Achieving Brouwer’s law with implicit Runge–Kutta methods

In high accuracy long-time integration of differential equations, round-off errors may dominate truncation errors. This article studies the influence of round-off on the conservation of first integrals such as the total energy in Hamiltonian systems. For implicit Runge–Kutta methods, a standard implementation shows an unexpected propagation. We propose a modification that reduces the effect of round-off and shows a qualitative and quantitative improvement for an accurate integration over long times. AMS subject classification (2000)  65L06, 65G50, 65P10     

Asymptotics for solutions of a defective renewal equation with applications

In this paper, we derive non-exponential asymptotic forms for solutions of defective renewal equations. These include as special cases asymptotics for compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the Gerber-Shiu discounted penalty function in the classical risk model and the reliability of a two-unit cold standby system in reliability theory.      

Spectrum Slicing for Multiple Access Channels with Heterogeneous Services

Wireless mobile networks from the fifth generation (5G) and beyond serve as platforms for flexible support of heterogeneous traffic types with diverse performance requirements. In particular, the broadband services aim for the traditional rate optimization, while the time-sensitive services aim for the optimization of latency and reliability, and some novel metrics such as Age of Information (AoI). In such settings, the key question is the one of spectrum slicing: how these services share the same chunk of available spectrum while meeting the heterogeneous requirements. In this work we investigated the two canonical frameworks for spectrum sharing, Orthogonal Multiple Access (OMA) and Non-Orthogonal Multiple Access (NOMA), in a simple, but insightful setup with a single time-slotted shared frequency channel, involving one broadband user, aiming to maximize throughput and using packet-level coding to protect its transmissions from noise and interference, and several intermittent users, aiming to either to improve their latency-reliability performance or to minimize their AoI. We analytically assessed the performances of Time Division Multiple Access (TDMA) and ALOHA-based schemes in both OMA and NOMA frameworks by deriving their Pareto regions and the corresponding optimal values of their parameters. Our results show that NOMA can outperform traditional OMA in latency-reliability oriented systems in most conditions, but OMA performs slightly better in age-oriented systems.     

Probabilistic Predictions with Federated Learning

Probabilistic predictions with machine learning are important in many applications. These are commonly done with Bayesian learning algorithms. However, Bayesian learning methods are computationally expensive in comparison with non-Bayesian methods. Furthermore, the data used to train these algorithms are often distributed over a large group of end devices. Federated learning can be applied in this setting in a communication-efficient and privacy-preserving manner but does not include predictive uncertainty. To represent predictive uncertainty in federated learning, our suggestion is to introduce uncertainty in the aggregation step of the algorithm by treating the set of local weights as a posterior distribution for the weights of the global model. We compare our approach to state-of-the-art Bayesian and non-Bayesian probabilistic learning algorithms. By applying proper scoring rules to evaluate the predictive distributions, we show that our approach can achieve similar performance as the benchmark would achieve in a non-distributed setting.     

随机压电智能桁架结构闭环控制概率动力响应分析

针对随机压电智能桁架结构研究了基于概率的结构闭环控制系统动力响应分析模型与方法．考虑结构的物理参数、几何尺寸、外荷载幅值以及闭环系统控制力同时具有随机性时，利用振型迭加法导出了结构动力响应随机变量的数字特征计算表达式．通过算例考察了智能结构物理参数、几何尺寸、外荷载幅值以及控制力的随机性对结构闭环控制系统动力响应的影响，并获得了若干有意义的结论．     

抗磨可靠性寿命的加速试验与预测

在工程实际中，对新机器零件的抗磨可靠性寿命进行评估或预测非常重要，但是，由于磨损是一种受多因素制约的随机过程，目前在实验室广泛采用的模拟磨损试验，不仅周期较长，而且预测误差也比较大。因此，提出了一种在保持磨损机相似的前提下合理选用高ＰＶ值的抗磨可靠性寿命加速试验的新方法。     

极值型风荷载作用下大型结构可靠性分析

研究了在极值型风荷载作用下大型结构的可靠性。结构的破坏以结构刚度矩阵奇异为依据，首先列举结构的主要破坏模式，其次利用增量载荷法求出的结构的安全余量方程，然后将极值型风荷载正态化，计算出各主要破坏模式的破坏概率，并用二阶窄界限理论计算大型结构的可靠性。最后以一大型输电塔为例进行了可靠性计算     

Evaluation of thermal resistance constitution for packaged A1GaN/GaN high electron mobility transistors by structure function method＊

The evaluation of thermal resistance constitution for packaged A1GaN/GaN high electron mobility transistor （HEMT） by structure function method is proposed in this paper. The evaluation is based on the transient heating measurement of the A1GaN/GaN HEMT by pulsed electrical temperature sensitive parameter method. The extracted chip-level and package-level thermal resistances of the packaged multi-finger A1GaN/GaN HEMT with 400μm SiC substrate are 22.5 K/W and 7.2 K/W respectively, which provides a non-invasive method to evaluate the chip-level thermal resistance of packaged A1GaN/GaN HEMTs. It is also experimentally proved that the extraction of the chip- level thermal resistance by this proposed method is not influenced by package form of the tested device and temperature boundary condition of measurement stage.     

A note on the existence of fractional f-factors in random graphs

Let G=Gn,p be a binomial random graph with n vertices and edge probability p=p(n),and f be a nonnegative integer-valued function defined on V(G) such that 0a≤f(x)≤bnp-2np ㏒n for every x ∈V(G). An fractional f-indicator function is an function h that assigns to each edge of a graph G a number h(e) in [0,1] so that for each vertex x,we have dh G(x)=f(x),where dh G(x) = x∈e h(e) is the fractional degree of x in G. Set Eh = {e:e ∈E(G) and h(e)=0}.If Gh is a spanning subgraph of G such that E(Gh)=Eh,then Gh is called an fractional f-factor of G. In this paper,we prove that for any binomial random graph Gn,p with p≥n-23,almost surely Gn,p contains an fractional f-factor.     

Interval optimization based line sampling method for fuzzy and random reliability analysis

For structural system with fuzzy variables as well as random variables, a novel algorithm for obtaining membership function of fuzzy reliability is presented on interval optimization based Line Sampling (LS) method. In the presented algorithm, the value domain of the fuzzy variables under the given membership level is firstly obtained according to their membership functions. Then, in the value domain of the fuzzy variables, bounds of reliability of the structure are obtained by the nesting analysis of the interval optimization, which is performed by modern heuristic methods, and reliability analysis, which is achieved by the LS method in the reduced space of the random variables. In this way the uncertainties of the input variables are propagated to the safety measurement of the structure, and the membership function of the fuzzy reliability is obtained. The presented algorithm not only inherits the advantage of the direct Monte Carlo method in propagating and distinguishing the fuzzy and random uncertainties, but also can improve the computational efficiency tremendously in case of acceptable precision. Several examples are used to illustrate the advantages of the presented algorithm.