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The eukaryotic cell cycle is regulated by a complicated chemical reaction network. Although many deterministic models have been proposed, stochastic models are desired to capture noise in the cell resulting from low numbers of critical species. However, converting a deterministic model into one that accurately captures stochastic effects can result in a complex model that is hard to build and expensive to simulate. In this paper, we first apply a hybrid (mixed deterministic and stochastic) simulation method to such a stochastic model. With proper partitioning of reactions between deterministic and stochastic simulation methods, the hybrid method generates the same primary characteristics and the same level of noise as Gillespie's stochastic simulation algorithm, but with better efficiency. By studying the results generated by various partitionings of reactions, we developed a new strategy for hybrid stochastic modeling of the cell cycle. The new approach is not limited to using mass-action rate laws. Numerical experiments demonstrate that our approach is consistent with characteristics of noisy cell cycle progression, and yields cell cycle statistics in accord with experimental observations.

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A computational tool was applied based on a two dimensional linear method to predict the hydrodynamic loads for damaged ships. Experimental tests on a ship model have also been carried out to predict the hydrodynamic loads in various design conditions. The results of the theoretical method and experimental tests are compared to validate the theoretical method. The extreme wave induced loads have been calculated by short term prediction. For the loads in intact condition, the prediction with duration of 20 years at sea state 5 is used, while for loads in damaged conditions the prediction in 96 hours exposure time at sea 3 is used. The maximum values of the most probable extreme amplitudes of dynamic wave induced loads in damaged conditions are much less than those in intact condition because of the reduced time. An opening could change the distribution of not only stillwater bending moment but also wave-induced bending moment. It is observed that although some cross sections are not structurally damaged, the total loads acting on these cross sections after damage may be increased dramatically compared to the original design load in intact condition

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