Decreased Resting-State Functional Complexity in Elderly with Subjective Cognitive Decline

Individuals with subjective cognitive decline (SCD) are at high risk of developing preclinical or clinical state of Alzheimer’s disease (AD). Resting state functional magnetic resonance imaging, which can indirectly reflect neuron activities by measuring the blood-oxygen-level-dependent (BOLD) signals, is promising in the early detection of SCD. This study aimed to explore whether the nonlinear complexity of BOLD signals can describe the subtle differences between SCD and normal aging, and uncover the underlying neuropsychological implications of these differences. In particular, we introduce amplitude-aware permutation entropy (AAPE) as the novel measure of brain entropy to characterize the complexity in BOLD signals in each brain region of the Brainnetome atlas. Our results demonstrate that AAPE can reflect the subtle differences between both groups, and the SCD group presented significantly decreased complexities in subregions of the superior temporal gyrus, the inferior parietal lobule, the postcentral gyrus, and the insular gyrus. Moreover, the results further reveal that lower complexity in SCD may correspond to poorer cognitive performance or even subtle cognitive impairment. Our findings demonstrated the effectiveness and sensitiveness of the novel brain entropy measured by AAPE, which may serve as the potential neuroimaging marker for exploring the subtle changes in SCD.     

Phase Space Prediction of Chaotic Time Series with Nu-Support Vector Machine Regression

A new class of support vector machine, nu-support vector machine, is discussed which can handle both classification and regression. We focus on nu-support vector machine regression and use it for phase space prediction of chaotic time series. The effectiveness of the method is demonstrated by applying it to the Hénon map. This study also compares nu-support vector machine with back propagation (BP) networks in order to better evaluate the performance of the proposed methods. The experimental results show that the nu-support vector machine regression obtains lower root mean squared error than the BP networks and provides an accurate chaotic time series prediction. These results can be attributable to the fact that nu-support vector machine implements the structural risk minimization principle and this leads to better generalization than the BP networks.     

Correction of Relativistic Center-of-Mass Vector on Electric Polarizability of Pion Meson

We estimate the correction of relativistic center-of-mass vector on electric polarizability of an equal-mass quark-antiquark system numerically. Effect on the system confined by different interactive potentials is analysed. A great improvement for the electric polarizability of pion meson is obtained.     

Exponential stabilization of nonlinear systems under saturated control involving impulse correction

This paper studies the problem of locally exponential stabilization (LES) of nonlinear systems under a class of hybrid control in the framework of actuator saturation, where the limitation of actuator saturation on both continuous state feedback control and impulsive control are fully considered. Based on impulsive control theory and differential inclusion approach, some sufficient conditions for LES are derived, where a novel set inclusion relation is proposed to handle the double saturation nonlinearities. Different from the existing results that each part of saturated hybrid control (SHC) is required to stabilize the system individually, our results relax the requirement by making full use of the correction effect of the impulse. Moreover, the maximum of estimation of domain of attraction is obtained by a convex optimal problem and corresponding algorithm. The result is applied to the robustness for a class of nonlinear systems. Finally, the validity of the results is shown by two examples and their simulations, where the synchronization problem of Chua’s oscillator is illustrated in the framework of actuator saturation.     

小波分析在经济预测模型中的应用

经济信号也是一种时间序列 ,它和小波分析中的信号具有相同的特性 .因此 ,可将经济时间序列看成经济信号 ,应用小波进行实际经济分析和预测 .论文针对最小二乘法的不足 ,提出了多分辨回归分析处理经济数据分析的方法 .本文在建立宏观模型时 ,利用小波分析对经济数据进行预处理 ,获得能反映宏观变化趋势的低频信息 ,再用最小二乘法进行拟合和预测 ,通过对传统最小二乘法建立的模型的对比分析 ,结果表明 :本方法优于一般最小二乘法 .     

