A theory of measurement with applications to spectrometry

An analytic function operating on experimental data is optimized for making the most accurate measurement of a parameter of the expected data, under the conditions of non-stationary shot noise. The value of the parameter is obtained by equating the operation on experimental data with the same operation on the expected data which contains the parameter as an unknown value. If the operation is represented by a weighting function, the form of the optimum weighting function depends on the initial transformation of the experimental data by the measuring instrument. The optimum weighting function always contains the derivative of the expected signal with respect to the unknown parameter, divided by the time-dependent variance of the received signal. Weighting functions for the logarithmic output of a spectrophotometer are described. The superiority over least-squares curve-matching is shown. A method for determination of peak position by optimum slope measurement is derived. In general, the optimum weighting function is not a matched filter. The optimum result is the same for center-of-gravity measurements. The optimum parameter measurement is equivalent to a least-squares error minimization weighted by the inverse variance or mean-square noise level. This variance weighting is significant in photometric measurements limited by shot noise or other measurements described by Poisson statistics, such that the mean-square noise level varies with time. The form of the optimum filter, for non-white, non-stationary noise is derived.     

Signal transduction in a coupled hormone system: selective explicit internal signal stochastic resonance and its control

Cooperative interactions of signal transduction and environmental noise are investigated with a coupled hormone system, in which selective explicit internal signal stochastic resonance (EISSR) is observed. More specifically, the large peak of a period-2 oscillation (i.e., a strong signal) is greatly amplified by the environmental noise while the small peak (i.e., a weak signal) does not exhibit cooperative interactions with noise. The EISSR phenomenon could be controlled by adjusting the frequency or amplitude of an external signal and a critical amplitude for external signal is found. Significantly, the maximal signal-to-noise ratio increases almost linearly with the increment of control parameter, despite that the magnitude of the large peak is decreased. In addition, the noise does not alter the fundamental frequencies of the strong signal and the weak signal, which implicates that the system can keep its intrinsic oscillatory state and resist the effect of environmental fluctuations.     

Two-parameter stochastic resonance in a model of electrochemical oxidation of formic acid on Pt

Stochastic resonance (SR) is shown in a two-parameter system, a model of electrochemical oxidation of formic acid on Pt. The driving current and the saturation coverage for carbon monoxide are two control parameters in this model. Modulation of an excitable focal stable state close to a Hopf bifurcation by a weak periodic signal in one parameter and noise in the other parameter is found to give rise to SR. The results indicate that the noise can enlarge a weak periodic signal and lead the system to be ordered. The scenario and novel aspects of SR in this system are discussed.     

Two-Parameter Stochastic Resonance in a Model of Electrodissolution of Fe in H_2SO_4

IntroductionStochastic resonance (SR) is a nonlinear effect which describes the optimal detection of a weak periodic signal by the action of external noise in nonlinear systems. SR was originally proposed to account for periodicity in the Earth's ice ages1, and it has been observed in a wide range of biological2-4 , physical5 and chemical6 systems. The systems mentioned above which may give rise to SR have a denominator despite many examples of SR in different scientific areas. It is noted…     

Influences of a periodic signal on a noisy synthetic gene network

The effects of noise and a periodic signal on a synthetic gene network have been investigated. By tuning the distance of a parameter from the Hopf bifurcation point, both implicit internal signal stochastic resonance and explicit internal signal stochastic resonance can be induced by noise. Furthermore, a switch process can also be elicited. When a periodic signal is coupled to the gene network, two interesting phenomena occur with the modulation of the frequency of the signal: the effect of noise amplifyin...     

Canard explosion and internal signal stochastic bi-resonance in the CO oxidation on platinum surface

Canard explosion means a dramatic change fromsmall amplitude quasi-harmonic oscillation to largeamplitude relaxation oscillation, accompanied by anexponential increase of period, of a limit cycle withina very narrow interval of a control parameter. Thisphenomenon was first found in the Van Der Pol equa-tions[1], and later has been found also in chemical[2]and biological[3] systems. Generally speaking, it is theresult of multi-time scales in the system, and can bedealt with singular perturbati…     

A method based on stochastic resonance for the detection of weak analytical signal

An effective method for detection of weak analytical signals with strong noise background is proposed based on the theory of stochastic resonance (SR). Compared with the conventional SR-based algorithms, the proposed algorithm is simplified by changing only one parameter to realize the weak signal detection. Simulation studies revealed that the method performs well in detection of analytical signals in very high level of noise background and is suitable for detecting signals with the different noise level by changing the parameter. Applications of the method to experimental weak signals of X-ray diffraction and Raman spectrum are also investigated. It is found that reliable results can be obtained.     

