Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq

International audienceThe verification of floating-point mathematical libraries requires computing numerical bounds on approximation errors. Due to the tightness of these bounds and the peculiar structure of approximation errors, such a verification is out of the reach of generic tools such as computer algebra systems. In fact, the inherent difficulty of computing such bounds often mandates a formal proof of them. In this paper, we present a tactic for the Coq proof assistant that is designed to automatically and formally prove bounds on univariate expressions. It is based on a formalization of floating-point and interval arithmetic, associated with an on-the-fly computation of Taylor expansions. All the computations are performed inside Coq's logic, in a reflexive setting. This paper also compares our tactic with various existing tools on a large set of examples

Differential anti-viral response to respiratory syncytial virus A in preterm and term infants

BACKGROUND: Preterm infants are more likely to experience severe respiratory syncytial virus (RSV) disease compared to term infants. The reasons for this are multi-factorial, however their immature immune system is believed to be a major contributing factor. METHODS: We collected cord blood from 25 preterm (gestational age 30.4-34.1 weeks) and 25 term infants (gestation age 37-40 weeks) and compared the response of cord blood mononuclear cells (CBMCs) to RSVA and RSVB stimulation using neutralising assays, high-dimensional flow cytometry, multiplex cytokine assays and RNA-sequencing. FINDINGS: We found that preterm and term infants had similar maternally derived neutralising antibody titres to RSVA and RSVB. Preterm infants had significantly higher myeloid dendritic cells (mDC) RSV infection compared to term infants. Differential gene expression analysis of RSVA stimulated CBMCs revealed enrichment of genes involved in cytokine production and immune regulatory pathways involving IL-10, IL-36γ, CXCL1, CXCL2, SOCS1 and SOCS3 in term infants, while differentially expressed genes (DEGs) in preterm infants were related to cell cycle (CDK1, TTK, ESCO2, KNL1, CDC25A, MAD2L1) without associated expression of immune response genes. Furthermore, enriched genes in term infants were highly correlated suggesting an increased co-ordination of their immune response to RSVA. When comparing DEGs in preterm and term infants following RSVB stimulation, no differences in immune response genes were identified. INTERPRETATION: Overall, our data suggests that preterm infants have a more restricted immunological response to RSVA compared with term infants. While further studies are required, these findings may help to explain why preterm infants are more susceptible to severe RSV disease and identify potential therapeutic targets to protect these vulnerable infants. FUNDING: Murdoch Children's Research Institute Infection and Immunity theme grant