Data processing device, data processing method, program, and chromatography system
By generating virtual multidimensional chromatograms through data processing devices and chromatographic systems, the problems of high cost and complexity of fully two-dimensional chromatographic systems are solved, condition studies are simplified, and separation capabilities and analytical efficiency are improved.
Patent Information
- Application Number
- CN202480036543.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2023-06-14
- Filing Date
- 2024-04-25
- Publication Date
- 2025-12-30
AI Technical Summary
Two-dimensional chromatography systems are expensive and complex, have high difficulty in condition research, long analysis time, insufficient separation capacity, and are difficult to identify when analytical conditions are incorrect or the equipment malfunctions.
A data processing device and chromatography system are provided, which can acquire multiple chromatograms through an interface, separate and display the correspondence between peak groups, generate virtual multidimensional chromatograms, and reduce the burden on users.
It provides detailed sample study information, while reducing the burden on users, simplifying the conditional study process, and improving separation capabilities and analytical efficiency.
Smart Images

Figure CN121241256A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to data processing, and particularly to processing of data related to sample analysis. BACKGROUND
[0002] In sample analysis, there is a technique called comprehensive two-dimensional chromatography. As described in, for example, Japanese Patent No. 5347932 (Patent Literature 1) or Japanese Patent No. 6828833 (Patent Literature 2), comprehensive two-dimensional chromatography uses a main chromatographic column and an auxiliary chromatographic column having different separation characteristics from the main chromatographic column. More specifically, comprehensive two-dimensional chromatography collects components eluted from the main chromatographic column at certain time intervals, and sends them to the auxiliary chromatographic column after compression in time.
[0003] Comprehensive two-dimensional chromatography separates a sample based on the mutually different separation characteristics of the main chromatographic column and the auxiliary chromatographic column. Thus, comprehensive two-dimensional chromatography makes it possible to separate two or more components in a sample that cannot be separated with only one of a one-dimensional chromatographic column or a two-dimensional chromatographic column. Therefore, comprehensive two-dimensional chromatography can provide a user with information that enables detailed investigation of a sample.
[0004] Prior Art Documents
[0005] Patent Literature
[0006] Patent Literature 1: Japanese Patent No. 5347932
[0007] Patent Literature 2: Japanese Patent No. 6828833 SUMMARY
[0008] Problem to be Solved by the Invention
[0009] However, comprehensive two-dimensional chromatography has many problems, and a user needs to bear a heavy burden when performing the above analysis.
[0010] That is, in order to send components eluted from the main chromatographic column to the auxiliary chromatographic column as described above, an expensive dedicated system is required.
[0011] Further, in comprehensive two-dimensional chromatography, a phenomenon called peak splitting easily occurs, and in order to avoid this phenomenon, a condition study is required. In this regard, in comprehensive two-dimensional chromatography, since the main chromatographic column and the auxiliary chromatographic column use mutually different separation systems, there are many parameters of the analysis conditions, and it is difficult to predict which parameter to change and how to change it in order to obtain a desired result, and the condition study is difficult.
[0012] Further, in comprehensive two-dimensional chromatography, the time required for one analysis is very long, ranging from 30 minutes to several hours. Therefore, the above condition study is not only difficult, but also requires a very long time to obtain research materials.
[0013] Further, since the system configuration for realizing the full two-dimensional chromatography is complicated, it is difficult to identify the cause when an analysis condition error or a device failure occurs, and the like.
[0014] Fundamentally, in the full two-dimensional chromatography, since the system configuration, the analysis through the auxiliary chromatographic column needs to be performed at an ultra-high speed of about 1 minute, and thus, in the analysis through the auxiliary chromatographic column, the sufficient separation ability cannot be realized in many cases.
[0015] The present application has been conceived in view of such a situation, and aims to provide a technique which can provide a user with information that can be used for detailed research on a sample and can reduce the burden on the user.
