On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Statsrådet K.-A. Fagerholm Julen 1970 Härstädes

Kirje

Genome-wide association study of major recurrent depression in the U.K. population.

OBJECTIVE: Studies of major depression in twins and families have shown moderate to high heritability, but extensive molecular studies have failed to identify susceptibility genes convincingly. To detect genetic variants contributing to major depression, the authors performed a genome-wide association study using 1,636 cases of depression ascertained in the U.K. and 1,594 comparison subjects screened negative for psychiatric disorders. METHOD: Cases were collected from 1) a case-control study of recurrent depression (the Depression Case Control [DeCC] study; N=1346), 2) an affected sibling pair linkage study of recurrent depression (probands from the Depression Network [DeNT] study; N=332), and 3) a pharmacogenetic study (the Genome-Based Therapeutic Drugs for Depression [GENDEP] study; N=88). Depression cases and comparison subjects were genotyped at Centre National de Génotypage on the Illumina Human610-Quad BeadChip. After applying stringent quality control criteria for missing genotypes, departure from Hardy-Weinberg equilibrium, and low minor allele frequency, the authors tested for association to depression using logistic regression, correcting for population ancestry. RESULTS: Single nucleotide polymorphisms (SNPs) in BICC1 achieved suggestive evidence for association, which strengthened after imputation of ungenotyped markers, and in analysis of female depression cases. A meta-analysis of U.K. data with previously published results from studies in Munich and Lausanne showed some evidence for association near neuroligin 1 (NLGN1) on chromosome 3, but did not support findings at BICC1. CONCLUSIONS: This study identifies several signals for association worthy of further investigation but, as in previous genome-wide studies, suggests that individual gene contributions to depression are likely to have only minor effects, and very large pooled analyses will be required to identify them.

Kenraali K. O. Leinonen 5/10 1973

Kirje 5.10.1973

Presidentti J.K. Paasikivi 27/11 1956

Kirje 27.11.1956