Planning under uncertainty solving large-scale stochastic linear programs

For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages

On the Power of Robust Solutions in Two-Stage Stochastic and Adaptive Optimization Problems

We consider a two-stage mixed integer stochastic optimization problem and show that a static robust solution is a good approximation to the fully adaptable two-stage solution for the stochastic problem under fairly general assumptions on the uncertainty set and the probability distribution. In particular, we show that if the right-hand side of the constraints is uncertain and belongs to a symmetric uncertainty set (such as hypercube, ellipsoid or norm ball) and the probability measure is also symmetric, then the cost of the optimal fixed solution to the corresponding robust problem is at most twice the optimal expected cost of the two-stage stochastic problem. Furthermore, we show that the bound is tight for symmetric uncertainty sets and can be arbitrarily large if the uncertainty set is not symmetric. We refer to the ratio of the optimal cost of the robust problem and the optimal cost of the two-stage stochastic problem as the stochasticity gap. We also extend the bound on the stochasticity gap for another class of uncertainty sets referred to as positive. If both the objective coefficients and right-hand side are uncertain, we show that the stochasticity gap can be arbitrarily large even if the uncertainty set and the probability measure are both symmetric. However, we prove that the adaptability gap (ratio of optimal cost of the robust problem and the optimal cost of a two-stage fully adaptable problem) is at most four even if both the objective coefficients and the right-hand side of the constraints are uncertain and belong to a symmetric uncertainty set. The bound holds for the class of positive uncertainty sets as well. Moreover, if the uncertainty set is a hypercube (special case of a symmetric set), the adaptability gap is one under an even more general model of uncertainty where the constraint coefficients are also uncertain.National Science Foundation (U.S.) (NSF Grant DMI-0556106)National Science Foundation (U.S.) (NSF Grant EFRI-0735905

Identifications of novel mechanisms in breast cancer cells involving duct-like multicellular spheroid formation after exposure to the Random Positioning Machine

Many cell types form three-dimensional aggregates (MCS; multicellular spheroids), when they are cultured under microgravity. MCS often resemble the organ, from which the cells have been derived. In this study we investigated human MCF-7 breast cancer cells after a 2 h-, 4 h-, 16 h-, 24 h-and 5d-exposure to a Random Positioning Machine (RPM) simulating microgravity. At 24 h few small compact MCS were detectable, whereas after 5d many MCS were floating in the supernatant above the cells, remaining adherently (AD). The MCS resembled the ducts formed in vivo by human epithelial breast cells. In order to clarify the underlying mechanisms, we harvested MCS and AD cells separately from each RPM-culture and measured the expression of 29 selected genes with a known involvement in MCS formation. qPCR analyses indicated that cytoskeletal genes were unaltered in short-term samples. IL8, VEGFA, and FLT1 were upregulated in 2 h/4 h AD-cultures. The ACTB, TUBB, EZR, RDX, FN1, VEGFA, FLK1 Casp9, Casp3, PRKCA mRNAs were downregulated in 5d-MCS-samples. ESR1 was upregulated in AD, and PGR1 in both phenotypes after 5d. A pathway analysis revealed that the corresponding gene products are involved in organization and regulation of the cell shape, in cell tip formation and membrane to membrane docking

A Geometric Characterization of the Power of Finite Adaptability in Multistage Stochastic and Adaptive Optimization

In this paper, we show a significant role that geometric properties of uncertainty sets, such as symmetry, play in determining the power of robust and finitely adaptable solutions in multistage stochastic and adaptive optimization problems. We consider a fairly general class of multistage mixed integer stochastic and adaptive optimization problems and propose a good approximate solution policy with performance guarantees that depend on the geometric properties of the uncertainty sets. In particular, we show that a class of finitely adaptable solutions is a good approximation for both the multistage stochastic and the adaptive optimization problem. A finitely adaptable solution generalizes the notion of a static robust solution and specifies a small set of solutions for each stage; the solution policy implements the best solution from the given set, depending on the realization of the uncertain parameters in past stages. Therefore, it is a tractable approximation to a fully adaptable solution for the multistage problems. To the best of our knowledge, these are the first approximation results for the multistage problem in such generality. Moreover, the results and the proof techniques are quite general and also extend to include important constraints such as integrality and linear conic constraints.National Science Foundation (U.S.) (Grant EFRI-0735905