[0016] Technical solution to the problem
[0017] According to an aspect of the present disclosure, a data processing apparatus that processes data is provided. The data processing apparatus includes an interface and an arithmetic apparatus that acquires, via the interface, a first chromatogram according to a first condition of a sample and a second chromatogram according to a second condition of the sample. The arithmetic apparatus separates the first chromatogram into a first peak group, separates the second chromatogram into a second peak group, performs correspondence between each of a plurality of peaks included in the first peak group and each of a plurality of peaks included in the second peak group, and displays a result of the correspondence.
[0018] According to another aspect of the present disclosure, a chromatographic system including a data processing apparatus and a chromatograph is provided. The data processing apparatus includes an arithmetic apparatus that acquires, from the chromatograph, a first chromatogram according to a first condition of a sample and a second chromatogram according to a second condition of the sample, separates the first chromatogram into a first peak group, separates the second chromatogram into a second peak group, performs correspondence between each of a plurality of peaks included in the first peak group and each of a plurality of peaks included in the second peak group, and displays a result of the correspondence.
[0019] Effects of the invention
[0020] According to an aspect of the present disclosure, a technique which can provide a user with information that can be used for detailed research on a sample and can reduce the burden on the user is provided. BRIEF DESCRIPTION OF DRAWINGS
[0021] [ Figure 1 FIG. 1 is a diagram showing the configuration of a chromatographic system 1 according to an embodiment.
[0022] [ Figure 2 FIG. 2 is a diagram for explaining a specific example of generation of a virtual multi-dimensional chromatogram.
[0023] [ Figure 3 FIG. 3 is a diagram for explaining another example of a processing result of two chromatograms G10, G20.
[0024] [ Figure 4 ] is a graph showing an example of the result of the mass spectrometric analysis of a certain sample.
[0025] [ Figure 5 ] is a graph showing three-dimensional data composed of a spectrum vector and a chromatogram.
[0026] [ Figure 6 ] is a graph showing an example of the relationship of the matrix representations of the spectrum, the chromatogram vector, and the spectrum vector, respectively.
[0027] [ Figure 7 ] is a graph showing another example of the relationship of the matrix representations of the spectrum, the chromatogram vector, and the spectrum vector, respectively.
[0028] [ Figure 8 ] is a graph for explaining the correspondence of peaks.
[0029] [ Figure 9 ] is a flowchart of the processing performed by the data processing apparatus 100 in order to perform the correspondence of peaks among a plurality of chromatograms.
[0030] [ Figure 10 ] is a graph showing a first specific example of the display of the result of the correspondence.
[0031] [ Figure 11 ] is a graph showing a second specific example of the display of the result of the correspondence.
[0032] [ Figure 12 ] is a graph showing the correspondence of peaks in the chromatogram 620 with peaks in the chromatogram 640. DETAILED DESCRIPTION
[0033] Hereinafter, an embodiment of the present disclosure will be described in detail with reference to the drawings. In addition, the same or corresponding portions are attached with the same symbols in the drawings, and the description thereof will not be repeated.
[0034] [Chromatographic system]
[0035] Referring to Figure 1 , the configuration of a chromatographic system 1 to which the embodiment is directed will be described. Figure 1 is a graph showing the configuration of the chromatographic system 1 to which the embodiment is directed. As Figure 1 indicated, the chromatographic system 1 includes a chromatograph 10, an analyzer 20, and a data processing apparatus 100.
[0036] (Chromatograph 10)
[0037] In the present specification, as a specific example of the chromatograph 10, a liquid chromatograph (LC) using a liquid as a mobile phase is described. Further, the chromatograph 10 can also be another kind of chromatograph such as a gas chromatograph using a gas as a mobile phase.
[0038] The chromatograph 10 includes a container 11, a delivery pump 12, a sample injector 13, a chromatographic column 14, and a UV detector 15.
