Parameter estimation in exponential models by linear and nonlinear fitting methods

Estimation of unknown parameters in exponential models by linear and nonlinear fitting methods is discussed. Based on the extreme value theorem and Taylor series expansion, it is proved theoretically that the parameters estimated by the linear fitting method alone cannot minimize the sum of the squared residual errors in the measurement data when measurement noise is involved in the data. Numerical simulation is performed to compare the performance of the linear and nonlinear fitting methods. Simulation results show that the linear method can obtain only a suboptimal estimate of the unknown parameters and that the nonlinear method gives more accurate results. Application of the fitting methods is demonstrated where the water spectral attenuation coefficient is estimated from underwater images and imaging distances, which supports the improvement in the accuracy of parameter estimation by the nonlinear fitting method.

Design of a new kind of chemical experiment container with virtual reality fusion

Background At present,the teaching of experiments in primary and secondary schools is affected by cost and security factors.Existing research on virtual experiment platforms has alleviated these problems.However,the lack of real experimental equipment and use of a single channel to understand user intentions weaken these platforms operationally and degrade the naturalness of interactions.Methods To solve these problems,we propose an intelligent experimental container structure and a situational awareness algorithm,both of which are verified and applied to a chemical experiment involving virtual-real fusion.First,the acquired images are denoised in the visual channel using the maximum diffuse reflection chroma to remove overexposure.Second,container situational awareness is realized by segmenting the image liquid level and establishing a relation-fitting model.Then,strategies for constructing complete behaviors and making priority comparisons among behaviors are adopted for information complementarity and independence,respectively.A multichannel intentional understanding model and an inter-active paradigm that integrates vision,hearing,and touch are proposed.Results The experimental results show that the accuracy of the intelligent container situation awareness proposed in this paper reaches 99%,and the accuracy of the proposed intention understanding algorithm reaches 94.7%.The test shows that the intelligent experimental system based on the new interaction paradigm also has better performance and a more realistic sense of operation experience in terms of experimental efficiency.Conclusion The results indicate that the proposed experimental container and algorithm can achieve a natural level of human-computer interaction in a virtual chemical experiment platform,enhance the user′s sense of operation,and achieve high levels of user satisfaction.

Overlapped peaks resolution for linear sweep polarography using Gaussian-like distribution

A resolution method based on Gaussian-like distribution for overlapped linear sweep polarographic peaks was proposed to simultaneously detect the polymetallic components, such as Zn（Ⅱ） and Co（Ⅱ）, coexisting in the leaching solution of zinc hydrometallurgy. A Gaussian-like distribution was constructed as the sub-model of overlapped peaks by analyzing the characteristics of linear sweep polarographic curve. Then, the abscissas of each peak and trough were pinpointed through multi-resolution wavelet decomposition, the curve and its derivative curves were fitted by using nonlinear weighted least squares （NWLS）. Finally, overlapped peaks were resolved into independent sub-peaks based on fitted reconstruction parameters. The experimental results show that the relative error of half-wave potential pinpointed by multi-resolution wavelet decomposition is less than 1% and the accuracy of Ip fitted by NWLS is higher than 96%. The proposed resolution method is effective for overlapped linear sweep polarographic peaks of Zn（Ⅱ） and Co（Ⅱ）.

Measurement of mouse liver glutathione S-transferase activity by the integrated method

Objective: The integrated method was investigated to measure Vm/Km of mouse liver glutathione S-transfer-ase (GST) activity on GSH and 7-Cl-4-nitrobenzofurazozan. Methods: Presetting concentration of one substrate twenty-fold above the other's and taking maximum product absorbance Am as parameter while Km as constant, Vm/Km was obtained by nonlinear fitting of GST reaction curve to the integrated Michaelis-Menten equation In [Am/(Am -Ai)] + Ai/ ( ξ× Km ) = ( Vm/Km )×ti (1). Results: Vm/Km for GST showed slight dependence on initial substrate concentration and data range, but it was resistant to background absorbance, error in reaction origin and small deviation in presetting Km. Vm/Km was proportional to the amount of GST with upper limit higher than that by initial rate. There was close correlation between Vm/Km and initial rate of the same GST. Consistent results were obtained by this integrated method and classical initial rate method for the measurement of mouse liver GST. Conclusion: With the concentration of one substrate twenty-fold above the other's, this integrated method was reliable to measure the activity of enzyme on two substrates , and substrate concentration of the lower one close to its apparent Km was able to be used.

