Testing of Multifractional Brownian Motion

Fractional Brownian motion (FBM) is a generalization of the classical Brownian motion. Most of its statistical properties are characterized by the self-similarity (Hurst) index 0<H<1. In nature one often observes changes in the dynamics of a system over time. For example, this is true in single-particle tracking experiments where a transient behavior is revealed. The stationarity of increments of FBM restricts substantially its applicability to model such phenomena. Several generalizations of FBM have been proposed in the literature. One of these is called multifractional Brownian motion (MFBM) where the Hurst index becomes a function of time. In this paper, we introduce a rigorous statistical test on MFBM based on its covariance function. We consider three examples of the functions of the Hurst parameter: linear, logistic, and periodic. We study the power of the test for alternatives being MFBMs with different linear, logistic, and periodic Hurst exponent functions by utilizing Monte Carlo simulations. We also analyze mean-squared displacement (MSD) for the three cases of MFBM by comparing the ensemble average MSD and ensemble average time average MSD, which is related to the notion of ergodicity breaking. We believe that the presented results will be helpful in the analysis of various anomalous diffusion phenomena.     

Adaptive Event-Triggered Synchronization of Uncertain Fractional Order Neural Networks with Double Deception Attacks and Time-Varying Delay

This paper investigates the problem of adaptive event-triggered synchronization for uncertain FNNs subject to double deception attacks and time-varying delay. During network transmission, a practical deception attack phenomenon in FNNs should be considered; that is, we investigated the situation in which the attack occurs via both communication channels, from S-C and from C-A simultaneously, rather than considering only one, as in many papers; and the double attacks are described by high-level Markov processes rather than simple random variables. To further reduce network load, an advanced AETS with an adaptive threshold coefficient was first used in FNNs to deal with deception attacks. Moreover, given the engineering background, uncertain parameters and time-varying delay were also considered, and a feedback control scheme was adopted. Based on the above, a unique closed-loop synchronization error system was constructed. Sufficient conditions that guarantee the stability of the closed-loop system are ensured by the Lyapunov-Krasovskii functional method. Finally, a numerical example is presented to verify the effectiveness of the proposed method.     

基于改进sigmoid激活函数的深度神经网络训练算法研究

针对深度神经网络训练过程中残差随着其传播深度越来越小而使底层网络无法得到有效训练的问题,通过分析传统sigmoid激活函数应用于深度神经网络的局限性,提出双参数sigmoid激活函数。一个参数保证激活函数的输入集中坐标原点两侧,避免了激活函数进入饱和区,一个参数抑制残差衰减的速度,双参数结合有效的增强了深度神经网络的训练。结合DBN对MNIST数据集进行数字分类实验,实验表明双参数 sigmoid激活函数能够直接应用于无预训练深度神经网络,而且提高了sigmoid激活函数在有预训练深度神经网络中的训练效果。     

人工神经网络分类鉴别苦丁茶红外光谱

为了分类鉴别苦丁茶,采用竞争神经网络(CNN)和反向传播人工神经网络(BP网络)两种模式的人工神经网络(ANN)分别分析了各种苦丁茶的红外谱图。作者采用25个样本作训练集,11个样本作检验集,用两种网络进行了训练。结果表明,CNN网络和BP网络均能够有效地实现苦丁茶产地的鉴别,但CNN网络能够进一步地区分苦丁茶的级别。实验表明,CNN速度快,预测结果准确,可望用竞争神经网络(CNN)和红外光谱法结合分类鉴别苦丁茶。     

Probability Density Function of the Output Current of Cascaded Multiplexer/Demultiplexers in Transparent Optical Networks

The influence of the concatenation of arbitrary optical multiplexers/demultiplexers (MUX/DEMUXs) on the probability density function (PDF) of the output current of a transparent optical network is assessed. All PDF results obtained analytically are compared with estimates from Monte Carlo simulation and an excellent agreement is achieved.

