Terahertz spectrum clustering of traditional Chinese medicine based on first derivative characteristics

In order to deal with the unclear absorption peak caused by the absorption peak overlap of traditional Chinese medicine(TCM)and other mixtures,a method of three unsupervised clustering algorithms as K-means,K-medoids and Fuzzy C-means(FCM)combined with the first derivative characteristics of terahertz absorption spectrum,is proposed to perform the terahertz spectra clustering of Sanchi and other three kinds of TCM compared with their easily-confused products(ECPs).These three unsupervised clustering methods complement the scope of the supervised learning classification method.The first derivative of the spectrum could amplify the difference in the absorption coefficient with different substances,so that the obvious absorption peak can be revealed.Experiments shows that these three clustering algorithms can achieve good results by combining the origin absorption coefficient with its first-order derivative as the characteristic data,and among which K-means does the best with the accuracy of95.32%.Compared with pure absorption coefficient data clustering,the accuracy in this study has been significantly improved,especially for the non-absorption-peak TCM classification.And the accuracy of K-means algorithm is improved by5.38%.Besides,clustering algorithms in this study have strong anti-interference ability to the error data.

A Dual Wavelength Differential First Derivative Spectrophotometric Method for Identification and Determination of Carbon Monoxide Generated During the Microsomal Metabolism of Xenobiotics in vitro

A dual wavelength differential first derivative spectrophotometric method has been developed to standardize the concentration of a saturated aqueous solution of carbon monoxide (CO) as the standard and to identify and to determine CO formed during the microsomal metabolism of xenobiotics in vitro. The method can significantly eliminate the background interference in the assay media and increase the quantitative accuracy and the sensitivity. There is a good linear relationship between CO concentration in the range of 2～10 μmol·L 1 CO and the distance D between the first derivative peak at 415 nm amd valley at 426 nm with r=0.9999(n=5),the regression equation being C (mmol·L 1 )=17.6D 0.4, the detection limit lower than 0.1 μmol·L 1 CO. The average recoveries of CO from the assay system and the sample were 102.1%, RSD=2.9% (n=7) and 79.7%, RSD=6.8% (n=12),respectively. The RSD of within day was 4.4%(n=18),and the RSD of day to day was 6.1%(n=16). By this method, four trihaloanilines and one trihalobenzene were tested, the results showed that only 2,4,5 trifluoroaniline could be converted to CO by the incubation with rat hepatic microsomes, NADPH and oxygen, the ability of phenobarbital or dexamethasone to induce rat hepatic microsomes to catalyze CO formation was 3 or 8 times higher than that of the control.

Smooth pulse recovery based on hybrid wavelet threshold denoising and first derivative adaptive smoothing filter

Based on the pulse-shaping unit in the front end of high-power laser facilities,we propose a new hybrid scheme in a closed-loop control system including wavelet threshold denoising for pretreatment and a first derivative adaptive smoothing filter for smooth pulse recovery,so as to effectively restrain the influence of electrical noise and FM-to-AM modulation in the time–power curve,and enhance the calibration accuracy of the pulse shape in the feedback control system.The related simulation and experiment results show that the proposed scheme can obtain a better shaping effect on the high-contrast temporal shape in comparison with the cumulative average algorithm and orthogonal matching pursuit algorithm combined with a traditional smoothing filter.The implementation of the hybrid scheme mechanism increased the signal-to-noise ratio of the laser pulse from about 11 dB to 30 dB,and the filtered pulse is smooth without modulation,with smoothness of about 98.8%.

