Automated Sensitivity Analysis for Probabilistic Loops

We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from symbolic computation, probability theory, and static analysis in order to automatically capture sensitivity information about probabilistic loops. Sensitivity information allows us to formally establish how value distributions of probabilistic loop variables influence the functional behavior of loops, which can in particular be helpful when choosing values of loop variables in order to ensure efficient/expected computations. Our work uses algebraic techniques to model higher moments of loop variables via linear recurrence equations and introduce the notion of sensitivity recurrences. We show that sensitivity recurrences precisely model loop sensitivities, even in cases where the moments of loop variables do not satisfy a system of linear recurrences. As such, we enlarge the class of probabilistic loops for which sensitivity analysis was so far feasible. We demonstrate the success of our approach while analyzing the sensitivities of probabilistic loops

Strong Invariants Are Hard: On the Hardness of Strongest Polynomial Invariants for (Probabilistic) Programs

We show that computing the strongest polynomial invariant for single-path loops with polynomial assignments is at least as hard as the Skolem problem, a famous problem whose decidability has been open for almost a century. While the strongest polynomial invariants are computable for affine loops, for polynomial loops the problem remained wide open. As an intermediate result of independent interest, we prove that reachability for discrete polynomial dynamical systems is Skolem-hard as well. Furthermore, we generalize the notion of invariant ideals and introduce moment invariant ideals for probabilistic programs. With this tool, we further show that the strongest polynomial moment invariant is (i) uncomputable, for probabilistic loops with branching statements, and (ii) Skolem-hard to compute for polynomial probabilistic loops without branching statements. Finally, we identify a class of probabilistic loops for which the strongest polynomial moment invariant is computable and provide an algorithm for it

Transfusion / Glycated hemoglobin concentrations of packed red blood cells minimally increase during storage under standard blood banking conditions

BACKGROUND Few and inconsistent data exist describing the effect of storage duration on glycated hemoglobin (HbA1c) concentrations of red blood cells (RBCs), impeding interpretation of HbA1c values in transfused diabetic patients. Hence the aim of this study was to evaluate to what extent HbA1c concentrations of RBCs change during the maximum allowed storage period of 42 days. STUDY DESIGN AND METHODS Blood was drawn from 16 volunteers, leukofiltered, and stored under standard blood banking conditions. HbA1c concentrations of RBCs were measured on Days 1 and 42 of storage using three different validated devices (ionexchange highperformance liquid chromatography Method A1 and A2, turbidimetric immunoassay Method B). RESULTS Mean HbA1c concentrations of RBCs on Day 1 were 5.3 0.3% (Method A1), 5.4 0.4% (Method A2), and 5.1 0.4% (Method B). HbA1c concentrations increased to 5.6 0.3% (A1, p < 0.0001), 5.7 0.3% (A2, p = 0.004), and 5.5 0.4% (B, p < 0.0001) on Day 42, respectively, corresponding to a 1.06fold increase across all methods. Glucose concentrations in the storage solution of RBCs decreased from 495 27 to 225 55 mg/dL (p < 0.0001), confirming that stored RBCs were metabolically active. CONCLUSION These results suggest a significant, albeit minor, and most likely clinically insignificant increase in HbA1c concentrations during storage of RBCs for 42 days.(VLID)341760