The non-Gaussian behavior of the PDFs, previously reported by other authors for square-law detectors, is significantly enhanced with the number of nodes increase due to the noise accumulation along the cascade of MUX/DEMUXs. The increase of the MUX/DEMUXs bandwidth and detuning also enhances the PDFs non-Gaussian behavior. The PDF shape variation with the detuning depends strongly on the number of nodes.

Explanations for the Gaussian approximation (GA) accuracy on the assessment of the performance of a concatenation of optical MUX/DEMUXs are also provided. For infinite extinction ratio and tuned MUX/DEMUXs, the GA error probabilities are, in general, pessimistic, due to the inaccurate estimation of the error probability for both bits. For low extinction ratio, the GA is very accurate due to a balance between the error probabilities estimated for the bits “1” and “0.” With the detuning increase, the GA estimates can become optimistic.     

Probability Density Function of the Output Current of Cascaded Multiplexer/Demultiplexers in Transparent Optical Networks

The influence of the concatenation of arbitrary optical multiplexers/demultiplexers (MUX/DEMUXs) on the probability density function (PDF) of the output current of a transparent optical network is assessed. All PDF results obtained analytically are compared with estimates from Monte Carlo simulation and an excellent agreement is achieved.

The non-Gaussian behavior of the PDFs, previously reported by other authors for square-law detectors, is significantly enhanced with the number of nodes increase due to the noise accumulation along the cascade of MUX/DEMUXs. The increase of the MUX/DEMUXs bandwidth and detuning also enhances the PDFs non-Gaussian behavior. The PDF shape variation with the detuning depends strongly on the number of nodes.

Explanations for the Gaussian approximation (GA) accuracy on the assessment of the performance of a concatenation of optical MUX/DEMUXs are also provided. For infinite extinction ratio and tuned MUX/DEMUXs, the GA error probabilities are, in general, pessimistic, due to the inaccurate estimation of the error probability for both bits. For low extinction ratio, the GA is very accurate due to a balance between the error probabilities estimated for the bits “1” and “0.” With the detuning increase, the GA estimates can become optimistic.     

应用荧光光谱和径向基函数神经网络定量检测三聚氰胺

实验发现三聚氰胺溶液在紫外光激发下产生较强荧光,测得其荧光峰在310～600 nm之间,荧光峰值波长为420 nm左右,荧光相对强度与三聚氰胺溶液浓度呈现复杂的非线性关系。提出了采用径向基函数神经网络结合荧光光谱对三聚氰胺溶液浓度进行测定的方法。对每个样本选取30个发射波长值所对应的荧光强度作为网络数据,训练、建立了径向基函数神经网络。应用训练好的径向基函数神经网络,对5种三聚氰胺溶液的浓度进行预测,结果相对误差分别为0.93%,0.09%,0.31%,1.55%,4.61%。该方法能快捷、准确地测定三聚氰胺在溶液中的含量,为三聚氰胺检测及食品安全监管提供了一种新方法。     

Analysis of Light Propagation in a Realistic Head Model by a Hybrid Method for Optical Brain Function Measurement

Near infrared spectroscopy (NIRS) is used to measure the change in blood volume and oxygenation in the brain cortex induced by functional brain activation. The development of an adequate model to calculate light propagation in the head is very important because the light is strongly scattered in the tissue and this causes ambiguity in the volume of tissue interrogated with a source–detector pair of the NIRS instrument. In this study, a two-dimensional realistic head model is generated from a MRI scan of a human adult head. The light propagation in the head model is calculated by the hybrid Monte Carlo–diffusion method to obtain the change in detected intensity caused by a focal absorption change in the grey matter or in the white matter to discuss the relationship between the depth of the activated region and the sensitivity of the NIRS signal. The sensitivity to the activated region in the white matter steeply decreases with an increase of the depth of the activated region because the spatial sensitivity profile is mainly confined to the grey matter. The contribution of the focal brain activity to the NIRS signal is determined by not only the depth of the activated region from the head surface but also the depth of the activated region from the brain surface.     