[0039] The container 11 contains a mobile phase. The delivery pump 12 draws the mobile phase from the container 11 and delivers it at a constant flow rate. The sample injector 13 injects a sample of an analysis target into the mobile phase delivered by the delivery pump 12. The chromatographic column 14 contains a stationary phase and separates various components contained in the sample injected by the sample injector 13. The UV detector 15 measures the absorbance of light of a given wavelength for an eluate from the chromatographic column 14.
[0040] The sample of the analysis target is injected into the mobile phase by the sample injector 13. The injected sample flows to the chromatographic column 14 along with the mobile phase delivered by the delivery pump 12 and passes through the chromatographic column 14.
[0041] The various components contained in the sample pass through the chromatographic column 14 at different times depending on the affinity with the stationary phase or the mobile phase. For example, among the components contained in the sample, a component that is easily adsorbed on the stationary phase takes a longer time (also referred to as "retention time") to pass through the chromatographic column 14 than a component that is difficult to adsorb on the stationary phase. Thus, the various components contained in the sample are separated in the time direction by the chromatographic column 14. An eluate containing the components separated in the chromatographic column 14 is introduced from the chromatographic column 14 to the UV detector 15.
[0042] The UV detector 15 includes a flow cell into which the eluate from the chromatographic column 14 is introduced, a UV lamp that irradiates ultraviolet light of a given wavelength to the eluate flowing in the flow cell, and a UV detection element that measures the intensity of the ultraviolet light transmitted through the flow cell. The UV detector 15 transmits the measurement results obtained for the eluate to the data processing apparatus 100. The eluate from the UV detector 15 is introduced to the analyzer 20.
[0043] (Analyzer 20)
[0044] The analyzer 20 acquires a sample from the eluate from the UV detector 15, performs analysis of the sample, and transmits the analysis results to the data processing apparatus 100. The analyzer 20 is, for example, an absorbance detector (PDA (Photo Diode Array) detector), a fluorescence detector, a differential refractive index detector, a conductivity detector, or a mass spectrometer.
[0045] (Data processing apparatus 100)
[0046] The data processing apparatus 100 is, for example, a general-purpose computer. The data processing apparatus 100 can also be a dedicated computer for processing detection data from the chromatograph 10. The data processing apparatus 100 includes an arithmetic apparatus 101, a memory 102, a storage apparatus 103, and an interface 104.
[0047] The arithmetic apparatus 101 is an arithmetic body (computer) that performs various processes by executing various programs. The arithmetic apparatus 101 is constituted by, for example, a processor such as a central processing unit (CPU) or a micro-processing unit (MPU). Further, the processor as an example of the arithmetic apparatus 101 has a function of performing various processes by executing programs. In addition, the data processing apparatus 100 can use a dedicated hardware circuit such as an application specific integrated circuit (ASIC) or a field-programmable gate array (FPGA) to realize a part or all of the functions in addition to or instead of the arithmetic apparatus 101. The "processor" is not limited to a narrow processor that executes processes in a stored-program manner like a CPU or an MPU, but can include a hardwired circuit such as an ASIC or an FPGA. Therefore, the "processor" as an example of the arithmetic apparatus 101 can be interpreted as a processing circuitry whose processes are defined in advance by computer-readable codes and / or a hardwired circuit. Further, the arithmetic apparatus 101 can be constituted by a single chip, or can be constituted by a plurality of chips. Further, the processor and the related processing circuitry can be constituted by a plurality of computers that are connected by a wired or wireless network such as a local area network. The processor and the related processing circuitry can also be constituted by a cloud computer that performs remote arithmetic based on input data and outputs the result of the arithmetic to another device located at a remote place.
[0048] The memory 102 includes a volatile storage area (for example, a work area) that temporarily stores program codes or work memories and the like when the arithmetic apparatus 101 executes various programs. As examples of the storage section, there can be mentioned a volatile memory such as a dynamic random access memory (DRAM) and a static random access memory (SRAM), or a non-volatile memory such as a read only memory (ROM) and a flash memory.
