The construction and approximation of feedforward neural network with hyp erb olic tangent function

In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tangent activation functionFirstly, an equation of partitions of unity for the hyperbolic tangent function is givenThen, two kinds of quasi-interpolation type neural network operators are constructed to approximate univariate and bivariate functions, respectivelyAlso, the errors of the approximation are estimated by means of the modulus of continuity of functionMoreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.     

半度量空间的刻画

We use the notions of weak base g-functions and pair networks to give some new characterizations of semi-metric spaces.     

On a problem of Hornik

In 1991,Hornik proved that the collection of single hidden layer feedforward neural networks(SLFNs)with continuous,bounded,and non-constant activation functionσis dense in C(K)where K is a compact set in R~s(see Neural Networks,4(2),251-257(1991)).Meanwhile,he pointed out"Whether or not the continuity assumption can entirely be dropped is still an open quite challenging problem".This paper replies in the affirmative to the problem and proves that for bounded and continuous almost everywhere(a.e.)activation functionσon R,the collection of SLFNs is dense in C(K)if and only ifσis un-constant a.e..     

Optimal Groomings with Grooming Ratios Six and Seven

Grooming uniform all‐to‐all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The determination of optimal C‐groomings has been considered for , and completely solved for . For , it has been shown that the lower bound for the drop cost of an optimal C‐grooming can be attained for almost all orders with 5 exceptions and 308 possible exceptions. For , there are infinitely many unsettled orders; especially the case is far from complete. In this paper, we show that the lower bound for the drop cost of a 6‐grooming can be attained for almost all orders by reducing the 308 possible exceptions to 3, and that the lower bound for the drop cost of a 7‐grooming can be attained for almost all orders with seven exceptions and 16 possible exceptions. Moreover, for the unsettled orders, we give upper bounds for the minimum drop costs.     

Asymptotic synchronization of continuous/discrete complex dynamical networks by optimal partitioning method

The synchronization problem for both continuous and discrete‐time complex dynamical networks with time‐varying delays is investigated. Using optimal partitioning method, time‐varying delays are partitioned into l subintervals and generalized results are derived in terms of linear matrix inequalities (LMIs). New delay‐dependent synchronization criteria in terms of LMIs are derived by constructing appropriate Lyapunov–Krasovskii functional, reciprocally convex combination technique and some inequality techniques. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria. © 2014 Wiley Periodicals, Inc. Complexity 21: 193–210, 2015     

Forwarding and optical indices of 4-regular circulant networks

An all-to-all routing in a graph G is a set of oriented paths of G, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing R is the number of times it is used (in either direction) by paths of R, and the maximum load of an edge is denoted by $\pi (G,R)$. The edge-forwarding index $\pi (G)$ is the minimum of $\pi (G,R)$ over all possible all-to-all routings R, and the arc-forwarding index $\overrightarrow{\pi }(G)$ is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by $w(G,R)$ the minimum number of colours required to colour the paths of R such that any two paths having an edge in common receive distinct colours. The optical index $w(G)$ is defined to be the minimum of $w(G,R)$ over all possible R, and the directed optical index $\overrightarrow{w}(G)$ is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for 4-regular circulant graphs with connection set $\{\pm 1,\pm s\}$, $1<s<n/2$. We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of 4-regular circulant graphs.     

纯电动汽车磷酸铁锂电池组的建模及优化

鉴于传统神经网络和支持向量机机理复杂、计算量大的缺陷,很难实时跟踪磷酸铁锂电池组复杂快速的内部反应,影响电池荷电状态的估算精度,提出应用一种简单、有效的极限学习机对一额定容量为100Ah、额定电压为72V的纯电动汽车磷酸铁锂电池组建模,并分别与BP神经网络、RBF神经网络、支持向量机进行对比。随后,以学习时间和泛化性能为优化目标,应用粒子群方法寻找最佳隐层节点个数。结果表明,基于极限学习机的磷酸铁锂电池组模型的学习时间、泛化性能优于BP神经网络、RBF神经网络、支持向量机;隐层节点优化后,模型的学习时间和泛化性能达到最优。     

基于GA-BP的移动通信设备故障诊断

针对通信设备故障发生随机性强,影响因素多,对应的故障诊断有高度非线性和不确定性的特点,采用BP神经网络算法,优化的GA-BP神经网络算法和POS-BP神经网络算法分别搭建基站设备故障诊断模型,提取设备故障历史数据进行MATLAB仿真,准确预测设备故障类型,帮助提高代维公司调度管理的智能化水平,提高基站设备运维的执行效率。仿真结果表明：本文的BP,GA-BP和POS-BP神经网络算法都能够实现设备故障类别的预测,且GA-BP神经网络算法相比BP和POS-BP神经网络算法对通信设备故障诊断有更好的适应性。     

基于光纤的光学频率传递研究

随着光钟研究的发展, 光钟的稳定度和不确定度均达到10^-18量级. 通过光纤可以实现光钟频率信号的高精度传输, 有望用于未来“秒”定义的复现. 演示了百公里级实验室光纤上的光学频率传递. 对于在实验室70 km光纤盘上实现的光频传递, 光纤相位噪声抑制在1-250 Hz傅里叶频率范围内均接近于光纤延时极限, 对应传输稳定度(Allan偏差)为秒级稳定度1.2×10^-15, 10000 s稳定度为1.4×10^-18. 实验室100 km光纤的光频传递秒级稳定度也达到了5×10^-15. 提出了光纤噪声用户端补偿的方案, 可以简化星形传递网络中心站的复杂度. 在25 km光纤上演示了该传递方案, 实现的传输稳定度接近传统前置补偿传递方案.     

Characteristics of Friedel pairs and diffraction contrast tomography with non‐perpendicular rotation axis

The characteristics of Friedel pairs in diffraction contrast tomography (DCT) are studied in the condition that the rotation axis of the sample is not exactly perpendicular to the incident X‐ray direction. For the rotation axis approximately aligned along the vertical direction, the Friedel pairs close to the horizontal plane are insensitive to the non‐perpendicularity of the rotation axis, and can be used to refine the sample‐to‐detector distance and X‐ray energy, while the Friedel pairs close to the vertical direction are sensitive to the non‐perpendicularity of the rotation axis, and can be used to determine the rotation axis orientation. The correct matching proportion of Friedel pairs decreases with increasing non‐perpendicularity of the rotation axis. A method of data processing considering rotation axis misalignment is proposed, which significantly increases the correct matching and indexing proportions of the diffraction spots. A pure aluminium polycrystalline sample is investigated using DCT at beamline 4W1A of Beijing Synchrotron Radiation Facility. Based on the analysis of Friedel pairs, the sample‐to‐detector distance and X‐ray energy are refined to be 8.67 mm and 20.04 keV, respectively. The non‐perpendicular angle of the rotation axis is calculated to be 0.10°. With these refined geometric parameters, the matching proportion of the spatial position of diffraction spots is 90.62%. Three‐dimensional reconstruction of the sample with 13 grains is realised using the algebraic reconstruction technique. It is demonstrated that the precise correction of the orientation of the sample rotation axis is effective in DCT suffering from rotation axis misalignment, and the higher accuracy in determining the rotation axis is expected to improve the reconstruction precision of grains.