Nonlinear identification of NMR spin systems by adaptive filtering

In this paper, we present two new methods for identifying NMR spin systems. These methods are based on nonlinear adaptive filtering. The spin system is assumed to be time-invariant with memory. The first method uses a truncated discrete Volterra series to describe the nonlinear relationship between excitation (input) and system response (output). First-, second-, and third-order kernels of this series are estimated employing the least mean square (LMS) algorithm. Three parallel filters can then model the NMR spin system so that its output is no more than simple sum of three convolution products between combinations of the input signal and filters coefficients. It is also shown that the contribution of the Volterra second-order term to the total system response is neglected compared with the contributions of the first- and the third-order terms. In the second identification method, the output signal is related to the input signal through a recursive nonlinear difference equation with constant coefficients. The LMS algorithm is used again to estimate the equation coefficients. The two methods are validated with a simulated NMR system model based on Bloch equations. The results and the performances of these methods are analyzed and compared. It is shown that our methods permit a simple identification of NMR spin systems. The field of applications of this study is promising in the optimization of NMR signal detection, especially in the cases of low signal-to-noise ratios where optimum signal filtering and analysis must be performed.     

Single infrared image super-resolution combining non-local means with kernel regression

In many infrared imaging systems, the focal plane array is not sufficient dense to adequately sample the scene with the desired field of view. Therefore, there are not enough high frequency details in the infrared image generally. Super-resolution (SR) technology can be used to increase the resolution of low-resolution (LR) infrared image. In this paper, a novel super-resolution algorithm is proposed based on non-local means (NLM) and steering kernel regression (SKR). Based on that there are a large number of similar patches within an infrared image, NLM method can abstract the non-local similarity information and then the value of high-resolution (HR) pixel can be estimated. SKR method is derived based on the local smoothness of the natural images. In this paper the SKR is used to give the regularization term which can restrict the image noise and protect image edges. The estimated SR image is obtained by minimizing a cost function. In the experiments the proposed algorithm is compared with state-of-the-art algorithms. The comparison results show that the proposed method is robust to the noise and it can restore higher quality image both in quantitative term and visual effect.     

False positive control of activated voxels in single fMRI analysis using bootstrap resampling in comparison to spatial smoothing

Functional magnetic resonance imaging (fMRI) is an effective tool for the measurement of brain neuronal activities. To date, several statistical methods have been proposed for analyzing fMRI datasets to select true active voxels among all the voxels appear to be positively activated. Finding a reliable and valid activation map is very important and becomes more crucial in clinical and neurosurgical investigations of single fMRI data, especially when pre-surgical planning requires accurate lateralization index as well as a precise localization of activation map.Defining a proper threshold to determine true activated regions, using common statistical processes, is a challenging task. This is due to a number of variation sources such as noise, artifacts, and physiological fluctuations in time series of fMRI data which affect spatial distribution of noise in an expected uniform activated region. Spatial smoothing methods are frequently used as a preprocessing step to reduce the effect of noise and artifacts. The smoothing may lead to a shift and enlargement of activation regions, and in some extend, unification of distinct regions.In this article, we propose a bootstrap resampling technique for analyzing single fMRI dataset with the aim of finding more accurate and reliable activated regions. This method can remove false positive voxels and present high localization accuracy in activation map without any spatial smoothing and statistical threshold setting.     

Nonlinear dynamics of DNA systems with inhomogeneity effects

We investigate the nonlinear dynamics of the Peyrard–Bishop DNA model taking into account site dependent inhomogeneities. By means of the multiple-scale expansion in the semi-discrete approximation, the dynamics is governed by the perturbed nonlinear Schrödinger equation. We carry out a multiple-scale soliton perturbation analysis to find the effects of the variety of nonlinear inhomogeneities on the breatherlike soliton solution. During the crossing of the inhomogeneities, the coherent structure of the soliton is found stable. The global shape of the inhomogeneous molecule is merged with the shape of the homogeneous molecule. However, the velocity, the wavenumber and the angular frequency undergo a time-dependent correction that is proportional to initial width of the soliton and depends on the nature of the inhomogeneities.     

Generalized regression theorem for open systems

A recently proposed method to treat open systems is applied to the evaluation of multitime correlation functions of operators of the open system itself. A general quantum-mechanical regression theorem is deduced, which holds also when the open system undergoes a non- markoffian motion. Such analysis extends the results previously obtained for singletime expectation values and further illustrates the advantages of the method.     

