A method and system for processing experimental data of bidentate extract
Patent Information
- Application Number
- CN202511754071.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-26
- Publication Date
- 2026-09-08
- Estimated Expiration
- 2045-11-26
AI Technical Summary
[0006]本发明提供一种蕲艾提取物试验数据处理方法及系统以解决上述现有技术中存在的特征峰识别精度低、变量重要性值稳定性较差、筛选阈值不够准确,导致蕲艾质量评估准确性较低的问题
[0017]The beneficial effects of this invention are as follows: By calculating the weighted fusion value of peak shape symmetry and local signal-to-noise ratio, this invention can identify true characteristic peaks from complex chromatographic or spectroscopic data, eliminating the interference of baseline noise and spurious peaks, and improving the quality of the initial variable set. By grouping candidate characteristic peaks using mutual information entropy and selecting the highest quality peak within each group as a representative, the problems of data collinearity and redundancy are solved, simplifying the model. In the key variable screening stage, this invention overcomes the defect of unstable variable importance values in single-modeling calculations by using Monte Carlo resampling technology, and constructs a comprehensive score that simultaneously measures importance and stability. The screening threshold is determined based on the overall distribution characteristics of the comprehensive importance scores of all variables, thereby enabling the screening of characteristic variables truly related to the efficacy of Artemisia argyi.
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Abstract
Description
Technical Field
[0001] This invention relates to the field of electronic data processing technology, specifically to a method and system for processing experimental data of Artemisia argyi extract. Background Technology
[0002] As an important traditional Chinese medicine, the quality control of Artemisia argyi is a crucial step in ensuring its clinical efficacy. To assess its quality, modern analytical techniques such as high-performance liquid chromatography (HPLC) and gas chromatography (GC) are commonly used to obtain the chemical fingerprints of its extracts. These chromatographic data typically exhibit complex characteristics such as high dimensionality, strong collinearity among multiple variables, and low signal-to-noise ratio.
[0003] In the data preprocessing stage, traditional peak identification methods mostly rely on simple signal intensity or signal-to-noise ratio thresholds. This approach not only easily misidentifies spurious peaks such as baseline noise and solvent peaks as valid chemical components, but may also miss real component peaks with low intensity but significant biological activity, thus affecting the accuracy of the initial variable set. In addition, spectral data generally contain a large number of highly correlated variables caused by homologues or isomers with similar chemical structures. This redundant information can interfere with the stability and accuracy of subsequent models.
[0004] To screen biomarkers directly related to drug efficacy from complex chemical fingerprints, chemometric methods, particularly partial least squares (PLS), are widely used to establish association models between chemical components and efficacy indicators. After model establishment, indicators such as projected importance (VIP) are typically used to assess the contribution of each variable. However, VIP values calculated in a single modeling iteration are highly sensitive to minor perturbations in the sample set, exhibiting poor stability and making it difficult to guarantee the reliability of the results. More importantly, when screening key variables, fixed empirical thresholds are commonly used for judgment. This "one-size-fits-all" approach ignores the inherent distribution characteristics of the data, exhibiting strong subjectivity and bias.
[0005] Therefore, how to establish a systematic data processing method to overcome the shortcomings of traditional methods and achieve accurate identification of characteristic peaks, effective removal of redundant variables, stable assessment of variable importance, and adaptive determination of screening thresholds is a technical problem that urgently needs to be solved in the field of traditional Chinese medicine quality control. Summary of the Invention
[0006] This invention provides a method and system for processing experimental data of Artemisia argyi extract to solve the problems of low accuracy in characteristic peak identification, poor stability of variable importance values, and inaccurate screening thresholds in the prior art, which lead to low accuracy in Artemisia argyi quality assessment.
