Information relaxations and duality in stochastic dynamic programs

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a "penalty" that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values. © 2010 INFORMS.

Prolactin receptor signaling is essential for perinatal brown adipocyte function: a role for insulin-like growth factor-2.

BACKGROUND: The lactogenic hormones prolactin (PRL) and placental lactogens (PL) play central roles in reproduction and mammary development. Their actions are mediated via binding to PRL receptor (PRLR), highly expressed in brown adipose tissue (BAT), yet their impact on adipocyte function and metabolism remains unclear. METHODOLOGY/PRINCIPAL FINDINGS: PRLR knockout (KO) newborn mice were phenotypically characterized in terms of thermoregulation and their BAT differentiation assayed for gene expression studies. Derived brown preadipocyte cell lines were established to evaluate the molecular mechanisms involved in PRL signaling on BAT function. Here, we report that newborn mice lacking PRLR have hypotrophic BAT depots that express low levels of adipocyte nuclear receptor PPARgamma2, its coactivator PGC-1alpha, uncoupling protein 1 (UCP1) and the beta3 adrenoceptor, reducing mouse viability during cold challenge. Immortalized PRLR KO preadipocytes fail to undergo differentiation into mature adipocytes, a defect reversed by reintroduction of PRLR. That the effects of the lactogens in BAT are at least partly mediated by Insulin-like Growth Factor-2 (IGF-2) is supported by: i) a striking reduction in BAT IGF-2 expression in PRLR KO mice and in PRLR-deficient preadipocytes; ii) induction of cellular IGF-2 expression by PRL through JAK2/STAT5 pathway activation; and iii) reversal of defective differentiation in PRLR KO cells by exogenous IGF-2. CONCLUSIONS: Our findings demonstrate that the lactogens act in concert with IGF-2 to control brown adipocyte differentiation and growth. Given the prominent role of brown adipose tissue during the perinatal period, our results identified prolactin receptor signaling as a major player and a potential therapeutic target in protecting newborn mammals against hypothermia.

Genome-wide association study of perioperative myocardial infarction after coronary artery bypass surgery.

OBJECTIVES: Identification of patient subpopulations susceptible to develop myocardial infarction (MI) or, conversely, those displaying either intrinsic cardioprotective phenotypes or highly responsive to protective interventions remain high-priority knowledge gaps. We sought to identify novel common genetic variants associated with perioperative MI in patients undergoing coronary artery bypass grafting using genome-wide association methodology. SETTING: 107 secondary and tertiary cardiac surgery centres across the USA. PARTICIPANTS: We conducted a stage I genome-wide association study (GWAS) in 1433 ethnically diverse patients of both genders (112 cases/1321 controls) from the Genetics of Myocardial Adverse Outcomes and Graft Failure (GeneMAGIC) study, and a stage II analysis in an expanded population of 2055 patients (225 cases/1830 controls) combined from the GeneMAGIC and Duke Perioperative Genetics and Safety Outcomes (PEGASUS) studies. Patients undergoing primary non-emergent coronary bypass grafting were included. PRIMARY AND SECONDARY OUTCOME MEASURES: The primary outcome variable was perioperative MI, defined as creatine kinase MB isoenzyme (CK-MB) values ≥10× upper limit of normal during the first postoperative day, and not attributable to preoperative MI. Secondary outcomes included postoperative CK-MB as a quantitative trait, or a dichotomised phenotype based on extreme quartiles of the CK-MB distribution. RESULTS: Following quality control and adjustment for clinical covariates, we identified 521 single nucleotide polymorphisms in the stage I GWAS analysis. Among these, 8 common variants in 3 genes or intergenic regions met p<10(-5) in stage II. A secondary analysis using CK-MB as a quantitative trait (minimum p=1.26×10(-3) for rs609418), or a dichotomised phenotype based on extreme CK-MB values (minimum p=7.72×10(-6) for rs4834703) supported these findings. Pathway analysis revealed that genes harbouring top-scoring variants cluster in pathways of biological relevance to extracellular matrix remodelling, endoplasmic reticulum-to-Golgi transport and inflammation. CONCLUSIONS: Using a two-stage GWAS and pathway analysis, we identified and prioritised several potential susceptibility loci for perioperative MI.