AIFS—A Tool for Biomorphic Fractal Modeling

A considerable class of fractal sets can be represented by using the attractors of Iterated Function Systems (Barnsley, 1988), with affine contractive mappings of a metric space . The modeling capabilities of such systems are heavily limited however. For example, it is not easy to predict the location of the attractor nor its global shape. Then, Iterated Systems are not affinely invariant (affine mappings of the elements of the system do not result in affine image of its attractor). In this paper a new setting, the affine invariant Iterated Function System is described in such a way that it removes the mentioned shortcomings and can be used for shape-predictable modeling of fractal based forms. The stress is put on modeling of biological forms and their atributes such as: continuous deformation of the attractor in desired way (like in growing), branching (plants, vascular or alveolar network), gradual changing of fractal dimension from smooth to space-filling fractals. The last is useful for creating images of tissues in different stages of development, symmetry, gradual transformation from one to another form, etc. The fractal images obtained by AIFS are merely to gain resemblance to bio-forms.     

Cantor集并的自相似性(英文)

本文研究了Cantor集和其并的自相似性.利用Cantor展式的方法,得到了关于Cantor集和迭代函数系的一个基本关系:T∪(T+α)为自相似的当且仅当存在一个非负整数n使得α=±(k2-k1)dn.进一步,若T∪(T+α)是自相似的,则它满足开集条件.     

Displacement exponent for loop-erased random walk on the Sierpiński gasket

We prove that loop-erased random walks on the finite pre-Sierpiński gaskets can be extended to a loop-erased random walk on the infinite pre-Sierpiński gasket by using the ‘erasing-larger-loops-first’ method, and obtain the asymptotic behavior of the walk as the number of steps increases, in particular, the displacement exponent and a law of the iterated logarithm.     

Optimal subsampling for large-scale quantile regression

To deal with massive data sets, subsampling is known as an effective method which can significantly reduce computational costs in estimating model parameters. In this article, an efficient subsampling method is developed for large-scale quantile regression via Poisson sampling framework, which can solve the memory constraint problem imposed by big data. Under some mild conditions, large sample properties for the estimator involving the weak and strong consistencies, and asymptotic normality are established. Furthermore, the optimal subsampling probabilities are derived according to the A-optimality criterion. It is shown that the estimator based on the optimal subsampling asymptotically achieves a smaller variance than that by the uniform random subsampling. The proposed method is illustrated and evaluated through numerical analyses on both simulated and real data sets.     

线性模型的最小二乘估计的中偏差及其重对数律

本文研究了线性模型的最小二乘估计的中偏差.通过估计Laplace渐近积分,得到了随机误差为取值于Rd的相互独立同分布随机变量情形下的中偏差与重对数律的结果.     

The Law of the Iterated Logarithm for Extreme Waiting Time in Multiphase Queueing Systems

The objective of this research in the queueing theory is the law of the iterated logarithm (LIL) under the conditions of heavy traffic in multiphase queueing systems (MQS). In this paper, the LIL is proved for the extreme values of some important probabilistic characteristics of the MQS, namely, maxima and minima of the summary waiting time of a customer, and maxima and minima of the waiting time of a customer.     

B值拟终鞅型序列与Banach空间的几何特征

设（Ω，，Ｐ）是概率空间，Ｂ是Ｂａｎａｃｈ空间．本文引入了一类新的鞅型序列──（Ｂ值）拟终鞅型序列，并研究了它们的收敛性与Ｂａｎａｃｈ空间的Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性，一致光滑性和ＵＭＤ性的依赖关系．     

B值拟鞅的原子分解

定义了B值拟鞅原子，建立了相应的B值拟鞅原子分解定理，由此进一步讨论了拟鞅空间p∑a，pQa，Ha，pHa，Da之间的嵌入关系，指出它们与值空间的几何性质密切相关。     

一类统计量的强大数律和重对数律的精确极限性质

设{xn,m≥1}是独立同分布随机变量序列,EX1=0,EX12=1．设Tn= Tn(X1,…,Xn)是随机函数且Tn=Sn Rn．本文证明在E|Rn|2∨r<∞或E|Rn|<∞下,对随机函数Tn成立着Baum-Katz强大数律和重对数律的精确极限性质的一般结果．由此作为推论,对U-统计量,Von-Mises统计量,线性过程,移动平均过程,线性模型中误差方差估计和功率和等在适当矩条件下均可写出Baum-Katz强大数律和重对数律的精确极限性质．     

B-值双随机Dirchlet级数的收敛性

主要研究了B-值双随机Dirichlet级数在不同条件(i){Xn}服从强大数定律,且 (ii){Xn}独立不同分布,且 等条件下的收敛性,得出了收敛横坐标的简洁公式．