Metric Theorems for Distribution Measures of Pseudorandom Sequences

 We improve a recent result of Mauduit and Sárk?zy (2000) on the well-distribution measure of pseudorandom sequences and complement another of their results on the correlation measure. Received 12 September 2000; in revised form 1 March 2001     

Measures on the Product of Compact Spaces

 If K is an uncountable metrizable compact space, we prove a “factorization” result for a wide variety of vector valued Borel measures μ defined on K ⁿ . This result essentially says that for every such measure μ there exists a measure μ′ defined on K such that the measure μ of a product A ₁ × ⋯ × A _n of Borel sets of K equals the measure μ′ of the intersection A ₁′∩⋯∩A _n ′, where the A _i ′’s are certain transforms of the A _i ’s. Partially supported by DGICYT grant PB97-0240. Received August 23, 2001; in revised form March 21, 2002     

Statistical Measures for Least Squares Using the αQβR Algorithm

This paper shows how the output derived from the α Qβ R algorithm can be used to calculate various statistical quantities needed to evaluate linear models. In particular, we show how to calculate standard statistical quantities like the coefficient of determination R², the F-statistics, and the t-statistics. These quantities serve as a measure of how well the model fits the data.     

Bayesian Case Influence Measures for Statistical Models With Missing Data

We examine three Bayesian case influence measures including the φ-divergence, Cook’s posterior mode distance, and Cook’s posterior mean distance for identifying a set of influential observations for a variety of statistical models with missing data including models for longitudinal data and latent variable models in the absence/presence of missing data. Since it can be computationally prohibitive to compute these Bayesian case influence measures in models with missing data, we derive simple first-order approximations to the three Bayesian case influence measures by using the Laplace approximation formula and examine the applications of these approximations to the identification of influential sets. All of the computations for the first-order approximations can be easily done using Markov chain Monte Carlo samples from the posterior distribution based on the full data. Simulated data and an AIDS dataset are analyzed to illustrate the methodology. Supplemental materials for the article are available online.     

The shape of the hazard function for cancer incidence

A population-based cohort consisting of 126,141 men and 122,208 women born between 1874 and 1931 and at risk for breast or colorectal cancer after 1965 was identified by linking the Utah Population Data Base and the Utah Cancer Registry. The hazard function for cancer incidence is estimated from left truncated and right censored data based on the conditional likelihood. Four estimation procedures based on the conditional likelihood are used to estimate the age-specific hazard function from the data; these were the life-table method, a kernel method based on the Nelson Aalen estimator, a spline estimate, and a proportional hazards estimate based on splines with birth year as sole covariate.The results are consistent with an increasing hazard for both breast and colorectal cancer through age 85 or 90. After age 85 or 90, the hazard function for female breast and colorectal cancer may reach a plateua or decrease, although the hazard function for male colorectal cancer appears to continue to rise through age 105. The hazard function for both breast and colorectal cancer appears to be higher for more recent birth cohorts, with a more pronounced birth-cohort effect for breast cancer than for colorectal cancer. The age specific for colorectal cancer appears to be higher for men than for women. The shape of the hazard function for both breast and colorectal cancer appear to be consistent with a two-stage model for spontaneous carcinogenesis in which the initiation rate is constant or increasing. Inheritance of initiated cells appears to play a minor role.     

Operator Semi-Selfdecomposable Measures and Related Nested Subclasses of Measures on Vector Spaces

T-semi-selfdecomposability, operator selfdecomposability, and subclasses L_m(b, (T_t)) and of measures on complete separable metric vector spaces are introduced and basic properties are proved. In particular, we show that is T-semi-selfdecomposable if and only if =T() where is infinitely divisible and is operator selfdecomposable if and only if L₀(b, (T_t)) for all 0<b<.     

On the Box Dimension of Typical Measures

 Let be a complete metric space and let be the space of all probability Borel measures on X. We give some estimations of the upper and lower box dimensions of the typical (in the sense of Baire category) measure in . Received 29 November 2000; in final form 8 January 2002     

Statistical approach to some ill-posed problems for linear partial differential equations

For linear partial differential equations, some inverse source problems are treated statistically based on nonparametric estimation ideas. By observing the solution in a small Gaussian white noise, the kernel type of estimators is used to estimate the unknown source function and its partial derivatives.. It is proved that such estimators are consistent as the noise intensity tends to zero. Depending on the principal part of the differential operator, the optimal asymptotic rate of convergence is ascertained within a wide class of risk functions in a minimax sense. Received: 5 May 1997 / Revised version: 18 June 1998     

Invariant Measures for Univalent Self-Maps of the Unit Disc

We develop a translation-type model for univalent self-maps φ of the unit disc having an interior fixed-point and use the model to classify the φ-invariant measures on . We are particularly interested in maps which can be embedded in continuous semigroups of holomorphic self-maps of . Received: February 2, 2007. Revised: June 18, 2007. Accepted: July 4, 2007.     