隧道二次衬砌监测的非线性回归分析研究

隧道二次衬砌性能劣化是影响隧道健康运营的主要病害,利用光纤通信技术对二次衬砌进行结构安全性分析,是保证隧道工程健康运营的重要手段。以埋入式光纤Bragg光栅应变传感器对田心隧道二次衬砌监测的实际数据为依据,选择最佳的典型函数模型对隧道的监测数据进行非线性回归分析,得出能够反映应变发展变化趋势的回归曲线,预测支护结构(监测点)的应变趋势,判断支护效果,对隧道支护结构当前的和最终的稳定性进行分析,从而实现对隧道结构部的稳定性判断。     

The identification of nonlinear molecular systems by spectroscopic methods

The Wiener functional expansion method for the analysis of nonlinear systems is applied to identify and analyze both nonlinear and linear molecular systems by spectroscopic methods. As the sampling filter (monochromator) of any spectroscopic apparatus may be defined by a Weber-Hermite polynomial, an analysis of the refracted or scattered light by orthogonal polynomials is easily achieved. Time averaging obtains the Weber-Hermite coefficients which permit the characterization of the molecular system with respect to the polarization of the incident and scattered light. In the case of two series of measurements made with incident and emerging light polarized in different directions: the identification of the JonesM matrices for the molecular system irradiated is possible. In the case of three series of measurements made, for example, with incident and emerging light (a) circularly polarized corotating, (b) circularly polarized contrarotating, and (c) plane polarized perpendicular: the identification of the molecular system's McClain invariants related to the vibrational symmetry group for Raman inelastic light scattering is possible. The analysis presents a unified picture of elastic and inelastic light scattering and one-photon and two-photon processes. The apparatus described would detect those instances in molecular systems for which Beer's law does not apply.     

隧道二次衬砌监测的非线性回归分析研究

隧道二次衬砌性能劣化是影响隧道健康运营的主要病害,利用光纤通信技术对二次衬砌进行结构安全性分析,是保证隧道工程健康运营的重要手段。以埋入式光纤Bragg光栅应变传感器对田心隧道二次衬砌监测的实际数据为依据,选择最佳的典型函数模型对隧道的监测数据进行非线性回归分析,得出能够反映应变发展变化趋势的回归曲线,预测支护结构(监测点)的应变趋势,判断支护效果,对隧道支护结构当前的和最终的稳定性进行分析,从而实现对隧道结构部的稳定性判断。     

生物系统中的非线性现象

文章通过用非线性科学的基本概念与系统方法分析了芽殖酵母细胞周期网络的动力学行为,说明非线性科学在定量研究生命过程所可能起到的重要作用,同时说明非线性科学现有的分析手段在研究生命系统中的局限性.这样利用非线性动力学研究生物系统的动力学问题,不但可以为系统生物学的研究提供强大的数学工具,同时也可以推动非线性科学本身的发展.这项研究从另一个角度显示了交叉学科的生命力.     

生物系统中的非线性现象

文章通过用非线性科学的基本概念与系统方法分析了芽殖酵母细胞周期网络的动力学行为，说明非线性科学在定量研究生命过程所可能起到的重要作用，同时说明非线性科学现有的分析手段在研究生命系统中的局限性．这样利用非线性动力学研究生物系统的动力学问题，不但可以为系统生物学的研究提供强大的数学工具，同时也可以推动非线性科学本身的发展．这项研究从另一个角度显示了交叉学科的生命力．     

Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints

Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the coarse-grained pure states correspond to the generalized coherent, i.e. generalized nonentangled states. Open system model of the coarse-graining is discussed. It is shown that in this model and in the weak coupling limit the constrained dynamical equations coincide with an equation for pointer states, based on Hilbert-Schmidt distance, that was previously suggested in the context of the decoherence theory.     

Nonlinear dynamics for magnetic systems with a single-spin potential with variable shapes

We discuss the influence of a zero-temperature environment on a coherent quantum system. First, we calculate the reduced density operator of the system in the framework of the well-known, exactly solvable model of an oscillator coupled to a bath of harmonic oscillators. Then, we propose the sketch of an Aharonov–Bohm-like interferometer showing, through interference measurements, the decrease of the coherence length of the system due to the interaction with the environment, even in the zero temperature limit.     

隧道围岩压力监测的非线性回归分析研究

隧道围岩压力的变化是导致公路隧道岩块错动、掉块、甚至塌方的重要因素。结合田心隧道工程,将一种可以把压力转变成光纤Bragg光栅波长移位的FBG土压力传感器应用于隧道围岩压力的监测;将40支土压力传感器安装在20个代表性断面中。采用非线性回归分析统计方法对隧道的量测数据进行分析,比较了监测数据的处理分析方法,选取最优的非线性回归分析模型。监测数据与回归拟合数据分析表明,非线性回归分析预测方法不仅可以反映隧道围岩变形和压力变化过程,还能根据其变化趋势进行结构异常判断。     

Nonlinear screening in multilayer graphene systems

Electrostatic screening in multilayer graphene is highly nonlinear due to the vanishing density of states at the Fermi level. Using a discrete model we study the charge screening normal to the layers. Our model shows a strong charge and temperature dependence and has a simple continuum limit at T=0 for undoped systems. Doped systems can exhibit more complex behavior due to minority-carrier screening. Most importantly we find that the screening length can vary more than an order of magnitude depending on the experimental conditions, reconciling the large range of screening lengths reported in previous experiments. This has important consequences for technological applications of multilayer graphene used in electrodes or transistor channels.