[0007] In a first aspect, the method for processing experimental data of Artemisia argyi extract according to the present invention includes the following steps: Obtain the chromatographic or spectroscopic test data matrix of Artemisia argyi extract; identify potential peaks in the data matrix, calculate the peak shape symmetry and the local signal-to-noise ratio within a preset window centered on the peak apex, and obtain a weighted fusion value. When the weighted fusion value is greater than a first threshold, the potential peak is identified as a candidate feature peak; establish an initial partial least squares model using all candidate feature peaks and the efficacy index data of Artemisia argyi extract, and calculate the cross-validation determination coefficient of the initial partial least squares model; determine the peak group division threshold based on the value of the cross-validation determination coefficient; calculate the mutual information entropy between the response intensity vectors of any two candidate feature peaks in all sample data. When the mutual information entropy is greater than the peak group division threshold, the two candidate feature peaks are grouped into the same peak group, and... Within each peak group, the peak with the highest weighted fusion value is selected as the representative characteristic peak of that peak group. A final partial least squares model is established using the representative characteristic peaks and efficacy index data. Multiple random samplings are performed on the samples using Monte Carlo resampling. In each sub-model established through sampling, the variable projection importance (VIP) value of each representative characteristic peak is calculated, resulting in a VIP value sequence for each representative characteristic peak. The mean of the VIP value sequence and the reciprocal of the coefficient of variation of the VIP value sequence are calculated, and their product is used as the comprehensive importance score of the representative characteristic peak. A screening threshold is calculated based on the kurtosis and skewness of the comprehensive importance scores of all representative characteristic peaks. Representative characteristic peaks with comprehensive importance scores greater than the screening threshold are identified as quality control characteristic variables.
[0008] Preferably, the calculation of the potential peak shape symmetry includes: For each potential peak, take 10 data points on each side of the peak's vertex, and calculate the area A on the left side of the peak's vertex and the area B on the right side of the peak's vertex. Then, calculate the peak's symmetry using the following formula. : .
[0009] Preferably, the local signal-to-noise ratio within the preset window centered on the potential peak vertex is calculated in the following manner: The local signal-to-noise ratio (SNR) is calculated using the peak height of the potential peak as the signal value and the standard deviation of the first 100 data points of the data matrix as the noise value.
[0010] Preferably, the weighted fusion value is calculated using the following formula: ; in, For weighted fusion values, The peak shape symmetry is represented by SNR, which is the local signal-to-noise ratio. This is the preset reference signal-to-noise ratio.
[0011] Preferably, the peak group division threshold is calculated using the following formula: ; in, Thresholds are assigned to peak groups. The coefficient of determination for cross-validation. The value range is [0, 1].
[0012] Preferably, the coefficient of variation of the VIP value sequence is equal to the ratio of the standard deviation to the mean of the VIP value sequence of the representative characteristic peak.
[0013] Preferably, the comprehensive importance score of the representative characteristic peak is calculated using the following formula: ; in, The overall importance score for the i-th representative characteristic peak is given. Let be the mean of the VIP value sequence of the i-th representative characteristic peak. Let be the standard deviation of the VIP value sequence of the i-th representative characteristic peak. To prevent the use of pre-defined tiny positive numbers with a denominator of zero.
[0014] Preferably, the step of calculating the screening threshold based on the kurtosis and skewness of the comprehensive importance score of all representative characteristic peaks includes: Calculate the mean of the overall importance scores for all representative characteristic peaks. Standard deviation Skewness S and kurtosis K; Calculate the screening threshold using the following formula. : .
[0015] Preferably, obtaining the chromatographic or spectroscopic test data matrix of Artemisia argyi extract includes: Chromatographic or spectroscopic experimental data matrix of Artemisia argyi extract was obtained by high performance liquid chromatography-mass spectrometry.
[0016] Secondly, the Artemisia argyi extract test data processing system of the present invention includes a memory and a processor. The memory stores computer instructions, and when the processor executes the computer instructions, it implements the above-mentioned Artemisia argyi extract test data processing method.
[0017] The beneficial effects of this invention are as follows: By calculating the weighted fusion value of peak shape symmetry and local signal-to-noise ratio, this invention can identify true characteristic peaks from complex chromatographic or spectroscopic data, eliminating the interference of baseline noise and spurious peaks, and improving the quality of the initial variable set. By grouping candidate characteristic peaks using mutual information entropy and selecting the highest quality peak within each group as a representative, the problems of data collinearity and redundancy are solved, simplifying the model. In the key variable screening stage, this invention overcomes the defect of unstable variable importance values in single-modeling calculations by using Monte Carlo resampling technology, and constructs a comprehensive score that simultaneously measures importance and stability. The screening threshold is determined based on the overall distribution characteristics of the comprehensive importance scores of all variables, thereby enabling the screening of characteristic variables truly related to the efficacy of Artemisia argyi. Attached Figure Description
[0018] Figure 1 This is a flowchart illustrating the data processing method for Artemisia argyi extract provided in an embodiment of the present invention. Detailed Implementation
[0019] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.
