带有加性噪声的阻尼吊桥方程随机吸引子的存在性

用算子分解技巧, 通过对方程的解进行先验估计, 给出随机动力系统的一致渐近紧性, 从而证明了随机吊桥方程在加性噪声下随机吸引子的存在性.     

基于空地协同采样的植被覆盖度随机森林估算方法

基于无人机高光谱影像, 建立地形复杂地区植被覆盖度的非参数随机森林回归估算模型。为获得构建随机森林模型所需的足够数量的训练样本, 利用低空无人机搭载的光学相机, 在从地面难以到达的山地、水域和植被茂密区, 通过垂直拍摄获得厘米分辨率的航拍影像, 作为对地面样方采样的补充。首先计算地面数码相机照片和无人机可见光影像的红绿蓝植被指数(red-green-blue vegetation index, RGBVI), 然后使用大津分割法提取样方的植被覆盖信息, 得到构建模型所需的训练样本。在此基础上, 基于2018年8月16—18日在内蒙古自治区察右中旗油娄沟矿区获取的GaiaSky-mini2无人机高光谱影像数据, 利用递归特征消除算法优选参与随机森林回归的特征变量集, 利用空地协同获取的训练样本构建植被覆盖度的随机森林回归估算模型。该模型在测试集上的确定系数R2为0.923, 均方根误差为0.087, 优于常用的像元二分模型, 可用于矿区植被动态信息的精细化监测。     

φ混合随机变量阵列加权和的收敛性质

利用φ混合随机变量的Rosenthal型矩不等式,考虑一定权重条件下,不同分布φ混合随机变量阵列的强收敛性质,得到了一些新结果.     

Two Tales of Return Predictability: The Case of Asia–Pacific Equity Markets

If past prices can successfully predict future price movements, it would contradict the notion of weak‐form market efficiency. Return predictability can be assessed via a variety of random walk statistical tests or via the application of mechanical trading rules. Findings of return predictability and state of market efficiency are compared by applying a battery of popular random walk statistical tests and a large set of mechanical trading rules to a family of equity indexes in Asia–Pacific equity markets over a 20‐year period of time. Inferences drawn from different random walk based econometric tests of market efficiency often disagree among themselves and tend to exaggerate the extent of predictability in returns. Testing of return predictability via a set of mechanical trading rules allows one to account for a possible data snooping bias, error measurements due to nonsynchronous trading and market frictions such as trading costs. Persistent predictability of returns that cannot be explained by the combination of data snooping bias, nonsynchronicity bias and moderate level of transaction costs is found in just two emerging equity markets in the region. Copyright © 2016 John Wiley & Sons, Ltd.     

近临界紧邻随机游动局部时的重整化极限

Lamperti于1961年证明了在适当条件下, 半直线上一类近临界的紧邻随机游动经过重整化会弱收敛到布朗运动. 考虑过程局部时重整化的极限问题, 运用随机游动的内蕴分枝结构以及非时齐分枝过程重整化极限的结果, 证明了其局部时经过适当的重整化会收敛到布朗运动的局部时.      

数学软件与解析几何教学的有效整合

从转变教学形式、加强实验课时以及调整考核形式等方面,探讨了Mathematica与解析几何课程整合的一些措施,整合的实质即建设解析几何实验课程.     

Semantic image annotation based on GMM and random walk model

Automatic image annotation has been an active topic of research in computer vision and patternrecognition for decades.A two stage automatic image annotation method based on Gaussian mixturemodel (GMM) and random walk model (abbreviated as GMM-RW) is presented.To start with,GMM fitted by the rival penalized expectation maximization (RPEM) algorithm is employed to estimatethe posterior probabilities of each annotation keyword.Subsequently, a random walk processover the constructed label similarity graph is implemented to further mine the potential correlations ofthe candidate annotations so as to capture the refining results, which plays a crucial role in semanticbased image retrieval.The contributions exhibited in this work are multifold.First, GMM is exploitedto capture the initial semantic annotations, especially the RPEM algorithm is utilized to train themodel that can determine the number of components in GMM automatically.Second, a label similaritygraph is constructed by a weighted linear combination of label similarity and visual similarity ofimages associated with the corresponding labels, which is able to avoid the phenomena of polysemyand synonym efficiently during the image annotation process.Third, the random walk is implementedover the constructed label graph to further refine the candidate set of annotations generated byGMM.Conducted experiments on the standard Corel5k demonstrate that GMM-RW is significantlymore effective than several state-of-the-arts regarding their effectiveness and efficiency in the task of automatic image annotation.     

Ho∞-based fault detection for nonlinear networked systems with random packet dropout and probabilistic interval delay

The fault detection problem for the nonlinear networked control system (NCS) with packet dropout and delay is investigated.A nonlinear stochastic system model is proposed to account for the NCS with random packet dropout and networkinduced non-uniformly distributed time-varying delay in both from sensor to controller (S/C) and from controller to actuator (C/A).Based on the obtained NCS model,employing an observer-based fault detection filter as the residual generator,the addressed fault detection problem is converted into an auxiliary nonlinear H∞ control problem.Then,with the help of Lyapunov functional approach,a sufficient condition for the desired fault detection filter is constructed in terms of certain linear matrix inequalities,which depend on not only the delay interval but also the delay interval occurrence rate and successful packet communication rate.Especially,a trade-off phenomenon between the maximum allowable delay bound and successful data packet transmission rate is found,which is typically resulted from the limited bandwidth of communication networks.The effectiveness of the proposed method is demonstrated by a simulation example.     

门诊到住院过程中病床负荷公平性的病人路由策略

在调研分析住院病人历史数据和医院业务流程基础上,建立了病人流路由分配的单排队多服务台队列倒V模型.以病房工作负荷公平性为目标,分析了RMI(randomized most-idle)随机路由分配策略的马尔科夫过程在倒V模型中的应用,得到了系统的阻塞概率及病床占用率等相关性能指标参数,从理论上分析了RMI路由分配策略的公平性.对比了两服务台队列占用率、单位时间内服务的病人数量,结果验证了RMI策略的公平性.     

古典概型问题的数学模型

在古典概型问题中引入了n次随机试验,n维样本点,n维随机事件和n维样本空间等概念,对解决古典概型的应用问题提供了相应的数学模型.