电感耦合等离子体原子发射光谱分析中导数光谱法研究——Ⅱ.数据平滑和扫描步长的影响

数据平滑和扫描步长是两个重要求导条件。本工作用五点三次多项式平滑技术对扫描数据进行平滑处理以消除随机噪音,但平滑次数增大会导致信号失真从而使导数光谱的分辨能力降低。扫描步长减小能提高导数光谱的分辨能力,但同时导致导数光谱灵敏度减小。导数光谱中干扰物等效浓度IEC的大小是上述因素的综合反映。本文以IEC为考察指标,讨论了平滑次数和扫描步长的优化。     

Spatial resolution and information transfer in scanning transmission electron microscopy

The relation between image resolution and information transfer is explored. It is shown that the existence of higher frequency transfer in the image is just a necessary but not sufficient condition for the achievement of higher resolution. Adopting a two-point resolution criterion, we suggest that a 10% contrast level between two features in an image should be used as a practical definition of resolution. In the context of scanning transmission electron microscopy, it is shown that the channeling effect does not have a direct connection with image resolution because sharp channeling peaks do not move with the scanning probe. Through a quantitative comparison between experimental image and simulation, a Fourier-space approach is proposed to estimate defocus and sample thickness. The effective atom size in Z-contrast imaging depends on the annular detector's inner angle. Therefore, an optimum angle exists for the highest resolution as a trade-off between reduced atom size and reduced signal with limited information transfer due to noise.     

Stability constants and thermodynamic functions of Y(III), Rh(III), Sm(III), Gd(III) and Dy(III) with juglone (5-hydroxy-1,4-naphthoquinone)

This work considers how the ratio signal/noise and the introduction of a cut-off frequency affect the calculus of the thermogenesis. In particular, the validity of the experimental criterion used to calculate this frequency inside the deconvolutive calculus is studied. The deconvolutive efficiency of the universal transference function is also presented comparatively.     

Solution of inverse problem of light beating spectroscopy using Tikhonov method of regularization for analyzing polydisperse suspensions of nanoparticles

The results of a numerical solution of the inverse problem of light beating spectroscopy using the Tikhonov regularization method are presented. The developed algorithm takes into account the positivity of the solution and the constant background signal. The regularization parameter of the method is determined based on the a priori information on the noise amplitude of the input signal. The results of the reconstruction of model uni-, bi-, and multimodal distributions are presented. For examples of numerically generated spectra, the effects of the measured spectrum noise, background signal, and frequency bandwidth of the signal measurement on the characteristics of the reconstructed distributions are studied.     

细胞体系中内噪声对弱信号检测的积极作用

在小尺度的生物化学反应体系中内噪声是普遍存在的,本文采用化学Langevin方程研究了细胞体系中内噪声对弱信号检测的作用. 研究发现, 在Hopf分岔点附近, 当弱信号非常小以至于不能独立地激发细胞内的钙尖峰振荡时, 内噪声能够帮助细胞内的钙振荡信号越过一个域值, 并且在一个最佳的内噪声强度下, 内噪声、内噪声诱导的钙振荡和弱信号之间会产生共振现象, 由此极大地增强了细胞体系对弱信号的检测能力. 由于内噪声是通过细胞尺度变化而改变的, 因此这种现象也说明了在对弱信号检测行为中最佳细胞尺度的存在. 研究还发现最佳的细胞尺度与真正的细胞体积是相吻合的, 并且基本不随外界刺激的改变而改变, 这具有重要的生物学意义.     

自动化色谱谱图解析——谱峰的自动识别与快速解析

结合基于高阶导数的谱峰识别方法和面积重现法,建立了一种完全自动化的对色谱曲线进行分割、识别与快速解析的方法。其中,DW(Durbin-Watson)测试的引入和区分信号与噪声判据的采用减少了在色谱解析过程中的人为干预,降低了对操作人员专业知识和经验的要求,为实现色谱解析的自动化奠定了基础。通过对模拟色谱和实验色谱的比较,验证了该方法是一个很有用的工具,可以为色谱分析工作提供有力的帮助。     

化学信号的近似高阶导数计算

提出了化学信号近似四阶导数计算的新方法——小波卷积法。该法通过信号与二阶样条小波函数的卷积运算对信号求导,能用于高噪音信号的直接求导,避免了普通导数运算将噪音放大的缺陷,即使对信噪比低至0．5的信号也能得到光滑的导数信号。详细讨论了尺度值、噪音、信号类型对求导的影响并建立了参数确定规则。将该法用于含噪音重叠分析化学信号的求导,能同时提高信号的分辨率和信噪比,结果满意。     