[0020] like Figure 1 As shown, an embodiment of the method for processing experimental data of Artemisia argyi extract provided by the present invention includes the following steps: S1. Obtain the chromatographic or spectroscopic test data matrix of Artemisia argyi extract; identify potential peaks in the data matrix, calculate the peak shape symmetry of the potential peaks and the local signal-to-noise ratio within a preset window centered on the peak apex, and obtain a weighted fusion value. When the weighted fusion value is greater than the first threshold, the potential peak is identified as a candidate feature peak.
[0021] High-performance liquid chromatography-mass spectrometry (HPLC-MS) was used to obtain chromatographic or spectroscopic experimental data matrices for Artemisia argyi extract. Specifically, HPLC-MS was used to detect different batches of Artemisia argyi extract samples, and a total ion current chromatogram was obtained for each sample. All chromatograms were aligned on a uniform time axis, with retention time as the x-axis and response intensity as the y-axis, to construct a data matrix X. In this matrix, each row represents one Artemisia argyi extract sample, and each column represents the response intensity at a retention time point.
[0022] The data matrix undergoes baseline correction and smoothing, and all potential peak vertices are initially identified using the first derivative method. To filter out spurious or noisy peaks by comprehensively evaluating peak shape quality, in an optional embodiment, the calculation of potential peak shape symmetry includes: For each potential peak, take 10 data points on each side of the peak's vertex, and calculate the area A on the left side of the peak's vertex and the area B on the right side of the peak's vertex. Then, calculate the peak's symmetry using the following formula. : .
[0023] The local signal-to-noise ratio within a preset window centered on the potential peak vertex is calculated in the following way: The local signal-to-noise ratio (SNR) is calculated using the peak height of the potential peak as the signal value and the standard deviation of the first 100 data points of the data matrix as the noise value.
[0024] The weighted fusion value is calculated using the following formula: ; in, For weighted fusion values, The peak shape symmetry is represented by SNR, which is the local signal-to-noise ratio. This is the preset reference signal-to-noise ratio.
[0025] For example, consider a potential peak: Through integration, the area of the 10 data points to the left of the peak's apex is calculated to be A = 12000, and the area of the 10 data points to the right is B = 11400. From this, the peak's symmetry is calculated to be S = 0.95. The peak height is 80000, and the baseline noise in the initial part of the data matrix (i.e., the standard deviation of the first 100 data points) is 400. Therefore, the local signal-to-noise ratio (SNR) of this peak is 200.
[0026] Assuming a preset reference signal-to-noise ratio The symmetry of 0.95 and the signal-to-noise ratio of 200 were substituted into the weighted fusion value formula for calculation. The resulting weighted fusion value (WIV) was approximately 0.96. This value is higher than the preset first threshold of 0.75, indicating that the potential peak has good symmetry and a high signal-to-noise ratio, and can be identified as a high-quality true chromatographic peak, thus retaining it for subsequent analysis. Conversely, if a peak exhibits severe tailing or an extremely low signal-to-noise ratio, its calculated weighted fusion value will be lower than 0.75, and it should be identified and discarded.
[0027] S2. An initial partial least squares model is established using all candidate characteristic peaks and efficacy index data of Artemisia argyi extract. The cross-validation determination coefficient of the initial partial least squares model is calculated. Based on the value of the cross-validation determination coefficient, the peak group division threshold is determined.
[0028] The peak area or peak height data of all candidate feature peaks in each sample are used to construct a new independent variable matrix. Simultaneously, efficacy index data (e.g., in vitro anti-inflammatory activity assay values) corresponding to each Artemisia argyi extract sample are obtained to form the dependent variable vector y. Partial least squares regression modeling is performed using the independent variable matrix as the independent variable and y as the dependent variable. Leave-one-out cross-validation is preferred during the modeling process, i.e., one sample is selected from n samples each time as the validation set, and the remaining n-1 samples are used as the training set, repeated n times. The sum of squared prediction errors (PRESS) and the sum of squared dependent variables are calculated. And according to the formula The cross-validation determination coefficient of the model is obtained. .