Factorisation Theorems for T-decomposable Measures on Groups

 For a real or p-adic unipotent algebraic group G, given a T∈ Hom(G, G) and T-decomposable measure on G which is either ‘full’ or symmetric, we get a decomposition , where μ₀ is T-invariant and , and this decomposition is unique upto a shift. We also show that ν₀ is T-decomposable under some additional sufficient condition and give a counter example to justify this. We generalise the above to power bounded operators on p-adic Banach spaces. We also prove some convergence-of-types theorems on p-adic groups as well as Banach spaces. (Received 21 October 2000; in revised form 21 February 2001)     

Vague集信息熵测量及其应用

引入了区别于现有文献的Vague集信息熵和Vague集的关联熵的概念,给出了一种改进的测量方法,并讨论了它们之间的关系。进而,我们揭示了Vague集的熵和Fuzzy集的熵之间的关系,并分析了本文所定义熵的意义。最后,讨论了这种关联熵在模糊识别和医疗诊断上的应用。     

Conformal Families of Measures for Fibred Systems

In this paper, we give sufficient conditions for the existence of (pseudo) weakly conformal and conformal families of measures for fibred systems. We describe a general construction principle for these families, modelled on the one developed by Denker and Urbanski for conformal measures. For those systems that are fibrewise local homeomorphisms, the constructed families are (pseudo) conformal. If a system is, moreover, weakly topologically exact along fibres, then each measure in the associated family is supported on the whole fibre where it is naturally defined.This research was partially supported by NSF Grant DMS 0100078.Received February 4, 2002; in final form October 24, 2002 Published online October 24, 2003     

miR-212 在乳腺浸润性导管癌 组织中的表达及效应分析

本文建立随机环境中具有随机控制函数的两性分枝过程,得到该模型概率母函数之间的关系式.当控制函数上可加时,证明配对单元平均增长率的极限是存在的,同时得到配对单元平均增长率一系列的极限性质,进而推进了前人的研究.     

统计测度与N上纯有限可加测度空间的表示定理

证明了N上纯有限可加测度空间的单位球正是统计测度的绝对凸包。     

聚类分析方法在机械故障部位诊断中的应用

润滑油光谱分析技术是不解体检测磨损故障的一种有效方法，但到目前为止，光谱分析的结论是关于整机是否正常，而不能指示出发生磨损故障的具体部位。本文提出了用聚类分析方法来诊断故障部位。通过对大量机车柴油的分析表明，该方法的诊断结果是令人满意的     

Nonnegative Linearization for Polynomials Orthogonal with Respect to Discrete Measures

We give conditions for the coefficients in three term recurrence relations implying nonnegative linearization for polynomials orthogonal with respect to measures supported on convergent sequences of points. The previous methods were unable to cover this case. January 14, 1999. Date revised: January 31, 2000. Date accepted: October 24, 2000.     

模糊数学在飞机故障诊断中的应用

飞机故障征兆与故障原因问的隶属关系是模糊的，为此，将模糊数学方法引入到飞机故障诊断中，提出由历史数据及专家优序数综合确定模糊隶属度的方法，建立模糊诊断模型，并在计算机上实现飞机故障的模糊诊断。     

Applications of computational homology to the analysis of treatment response in breast cancer patients

The experimental method comparative genomic hybridization (CGH) array provides a full picture of chromosome amplifications and deletions of an individual's genome. The multi-dimensional nature of these data, however, has not been fully explored. Current methods for CGH analysis focus on specific markers, but deeper understanding can be gained by examining the properties of the overall genomic profile. In this paper we propose a novel method for characterizing CGH profiles mathematically using algebraic homology. We apply our method to breast cancer CGH profiles from patients that have been subjected to different treatments. We show that our results obtained using homology are in agreement with previous studies and are able to distinguish between frequency of cancer recurrence in chemotherapy and non-treated patient populations.     

Diagnosis for uncertain,dynamic and hybrid domains using Bayesian networks and arithmetic circuits

System failures, for example in electrical power systems, can have catastrophic impact on human life and high-cost missions. Due to an electrical fire in Swissair flight 111 on September 2, 1998, all 229 passengers and crew on board sadly lost their lives. A battery failure most likely took place on the Mars Global Surveyor, which unfortunately last communicated with Earth and thus ended its mission on November 2, 2006. Fault diagnosis techniques that seek to hinder similar accidents in the future are being developed in this article. We present comprehensive fault diagnosis methods for dynamic and hybrid domains with uncertainty, and validate them using electrical power system data. Our approach relies on the use of Bayesian networks, which model the electrical power system, compiled to arithmetic circuits. We handle in an integrated way varying fault dynamics (both persistent and intermittent faults), fault progression (both abrupt and drift faults), and fault behavior cardinality (both discrete and continuous behaviors). Our work has resulted in a software system for fault diagnosis, ProDiagnose, that has been the top performer in three of the four international diagnostics competitions in which it participated. In this paper we comprehensively present our methods as well as novel and extensive experimental results on data from a NASA electrical power system.     

Breast cancer prediction using the isotonic separation technique

A recently developed data separation/classification method, called isotonic separation, is applied to breast cancer prediction. Two breast cancer data sets, one with clean and sufficient data and the other with insufficient data, are used for the study and the results are compared against those of decision tree induction methods, linear programming discrimination methods, learning vector quantization, support vector machines, adaptive boosting, and other methods. The experiment results show that isotonic separation is a viable and useful tool for data classification in the medical domain.