[0049] The storage device 103 stores various programs or various data, and the like, which the arithmetic device 101 executes. The storage device 103 can be one or a plurality of non-transitory computer readable medium, and can be one or a plurality of computer readable storage medium. As examples of the storage device 103, a Hard Disk Drive (HDD) and a Solid State Drive (SSD), and the like can be cited. The storage device 103 involved in the embodiment stores a data processing program 130 for the arithmetic device 101 to execute processing of data processing of detection data acquired from the chromatograph 10.
[0050] The interface 104 transmits and receives data with an external device or an external machine through wired communication or wireless communication. For example, the interface 104 acquires detection data output from the chromatograph 10 by communicating with the chromatograph 10. Further, the interface 104 can also be a communication device that transmits detection data acquired from the chromatograph 10 to a cloud server or causes the arithmetic device 101 to transmit the execution result of data processing to the cloud server by communicating with the cloud server not illustrated. Further, the interface 104 can also transmit and receive data with the display portion 110 or the input portion 120 as a user interface through wired communication or wireless communication. The data processing device 100 is not limited to one interface 104, and a plurality of interfaces 104 can be provided according to the number of communication objects.
[0051] The display portion 110 is, for example, a display constituted by a liquid crystal panel or the like, and displays the execution result of data processing of the data processing device 100 (for example, a calculated Levenshtein distance). The input portion 120 is, for example, a pointing device such as a keyboard or a mouse, and accepts an instruction from a user. When a touch panel is used as a user interface, the display portion 110 and the input portion 120 can be integrated. Further, the display portion 110 and the input portion 120 can also be a configuration provided to the data processing device 100.
[0052] In the chromatographic system 1 constituted as described above, the data processing device 100 acquires detection data from the chromatograph 10 via the interface 104. The detection data contains a signal intensity measured by the UV detector 15. The data processing device 100 generates a chromatogram representing a time change of the signal intensity contained in the detection data.
[0053] The data processing device 100 also acquires an analysis result of a sample that is a target of chromatogram generation from the analyzer 20.
[0054] [Data Processing (1)]
[0055] In the chromatographic system 1, a user performs measurement using the chromatograph 10 on a certain sample in a plurality of cases different from each other in conditions. An example of the conditions is the kind of mobile phase used. For example, on a certain sample, after performing first analysis according to a condition using water as a mobile phase, second analysis is performed according to a condition using methanol as a mobile phase. Another example of the conditions is the kind of stationary phase used. Still another example of the conditions is the kind of combination of mobile phase and stationary phase used.
[0056] Through the above plurality of measurements different from each other in conditions, the data processing apparatus 100 generates a plurality of chromatograms acquired under conditions different from each other on a certain sample. Then, the data processing apparatus 100 integrates the plurality of chromatograms to generate a virtual multi-dimensional chromatogram.
[0057] Figure 2 is a view for explaining a specific example of generation of a virtual multi-dimensional chromatogram. Figure 2 Four stages ST1, ST2, ST3, ST4 are shown in FIG. 1. The stage ST1 is that the data processing apparatus 100 acquires (generates) two chromatograms G10, G20. In each of the chromatograms G10, G20, the horizontal axis indicates retention time, and the vertical axis indicates signal intensity.
[0058] The chromatogram G10 includes four peaks P0, P1, P2, P3 in appearance. The peak P0 and the peak P3 each have an outer shape like a plurality of peaks.
[0059] The chromatogram G20 includes six peaks P4, P5, P6, P7, P8, P9 in appearance. The peak P9 has an outer shape like a plurality of peaks.
[0060] In the stage ST2, the data processing apparatus 100 performs processing for separation of peaks on each of the chromatograms G10, G20.
[0061] Through the processing for separation of peaks, a peak group is determined from the chromatogram G10. The peak group determined from the chromatogram G10 is shown as seven peaks P11 to P17 in the chromatogram G11. Further, a peak group is determined from the chromatogram G20. The peak group determined from the chromatogram G20 is shown as seven peaks P21 to P27 in the chromatogram G21. In addition, in each of the chromatograms G11, G21, as with the chromatograms G10, G20, the horizontal axis indicates retention time, and the vertical axis indicates signal intensity.
