On random walks on affine group

Diaconis' presumption that the number of steps required to get close to uniform for a random walk on the affine group A _pis c(p)p ²with c(p) →ã is verified. We also discuss the random number generation associated with the random walk on the affine group. The number of steps to force the generated number to become random is improved. A modified version of Diacohis-Shahshahani's upper bound lemma is given and applied     

Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications to Image Restoration

Abstract

In this paper, we show how the time for convergence to stationarity of a Markov chain can be assessed using the Wasserstein metric, rather than the usual choice of total variation distance. The Wasserstein metric may be more easily applied in some applications, particularly those on continuous state spaces. Bounds on convergence time are established by considering the number of iterations required to approximately couple two realizations of the Markov chain to within ε tolerance. The particular application considered is the use of the Gibbs sampler in the Bayesian restoration of a degraded image, with pixels that are a continuous grey-scale and with pixels that can only take two colours. On finite state spaces, a bound in the Wasserstein metric can be used to find a bound in total variation distance. We use this relationship to get a precise O(N log N) bound on the convergence time of the stochastic Ising model that holds for appropriate values of its parameter as well as other binary image models. Our method employing convergence in the Wasserstein metric can also be applied to perfect sampling algorithms involving coupling from the past to obtain estimates of their running times.     

Sikkema-Bézier型算子对有界变差函数的点态逼近度

构造了两种Sikkema -B啨ｚｉｅｒ型算子Ｓｎ,a(f,x) ,S n ,a(f,x) (它们是Sikkema算子的两种推广 ) ,并研究了它们对有界变差函数的点态逼近 ,得到它们对这类函数点态逼近的最优估计式     

中国古典词学正变批评的发展及其特征

我国古典词学正变批评的发展主要经历了三个阶段,即:明代为彰显期,清代前中期为兴盛期,晚清为深化期;其特征则主要体现在体派性、源流性、导引性三个方面.     

中学、西学与东学——现代汉语诗学话语主体的知识结构与话语立场

由于代际与经历的不同,现代汉语诗学话语主体呈现出复杂的知识结构,要么侧重“中学”,要么侧重“西学”,要么学贯中西,但在中学与西学的两极之外,还有关于日本的学问与经由日本传入中国的学问,我们称之为“东学”。中学、西学与东学的知识变奏,使得现代汉语诗学话语主体也在理性、自由、激进、保守等不同话语立场的辩驳与冲撞中,将现代汉语诗学话语演绎得淋漓尽致、丰富多彩。     

湖北汤孙湖菱属植物果实性状的变异式样及其分类学意义

本文用居群方法采集湖北汤孙湖菱属（Trapa.L.）植物果实140个，分别测量了18个性状，以柱形图、形象化散点图分析了性状的可塑性，变异式样及其相关性。并探讨了其分类学意义，结果表明，腰角的有无和长度可作为分类的主要性状，依此，可将汤孙湖的菱属确认为格菱和野菱两个种。     

Within-Animal Variation as an Indication of the Minimal Magnitude of the Critical Effect Size for Continuous Toxicological Parameters Applicable in the Benchmark Dose Approach

In this study, the within-animal variation in routinely studied continuous toxicological parameters was estimated from temporal fluctuations in individual healthy nonexposed animals. Assuming that these fluctuations are nonadverse, this within-animal variation may be indicative of the minimal magnitude of the critical effect size (CES). The CES is defined as the breaking point between adverse and nonadverse changes in a continuous toxicological parameter, at the level of the individual organism. The total variation in the data from individual nonexposed animals was divided in variation parts due to known factors (differences in sex, animal, and day) and a residual variation, by means of analysis of variance. Using the residual variation and the estimated analytical measurement error of a toxicological parameter, the within-animal variation can be estimated. The data showed within-animal variations ranging between 0.6% and 34% for different clinical chemistry and hematological parameters in 90-day rat studies. This indicates that different (minimal) CES values may be applicable for different parameters.