Scale-free Networks with Self-Similarity Degree Exponents

Ravasz et al. structured a deterministic model of a geometrically growing network to describe metabolic networks. Inspired by the model of Ravasz et al., a random model of a geometrically growing network is proposed. It is a model of copying nodes continuously and can better describe metabolic networks than the model of Ravasz et al. Analysis shows that the analytic method based on uniform distributions （i.e., Barabási-Albert method） is not suitable for the analysis of the model and the simulation process is beyond computing power owing to its geometric growth mechanism. The model can be better analyzed by the Poisson process. Results show that the model is scale-free with a self-similarity degree exponent, which is dependent on the common ratio of the growth process and similar to that of fractal networks.     

Novel Woods-Saxon stochastic resonance system for weak signal detection

We propose a joint exponential function and Woods–Saxon stochastic resonance(EWSSR)model.Because change of a single parameter in the classical stochastic resonance model may cause a great change in the shape of the potential function,it is difficult to obtain the optimal output signal-to-noise ratio by adjusting one parameter.In the novel system,the influence of different parameters on the shape of the potential function has its own emphasis,making it easier for us to adjust the shape of the potential function.The system can obtain different widths of the potential well or barrier height by adjusting one of these parameters,so that the system can match different types of input signals adaptively.By adjusting the system parameters,the potential function model can be transformed between the bistable model and the monostable model.The potential function of EWSSR has richer shapes and geometric characteristics.The effects of parameters,such as the height of the barrier and the width of the potential well,on SNR are studied,and a set of relatively optimal parameters are determined.Moreover,the EWSSR model is compared with other classical stochastic resonance models.Numerical experiments show that the proposed EWSSR model has higher SNR and better noise immunity than other classical stochastic resonance models.Simultaneously,the EWSSR model is applied to the detection of actual bearing fault signals,and the detection effect is also superior to other models.     

Analogue correction method of errors and its application to numerical weather prediction

In this paper, an analogue correction method of errors (ACE) based on a complicated atmospheric model is further developed and applied to numerical weather prediction (NWP). The analysis shows that the ACE can effectively reduce model errors by combining the statistical analogue method with the dynamical model together in order that the information of plenty of historical data is utilized in the current complicated NWP model. Furthermore, in the ACE, the differences of the similarities between different historical analogues and the current initial state are considered as the weights for estimating model errors. The results of daily, decad and monthly prediction experiments on a complicated T63 atmospheric model show that the performance of the ACE by correcting model errors based on the estimation of the errors of 4 historical analogue predictions is not only better than that of the scheme of only introducing the correction of the errors of every single analogue prediction, but is also better than that of the T63 model.     

An Improved Local Weighted Linear Prediction Model for Chaotic Time Series

Previous research working on local prediction state with some unsuitable neighbor points （such as false points and pseudo-false neighbor points） are the main source of errors of local prediction and these unsuitable neighbors cannot be eliminated entirely. Therefore, an improved local weighted linear prediction model based on local integrated correlation, which can reduce the influence of the residual unsuitable neighbors, is proposed to predict chaotic time series in our study. Simulation results show that the performance of the improved model is superior to the other local prediction models in the prediction of chaotic time series without and with additive white Gaussian noise.     

GEKF, GUKF and GGPF based prediction of chaotic time-series with additive and multiplicative noises

On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented Kalman filtering （UKF） and the Gaussian particle filtering （GPF） to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal （These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper）. Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey-Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.     

Measurement of avalanche size and position resolution of RPCs with different surface resistivities of the high voltage provider

The effects of surface resistivity of the high voltage provider on the space dispersion of the induced charge of a prototype Resistive Plate Chamber （RPC） have been studied experimentally and theoretically. The results of both experiment and theory agree and confirm that a two-Gaussian function can be used to fit the dispersion of the induced charge of the RPC. It is shown that the Gaussian function with the narrower width is mainly due to the expansion of the avalanche charge in the gas gap of the RPC, and the Gaussian function with the larger width is due to the charge dispersion when it passes through the resistive carbon film. This will be useful in the RPC design when one wants to make an RPC with high position resolution.     

