-Pochhammer symbols in terms of (generalized) Dwork maps. We also obtain a criterion for the $q$-integrality of basic hypergeometric series in terms of certain step functions, which generalize Christol step functions. This provides suitable $q$-analogs of two results proved by Christol: a formula for the $p$-adic valuation of Pochhammer symbols and a criterion for the $N$-integrality of hypergeometric series

New Finite Rogers-Ramanujan Identities

We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson's transformation formula by specialization or through Bailey's method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.Comment: 19 pages. to appear in Ramanujan

Multinational characterization of neurological phenotypes in patients hospitalized with COVID-19

Neurological complications worsen outcomes in COVID-19. To define the prevalence of neurological conditions among hospitalized patients with a positive SARS-CoV-2 reverse transcription polymerase chain reaction test in geographically diverse multinational populations during early pandemic, we used electronic health records (EHR) from 338 participating hospitals across 6 countries and 3 continents (January–September 2020) for a cross-sectional analysis. We assessed the frequency of International Classification of Disease code of neurological conditions by countries, healthcare systems, time before and after admission for COVID-19 and COVID-19 severity. Among 35,177 hospitalized patients with SARS-CoV-2 infection, there was an increase in the proportion with disorders of consciousness (5.8%, 95% confidence interval [CI] 3.7–7.8%, pFDR < 0.001) and unspecified disorders of the brain (8.1%, 5.7–10.5%, pFDR < 0.001) when compared to the pre-admission proportion. During hospitalization, the relative risk of disorders of consciousness (22%, 19–25%), cerebrovascular diseases (24%, 13–35%), nontraumatic intracranial hemorrhage (34%, 20–50%), encephalitis and/or myelitis (37%, 17–60%) and myopathy (72%, 67–77%) were higher for patients with severe COVID-19 when compared to those who never experienced severe COVID-19. Leveraging a multinational network to capture standardized EHR data, we highlighted the increased prevalence of central and peripheral neurological phenotypes in patients hospitalized with COVID-19, particularly among those with severe disease

The Cyst-Dividing Bacterium Ramlibacter tataouinensis TTB310 Genome Reveals a Well-Stocked Toolbox for Adaptation to a Desert Environment

Ramlibacter tataouinensis TTB310T (strain TTB310), a betaproteobacterium isolated from a semi-arid region of South Tunisia (Tataouine), is characterized by the presence of both spherical and rod-shaped cells in pure culture. Cell division of strain TTB310 occurs by the binary fission of spherical “cyst-like” cells (“cyst-cyst” division). The rod-shaped cells formed at the periphery of a colony (consisting mainly of cysts) are highly motile and colonize a new environment, where they form a new colony by reversion to cyst-like cells. This unique cell cycle of strain TTB310, with desiccation tolerant cyst-like cells capable of division and desiccation sensitive motile rods capable of dissemination, appears to be a novel adaptation for life in a hot and dry desert environment. In order to gain insights into strain TTB310's underlying genetic repertoire and possible mechanisms responsible for its unusual lifestyle, the genome of strain TTB310 was completely sequenced and subsequently annotated. The complete genome consists of a single circular chromosome of 4,070,194 bp with an average G+C content of 70.0%, the highest among the Betaproteobacteria sequenced to date, with total of 3,899 predicted coding sequences covering 92% of the genome. We found that strain TTB310 has developed a highly complex network of two-component systems, which may utilize responses to light and perhaps a rudimentary circadian hourglass to anticipate water availability at the dew time in the middle/end of the desert winter nights and thus direct the growth window to cyclic water availability times. Other interesting features of the strain TTB310 genome that appear to be important for desiccation tolerance, including intermediary metabolism compounds such as trehalose or polyhydroxyalkanoate, and signal transduction pathways, are presented and discussed