Dynamics of the coronavirus disease 2019(COVID-19)epidemic in Wuhan City,Hubei Province and China:a second derivative analysis of the cumulative daily diagnosed cases during the first 85 days

Background:Controlling the coronavirus disease 2019(COVID-19)epidemic requires information beyond new and cumulative cases.This study aims to conduct an in-depth analysis by geographic strata:Wuhan City(hereafter referred to as Wuhan)only,Hubei Province(hereafter referred to as Hubei)excluding Wuhan,and China excluding Hubei.Methods:Daily cumulative confirmed COVID-19 cases between December 8,2019(the date of symptom onset based on patients'recall during the investigation),and March 1,2020,from official sources and published studies were analyzed.The second derivative model was used for information extraction.Data analysis was conducted separately for the three strata.Results:A total of 80026 diagnosed COVID-19 cases were reported during the first 85 days of the epidemic,with 49315 cases from Wuhan,17788 from Hubei excluding Wuhan,and 12923 from China excluding Hubei.Analytical results indicate that the COVID-19 epidemic consists of an Acceleration,a Deceleration,and a Stabilization Phase in all three geographic strata,plus a Silent Attack Phase for Wuhan only.Given the reported incubation period of 14 days,effects of the massive anti-epidemic actions were revealed by both the Acceleration and Deceleration Phases.The Acceleration Phase signaled the effect of the intervention to detect the infected;the Deceleration Phase signaled the declines in new infections after the infected were detected,treated and quarantined.Conclusion:Findings of the study provide new evidence to better monitor the epidemic,evaluate its response to intervention,and predict the trend long.In addition to re-evaluating the control of the COVID-19 epidemic in China,this study provided a model for monitoring outbreaks of COVID-19 in different countries across the world.

Using Transformation Thought to Simplify Reciprocal Function Derivatives

Derivatives are the foundation of mathematical calculations,however,for some functions, using the rules of finding a derivative may lead to cumbersome steps. Therefore, this paper provides a simple way using transformation thought for the reciprocal function derivative.

Numerical implementation of a modified Mohr–Coulomb model and its application in slope stability analysis

The hyperbolic function proposed by Abbo- Sloan was employed not only to approach the Mohr- Coulomb criterion but also to express the plastic potential function. A better approximation to the Mohr-Coulomb yield and potential surfaces was achieved by increasing the transition angle and proven to be highly efficient in numerical convergence. When a Gaussian integral point goes into plastic state, two cases on yield stress adjustments were introduced. They may avoid solving the second derivative of the plastic potential function and the inverse matrix compared with the existing subroutine. Based on the above approaches, a fully implicit backward Euler integral regression algorithm was adopted. The two- and three-di- mensional user subroutines which can consider the asso- ciated or non-associated flow rule were developed on the platform of the finite element program--ABAQUS. To verify the reliability of these two subroutines, firstly, the numerical simulations of the indoor conventional triaxial compression and uniaxial tensile tests were performed, and their results were compared with those of the embedded Mohr-Coulomb model and the analytical approach. Then the main influential factors including the associated or non- associated flow rule, the judgment criteria of slope failure, and the tensile strength of soil were analyzed, and the application of the two-dimensional subroutine in the sta- bility analysis of a typical soil slope was discussed in detail through comparisons with the embedded model and the limit analysis method, which shows that this subroutine is more applicable and reliable than the latter two.

Rapid determination of production date for green tea by near-infrared spectroscopy

Coupled with partial least squares(PLS),near infrared(NIR)spectroscopy was applied to develop a fast and nondestructive method to identify the production date of Rizhao green tea aiming at the deficiencies of the existing methods.In the modeling process,the raw spectra were first processed by five-point smoothing and first derivative.And then,moving window back propagation artificial neural network(MW-BP-ANN)was applied to select the characteristic spectral variables.After that,the calibration model was built by PLS,and the optimum model was achieved when 9 principal component scores(PCs)were included.The performances of the calibration models were evaluated according to root mean square error of predictionεRMSEP,correlation coefficient(C p)and residual prediction deviation(σRPD).The optimum results of the calibration model was achieved,andεRMSEP=19.965,C p=0.943 andσRPD=3.07.The overall results sufficiently demonstrate that NIR spectroscopy combined with PLS can be efficiently applied in the rapid identification of green tea production date.