[0029] To allow the stringency of peak group partitioning to be adjusted based on the predictive power of the model within the dataset, in an optional embodiment, the peak group partitioning threshold is calculated using the following formula: ; in, Thresholds are assigned to peak groups. The coefficient of determination for cross-validation. The value range is [0, 1].
[0030] For example, when using a partial least squares discriminant analysis model to process data, the model calculated through seven-fold cross-validation... This indicates that the model has strong predictive power and stability. At this point, the peak group segmentation threshold... The threshold was set at 0.78. A higher threshold means that only highly correlated peaks will be grouped into the same peak group, which helps to identify functionally relevant metabolites in high-quality data.
[0031] If the dataset is of poor quality or the differences between groups are not significant, the model will suffer. At this point, the peak group segmentation threshold... The threshold is correspondingly reduced to 0.34. This relatively low threshold relaxes the criteria for peak grouping, allowing peaks with weaker correlations to cluster together, thus avoiding the loss of potentially important information in data with low signal-to-noise ratios.
[0032] S3. Calculate the mutual information entropy between the response intensity vectors of any two candidate feature peaks in all sample data. When the mutual information entropy is greater than the peak group division threshold, the two candidate feature peaks are assigned to the same peak group. Within each peak group, the peak with the highest weighted fusion value is selected as the representative feature peak of that peak group. The final partial least squares model is established using the representative feature peaks and efficacy index data. The samples are randomly sampled multiple times through Monte Carlo resampling. In the sub-model established in each sampling, the variable projection importance (VIP) value of each representative feature peak is calculated to obtain the VIP value sequence of each representative feature peak.
[0033] Specifically, for any two candidate feature peaks i and j, extract their response intensity vectors across all n samples. and Discretize the data from these two vectors (e.g., divide them into 10 intervals), and calculate the marginal entropy for each interval. , and their joint entropy The formula for calculating mutual information entropy (MI) is as follows: Traverse all peak pairs to construct a mutual information entropy matrix. Use clustering to group two feature peaks with an MI value greater than the peak grouping threshold into one class, iterating until all peaks are grouped. Within each divided peak group, compare the weighted fusion values of all candidate feature peaks calculated in the previous steps, and select the peak with the highest weighted fusion value as the representative feature peak of that peak group.
[0034] Construct an independent variable matrix from all representative characteristic peaks A final partial least squares (PLS) model is established using the efficacy index vector y. The number of resampling iterations is set to M=500. In the i-th iteration, n samples are randomly drawn with replacement from a total of n samples to form a bootstrap resampling sample set. A PLS sub-model is built using the data in this sample set, and the VIP value of each representative feature peak is calculated based on this sub-model. The VIP value is calculated based on its cumulative contribution to the independent and dependent variables. This process is repeated M times, resulting in a sequence of M VIP values for each representative feature peak.
[0035] S4. Calculate the mean of the VIP value sequence and the reciprocal of the coefficient of variation of the VIP value sequence, and use the product of the two as the comprehensive importance score of the representative feature peak. Calculate the screening threshold based on the kurtosis and skewness of the comprehensive importance scores of all representative feature peaks, and determine the representative feature peaks with comprehensive importance scores greater than the screening threshold as quality control feature variables.
[0036] In order to screen out characteristic peaks that are both highly important and stable, in an optional embodiment, the coefficient of variation of the VIP value sequence is equal to the ratio of the standard deviation to the mean of the VIP value sequence of the representative characteristic peak.
[0037] The comprehensive importance score of the representative characteristic peaks is calculated using the following formula: ; in, The overall importance score for the i-th representative characteristic peak is given. Let be the mean of the VIP value sequence of the i-th representative characteristic peak. Let be the standard deviation of the VIP value sequence of the i-th representative characteristic peak. To prevent the use of pre-defined tiny positive numbers with a denominator of zero.
