Data analysis for accelerated life tests via Weibull-gamma frailty regression models

In this article, we study data analysis methods for accelerated life test (ALT) with blocking. Unlike the previous assumption of normal distribution for random block effects, we advocate the use of Weibull regression model with gamma random effects for making statistical inference of ALT data. To estimate the unknown parameters in the proposed model, maximum likelihood estimation and Bayesian estimation methods are provided. We illustrate the proposed methods using real data examples and simulation examples. Numerical results suggest that distribution of random effects has minimal impact on the estimation of fixed effects in the Weibull regression models. Furthermore, to demonstrate the advantage of our proposed model, we also provide methods to compare ALT plans and thus identify the optimal ALT plans.     

Hierarchies of exact solutions for the discrete third Painlevé equation

In this paper, we construct hierarchies of rational solutions of the discrete third Painlevé equation (d-PIII) by applying Schlesinger transformations to simple initial solutions. We show how these solutions reduce in the continuous limit to the hierarchies of rational solutions of the third Painlevé equation (PIII). We also study the solutions of d-PIII which are expressed in terms of discrete Bessel functions and show that these solutions reduce in the continuous limit the hierarchies of special function solutions of PIII.     

Chimera state and route to explosive synchronization

Transition to explosive synchronization is exhibited in networks of Kuramoto oscillators with a positive correlation between the oscillator dynamics and their inner topological structure encoded in the vertex degrees relations, shedding a light over the explosive critical phenomena. Here we study emergence of chimera states for the large amplitude oscillations when degree-frequency correlation is established only for the vertices with the highest degrees. For the strong coupling regime no simultaneous coexistence of coherence and incoherence signatures is observed. The connection between the network dynamics and the range and strength of coupling is elucidated through extensive analytical investigation, presenting realistic simulations of a scale-free neural network of Caenorhabditis elegans.     

Counterparty risk valuation on credit-linked notes under a Markov Chain framework

A credit-linked note(CLN) is a note paying an enhanced coupon to investors for bearing the credit risk of a reference entity. In this paper, we study the counterparty risk on CLNs under a Markov chain framework, and introduce a Markov copula model to describe joint defaults between the reference entity underlying the CLN and CLN issuer. Assuming that the respective default intensities are directly and inversely proportional to the interest rate, which follows a CIR process, we obtain the explicit formulae for CLN values through a PDE approach.Finally, credit valuation adjustment(CVA) formula is derived to price counterparty credit risk.     

Some sufficient conditions for stabilizing periodic orbits without the odd-number property by delayed feedback control in continuous-time systems

One of the important topics in the study of delayed feedback control (DFC) for chaotic systems is stability analysis. In the present Letter, we give some sufficient conditions for stabilizing periodic orbits by the DFC without the odd-number property in continuous-time systems. Our results naturally connect the stability condition for inversely unstable orbits and the odd-number limitation.     

Derivatives of meromorphic functions and exponential functions

We take up a new method to prove a Picard type theorem. Let f be a meromorphic function in the complex plane, whose zeros are multiple, and let R be a Möbius transformation. If \({\overline {\lim } _{r \to \infty }}\frac{{T\left( {r,f} \right)}}{{{r^2}}} = \infty \) then f′z) = R(e ^z ) has infinitely many solutions in the complex plane.     

李代数W(2,2)上的Hom-李代数结构

李代数W（2，2）是一类重要的无限维李代数，它是在研究权为2的向量生成的顶点算子代数的过程当中提出来的.Hom-李代数是指同时具备代数结构和李代数结构的一类代数，并且乘法与李代数乘法运算满足Leibniz法则.本文确定了李代数W（2，2）上的Hom-李代数结构.主要结论是李代数W（2，2）上没有非平凡的Hom-李代数结构.本文的研究结果对于W（2，2）代数的进一步研究有一定的帮助作用.     

Variable selection via quantile regression with the process of Ornstein-Uhlenbeck type

Based on the data-cutoff method,we study quantile regression in linear models,where the noise process is of Ornstein-Uhlenbeck type with possible jumps.In single-level quantile regression,we allow the noise process to be heteroscedastic,while in composite quantile regression,we require that the noise process be homoscedastic so that the slopes are invariant across quantiles.Similar to the independent noise case,the proposed quantile estimators are root-n consistent and asymptotic normal.Furthermore,the adaptive least absolute shrinkage and selection operator(LASSO)is applied for the purpose of variable selection.As a result,the quantile estimators are consistent in variable selection,and the nonzero coefficient estimators enjoy the same asymptotic distribution as their counterparts under the true model.Extensive numerical simulations are conducted to evaluate the performance of the proposed approaches and foreign exchange rate data are analyzed for the illustration purpose.     

基于后悔理论的灰色应急决策方案动态调整方法

突发事件发展具有可变性、动态性、随机性等特点,这要求决策者能根据实际情况及时调整应急方案,在此过程中决策者往往表现出“有限理性”的心理特征。针对以上情形,提出一种基于后悔理论的决策方法,以解决不确定环境下考虑决策者心理因素的应急方案动态调整问题。该方法首先描述分析了基于灰数信息的应急调整方案的生成过程;然后从后悔规避的视角构造了调整方案集关于处置效果、调整成本、应对损失三方面的灰色感知效用矩阵;进一步,用转移概率矩阵预测突发事件的演化概率,计算各调整方案的灰色综合感知效用值以选出最佳调整方案;最后,通过实例验证了该方法的可行性和有效性。结果表明,该方法贴近决策实际、具有较强的实用性;能够为应急决策的方案调整问题提供方法指导和理论支持。