Risk Minimization, Regret Minimization and Progressive Hedging Algorithms

This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomposition scheme, called progressive hedging, for solving multistage risk minimization and regret minimization problems. In particular, the classical progressive hedging algorithm is modified in order to handle a new class of linkage constraints that arises from reformulations and other applications of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms.Comment: 21 pages, 2 figure

The function of RNA Binding Protein 9 in germ cell differentiation in Drosophila ovary

Germ cell development is an essential process to ensure continuity of species. Drosophila oogenesis has long been served as a model system to study germ cell development. Previously, the Elav-Hu family protein RNA-binding protein 9 (rbp9) has been reported important for germ cell differentiation in Drosophila ovary, but its mechanism of function is largely unknown. In this study, we aimed to further study the function of Rbp9 in germ cell differentiation. Firstly, we confirmed rbp9 mutant phenotype by using rbp9 germline specific RNAi knock-down. We further confirmed that Rbp9 is highly expressed in sixteen-cell cyst and early egg chambers by using BAC transgenic reporter. Rbp9 mutant germarium contains accumulated early cysts. BMP signaling and Bam regulation is not affected in rbp9 mutant, but early differentiation cysts expressing Nanos, Sxl and Bam are accumulated in rbp9 mutant. Moreover, sixteen-cell cysts are failed to further differentiate in rb9 mutant. Both Bruno and Orb expression cysts are present in rbp9 mutant, but they are blocked before oocyte specification and begin to degenerate. And meiosis is also failed initiated in rbp9 mutant. The function of rbp9 in germ cell differentiation is required for both adult stage and before adult stage. Though Rbp9 is critical for cyst differentiation, over-expression of Rbp9 does not affect germ cell development in germarium region. But Rbp9 over-expression will affect number of cyst division times and mid stage egg chamber development. Moreover, we identified that rbp9 genetically interacts with bam in regulating cystoblast differentiation. Rbp9 functions as downstream of Bam in germline differentiation, as Rbp9 over-expression can partially drive germ cell differentiation in bam mutant, but lack of Rbp9 blocks Bam driving germ cell differentiation. In all, this study will help better understand function of rbp9 in germ cell differentiation in Drosophila ovary, and may also provide insights in general germ cell development

Heat transfer in vertical concentric cylinders in a high level nuclear waste repository

Modeling free convection heat transfer in a cylindrical annular enclosure is still an active area of research and an important problem to be addressed in the high level nuclear waste repository. The waste containers are vertically emplaced in the borehole 300 meters below ground. and in a horizontal grid of 30 x 8 meters apart. The borehole will be capped after the container emplacement and the container is surrounded by an enclosed vertically concentric air-gap inside the borehole. The expected initial heat generated is 4.74 kW per container and it degenerates exponentially with time. A computer simulation model is used to find the thermal performance for the air-gap and the problem is solved in two steps. The first step is to solve for the heat conduction in the rock. The second step proceeds by using the results of the first step as boundary condition to solve the more complicated convection and radiation in the air-gap. Finally a parametric study was done for three different air-gap thicknesses (5 cm, 10 cm, and 15 cm) to obtain the effect of the gap thickness on that heat transfer. Eventually the goal of this study is to obtain the temperature at the central axis of the vertical container as a function of time so that the maximum temperature of the zirconium cladding on the fuel pellets can be determined