DMPFIT: A Tool for Atomic-Scale Metrology via Nonlinear Least-Squares Fitting of Peaks in Atomic-Resolution TEM Images

Despite the wide availability and usage of Gatan’s DigitalMicrograph software in the electron microscopy community for image recording and analysis, nonlinear least-squares fitting in DigitalMicrograph is less straightforward. This work presents a ready-to-use tool, the DMPFIT software package, written in DigitalMicrograph script and C++ language, for nonlinear least-squares fitting of the intensity distribution of atomic columns in atomic-resolution transmission electron microscopy (TEM) images with a general two-dimensional (2D) Gaussian model. Applications of the DMPFIT software are demonstrated both in atomic-resolution conventional coherent TEM (CTEM) images recorded by the negative spherical aberration imaging technique and in high angle annular dark field (HAADF) scanning TEM (STEM) images. The implemented peak-finding algorithm based on the periodicity of 2D lattices enables reliable and convenient atomic-scale metrology as well as intuitive presentation of the resolved atomic structures.

Memristive neuron model with an adapting synapse and its hardware experiments

Electromagnetic induction effect caused by neuron potential can be mimicked using memristor.This paper considers a fluxcontrolled memristor to imitate the electromagnetic induction effect of adapting feedback synapse and presents a memristive neuron model with the adapting synapse.The memristive neuron model is three-dimensional and non-autonomous.It has the time-varying equilibria with multiple stabilities,which results in the global coexistence of multiple firing patterns.Multiple numerical plots are executed to uncover diverse coexisting firing patterns in the memristive neuron model.Particularly,a nonlinear fitting scheme is raised and a fitting activation function circuit is employed to implement the memristive mono-neuron model.Diverse coexisting firing patterns are observed from the hardware experiment circuit and the measured results verify the numerical simulations well.

Inelastic Deformation Analysis of Aluminum Bending Members

Aluminum alloys are typical nonlinear materials, and consequently bending members made of this material exhibit a nonlinear behavior. Most design codes do not pay much attention to such deformations and adopt a simple linear analysis for the calculation of deflections. This paper presents an investigation of the nonlinear deformation of aluminum bending members using the finite-element analysis （FEA）. The plastic adaptation coefficient, which can be used to limit the residual deflection, is introduced, and the influence of residual deflection is investigated. A method for evaluating the plastic adoption coefficient is proposed. This paper also shows the load-deflection curve of aluminum bending members and the influence of several parameters. A semi-empirical formula is derived, and some numerical examples are given by FEA. The coefficients of the semi-empirical formula are modified by the FEA results using the nonlinear fitting method. Based on these results, two improved design methods for strength and deformation of aluminum bending members are proposed. Through the comparison with test data, these methods are proved to be suitable for structural design.

Statistical distribution based detector response function of a Si(PIN) detector for K_α and K_β X-ray

A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for each single peak contains a step function, a Gaussian function and an exponential tail function. Parameters in the model are obtained by weighted nonlinear least-squares fitting method. In the application, six kinds of elements＇ characteristic X-ray spectra are obtained by Si （PIN） detector, and fitted out by the established DRF model. Reduced chi-square values are at the interval of 1.11-1.25. Other applications of the method are also discussed.

Numerical partitioning of components for four-modal sedimentary grain-size distribution based on gradient descent method

The gradient descent(GD)method is used to fit the measured data(i.e.,the laser grain-size distribution of the sediments)with a sum of four weighted lognormal functions.The method is calibrated by a series of ideal numerical experiments.The numerical results indicate that the GD method not only is easy to operate but also could effectively optimize the parameters of the fitting function with the error decreasing steadily.The method is applied to numerical partitioning of laser grain-size components of a series of Garzêloess samples and three bottom sedimentary samples of submarine turbidity currents modeled in an open channel laboratory flume.The overall fitting results are satisfactory.As a new approach of data fitting,the GD method could also be adapted to solve other optimization problems.