Quantifying biochemical variables of corn by hyperspectral reflectance at leaf scale

To further develop the methods to remotely sense the biochemical content of plant canopies,we report the results of an experiment to estimate the concentrations of three biochemical variables of corn,i.e.,nitrogen(N),crude fat(EE) and crude fiber(CF) concentrations,by spectral reflectance and the first derivative reflectance at fresh leaf scale. The correlations between spectral reflectance and the first derivative transformation and three biochemical variables were analyzed,and a set of estimation models were established using curve-fitting analyses. Coefficient of determination(R2),root mean square error(RMSE) and relative error of prediction(REP) of estimation models were calculated for the model quality evaluations,and the possible opti-mum estimation models of three biochemical variables were proposed,with R2 being 0.891,0.698 and 0.480 for the estimation models of N,EE and CF concentrations,respectively. The results also indicate that using the first derivative reflectance was better than using raw spectral reflectance for all three biochemical variables estimation,and that the first derivative reflectances at 759 nm,1954 nm and 2370 nm were most suitable to develop the estimation models of N,EE and CF concentrations,respectively. In addition,the high correlation coefficients of the theoretical and the measured biochemical parameters were obtained,especially for nitrogen(r=0.948).

Non-Parametric Local Maxima and Minima Finder with Filtering Techniques for Bioprocess

Typically extrema filtration techniques are based on non-parametric properties such as magnitude of prominences and the widths at half prominence, which cannot be used with data that possess a dynamic nature. In this work, an extrema identification that is totally independent of derivative-based approaches and independent of quantitative attributes is introduced. For three consecutive positive terms arranged in a line, the ratio (R) of the sum of the maximum and minimum to the sum of the three terms is always 2/n, where n is the number of terms and 2/3 ≤ R ≤ 1 when n = 3. R > 2/3 implies that one term is away from the other two terms. Applying suitable modifications for the above stated hypothesis, the method was developed and the method is capable of identifying peaks and valleys in any signal. Furthermore, three techniques were developed for filtering non-dominating, sharp, gradual, low and high extrema. Especially, all the developed methods are non-parametric and suitable for analyzing processes that have dynamic nature such as biogas data. The methods were evaluated using automatically collected biogas data. Results showed that the extrema identification method was capable of identifying local extrema with 0% error. Furthermore, the non-parametric filtering techniques were able to distinguish dominating, flat, sharp, high, and low extrema in the biogas data with high robustness.

Spectral square moments of a resonance sum for Maass forms

Let f be a Maass cusp form for Г0（N） with Fourier coefficients 1 k2. λf（n） and Laplace eigenvalue 1/4 ＋k2 For real α≠0 and β 〉 0, consider the sum Sx（f; α,β） = ∑n λf（n）e（αnβ）φ（n/X）, where φ is a smooth function of compact support. We prove bounds for the second spectral moment of Sx （f;α, β）, with the eigenvalue tending towards infinity. When the eigenvalue is sufficiently large, we obtain an average bound for this sum in terms of X. This implies that if f has its eigenvalue beyond X1/2＋ε, the standard resonance main term for Sx（f; ±2√q 1/2）, q ∈Z＋, cannot appear in general. The method is adopted from proofs of subconvexity bounds for Rankin-Selberg L-functions for GL（2） × GL（2）. It contains in particular a proof of an asymptotic expansion of a well-known oscillatory integral with an enlarged range of Kε≤ L≤ K1-ε. The same bounds can be proved in a similar way for holomorphie cusp forms.

Weighted stationary phase of higher orders

The subject matter of this paper is an integral with exponential oscillation of phase f（x） weighted by g（x） on a finite interval [α, β]. When the phase f（x） has a single stationary point in （α,β）, an nth-order asymptotic expansion of this integral is proved for n ≥ 2. This asymptotic expansion sharpens the classical result for n = 1 by M. N. Huxley. A similar asymptotic expansion was proved by V. Blomer, R. Khan and M. Young under the assumptions that f（x） and g（x） are smooth and g（x） is compactly supported on R. In the present paper, however, these functions are only assumed to be continuously differentiable on [α,β] 2n ＋ 3 and 2n ＋ 1 times, respectively. Because there are no requirements on the vanishing of g（x） and its derivatives at the endpoints α and β, the present asymptotic expansion contains explicit boundary terms in the main and error terms. The asymptotic expansion in this paper is thus applicable to a wider class of problems in analysis, analytic number theory, and other fields.