This paper summarizes the intermediate lessons learned from the analyses of the risk management problems in three technological endeavors. These problems are: the absence of a structure for rewarding successful project risk management; the need for an ever-more accurate economic measure of risk; and the difficulty of transferring risks to contract-bound independent outsourcing entity. This paper also describes recent advancement towards providing answers to these challenges and future research endeavors in this field.

Many applications of scientific computing rely on computations on sparse matrices, thus the design of efficient implementations of sparse matrix kernels is crucial for the overall efficiency of these applications. Due to the high compute-to-memory ratio and irregular memory access patterns, the performance of sparse matrix kernels is often far away from the peak performance on a modern processor. Alternative data structures have been proposed, which split the original matrix A into A{sub d} and A{sub s}, so that A{sub d} contains all dense blocks of a specified size in the matrix, and A{sub s} contains the remaining entries. This enables the use of dense matrix kernels on the entries of A{sub d} producing better memory performance. In this work, we study the problem of finding a maximum number of non overlapping rectangular dense blocks in a sparse matrix, which has not been studied in the sparse matrix community. We show that the maximum non overlapping dense blocks problem is NP-complete by using a reduction from the maximum independent set problem on cubic planar graphs. We also propose a 2/3-approximation algorithm for 2 times 2 blocks that runs in linear time in the number of nonzeros in the matrix. We …

We analyze results of 15 global climate simulations contributed to the Coupled Model Intercomparison Project (CMIP). Focusing on the western U.S., we consider both present climate simulations and predicted responses to increasing atmospheric CO{sub 2}. The models vary in their ability to predict the present climate. Over the western U.S., a few models produce a seasonal cycle for spatially-averaged temperature and/or precipitation in good agreement with observational data. Other models tend to overpredict precipitation in the winter or exaggerate the amplitude of the seasonal cycle of temperature. The models also differ in their ability to reproduce the spatial patterns of temperature and precipitation in the U.S. Considering the monthly mean precipitation responses to doubled atmospheric CO{sub 2}, averaged over the western U.S., we find some models predict increases while others predict decreases. The predicted temperature response, on the other hand, is invariably positive over this region; however, for each month, the range of values given by the different models is large compared to the mean model response. We look for possible relationships between the models' temperature and precipitation responses to doubled CO{sub 2} concentration and their ability to simulate some aspects of the present climate. We find that these relationships …

We show that a simple plane wave analysis can be used even under tight focusing conditions to predict the dependence of third-harmonic generation on the polarization state of the incident beam. Exploiting this fact, we then show that circularly polarized beams may be used to spatially characterize the beam focus and temporally characterize ultrashort pulses in high numerical aperture systems by experimentally demonstrating, for the first time, novel collinear, background-free, third-harmonic intensity autocorrelations in time and space in a high numerical aperture microscope. We also discuss the possibility of using third harmonic generation with circularly polarized beams for background-free collinear frequency resolved optical gating.

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