Partially observed optimal stopping problem for discrete-time Markov processes

This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization procedure based on optimal quantization. First,we discretize the state space of the unobserved variable by quantizing an underlying reference measure. Then we jointly discretize the resulting approximate filter and the observation process. We obtain a fully computable approximation of the value function with explicit error bounds for its convergence towards the true value fonction

X chromosome gene dosage as a determinant of congenital malformations and of age-related comorbidity risk in patients with Turner syndrome, from childhood to early adulthood

International audienceObjective Turner Syndrome is associated with several phenotypic conditions associated with a higher risk of subsequent comorbidity. We aimed to evaluate the prevalence of congenital malformations and the occurrence of age-related comorbid conditions and to determine whether the frequencies of congenital and acquired conditions depend on X chromosome gene dosage, as a function of karyotype subgroup. Design and methods This national retrospective observational cohort study includes 1501 patients. We evaluated the prevalence of congenital malformations and the cumulative incidence of subsequent specific comorbidities at five-year intervals, from the ages of 10 to 30 years, with stratification by karyotype subgroup: 45,X (n = 549), 45,X/46,isoXq (n = 280), 46,X,r(X)/46,XX (n = 106), 45,X/46,XX (n = 221), presence of Y (n = 87). Results Median age was 9.4 (3.7-13.7) years at first evaluation and 16.8 (11.2-21.4) years at last evaluation. Congenital heart (18.9%) malformations were more frequent in 45,X patients, and congenital renal (17.2%) malformations were more frequent in 45,X, 45,X/46,isoXq and 46,X,r(X)/46,XX patients than in those with 45,X/46,XX mosaicism or a Y chromosome (P < 0.0001). The cumulative incidence of subsequent acquired conditions, such as thyroid disease, hearing loss, overweight/obesity, dyslipidemia and, to a lesser extent, celiac disease, glucose intolerance/type 2 diabetes, hypertension and liver dysfunction increased with age, but less markedly for patients with mosaicism than for those with other karyotypes. Patients with a ring chromosome were more prone to metabolic disorders. Conclusion These data suggest that X gene chromosome dosage, particularly for Xp genes, contributes to the risk of developing comorbidities