基于荧光光谱和径向基函数神经网络的合成食品色素测定和鉴别

以合成食品色素胭脂红、苋菜红溶液为例,提出了应用荧光光谱结合径向基函数神经网络对合成食品色素溶液进行浓度测定和种类鉴别的方法。应用SP-2558多功能光谱测量系统,测得胭脂红和苋菜红溶液分别在波长为300和400 nm的光激发下产生的荧光光谱。对每个胭脂红溶液样本选取15个发射波长值所对应的荧光强度作为网络特征参数,训练、建立用于浓度预测的径向基函数神经网络。据此,对3种胭脂红溶液样本的浓度进行预测,预测结果相对误差分别为1.42%,1.44%和3.93%。另外,以胭脂红和苋菜红溶液荧光波长值所对应的荧光强度作为特征参数,训练、建立了用于种类鉴别的径向基函数神经网络,进行合成食品色素溶液种类识别,准确率达100%。这些结果表明,该方法方便、快捷、准确度较高,可应用于合成食品色素检测及食品安全监管。     

A Monte Carlo simulation to the performance of the R/S and V/S methods—Statistical revisit and real world application

A correct or precise estimation of the Hurst exponent is one of the fundamentally important problems in the financial economics literature. There are three widely used tools to estimate the Hurst exponent, the canonical rescaled range (R/S), the variance rescaled statistic (V/S) and the Modified rescaled range (Modified R/S). To clarify their performance, we compare them by Monte Carlo simulations; we generate many time-series of a fractal Brownian motion, of a Weierstrass–Mandelbrot cosine fractal function and of a fractionally integrated process, whose theoretical Hurst exponents are known, to compare the Hurst exponents estimated by the three methods. To better understand their pragmatic performance, we further apply all of these methods empirically in real-world applications. Our results imply it is not appropriate to conclude simply which method is better as V/S performs better when the analyzed market is anti-persistent while R/S seems to be a reliable tool used in persistent market.     

小波软阈值径向基神经网络同时测定多组分混合物

建立了一种小波软阈值径向基函数神经网络 (STWRBFN)方法 ,同时定量分析了多组分混合物。结合小波软阈值法和径向基函数神经网络改进了回归质量。通过最佳化 ,选择了小波函数、小波分解水平(L)、阈值法类型和网络的伸展参数 (σ)。两个程序PSTWRBFN和PRBFN被设计执行STWRBFN和径向基函数神经网络 (RBFN)计算。实验结果表明STWRBFN是成功的且优于RBFN法 ,和经典的多变量线性回归(MLR)方法相比较 ,这两个方法更为有效     

径向基函数神经网络和近红外光谱用于大黄中有效成分的定量预测

采用近红外光谱(NIRS)法和人工神经网络定量预测大黄样品中４种有效成分的含量,包括：蒽醌及其单糖甙类、水溶性蒽甙类、芪芪甙类、鞣质及其有关化合物。在1 100～2 500 nm波长范围内扫描大黄粉末样品,采用径向基函数神经网络(RBFNN)建立了近红外光谱与HPLC分析值之间的校正模型。上述四类化合物的交叉验证均方差(RMSECV)分别为2.572,0.442,2.794,9.438;预测均方差(RMSEP)分别为4.598,8.657,0.458 6,5.106。该方法快速,无损,结果令人满意,可作为中药材复杂体系中化学组分定量测定的方法。     

三种光电混合神经网络系统衍射误差的仿真研究

介绍了三种类型的光电混合神经网络系统,重点研究了衍射引起的误差对系统输出的影响。根据衍射、光学信息处理和神经网络理论,采用实验中的参量和输入数据,对衍射造成的输出误差做了仿真分析。分析表明,近场衍射造成较大的输出误差。近场与远场衍射综合作用时,误差因输入图像模式不同而差异较大;其中,当输入较小的简单图像时相对误差较大;而对实验中实际采用的复杂图像,相对误差较小。利用线性回归方法对输出数据做了校正,并分析了其可行性,校正后的数据误差降低一个量级。衍射误差对实验中识别率的影响可以控制在较小的范围内,识别率可以保持在97.7%以上。