Influence of Velocity Shell Correlations on Anomalous Scaling Exponents of Passive Scalars in Shell Models

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of passive scalars of turbulence. Different to the original problem, the distribution function of the prescribed random velocity field is multi-dimensional normal and delta-correlated in time. Here, our random velocity field is spatially correlative. For comparison, we also give the result obtained by the Gaussian random velocity field without spatial correlation. The anomalous scaling exponents H（p） of passive scalar advected by two kinds of random velocity above are determined for structure function up to p= 15 by numerical simulations of the random shell model with Runge-Kutta methods to solve the stochastic differential equations. We observed that the H（p） ＇s obtained by the multi-dimeasional normal distribution random velocity are more anomalous than those obtained by the independent Gaussian random velocity.     

Monte Carlo Simulation of Magnetization Behaviour of Co Nanowires

Based on the Monte Carlo method, we simulate the magnetization curves with various magnetic field orientations for various single Co nanowires at room temperature. The simulated switching field as a function of angle between the field and the wire axis is consistent well with the experimental data. Correspondingly, the coercivity as a function of angle θ is presented, which together with the switching field plays an important role on explaining the magnetic reversal mechanism. It is found that the angular dependence of coercivity depends on the diameter of nanowires, and the coercivity and switching field versus θ deviate markedly from the prediction from the classical uniform rotation mode in the chain-of-sphere model. Furthermore, the magnetic reversal configurations display that magnetization reversal in the wires with small diameters is a nucleation-propagation process, and it is similar to the curling spread process in the larger wires.     

Classifying land cover based on calibrated full-waveform airborne light detection and ranging data

The capability of the parameters derived from waveform data in discriminating objects is assessed and the effect of the relative calibration of full-waveform data in discriminating land-cover classes is evaluated. Firstly, a non-linear least-squares method with the Levenberg-Marquardt algorithm is used to fit the return waveforms by a Gaussian function. Gaussian amplitude, standard deviation, and energy are extracted. Secondly, a relative calibration method using the range between the sensor and the target based on a radar equation is applied to calibrate amplitude and energy. The change in transmit pulse energy is also considered in this process. A support vector machine classifier is used to distinguish the study area into non-vegetated area （including roads, buildings, and vacant lots）, grassland, needle-leaf forests, and broad- leaf forests. The overall classification accuracy ranges from 79.33% to 87.6%, with the combination of the two groups of the three studied parameters. Calibrated data classification accuracy is improved from 1.20% to 6.44%, thus resulting in better forest type discrimination. The result demonstrates that the parameters extracted from the waveforms can be applied effectively in identifying objects and that relative calibrated data can improve overall classification accuracy.     

Statistical Elmore delay of RC interconnect tree

As feature size keeps scaling down,process variations can dramatically reduce the accuracy in the estimation of interconnect performance.This paper proposes a statistical Elmore delay model for RC interconnect tree in the presence of process variations.The suggested method translates the process variations into parasitic parameter extraction and statistical Elmore delay evaluation.Analytical expressions of mean and standard deviation of interconnect delay can be obtained in a given fluctuation range of interconnect geometric parameters.Experimental results demonstrate that the approach matches well with Monte Carlo simulations.The errors of proposed mean and standard deviation are less than 1% and 7%,respectively.Simulations prove that our model is efficient and accurate.     