Inverse Optimal Filtering Method for the Instrumental Spreading Correction in Size Exclusion Chromatography

Abstract

The Kalman filter based techniques are adapted to solve the most general form of Tung's integral formula, i. e. when a non-uniform, non-symmetric calibration model is employed to correct chromatograms obtained in size exclusion chromatography from instrumental broadening errors. Through this method, the inverse smoothing of a chromatogram contaminated with measurement noise of known statistics is optimally performed by minimizing the estimation error variance. The method is numerically very “robust”, improves the signal to noise ratio, provides good validation checks, and does not involve any previous parameter estimation procedure.     

The Evaluation Method of Smoothing Algorithms in Voltammetry

The criterion for testing the influence of smoothing algorithms for the relevant parameters considered in analytical experiment is presented. The proposed approach assumes that the improvement of the whole set of measured curves should be considered. The calibration curve parameters with confidence intervals, correlation coefficient, detection limit, signal to noise ratio and parameters of recovery function are utilized for the evaluation. Performance of evaluation method is presented for several kinds of experimental noises.     

耦合生物细胞体系中噪声诱导钙信号的传递和增强

Dynamics of calcium oscillation in a coupled cell system is discussed. It shows that when one end of the cell chain is perturbed by noise, the signal induced by noise can propagate along a linearly coupled cell chain with considerable enhancement, a rather ordered internal signal can be obtained on the other end, and the signal itself can also be enhanced. The effects of coupling constant, noise intensity and coupling means on the propagation of the signal are investigated. It is found that there exist an optimal coupling constant and noise intensity in favor of the signal propagation. What′s more, a qualitative explanation via the signal and the noise background is given. And the one way coupling is better for the signal propagation and enhancement than for the two way coupling. The results may have important applications in living cell systems, where information is transmitted along a cell chain.     

Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform

Spectral signals are often corrupted by noise during their acquisition and transmission. Signal processing refers to a variety of operations that can be carried out on measurements in order to enhance the quality of information. In this sense, signal denoising is used to reduce noise distortions while keeping alterations of the important signal features to a minimum. The minimization of noise is a highly critical task since, in many cases, there is no prior knowledge of the signal or of the noise. In the context of denoising, wavelet transformation has become a valuable tool. The present paper proposes a noise reduction technique for suppressing noise in laser-induced breakdown spectroscopy (LIBS) signals using wavelet transform. An extension of the Donoho's scheme, which uses a redundant form of wavelet transformation and an adaptive threshold estimation method, is suggested. Capabilities and results achieved on denoising processes of artificial signals and actual spectroscopic data, both corrupted by noise with changing intensities, are presented. In order to better consolidate the gains so far achieved by the proposed strategy, a comparison with alternative approaches, as well as with traditional techniques, is also made.     

Constructive Role of Internal Noise for the Detection of Weak Signal in Cell System

Taking into account the existence of internal noise in small scale biochemical reaction systems, we studied how the internal noise would influence the detection of weak external signal in the cell system using chemical Langevin equation. The weak signal was too small to, separately, fire calcium spikes for the cell. We found that, near the Hopf bifurcation point, the internal noise could help the calcium oscillation signal cross a threshold value, and at an optimal internal noise level, a resonance occurred among the internal noise, the internal noise-induced calcium oscillations, and the weak signal, so as to enhance intensively the ability of the cell system to detect the weak signal. Since the internal noise was changed via the cell size, this phenomenon demonstrated the existence of an optimal cell size for the signal detection. Interestingly, it was found that the optimal size matched well with the real cell size, which was robust to external stimulus, this was of significant biological meaning.     

Noise normalisation in capillary electrophoresis using a diode array detector

When using capillary electrophoresis with a diode array detector, the wavelength at maximum absorbance is often chosen to quantify a given analyte. However, the background noise for every wavelength should be taken into account as it is by maximising the signal to noise ratio that the lowest limit of detection will be obtained. Here, we proposed an algorithm allowing to correct an electropherogram from its background absorption and to estimate the background noise. Applying it to all the electropherograms obtained in each wavelength channel allows obtaining the background noise as a function of the wavelength, which can be used to calculate the signal to noise ratio. This not only allows selecting the best wavelength to maximise the limit of detection of a given analyte, but also to generate a noise normalised base peak electropherogram (nn-BPE). It is shown that the noise normalised base peak electropherograms substantially improve the peaks visualisation. The algorithm is part of a graphic user interface that runs under MatLab environment; it does not require any programming knowledge and is freely available.