On the matricial version of Fermat–Euler congruences

The congruences modulo the primary numbers n=p ^a are studied for the traces of the matrices A ⁿ and A ^n-φ(n), where A is an integer matrix and φ(n) is the number of residues modulo n, relatively prime to n. We present an algorithm to decide whether these congruences hold for all the integer matrices A, when the prime number p is fixed. The algorithm is explicitly applied for many values of p, and the congruences are thus proved, for instance, for all the primes p ≤ 7 (being untrue for the non-primary modulus n=6). We prove many auxiliary congruences and formulate many conjectures and problems, which can be used independently. Partially supported by RFBR, grant 05-01-00104. An erratum to this article is available at .     

A functional central limit theorem for a generalized occupancy problem

A functional central limit theorem is proved for a class of finitely exchangeable random variables which are based on an occupancy scheme.     

论Suslov误解和Holder缺陷

本文根据变分学的基本原理，从产生ｄ－δ交换性问题的根源出发，证明了Ｓｕｓｌｏｖ观点实际上是一种误解；还证明了Ｈｏｌｄｅｒ观点基本正确，但存在缺陷。本文的工作表明，微分运算ｄ和变分运算δ次序可以交换，这是变分学中的一个基本原理，这一基本原理也适用于非完整系统。     

PHS网络MOS优化的研究

通过对PHS网络中MOS(平均意见得分)测试的分析,结合PHS网络现状和寻呼区结构,发现PHS网络中潜在的寻呼区边界问题,进一步研究寻呼区的规划和特性,提出寻呼区规划和优化的两种方法,用来提高PHS网络的MOS值和用户感知。通过MOS测试及效果评估,验证了所提出的优化方法对改善PHS网络的MOS值具有一定的效果,尤其对MOS分值偏低的改善幅度更为明显,能够提高用户对PHS网络的满意度。     

投资者看法差异与风险资产定价

股票市场中投资者的看法差异是否影响定价?将投资者之间由于信息不对称引起的看法差异和对称信息下由于信念异质引起的看法差异,纳入统一的一个理性预期模型,推导出基于信息性风险和异质信念下的风险资产定价模型,对几种不同来源性质的看法差异进行剥离并通过对均衡价格的比较静态分析证明了:由信息不对称造成的看法差异与投资者要求的预期收益率正相关,而由信念异质引起的看法差异与预期收益率负相关.这表明:投资者对逆向选择风险要求额外的风险贴水,而相反会忽视赢者诅咒风险,投资者的看法差异越大越会造成股票价格的高估.     

Conditional Logistic Regression With Longitudinal Follow-up and Individual-Level Random Coefficients: A Stable and Efficient Two-Step Estimation Method

The analysis of data generated by animal habitat selection studies, by family studies of genetic diseases, or by longitudinal follow-up of households often involves fitting a mixed conditional logistic regression model to longitudinal data composed of clusters of matched case-control strata. The estimation of model parameters by maximum likelihood is especially difficult when the number of cases per stratum is greater than one. In this case, the denominator of each cluster contribution to the conditional likelihood involves a complex integral in high dimension, which leads to convergence problems in the numerical maximization. In this article we show how these computational complexities can be bypassed using a global two-step analysis for nonlinear mixed effects models. The first step estimates the cluster-specific parameters and can be achieved with standard statistical methods and software based on maximum likelihood for independent data. The second step uses the EM-algorithm in conjunction with conditional restricted maximum likelihood to estimate the population parameters. We use simulations to demonstrate that the method works well when the analysis is based on a large number of strata per cluster, as in many ecological studies. We apply the proposed two-step approach to evaluate habitat selection by pairs of bison roaming freely in their natural environment. This article has supplementary material online.     

与格路有关的组合恒等式

通过研究格路径的性质得到一类组合恒等式的通式,代入不同的参数给出已有的一些组合恒等式新的简洁证明,并得到一些新的组合恒等式.最后推广得到多项式系数的恒等式.     

A comparison of generalized multinomial logit and latent class approaches to studying consumer heterogeneity with some extensions of the generalized multinomial logit model

We calibrate and contrast the recent generalized multinomial logit model and the widely used latent class logit model approaches for studying heterogeneity in consumer purchases. We estimate the parameters of the models on panel data of household ketchup purchases, and find that the generalized multinomial logit model outperforms the best‐fitting latent class logit model in terms of the Bayesian information criterion. We compare the posterior estimates of coefficients for individual customers based on the two different models and discuss how the differences could affect marketing strategies (such as pricing), which could be affected by applying each of the models. We also describe extensions to the scale heterogeneity model that includes the effects of state dependence and purchase history. Copyright © 2011 John Wiley & Sons, Ltd.     

齐次Poisson过程中到达时刻的分布

利用多项分布、区间分解等方法研究了齐次Poi8son过程中粒子到达时刻的分布规律,对许多定理进行研究和推广,得到了更为一般的结果.     

基于网络舆情倾向性分析的机器学习方法研究

本文重点是对网络用户中的网络舆情倾向性进行分析,构建一种准确率更高的模型来实现情感倾向判断.网络舆情倾向性分析主要是通过机器学习的方法和制定部分规则的方法,从而能够更加准确地判断出句子的情感倾向性,进而能在实际生活中进行有针对性地积极引导调控.基于此,提出一个设想,对于机器学习的方法之间的结合与本身的改进,再加入规则的制定,能够提高机器对情感句子的分析准确率.对于模型应用之前的特征提取的方法进行比较选取,通过特定的特征选取方式使得构造向量空间更加准确,再通过比较不同分类算法进行比较选取.