Throughput and delay analysis of an opportunistic tree algorithm

Tree algorithms are a well-known class of random access algorithms with a provable maximum stable throughput under the infinite population model (as opposed to ALOHA or the binary exponential backoff algorithm). In this article, we propose a tree algorithm for opportunistic spectrum usage in cognitive radio networks. A channel in such a network is shared among so-called primary and secondary users, where the secondary users are allowed to use the channel only if there is no primary user activity. The tree algorithm designed in this article can be used by the secondary users to share the channel capacity left by the primary users.

We analyze the maximum stable throughput and mean packet delay of the secondary users by developing a tree structured Quasi-Birth Death Markov chain under the assumption that the primary user activity can be modeled by means of a finite state Markov chain and that packets lengths follow a discrete phase-type distribution.

Numerical experiments provide insight on the effect of various system parameters and indicate that the proposed algorithm is able to make good use of the bandwidth left by the primary users.     

A combinatorial study of two-periodic random walks

Two-periodic random walks have up-steps and down-steps of one unit as usual, but the probability of an up-step is α after an even number of steps and β = 1 ? α after an odd number of steps, and reversed for down-steps. This concept was studied by Böhm and Hornik^{[2 Böhm, W.; Hornik, K. On two-periodic random walks with boundaries. Stoch. Models 2010, 26, 165–194.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]}. We complement this analysis by using methods from (analytic) combinatorics. By using two steps at once, we can reduce the analysis to the study of Motzkin paths, with up-steps, down-steps, and level-steps. Using a proper substitution, we get the generating functions of interest in an explicit and neat form. The parameters that are discussed here are the (one-sided) maximum (already studied by Böhm and Hornik^{[2 Böhm, W.; Hornik, K. On two-periodic random walks with boundaries. Stoch. Models 2010, 26, 165–194.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]}) and the two-sided maximum. For the asymptotic evaluation of the average value of the two-sided maximum after n random steps, more sophisticated methods from complex analysis (Mellin transform, singularity analysis) are required. The approach to transfer the analysis to Motzkin paths is, of course, not restricted to the two parameters under consideration.     

一类含有随机参数的混沌系统的Hopf分岔研究

文章选取随机变量为系统的随机变量研究含有随机参数混沌系统的Hopf分岔,利用Chebyshev正交多项式逼近理论将含有随机变量的系统转化为等价的确定性系统,通过Hopf分岔定理和Lyapunov系数讨论了随机参数系统的Hopf分岔及稳定性,发现随机系统的渐进稳定性参数区间大小不仅和确定性参数有关,还与随机参数有非常密切的关系.     

基于模糊理论评估连续梁桥地震破坏状况

为了研究不同强度等级地震作用下连续梁桥的破坏模式及破坏程度,采用多级模糊综合评判方法建立连续梁桥的综合评估模型。根据连续梁桥的特点,利用连续梁桥各单元及各构件的破坏程度建立多个因素集,根据各因素的权重和评价标准,对多个因素集进行逐级评判,根据最大隶属度原则得到地震作用下连续梁桥的破坏情况,并通过等级参数评判法对不同地震强度下连续梁桥的破坏情况进行等级评判,得到连续梁桥破坏情况与地震强度之间的关系。最后,基于多级模糊综合评判方法对一座连续梁桥实例进行评判     

Linear Increments with Non‐monotone Missing Data and Measurement Error

Linear increments (LI) are used to analyse repeated outcome data with missing values. Previously, two LI methods have been proposed, one allowing non‐monotone missingness but not independent measurement error and one allowing independent measurement error but only monotone missingness. In both, it was suggested that the expected increment could depend on current outcome. We show that LI can allow non‐monotone missingness and either independent measurement error of unknown variance or dependence of expected increment on current outcome but not both. A popular alternative to LI is a multivariate normal model ignoring the missingness pattern. This gives consistent estimation when data are normally distributed and missing at random (MAR). We clarify the relation between MAR and the assumptions of LI and show that for continuous outcomes multivariate normal estimators are also consistent under (non‐MAR and non‐normal) assumptions not much stronger than those of LI. Moreover, when missingness is non‐monotone, they are typically more efficient.     

Robust Smoothed Rank Estimation Methods for Accelerated Failure Time Model Allowing Clusters

Smoothed Gehan rank estimation methods are widely used in accelerated failure time (AFT) models with/without clusters. However, most methods are sensitive to outliers in the covariates. In order to solve this problem, we propose robust approaches based on the smoothed Gehan rank estimation methods for the AFT model, allowing for clusters by employing two different weight functions. Simulation studies show that the proposed methods outperform existing smoothed rank estimation methods regarding their biases and standard deviations when there are outliers in the covariates. The proposed methods are also applied to a real dataset from the “Major cardiovascular interventions” study.     

Influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes

In this paper, we propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest follows the Negative Binomial distribution and the time to event follows a Weibull distribution. Indeed, we introduce the Weibull-Negative-Binomial (WNB) distribution, which can be used in order to model survival data when the hazard rate function is increasing, decreasing and some non-monotonous shaped. Another advantage of the proposed model is that it has some distributions commonly used in lifetime analysis as particular cases. Moreover, the proposed model includes as special cases some of the well-know cure rate models discussed in the literature. We consider a frequentist analysis for parameter estimation of a WNB model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, the methodology is illustrated on a medical data.     

Combining Inverse Probability Weighting and Multiple Imputation to Improve Robustness of Estimation

Inverse probability weighting (IPW) and multiple imputation are two widely adopted approaches dealing with missing data. The former models the selection probability, and the latter models data distribution. Consistent estimation requires correct specification of corresponding models. Although the augmented IPW method provides an extra layer of protection on consistency, it is usually not sufficient in practice as the true data‐generating process is unknown. This paper proposes a method combining the two approaches in the same spirit of calibration in sampling survey literature. Multiple models for both the selection probability and data distribution can be simultaneously accounted for, and the resulting estimator is consistent if any model is correctly specified. The proposed method is within the framework of estimating equations and is general enough to cover regression analysis with missing outcomes and/or missing covariates. Results on both theoretical and numerical investigation are provided.