Expected reliability of communication protocols

We consider the problem of sending a message from a sender $s$ to a receiver $r$ through an unreliable network by specifying in a protocol what each vertex is supposed to do if it receives the message from one of its neighbors. A protocol for routing a message in such a graph is finite if it never floods $r$ with an infinite number of copies of the message. The expected reliability of a given protocol is the probability that a message sent from $s$ reaches $r$ when the edges of the network fail independently with probability $1?p$.We discuss, for given networks, the properties of finite protocols with maximum expected reliability in the case when $p$ is close to 0 or 1, and we describe networks for which no one protocol is optimal for all values of $p$. In general, finding an optimal protocol for a given network and fixed probability is challenging and many open problems remain.     

一类改进最大熵方法的可调参数分析

在结构可靠性分析中,引入含可调参数的转换函数能对传统的最大熵方法进行改进,获得更高的失效概率预测精度。但是,此可调参数的最佳取值很难确定。针对这一问题,引入概率守恒方程,从功能函数转换前后所得概率密度函数出发,建立其最大熵值的变化关系,给出转换前后最大熵值之差的理论形式。通过对三种典型单调非线性转换函数开展算例研究,发现功能函数转换前后的最大熵值之差与转换函数的最佳可调参数值有关。改变可调参数值驱使最大熵值之差变化的同时,改进最大熵方法能遍历到更好的失效概率估计值。     

空间机器人捕获航天器后基于无源性理论的鲁棒镇定控制

研究了漂浮基空间机器人捕获非合作航天器过程对系统产生的冲击效应及其后联合体系统镇定运动的控制问题。为此,利用拉格朗日方法及牛顿-欧拉法分别获得了捕获前空间机器人及目标航天器的动力学模型;结合动量守恒定律、系统运动几何关系及力的传递规律,分析了捕获过程相互碰撞所产生的冲击效应,建立了捕获完成后两者联合体的系统动力学模型。在此基础上,针对同时存在不确定参数及外部扰动的联合体系统,设计了基于无源性理论的镇定运动神经网络H_∞鲁棒控制算法。本文提出的基于无源性理论设计的鲁棒控制算法具有良好的动态特性及较强的鲁棒性,可快速完成系统的镇定控制,实现轨迹的精确跟踪。系统数值模拟仿真验证了本文控制方案的正确性。     

Stochastic modeling of quality of systems operating in a heterogeneous environment

We consider systems that are subject to an external mixed Poisson shock process. Each shock can result in a failure of a system with a given probability and is survived with the complementary probability. Each shock additionally decreases the quality function that describes the performance of a system, thus forming the corresponding stochastic process. Expectations (unconditional and conditional on survival) and relevant variability characteristics for the stochastic quality function are derived. Some monotonicity properties of the conditional quality function are investigated and the future values of this function are derived.     

An interview with Sam C. Saunders

Sam C. Saunders, the son of Elizabeth Cundiff and Winston E. Saunders, was born in Richland, OR, on February 24, 1931. The family moved to La Grande, OR, in 1944, where Sam completed high school and two years at Eastern Oregon College. He then received the BSc degree in Mathematics from the University of Oregon, Eugene, OR, in 1952, and he attended the University of Washington, Seattle, WA, receiving a PhD degree under Z. W. Birnbaum. After graduating, he accepted employment at the Boeing Company in its Mathematical Services Unit and, in 1972, a position as a Full Professor at Washington State University, Pullman, WA, from which he retired in 1996.     

A distributionally robust area under curve maximization model

Area under ROC curve (AUC) is a performance measure for classification models. We propose new distributionally robust AUC models (DR-AUC) that rely on the Kantorovich metric and approximate AUC with the hinge loss function, and derive convex reformulations using duality. The DR-AUC models outperform deterministic AUC and support vector machine models and have superior worst-case out-of-sample performance, thereby showing their robustness. The results are encouraging since the numerical experiments are conducted with small-size training sets conducive to low out-of-sample performance.     

On Default Priors for Robust Bayesian Estimation with Divergences

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum γ-divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the γ-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.     

Computational analysis for the determination of deleterious nsSNPs in human MTHFD1 gene

Single nucleotide polymorphisms (SNPs) are the most common genetic polymorphisms and play a major role in many inherited diseases. Methylenetetrahydrofolate dehydrogenase 1 (MTHFD1) is one of the enzymes involved in folate metabolism. In the present study, the functional and structural consequences of nsSNPs of human MTHFD1 gene was analyzed using various computational tools like SIFT, PolyPhen2, PANTHER, PROVEAN, SNAP2, nsSNPAnalyzer, PhD-SNP, SNPs&GO, I-Mutant, MuPro, ConSurf, InterPro, NCBI Conserved Domain Search tool, ModPred, SPARKS-X, RAMPAGE, FT Site and PyMol. Out of 327 nsSNPs form human MTHFD1 gene, total 45 SNPs were predicted as functionally most significant SNPs, among which 17 were highly conserved and functional, 17 were highly conserved and structural residues. Among 45 most significant SNPs, 15 were predicted to be involved in post translational modifications. The p.Gly165Arg may interfere in homodimer interface formation. The p.Asn439Lys and p.Asp445Asn may interfere in binding interactions of MTHFD1 protein with cesium cation and potassium. The two SNPs (p.Asp562Gly and p.Gly637Cys) might interfere in interactions of MTHFD1 with ligand.