[0062] In the stage ST3, the data processing apparatus 100 performs correspondence of peaks between the chromatogram G11 and the chromatogram G21. Thereby, each of the seven peaks included in the chromatogram G11 corresponds to each of the seven peaks included in the chromatogram G21.
[0063] In the correspondence of the peaks, a certain peak in the chromatogram G11 is selected, and in the chromatogram G21, a peak considered to represent the same component as the component represented by the selected peak is determined as the peak corresponding to the selected peak. Then, for all the peaks in the chromatogram G11, the corresponding peaks are determined in the chromatogram G21.
[0064] In the correspondence of the peaks, a certain peak in the chromatogram G11 is selected, and in the chromatogram G21, a peak considered to represent the same component as the component represented by the selected peak is determined as the peak corresponding to the selected peak. Then, for all the peaks in the chromatogram G11, the corresponding peaks are determined in the chromatogram G21. Figure 2 In the correspondence of the peaks, a certain peak in the chromatogram G11 is selected, and in the chromatogram G21, a peak considered to represent the same component as the component represented by the selected peak is determined as the peak corresponding to the selected peak. Then, for all the peaks in the chromatogram G11, the corresponding peaks are determined in the chromatogram G21.
[0065] In the correspondence of the peaks, a certain peak in the chromatogram G11 is selected, and in the chromatogram G21, a peak considered to represent the same component as the component represented by the selected peak is determined as the peak corresponding to the selected peak. Then, for all the peaks in the chromatogram G11, the corresponding peaks are determined in the chromatogram G21.
[0066] The chromatogram G30 is an example of a display of the result of the correspondence of the peaks in the stage ST3. More specifically, the chromatogram G30 contains seven peaks P31, P32, P33, P34, P35, P36, P37.
[0067] Each of the peaks P31, P32, P33, P34, P35, P36, P37 is located at the intersection of the respective retention time of the peaks P11, P12, P13, P14, P15, P16, P17 and the respective retention time of the peaks P22, P23, P21, P25, P26, P24, P27 of the chromatogram G21. For example, the peak P31 is located at the intersection of the peak P11 and the peak P22. Further, the peak P32 is located at the intersection of the peak P12 and the peak P23.
[0068] The intensity of each of the peaks P31, P32, P33, P34, P35, P36, P37 is determined by the product of the respective signal intensity of the peaks P11, P12, P13, P14, P15, P16, P17 and the respective signal intensity of the peaks P22, P23, P21, P25, P26, P24, P27 of the chromatogram G21. For example, the intensity of the peak P31 is determined by the product of the signal intensity of the peak P11 and the signal intensity of the peak P22. Further, the intensity of the peak P32 is determined by the product of the signal intensity of the peak P12 and the signal intensity of the peak P23.
[0069] In the chromatogram G30, the intensity of the peaks shown at the intersections of the peaks of the chromatogram G10 and the peaks of the chromatogram G20 is determined by the product of the signal intensity of the peaks of the chromatogram G10 and the signal intensity of the peaks of the chromatogram G20, so that the signal intensity of the peaks of the chromatogram G10 and the signal intensity of the peaks of the chromatogram G20 are more strongly represented in the chromatogram G30.
[0070] The chromatogram G30 is an example of "three-dimensional representation" of the three dimensions of (1) the retention time in the chromatogram G11, (2) the retention time in the chromatogram G21, and (3) the product of the signal intensity in the chromatogram G11 and the signal intensity in the chromatogram G21, with respect to the sample that is the object of analysis of the chromatogram G11 and the chromatogram G21. The product of the signal intensity in the chromatogram G11 and the signal intensity in the chromatogram G21 is an example based on the values of the signal intensity in the chromatogram G11 and the signal intensity in the chromatogram G21. Another example is the sum of these signal intensities. Still another example is a calculated value following a function having these signal intensities.