A new estimator method for GARCH models

The GARCH (p, q) model is a very interesting stochastic process with widespread applications and a central role in empirical finance. The Markovian GARCH (1, 1) model has only 3 control parameters and a much discussed question is how to estimate them when a series of some financial asset is given. Besides the maximum likelihood estimator technique, there is another method which uses the variance, the kurtosis and the autocorrelation time to determine them. We propose here to use the standardized 6th moment. The set of parameters obtained in this way produces a very good probability density function and a much better time autocorrelation function. This is true for both studied indexes: NYSE Composite and FTSE 100. The probability of return to the origin is investigated at different time horizons for both Gaussian and Laplacian GARCH models. In spite of the fact that these models show almost identical performances with respect to the final probability density function and to the time autocorrelation function, their scaling properties are, however, very different. The Laplacian GARCH model gives a better scaling exponent for the NYSE time series, whereas the Gaussian dynamics fits better the FTSE scaling exponent.     

基于高斯过程的混沌时间序列单步与多步预测

针对混沌时间序列单步和多步预测,提出基于复合协方差函数的高斯过程 (GP)模型方法.GP模型的确立由协方差函数决定,通过对训练数据集的学习,在证据最大化框架内,利用矩阵运算和优化算法自适应地确定协方差函数和均值函数中的超参数.GP模型与神经网络、模糊模型相比,其可调整参数很少.将不同复合协方差函数的GP模型应用在混沌时间序列单步及多步提前预测中,并与单一协方差函数的GP、支持向量机、最小二乘支持向量机、径向基函数神经网络等方法进行了比较.仿真结果表明,基于不同复合协方差函数的GP方法能精确地预测混沌时间序 关键词： 高斯过程 混沌时间序列 预测 模型比较     

近红外光谱的北方寒地土壤含水率预测模型研究

我国北方寒地温差大,土壤温差对近红外光谱测量土壤墒情有较大影响。针对这一问题,以北方寒地土壤为研究对象,探究大范围温度胁迫下（-20～40 ℃）土壤的近红外光谱与土壤不同含水率之间的关系预测模型方法。选取黑龙江八一农垦大学农学院试验基地中的黑土,经烘干、过筛等操作处理后配置含水率范围在15%～50%内八种不同湿度的土壤样品,建立北方寒地土壤大范围温度胁迫下土壤的近红外光谱信息与含水率之间的定量预测模型。在全波段光谱数据的基础上,结合五种不同光谱信号预处理方法,采用BP神经网络算法、优化支持向量机算法（SVM）、高斯过程算法（GP）三种智能算法建立北方寒地土壤近红外光谱与含水率的预测模型并验证模型的效果。利用69组数据进行训练建模, BP神经网络相关参数设置为学习速率0.05,最大训练次数设置为5 000,隐层单元数确定为20;SVM采用径向基函数,并利用leave-one-out cross validation确定了最佳惩罚参数为0.87,使模型预测的准确性提高;高斯过程算法内部采用马顿核。模型的定量评估采用决定系数(R2)和均方根误差（RMSE）。结果表明,在建立的全部BP神经网络模型中,效果最佳的为S_G-BP神经网络模型,模型的R2为0.960 9,RMSE为2.379 7;在SVM模型中SNV-SVM模型的效果最好,模型的R2为0.991 1,RMSE为1.081 5;在GP模型中S_G-GP模型的效果最好,模型的R2为0.928,RMSE为3.258 1,综上基于SNV预处理的SVM模型训练效果最优。利用剩余的35组光谱数据作为预测集验证模型性能,经模型对比分析发现基于SVM算法的预测模型效果优于其他两种算法,其中基于S_G的SVM模型效果最优,其预测模型的R2和差RMSE分别为0.992 1和0.736 9。综合建模集与预测集的参数最终确定基于S_G的SVM模型为最佳模型。此模型可以作为大范围温度胁迫条件下（寒地）的土壤含水率有效预测方法,为设计优化适宜寒地便携式近红外土壤含水率快速测量仪提供科学依据。     

