Leading strategies in competitive on-line prediction

We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a “leading prediction strategy”, which not only asymptotically performs at least as well as any continuous limited-memory strategy, but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space, we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.     

紊流边界层脉动壁压研究

通过试验获得了紊流边界层脉动壁压信号,讨论了不同雷诺数条件下水流脉动壁压的统计特性,并对实测的脉动壁压进行了正交分解与低阶近似的研究．计算结果表明,紊流边界层的脉动壁压可用正交分解进行描述,其特征值随阶数的增加而减小,说明雷诺数越高,紊流中含能模态的激发越多．对脉动壁压进行低阶近似所须的阶数也与雷诺数的大小有关．