[0071] The data processing apparatus 100 can display the chromatogram G30 as an example of the processing result of the two chromatograms G10, G20. The data processing apparatus 100 can also display the chromatogram G10, G20 simultaneously with the chromatogram G30 as an example of the processing result.
[0072] The chromatogram G30 is a virtual two-dimensional chromatogram, and the three-dimensional representation is achieved by a two-dimensional graph and the concentration of the region in the graph. In addition, the chromatogram G30 can also be represented by a three-dimensional graph having the above three dimensions as three axes.
[0073] The data processing apparatus 100 can also generate a virtual multi-dimensional chromatogram from three or more chromatograms obtained from experiments under mutually different conditions.
[0074] For example, the data processing apparatus 100 can perform separation of peaks in each of three chromatograms (first chromatogram, second chromatogram, and third chromatogram) by deconvolution, correspond the peaks in the three chromatograms to the respective peaks in the remaining two chromatograms by peak tracking, and then combine the three chromatograms to generate a virtual three-dimensional chromatogram.
[0075] The virtual three-dimensional chromatogram is, for example, a three-dimensional graph having the respective retention times of the first to third chromatograms as axes. In this three-dimensional graph, the color of each peak is displayed, and the concentration of the color is adjusted according to the product value of the signal intensity of the corresponding point in the first chromatogram, the signal intensity of the corresponding point in the second chromatogram, and the signal intensity of the corresponding point in the third chromatogram.
[0076] [Data processing (2)]
[0077] Figure 3is a graph for explaining another example of the processing result of the two chromatograms G10, G20. Figure 3 The table is shown in FIG. 12. The data processing apparatus 100 can display the table as an example of the processing result of the two chromatograms G10, G20. Figure 3 The table is shown in FIG. 12. The data processing apparatus 100 can display the table as an example of the processing result of the two chromatograms G10, G20.
[0078] The table contains information of the seven peaks of the chromatogram G20 corresponding to each of the seven peaks separated in the chromatogram G10.
[0079] In the table shown in FIG. 12, the peaks extracted from each of the chromatograms G10, G20 are arranged in the order of the peak numbers. Then, the peaks of the chromatogram G10 and the peaks of the chromatogram G20 corresponding to the peaks are connected with dotted lines. For example, the peak P11 and the peak P22 are connected with dotted lines. Figure 3 In the table shown in FIG. 12, the peaks extracted from each of the chromatograms G10, G20 are arranged in the order of the peak numbers. Then, the peaks of the chromatogram G10 and the peaks of the chromatogram G20 corresponding to the peaks are connected with dotted lines. For example, the peak P11 and the peak P22 are connected with dotted lines.
[0080] Figure 2 The data processing apparatus 100 generates and displays a table as shown in FIG. 13 using the correspondence of the peaks explained in the stage ST3. Figure 3 The table is shown in FIG. 13. The data processing apparatus 100 can display the table as an example of the processing result of the two chromatograms G10, G20.
[0081] In the table shown in FIG. 13, the peaks extracted from each of the chromatograms G10, G20 are arranged in the order of the peak numbers. Then, the peaks of the chromatogram G10 and the peaks of the chromatogram G20 corresponding to the peaks are connected with dotted lines. For example, the peak P11 and the peak P22 are connected with dotted lines. Figure 3
[0082] The table shown in FIG. 13 indicates the correspondence of the peak numbers of each peak of the chromatogram G10 and the peak numbers of each peak of the chromatogram G20 with dotted lines. The peak number is an example of the peak information. The peak information can be the retention time itself, or the analysis result of the analyzer 20 corresponding to each peak. That is, the data processing apparatus 100 can display the retention time between the corresponding peaks instead of the table shown in FIG. 13, or in addition to the table shown in FIG. 13, or can display the analysis result between the corresponding peaks. Figure 3 Figure 3 Figure 3 The data processing apparatus 100 generates and displays a table as shown in FIG. 13 using the correspondence of the peaks explained in the stage ST3.