[0038] For example, suppose that through multiple cross-validation or bootstrap sampling, representative feature peak A yields a sequence of projected importance (VIP) values for ten variables, as shown below: {2.5, 2.6, 2.4, 2.5, 2.7, 2.5, 2.4, 2.6, 2.5, 2.3}. The calculated mean of this sequence is 2.5, and the standard deviation is 0.11. Therefore, its composite importance score (CIS) is approximately 2.52 divided by 0.11, resulting in approximately 56.8. In contrast, another representative feature peak, B, has a VIP value sequence of {1.5, 3.5, 2.8, 1.2, 3.1, 2.5, 1.8, 3.2, 1.4, 3.0}. Although the mean of this sequence is also approximately 2.4, similar to peak A, its standard deviation is 0.82, resulting in a composite importance score (CIS) of only 7.0. Thus, although the average importance of the two feature peaks is similar, peak A has a significantly higher importance score than peak B. This is mainly because peak A consistently exhibits high importance across different subsets of data, indicating greater stability. By penalizing the unstable nature of importance, this method can prioritize the selection of more reliable biomarkers.
[0039] In an optional embodiment, calculating the screening threshold based on the kurtosis and skewness of the comprehensive importance score of all representative characteristic peaks includes: Calculate the mean of the overall importance scores for all representative characteristic peaks. Standard deviation Skewness S and kurtosis K; Calculate the screening threshold using the following formula. : .
[0040] For example, instead of using a fixed empirical threshold, the overall shape of the data distribution is used to set the screening criteria. Suppose that after analyzing a batch of sample data, a set of Comprehensive Importance Score (CIS) values for all representative characteristic peaks is obtained. Statistical analysis of this set yields a mean of 20, a standard deviation of 15, a skewness of 3.0, and a kurtosis of 5.0. High skewness and high kurtosis indicate that the score distribution exhibits a clear right-skewed, peak-like shape, meaning that there are a few characteristic peaks with extremely high scores. In this case, the multiplier term in the threshold calculation formula is 1.1, which is greater than the preset minimum value of 0.5; therefore, 1.1 is chosen as the final multiplier. The final screening threshold is thus determined. The calculated value is 36.5. A higher threshold can effectively monitor important features in the long tail of the distribution. If the rating distribution of another dataset is close to normal, with a skewness of 0.1 and a kurtosis of 0.2, the multiplier term is calculated to be 0.04. This value is less than 0.5, so the default value of 0.5 is used as the multiplier. In this case, the threshold will be 27.5, which is a relatively lenient standard, thus adapting to the screening needs of different data features. By traversing all representative feature peaks, the comprehensive importance score is compared with the screening threshold. All representative feature peaks with a comprehensive importance score greater than the screening threshold are identified as quality control feature variables related to efficacy.
[0041] The implementation principle of the data processing method for Artemisia argyi extract in this invention is as follows: By calculating the weighted fusion value of peak symmetry and local signal-to-noise ratio, this invention can accurately identify true characteristic peaks from complex chromatographic or spectroscopic data, effectively filtering out baseline noise and spurious peak interference, thereby significantly improving the quality of the initial variable set. Secondly, to address the issues of data collinearity and redundancy, this invention uses mutual information entropy to group candidate characteristic peaks and selects the highest-quality peak within each group as a representative to simplify the model. In the key variable screening stage, this invention introduces Monte Carlo resampling technology to overcome the instability of variable importance obtained from a single modeling iteration and constructs a comprehensive scoring system that can simultaneously assess importance and stability. Finally, this invention no longer relies on fixed empirical thresholds but dynamically determines the screening criteria based on the overall distribution characteristics of the comprehensive scores of all variables, thereby achieving accurate identification of characteristic variables truly related to the efficacy of Artemisia argyi.
[0042] An embodiment of the Artemisia argyi extract test data processing system provided by the present invention includes a memory and a processor. The memory stores computer instructions, and when the processor executes the computer instructions, it implements the Artemisia argyi extract test data processing method in the above embodiment.
[0043] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.