NADPH oxidase elevations in pyramidal neurons drive psychosocial stress-induced neuropathology

Oxidative stress is thought to be involved in the development of behavioral and histopathological alterations in animal models of psychosis. Here we investigate the causal contribution of reactive oxygen species generation by the phagocyte NADPH oxidase NOX2 to neuropathological alterations in a rat model of chronic psychosocial stress. In rats exposed to social isolation, the earliest neuropathological alterations were signs of oxidative stress and appearance of NOX2. Alterations in behavior, increase in glutamate levels and loss of parvalbumin were detectable after 4 weeks of social isolation. The expression of the NOX2 subunit p47phox was markedly increased in pyramidal neurons of isolated rats, but below detection threshold in GABAergic neurons, astrocytes and microglia. Rats with a loss of function mutation in the NOX2 subunit p47phox were protected from behavioral and neuropathological alterations induced by social isolation. To test reversibility, we applied the antioxidant/NOX inhibitor apocynin after initiation of social isolation for a time period of 3 weeks. Apocynin reversed behavioral alterations fully when applied after 4 weeks of social isolation, but only partially after 7 weeks. Our results demonstrate that social isolation induces rapid elevations of the NOX2 complex in the brain. Expression of the enzyme complex was strongest in pyramidal neurons and a loss of function mutation prevented neuropathology induced by social isolation. Finally, at least at early stages, pharmacological targeting of NOX2 activity might reverse behavioral alterations

Analysis of miRNA and mRNA Expression Profiles Highlights Alterations in Ionizing Radiation Response of Human Lymphocytes under Modeled Microgravity

BACKGROUND: Ionizing radiation (IR) can be extremely harmful for human cells since an improper DNA-damage response (DDR) to IR can contribute to carcinogenesis initiation. Perturbations in DDR pathway can originate from alteration in the functionality of the microRNA-mediated gene regulation, being microRNAs (miRNAs) small noncoding RNA that act as post-transcriptional regulators of gene expression. In this study we gained insight into the role of miRNAs in the regulation of DDR to IR under microgravity, a condition of weightlessness experienced by astronauts during space missions, which could have a synergistic action on cells, increasing the risk of radiation exposure. METHODOLOGY/PRINCIPAL FINDINGS: We analyzed miRNA expression profile of human peripheral blood lymphocytes (PBL) incubated for 4 and 24 h in normal gravity (1 g) and in modeled microgravity (MMG) during the repair time after irradiation with 0.2 and 2Gy of \u3b3-rays. Our results show that MMG alters miRNA expression signature of irradiated PBL by decreasing the number of radio-responsive miRNAs. Moreover, let-7i*, miR-7, miR-7-1*, miR-27a, miR-144, miR-200a, miR-598, miR-650 are deregulated by the combined action of radiation and MMG. Integrated analyses of miRNA and mRNA expression profiles, carried out on PBL of the same donors, identified significant miRNA-mRNA anti-correlations of DDR pathway. Gene Ontology analysis reports that the biological category of "Response to DNA damage" is enriched when PBL are incubated in 1 g but not in MMG. Moreover, some anti-correlated genes of p53-pathway show a different expression level between 1 g and MMG. Functional validation assays using luciferase reporter constructs confirmed miRNA-mRNA interactions derived from target prediction analyses. CONCLUSIONS/SIGNIFICANCE: On the whole, by integrating the transcriptome and microRNome, we provide evidence that modeled microgravity can affects the DNA-damage response to IR in human PBL