[0083] [Separation of peaks]
[0084] As an example of the separation of the peaks in the above stage ST2, deconvolution is explained.
[0085] In the deconvolution, it is assumed that there is a "chromatogram vector" generated from a chromatogram for a certain sample. In addition, for the sample, a "spectrum" is obtained by a given analysis method (implemented in the analyzer 20), and a "spectrum vector" is generated from the spectrum.
[0086] In addition, the deconvolution follows the premise that when the above spectrum is expressed as a matrix, the matrix can be expressed as the product of the matrix of the above one or more "chromatogram vectors" and the matrix of the above "spectrum vector".
[0087] On the basis of the foregoing, in the deconvolution, the above-described matrix of the chromatogram is decomposed into two matrices, one of which is regarded as a matrix of the chromatogram vector and the other of which is regarded as a matrix of the spectrum vector. Each column of the matrix of the chromatogram vector obtained by the above-described decomposition is regarded as a vector representing a peak of each component of the sample. Then, from the chromatogram (of the entire sample), as a waveform equivalent to the vector representing the peak of each component, the peak of each component is extracted. Hereinafter, the deconvolution is described more specifically.
[0088] In the following example, as an example of the above-described "given analysis method", mass spectrometry is adopted. Figure 4 is a graph showing an example of the result of the mass spectrometry of a certain sample. Referring to Figure 4 , the calculation of the spectrum vector is described. Figure 4 shows the result of the mass spectrometry of a certain sample.
[0089] The calculation of the spectrum vector is based on the spectrum shown in Figure 4 , and is calculated using the signal intensities. In the example of Figure 4 , the signal intensities include the signal intensity "30" at the mass-to-charge ratio "100", the signal intensity "50" at the mass-to-charge ratio "200", and the signal intensity "400" at the mass-to-charge ratio "300".
[0090] Then, the spectrum vector is generated using the signal intensities of the plurality of points on the spectrum.
[0091] Further, the chromatogram vector is also generated using the signal intensities of the plurality of points on the chromatogram in the same manner as the generation of the spectrum vector from the spectrum.
[0092] Figure 5 is a graph showing three-dimensional data constituted by the spectrum vector and the chromatogram. Figure 5 The graph shown in is a three-dimensional graph with the mass-to-charge ratio as the first axis, the retention time as the second axis, and the signal intensity as the third axis.
[0093] Figure 4 The spectrum shown in Figure 5 is acquired with respect to the eluate introduced from the chromatograph 10 to the analyzer 20 at a certain time. The data processing apparatus 100 can calculate the spectrum vector with respect to the spectrum acquired at each of a plurality of times, and generate three-dimensional vector data as shown in by arranging these spectrum vectors in time series in order of the retention time.
[0094] The chromatogram can be considered as arranging the retention time of Figure 5 as the horizontal axis and the value equivalent to the signal intensity of Figure 5 as the vertical axis, thereby arranging Figure 5a three-dimensional chart is projected onto a two-dimensional chart. Thus, in the present embodiment, it is assumed that the chromatogram represents a time variation of the spectrum vector.
[0095] Based on the above assumption, in the present embodiment, the following premise is set: when the spectrum is expressed as a matrix, the matrix is a product of a matrix of the one or more "chromatogram vectors" and a matrix of the "spectrum vector".
[0096] Figure 6 is a diagram showing an example of the relationship of the matrix representations of the spectrum, the chromatogram vector, and the spectrum vector.
[0097] In Figure 6 , the matrix M10 represents a matrix of the chromatogram vector. The line L10 represents an example of the chromatogram corresponding to the matrix M10. The matrix M20 represents a matrix of the spectrum vector. The line L20 represents an example of the spectrum corresponding to the matrix M20. The matrix M30 represents a matrix of the spectrum. In the matrix M30, the row direction corresponds to a variation of time (retention time in the chromatogram), and the column direction corresponds to a variation of the mass-to-charge ratio in the spectrum.