Claims
1. A method for processing experimental data of Artemisia argyi extract, characterized in that, include: Acquire the chromatographic or spectroscopic test data matrix of Artemisia argyi extract; identify potential peaks in the data matrix, calculate the peak shape symmetry of potential peaks and the local signal-to-noise ratio within a preset window centered on the peak apex, and obtain a weighted fusion value. When the weighted fusion value is greater than a first threshold, the potential peak is identified as a candidate feature peak; establish an initial partial least squares model using all candidate feature peaks and efficacy index data of Artemisia argyi extract, and calculate the cross-validation determination coefficient of the initial partial least squares model; determine the peak group division threshold based on the value of the cross-validation determination coefficient; calculate the mutual information entropy between the response intensity vectors of any two candidate feature peaks in all sample data. When the mutual information entropy is greater than the peak group division threshold, the two candidate feature peaks are assigned to the same peak group, and the peak with the highest weighted fusion value in each peak group is selected as the representative feature peak of that peak group; A final partial least squares model is established using representative characteristic peaks and efficacy index data. Multiple random samplings are performed on the sample using Monte Carlo resampling. In each sub-model established by the sampling, the variable projection importance (VIP) value of each representative characteristic peak is calculated, resulting in a VIP value sequence for each representative characteristic peak. The mean of the VIP value sequence and the reciprocal of the coefficient of variation of the VIP value sequence are calculated, and their product is used as the comprehensive importance score of the representative characteristic peak. A screening threshold is calculated based on the kurtosis and skewness of the comprehensive importance scores of all representative characteristic peaks. Representative characteristic peaks with comprehensive importance scores greater than the screening threshold are identified as quality control characteristic variables.
2. The method for processing experimental data of Artemisia argyi extract according to claim 1, characterized in that, The calculation of the potential peak shape symmetry includes: For each potential peak, take 10 data points on each side of the peak's vertex, and calculate the area A on the left side of the peak's vertex and the area B on the right side of the peak's vertex. Then, calculate the peak's symmetry using the following formula. : 。 3. The method for processing experimental data of Artemisia argyi extract according to claim 2, characterized in that, The local signal-to-noise ratio within a preset window centered on the potential peak vertex is calculated in the following way: The local signal-to-noise ratio (SNR) is calculated using the peak height of the potential peak as the signal value and the standard deviation of the first 100 data points of the data matrix as the noise value.
4. The method for processing experimental data of Artemisia argyi extract according to claim 3, characterized in that, The weighted fusion value is calculated using the following formula: ; in, For weighted fusion values, The peak shape symmetry is represented by SNR, which is the local signal-to-noise ratio. This is the preset reference signal-to-noise ratio.
5. The method for processing experimental data of Artemisia argyi extract according to claim 1, characterized in that, The peak group division threshold is calculated using the following formula: ; in, Thresholds are assigned to peak groups. The coefficient of determination for cross-validation. The value range is [0, 1].
6. The method for processing experimental data of Artemisia argyi extract according to claim 1, characterized in that, The coefficient of variation of the VIP value sequence is equal to the ratio of the standard deviation to the mean of the VIP value sequence of the representative characteristic peak.
7. The method for processing experimental data of Artemisia argyi extract according to claim 6, characterized in that, The comprehensive importance score of the representative characteristic peaks is calculated using the following formula: ; in, The overall importance score for the i-th representative characteristic peak is given. Let be the mean of the VIP value sequence of the i-th representative characteristic peak. Let be the standard deviation of the VIP value sequence of the i-th representative characteristic peak. To prevent the use of pre-defined tiny positive numbers with a denominator of zero.
8. The method for processing experimental data of Artemisia argyi extract according to claim 1, characterized in that, The calculation of the screening threshold based on the kurtosis and skewness of the comprehensive importance score of all representative characteristic peaks includes: Calculate the mean of the overall importance scores for all representative characteristic peaks. Standard deviation skewness S and kurtosis K; Calculate the screening threshold using the following formula. : 。 9. The method for processing experimental data of Artemisia argyi extract according to claim 1, characterized in that, The method for obtaining the chromatographic or spectroscopic test data matrix of Artemisia argyi extract includes: Chromatographic or spectroscopic experimental data matrix of Artemisia argyi extract was obtained by high performance liquid chromatography-mass spectrometry.
10. A data processing system for Artemisia argyi extract experiments, characterized in that, It includes a memory and a processor. The memory stores computer instructions. When the processor executes the computer instructions, it implements the test data processing method for Artemisia argyi extract as described in any one of claims 1-9.
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