康熙己卯顺天乡试案考辨

康熙三十八年发生的己卯顺天乡试案,是康熙朝科场大案之一,不仅牵涉甚广,而且对此后的科举制度发展产生了深远影响.文章主要考察了己卯顺天乡试案的案情始末,并对整个案件的处理情况进行了分析,指出此次科场案件不仅体现了康熙皇帝高明的政治手段和治国策略,更成为清朝科举制度改革的重要契机,由此而生发的各种科场改革对有清一代亦发挥重要作用.     

Global Optimization in Any Minkowski Metric: A Permutation-Translation Simulated Annealing Algorithm for Multidimensional Scaling

It is well known that considering a non-Euclidean Minkowski metric in Multidimensional Scaling, either for the distance model or for the loss function, increases the computational problem of local minima considerably. In this paper, we propose an algorithm in which both the loss function and the composition rule can be considered in any Minkowski metric, using a multivariate randomly alternating Simulated Annealing procedure with permutation and translation phases. The algorithm has been implemented in Fortran and tested over classical and simulated data matrices with sizes up to 200 objects. A study has been carried out with some of the common loss functions to determine the most suitable values for the main parameters. The experimental results confirm the theoretical expectation that Simulated Annealing is a suitable strategy to deal by itself with the optimization problems in Multidimensional Scaling, in particular for City-Block, Euclidean and Infinity metrics.