Evaluation of Dead Time Calculation in Reversed-Phase Liquid Chromatography Using a Multiparametric Mathematical Method

In reversed phase liquid chromatography (RP-HPLC), the validity of a multiparametric non-linear least-squares regression iterative method for the determination of the column dead time t_M and the regression parameter (slope b), based on the use of alkan-2-ones, alkyl aryl ketones, and 1-nitroalkanes has been evaluated. The determination of t_M and b has been extensively studied for two mobile phase systems acetonitrile-water and methanol-water on seven octadecyl-C₁₈ and one octyl C₈ analytical columns. The calculated t_M and b values were compared with those obtained by Guardino's and Grobler's methods. The influence exerted thereon by the nature of the homologous series, the mobile phase composition, and the packing materials were investigated.     

A time-series approach to measuring node similarity in networks and its application to community detection

A central concept in network analysis is that of similarity between nodes. In this paper, we introduce a dynamic time-series approach to quantifying the similarity between nodes in networks. The problem of measuring node similarity is exquisitely embedded into the framework of time series for state evolution of nodes. We develop a deterministic parameter-free diffusion model to drive the dynamic evolution of node states, and produce a unique time series for each source node. Then we introduce a measure quantifying how far all the other nodes are located from each source one. Following this measure, a quantity called dissimilarity index is proposed to signify the extent of similarity between nodes. Thereof, our dissimilarity index gives a deep and natural integration between the local and global perspectives of topological structure of networks. Furthermore, we apply our dissimilarity index to unveil community structure in networks, which verifies the proposed dissimilarity index.     

尾流激励的叶片气动力降阶模型

气动力降阶模型是研究叶片气动弹性振动快速高效的新方法。现有气动力降阶模型的研究主要集中在叶片颤振方面,没有涉及更为常见的上游尾流激励的叶片振动问题。本文提出基于Volterra级数的尾流激励叶片气动力降阶模型,为尾流激励下叶片振动和动静叶干涉振动研究提供了新的思路。采用行波法简化尾流的参数个数,用阶跃信号法识别降阶模型的核函数。二维叶片的算例结果表明,本文方法可以较准确地描述尾流激励引起的叶片气动力振荡,而且计算效率极高。     

A DAMAGE CONSTITUTIVE MODEL OF ROCK WITH CONSIDERATION OF RESIDUAL STRENGTH

基于岩石微元强度服从Weibull分布规律,引入损伤变量修正因子,建立了考虑残余强度影响的岩石损伤本构模型.运用多元函数求极值的方法,推导了含修正系数的模型参数\(m\)和\(F_{0}\)的理论表达式;对模型修正因子的选取进行了讨论分析. 结果表明：本文修正模型的实质是增加了一个含有修正系数的线性项;修正系数 \(\delta \)主要反映岩石的残余强度特征,选取合适的 \(\delta \) 值可以提高修正后本构模型的准确性.     

多体系统指标2运动方程HHT方法违约校正1）

采用Cartesian绝对坐标建模方法,完整约束多体系统运动方程是指标3的微分--代数方程（differentialalgebraic equations,DAEs）,数值求解指标3的DAEs属于高指标问题,通过对位置约束方程求导,可使运动方程的指标降为2.位置约束方程求导得到的是速度约束方程.直接求解指标3的运动方程,速度约束方程得不到满足,而且高指标DAEs的数值求解存在一些问题.论文首先采用HHT（Hilber--Hughes--Taylor）直接积分方法求解降指标得到的指标2运动方程,此时速度约束方程参与离散计算,从机器精度上讲速度约束自然得到满足,而位置约束方程没有参与计算,存在“违约”.针对违约问题,采用基于Moore--Penrose广义逆理论的违约校正方法,消除位置约束方程的违约.指标2运动方程HHT方法违约校正,将HHT方法和违约校正方法很好地结合,在数值求解指标2运动方程的过程中,位置约束方程和速度约束方程都不存在违约问题,而且新方法没有引入新的未知数向量,离散得到的非线性方程组的方程数量与原指标2运动方程的方程数量相同,求解规模没有扩大.新方法的实用和有效性通过算例的数值实验得到验证,数值实验也说明新方法保持了HHT方法本身具有的数值阻尼可以控制和二阶精度的特性.最后从非线性方程组的求解规模和计算速度上与其他方法进行了比较分析,说明新方法的优势所在.