Possible values for 2

From GCH and P^{m(κ)-hypermeasurable} (1 <m<gw), we construct a model satisfying 2_ⁿ = _a(n) and 2_^ω = _ω+m for a monotone a:ω→ω satisfying a(n)>n.     

On box products

We prove two theorems about box products. The first theorem says that the box product of countable spaces is pseudonormal, i.e. any two disjoint closed sets one of which is countable can be separated by open sets. The second theorem says that assuming CH a certain uncountable box product is normal (i.e. <_ω1?□_α<ω1X_α where each Xα is a compact metric space).     

On the functional optimization of a certain class of nonstationary spatial functions

Procedures are developed in order to obtain optimal estimates of linear functionals for a wide class of nonstationary spatial functions. These procedures rely on well-established constrained minimum-norm criteria, and are applicable to multidimensional phenomena which are characterized by the so-called hypothesis of inherentity. The latter requires elimination of the polynomial, trend-related components of the spatial function leading to stationary quantities, and also it generates some interesting mathematics within the context of modelling and optimization in several dimensions. The arguments are illustrated using various examples, and a case study computed in detail.The authors acknowledge with appreciation the comments and criticisms made by Dr. L. C. W. Dixon of the Numerical Optimization Centre, Hatfield Polytechnic, Hatfield, Hertfordshire, England.     

二维正态分布的假设检验

将二维随机向量分解成互不相关的主成分,通过对两主成分的正态独立性检验达到二维随机向量正态性检验的目的.     

The theta-Laguerre calculus formulation of the Li/Keiper constants

The Riemann hypothesis is equivalent to the nonnegativity of a sequence of real constants , that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. We re-express these constants using the theta-Laguerre calculus. By using integral representations, we reformulate the coefficients together with a closely related sequence . We present a decomposition of the quantities a_j into superdominant and subdominant components and give an upper bound on the former and an asymptotic lower bound for the latter. Sufficient estimation of these quantities would lead to confirmation of the Riemann hypothesis.     

基于概率假设密度的无线传感器网络多目标跟踪算法

针对无线传感器网络多目标跟踪过程中杂波难以去除以及由数据关联复杂带来的计算复杂度高的问题,将概率假设密度滤波器应用于无线传感器网络,以更好地对多目标状态信息进行融合估计;首先,建立簇-树型无线传感器网络模型,并运用随机有限集理论对目标状态模型和传感器观测模型进行描述;然后,根据目标与节点之间的距离设置观测阈值,当传感器节点测量值小于观测阈值时,概率假设密度滤波器将实时对该组测量数据进行处理,从而实现传感器网络对目标状态的联合检测与跟踪;仿真结果表明,在无线传感器网络的多目标跟踪应用中,该算法比粒子滤波算法具有更高的跟踪效率和精度。     

Direction-Projection-Permutation for High-Dimensional Hypothesis Tests

High-dimensional low sample size (HDLSS) data are becoming increasingly common in statistical applications. When the data can be partitioned into two classes, a basic task is to construct a classifier that can assign objects to the correct class. Binary linear classifiers have been shown to be especially useful in HDLSS settings and preferable to more complicated classifiers because of their ease of interpretability. We propose a computational tool called direction-projection-permutation (DiProPerm), which rigorously assesses whether a binary linear classifier is detecting statistically significant differences between two high-dimensional distributions. The basic idea behind DiProPerm involves working directly with the one-dimensional projections of the data induced by binary linear classifier. Theoretical properties of DiProPerm are studied under the HDLSS asymptotic regime whereby dimension diverges to infinity while sample size remains fixed. We show that certain variations of DiProPerm are consistent and that consistency is a nontrivial property of tests in the HDLSS asymptotic regime. The practical utility of DiProPerm is demonstrated on HDLSS gene expression microarray datasets. Finally, an empirical power study is conducted comparing DiProPerm to several alternative two-sample HDLSS tests to understand the advantages and disadvantages of each method.     

Note on zeros of the derivative of the Selberg zeta-function

Wenzhi Luo studied the distribution of nontrivial zeros of the derivatives of Selberg zeta-functions on cocompact hyperbolic surfaces, and obtained an asymptotic formula for zero density with bounded height. Then he related the distribution of zeros to the multiplicities of Laplacian eigenvalues. Using better bounds for the growth of the Selberg zeta-functions we improve some of the above results. This work was partially supported by a Grant from the Lithuanian Foundation of Studies and Science.