Modeling nonlinear relationships in ERP data using mixed‐effects regression with R examples

In the analysis of psychological and psychophysiological data, the relationship between two variables is often assumed to be a straight line. This may be due to the prevalence of the general linear model in data analysis in these fields, which makes this assumption implicitly. However, there are many problems for which this assumption does not hold. In this paper, we show that, in the analysis of event‐related potential (ERP) data, the assumption of linearity comes at a cost and may significantly affect the inferences drawn from the data. We demonstrate why the assumption of linearity should be relaxed and how to model nonlinear relationships between ERP amplitudes and predictor variables within the familiar framework of generalized linear models, using regression splines and mixed‐effects modeling.     

非线性偏最小二乘法在紫外分光光度分析中的应用——沃古林眼药水有机组分的测定

Lambert-Beer定律是以稀溶液为假设前提,不考虑吸光溶质分子和邻近分子的作用,实际分析样品溶液的吸收值和浓度之间不完全呈线性关系,采用线性处理会给结果带来一定的偏差。本文将非线性偏最小二乘法应用于沃古林眼药水紫外分光光度分析,盐酸普鲁卡因、盐酸黄连素和尼泊金乙酯的平均回收率依次为99.9%、100.0%和100.1%,CC依次为1.1%、0.6%和1.1%,结果明显好于线性偏最小二乘法。本法为复方制剂的分光光度分析提供了更为理想的新途径。     

Incorporating vessel taper and compliance properties in Navier-Stokes based blood flow models

A popular and useful technique used to model blood flow in cardiovascular simulations is to divide each blood vessel into a series of segments, each with its own lumped resistance, intertance, and compliance parameters. The values of these parameters are usually obtained through a simplification of the Navier-Stokes equations for fluid flow. However, the simplification often ignores the nonlinear and convective terms of the equations, resulting in errors in the parameter values, especially in the value found for resistance per unit length. We report a new method for the calculation of vessel resistance per unit length which takes into account the effects of vessel taper and wall compliance. It is shown that these effects can be addressed by the addition of two time-varying terms to the calculation of resistance per unit length. One term, due to vessel taper, is proportional to volumetric flow rateQ. The other term, due to vessel compliance, is proportional to ∂p/∂t. These variables are readily available in computer simulations of blood flow in lumped parameter systems. Using data for the descending aorta, the new parameter values, when averaged over a cardiac cycle, compare favorably with results in the literature.     

肾综合征出血热发病率的ANN预测模型

目的 :探讨ANN时间序列预测模型在疾病发病率或死亡率预测上的应用前景。方法 :利用动态学习比率BP算法以双曲正切函数为功能函数的非线性时间序列预测方法。结果 :建立HFRS发病率的ANN预测模型 ,其预测精度高。结论 :BP人工神经网络可以用于疾病发病率或死亡率的预测     

A sequential procedure for determining the number of regimes in a threshold autoregressive model

Summary In this paper, we propose a sequential method for determining the number of regimes in threshold autoregressive models. The proposed method relies on the superconsistency of sequential threshold estimates and uses general linearity tests to determine the number of thresholds. A simulation study is performed in order to find out the finite‐sample properties of our procedure and to compare it with two other procedures available in the literature. We find that our method works reasonably well for both single and multiple threshold models.     

非线性生物模型回归参数计算的一个新方法及应用

目的：研究变量代换对非线性生物模型回归参数的干扰，寻找消除或减少该干扰的新方法。方法：利用空间变换、泰勒(Taylor)级数和加权处理的组合方式消除或减少变量代换带来的严重影响。结果：给出一个计算非线性生物模型回归参数的新方法。结论：新方法消除或减少了变量代换带来的严重影响，保留了变量代换便于计算的优点；不但显著提高了非线性生物模型回归参数的精度，而且还能发现原始数据中隐藏的问题。     

Minimization of EOG artefacts from corrupted eeg signals using a neural network approach

In this paper, we propose a neural network (NN) approach to the enhancement of EEG signals in the presence of EOG artefacts. We recast the EEG enhancement problem into the optimization framework by developing an appropriate cost function. The cost function is nothing but the energy in the enhanced EEG signal obtained through a nonlinear filter formulation, unlike the conventionally-used linear filter formulation. The minimization property of feedback-type neural networks is exploited to solve this problem. An analysis has been performed to characterize the stationary points of the suggested energy function. The hardware set-up of the developed neural network has also been derived. The optimum nonlinear filter coefficients obtained from this minimization algorithm are used to estimate the EOG artefact which is then subtracted from the corrupted EEG signal, sample by sample, to get the artefact minimized signal. The time plots as the LP spectrum show that the proposed method is very effective. Thus the power and efficacy of the NN approach have been exploited for the purpose of minimizing EOG artefacts from corrupted EEG signals.     

Exact orthogonal kernel estimation from finite data records: Extending Weiner's identification of nonlinear systems

A technique is described for exact estimation of kernels in functional expansions for nonlinear systems. The technique operates by orthogonalizing over the data record and in so doing permits a wide variety of input excitation. In particular, the excitation is not limited to inputs that are white, Gaussian, or lengthy. Diagonal kernel values can be estimated, without modification, as accurately as off-diagonal values. Simulations are provided to demonstrate that the technique is more accurate than the Lee-Schetzen method with a white Gaussian input of limited duration, retaining its superiority when the system output is corrupted by noise.     

Computer-aided calculation of dose response curves in behavioral pharmacology by using a nonlinear regression procedure

In a variety of behavioral pharmacological experiments drug induced graded responses can be recorded even if one animal can be tested only once. In this case the analysis of dose response relationships will be accompanied with theoretical and practical problems additional to those known for dose response curves in single subjects as well as for the all-or-none type of responses. An experimental design was considered where one quantitatively measurable response of each animal tested contributed to an average dose response relationship. Use was made of a four parameter model capable of fitting s-shaped dose response curves over the whole feasible dose range for solving this nonlinear regression problem. Two examples, the dose dependent increased locomotor activity induced by apomorphine and the inhibited locomotor activity after pimozide treatment, were given to demonstrate the use of the method described and to direct the reader's attention to the wide range of its possible applications.