联合区间高斯过程的近红外光谱波长选择方法及应用

针对近红外光谱应用,提出了一种基于高斯过程(GP)模型的波长选择算法,即联合区间高斯过程(synergy interval gaussian process,siGP)算法。首先将全光谱区域划分为一系列无重复且间距相等的区间,再选取最优的若干个区间联合建立GP模型,由于GP模型具有非线性处理能力,因此该方法可以减少非线性的影响。以红曲菌固态发酵过程中过程参数水分含量和pH值的检测为例,新算法对水分含量、pH值的预测集相关系数(r_p)分别为0.956 4和0.977 3,预测均方根误差(RMSEP)分别为0.012 7和0.161 0,参与建模的数据点由全谱的1 500个分别减少到225个、375个,在对独立样本的预测上,表现出较好的精度。与传统联合区间偏最小二乘(siPLS)波长选择算法对比,siGP算法预测效果更好：对水分含量和pH值,r_p在GP模型预测时提高了3.37%和3.51%,RMSEP在GP模型预测时提高了29.4%和34.8%。表明siGP结合GP模型能够有效选择波长区间以及提高近红外模型的准确性,对进一步实现近红外光谱技术在线检测具有参考价值。     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

基于开关电流技术的小波变换的滤波器电路实现

提出基于开关电流技术的小波变换的滤波器电路实现方法. 小波变换的开关电流滤波器实现电路由冲激响应为高斯一阶导数及其膨胀函数的滤波器组构成. 开关电流滤波器的膨胀系数(尺度)通过控制宽长比(W/L)或时钟频率可得到精确地控制. Padé逼近是一种有效的有理逼近，小波函数经过Padé变换可以得到其有理分式逼近，十分利于其开关电流滤波器电路实现. 仿真结果证实了其可行性. 关键词： 小波变换 开关电流 滤波器 Padé逼近     

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.     

Singular Values of Products of Ginibre Random Matrices,Multiple Orthogonal Polynomials and Hard Edge Scaling Limits

Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation kernel that can be expressed in terms of Meijer G-functions. We show that this point process can be interpreted as a multiple orthogonal polynomial ensemble. We give integral representations for the relevant multiple orthogonal polynomials and a new double contour integral for the correlation kernel, which allows us to find its scaling limits at the origin (hard edge). The limiting kernels generalize the classical Bessel kernels. For M = 2 they coincide with the scaling limits found by Bertola, Gekhtman, and Szmigielski in the Cauchy–Laguerre two-matrix model, which indicates that these kernels represent a new universality class in random matrix theory.     

近红外光谱分析中的高斯过程回归方法

将高斯过程算法引入化学计量学领域,用于挖掘近红外光谱与被测物组分之间的复杂关系.为增加模型的稳健性,首先采用了蒙特卡罗交叉验证方法以去除异常样本,而后多元散射校正、平滑、导数等方法被用于模型的预处理.近红外光谱在经过无信息变量去除算法处理后,在保留有用信息的基础上大大缩减了波长点数,以这些特征波长点作为输入建立的分析模型更具有解释能力和稳健性.为验证算法的有效性,使用了一组公开的数据集,它包含了80个玉米样品的近红外光谱以及油、淀粉、蛋白质的含量值.GP回归算法被用于分析这三种组分的含量,所得模型的评价指标分别采用校正、校正集交叉验证均方根误差、预测均方根误差以及各自的相关系数.结果显示,模型的校正相关系数r达到0.99以上,预测时的相关系数r也在0.96以上,验证了该算法的有效性.     

基于鲁棒极端学习机的混沌时间序列建模预测

针对混沌时间序列预测模型易受异常点影响,导致模型预测精度低的问题,在贝叶斯框架下提出一种鲁棒极端学习机.所提模型将具有重尾分布特性的高斯混合分布作为模型输出似然函数,得到一种对异常点和噪声更具鲁棒性的预测模型.但由于将高斯混合分布作为模型输出似然函数后,模型输出的边缘似然函数变成难以解析处理的形式,因此引入变分方法进行近似推理,实现模型参数的估计.在加入异常点和噪声的情况下,将所提模型应用于大气环流模拟模型方程Lorenz序列以及Rossler混沌时间序列和太阳黑子混沌时间序列的预测中,预测结果验证了所提模型的有效性.