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It has been suggested that a νp-process can occur when hot, dense, and proton-rich matter is expanding within a strong flux of antineutrinos. In such an environment, proton-rich nuclides can be produced in sequences of proton captures and (n, p) reactions, where the free neutrons are created in situ by |$\overline{\nu }_\mathrm{e}+\mathrm{p} {\rightarrow} \mathrm{n}+\mathrm{e}^+$| reactions. The detailed hydrodynamic evolution determines where the nucleosynthesis path turns off from N  = Z line and how far up the nuclear chart it runs. In this work, the uncertainties on the final isotopic abundances stemming from uncertainties in the nuclear reaction rates were investigated in a large-scale Monte Carlo approach, simultaneously varying more than 10 000 reactions. A large range of model conditions was investigated because a definitive astrophysical site for the νp-process has not yet been identified. The present parameter study provides, for each model, identification of the key nuclear reactions dominating the uncertainty for a given nuclide abundance. As all rates appearing in the νp-process involve unstable nuclei, and thus only theoretical rates are available, the final abundance uncertainties are larger than those for nucleosynthesis processes closer to stability. Nevertheless, most uncertainties remain below a factor of 3 in trajectories with robust nucleosynthesis. More extreme conditions allow production of heavier nuclides but show larger uncertainties because of the accumulation of the uncertainties in many rates and because the termination of nucleosynthesis is not at equilibrium conditions. It is also found that the solar ratio of the abundances of 92Mo and 94Mo could be reproduced within uncertainties. [ABSTRACT FROM AUTHOR]

Abstract   We obtain faster algorithms for problems such as r-dimensional matching and r-set packing when the size k of the solution is considered a parameter. We first establish a general framework for finding and exploiting small problem kernels (of size polynomial in k). This technique lets us combine Alon, Yuster and Zwick’s color-coding technique with dynamic programming to obtain faster fixed-parameter algorithms for these problems. Our algorithms run in time O(n+2 O(k)), an improvement over previous algorithms for some of these problems running in time O(n+k O(k)). The flexibility of our approach allows tuning of algorithms to obtain smaller constants in the exponent. [ABSTRACT FROM AUTHOR]