From coinductive proofs to exact real arithmetic: theory and applications

Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. We discuss several examples including the extraction of programs for polynomials up to degree two and the definite integral of continuous maps

Progress in the development of selective heme oxygenase-1 inhibitors and their potential therapeutic application

Heme oxygenases (HOs) are a family of enzymes involved in the selective catabolism of free circulating heme. While HO-2 is constitutively expressed, HO-1 is strongly overexpressed under stressful stimuli (e.g., oxidative stress). Under these conditions, HO-1 exerts its strong cytoprotective activities and plays a crucial role in stimulating cell survival by removing the pro-oxidant heme and by producing carbon monoxide and biliverdin (promptly reduced to bilirubin). Unfortunately, the broad spectrum of HO-1 cytoprotective effects has been well experimentally documented both in normal and tumor cells, where the enzyme can be overexpressed, making it an exciting target in the management of some type of tumors. Development of non-competitive HO-1 inhibitors dates back in 2002 with the discovery of Azalanstat. Since then, many efforts have been devoted to the identification of selective HO-1 and HO-2 inhibitors and to unravel the molecular determinants responsible for selectivity. Molecular modeling studies supported the identification of chemical features involved in the recognition and inhibition of these enzymes. Herein, medicinal chemistry aspects and in silico studies related to the development of HO inhibitors will be discussed. The purpose of this review is to highlight recent advances in the development of new selective HO-1 and HO-2 inhibitors and covers the last six years (2013–2018)

Folliculogenesis in random start protocols for oocytes cryopreservation: quantitative and qualitative aspects

Random start protocols are commonly used for oocytes cryopreservation in women with cancer. However, evidence to support their effectiveness is yet modest. This study aims to compare the quality of ovarian response between the ovary carrying the dominant follicle or the corpus luteum (active ovary) and the contralateral ovary (resting ovary). Women with a diagnosis of malignancy who underwent oocytes cryopreservation were reviewed. The main inclusion criterion was the presence of a unilateral dominant follicle or a unilateral corpus luteum on the first day of ovarian hyperstimulation. The primary outcome was the number of mature oocytes retrieved. Intra-patient comparisons between the two ovaries were made using the nonparametric Wilcoxon test for paired data. Forty-three women were included. The number of mature oocytes retrieved from the active and the resting ovaries did not differ, the median [interquartile range—IQR] being 4 [2–7] and 5 [2–8], respectively (p = 0.09). The rate [IQR] of mature oocytes per developed follicle was 58% [40–80%] and 65% [33–87%], respectively (p = 0.42). In addition, no significant difference emerged when repeating the analyses separately for women carrying dominant follicles and for those carrying corpora lutea. This study failed to detect any detrimental effect of the presence of a dominant follicle or a corpus luteus on the ovarian response to hyperstimulation, thus supporting the validity of random start protocols

Polynomial time over the reals with parsimony

International audienceWe provide a characterization of Ko's class of polynomial time computable functions over real numbers. This characterization holds for a stream based language using a parsimonious type discipline, a variant of propositional linear logic. We obtain a first characterization of polynomial time computations over the reals on a higher-order functional language using a linear/affine type system

From Coinductive Proofs to Exact Real Arithmetic

Abstract. We give a coinductive characterisation of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. This is a pilot study in using proof-theoretic methods for obtaining certified algorithms in exact real arithmetic.