[0098] The matrix M30 of the spectrum corresponds to three-dimensional data as shown in Figure 5 . More specifically, in the matrix M30, one row represents a spectrum at a certain time, i.e., signal intensities of each mass-to-charge ratio detected at a certain time. For example, the row R31 represents a set of mass spectrometry signal intensities of the eluate introduced from the chromatograph 10 to the analyzer 20 at the first time, and the row R32 represents a set of mass spectrometry signal intensities of the eluate introduced from the chromatograph 10 to the analyzer 20 at the second time.
[0099] In the matrix M30, one column represents a time variation of the signal intensity of a certain mass-to-charge ratio. For example, the column C31 represents a time variation of the signal intensity of a component having a certain mass-to-charge ratio. More specifically, the column C31 represents a time variation of the content of the component having a certain mass-to-charge ratio in the eluate introduced from the chromatograph 10 to the analyzer 20.
[0100] Figure 7 is a diagram showing another example of the relationship of the matrix representations of the spectrum, the chromatogram vector, and the spectrum vector. In Figure 6 , an example in which the sample contains only one component is explained. In Figure 7 , an example in which the sample contains two or more kinds of components is explained.
[0101] In Figure 7 , the line L11 represents a chromatogram of a sample containing only a first component of two or more kinds of components. The line L12 represents a chromatogram of a sample containing only a second component of two or more kinds of components.
[0102] Further, inFigure 7 In the diagram, line L21 represents the spectrum of a sample containing only the first component from two or more types of components. Line L22 represents the spectrum of a sample containing only the second component from two or more types of components.
[0103] When a sample contains two or more types of components, matrix M10, representing the chromatogram vector, as shown in columns C11 and C12, contains two or more columns. Each of these two or more columns corresponds to each of the two or more types. Furthermore, matrix M20, representing the chromatogram vector, as shown in rows R21 and R22, contains two or more rows. Each of these two or more rows corresponds to each of the two or more types.
[0104] exist Figure 7 In the example, matrix M30 is the product of matrices M10 and M20. For example, element F1 of matrix M30 is the sum of the product of the first row and first column of matrix M10 and the first row and first column of matrix M20, the product of the first row and second column of matrix M10 and the second row and first column of matrix M20, and so on.
[0105] In deconvolution, the relationship between matrices M10, M20, and M30 is used to decompose the matrix equivalent to matrix M30 into matrices equivalent to matrix M10 and matrix equivalent to matrix M20.
[0106] More specifically, the analyzer 20 generates chromatograms for a given sample at each of multiple time points, for each eluent input from the chromatograph 10. The data processing unit 100 uses the chromatograms generated at multiple time points to generate a matrix equivalent to matrix M30. Then, the data processing unit 100 decomposes the generated matrix into a matrix of chromatogram vectors (equivalent to...). Figure 7 The matrix M10) and the matrix of the spectral vector (equivalent to the matrix of the spectral vector) Figure 7 Matrix M20).
[0107] There are infinitely many ways to decompose a matrix mathematically. For example, according to prime factorization, when the element value of matrix M30 is 24, it can be imagined to be decomposed into "2" and "12", "5" and "4.8", "-3" and "-8", and so on, in infinitely many combinations.
[0108] Therefore, in this embodiment, a constraint is set in the matrix decomposition, namely, the values of each column of the matrix M10 generated by the decomposition follow the EMG distribution function (a function with positive values and a Gaussian shape). Thus, the matrix M30 is equivalent to undergoing appropriate matrix decomposition.
[0109] For example, in the matrix M30, the values of the 1st column (the leftmost column) change as 12→36→12, which can be understood as a Gaussian shape. Further, in the matrix M30, if the values of a column change as small→large→medium→large→small, the change of the values of the column can be understood as two Gaussian shapes, and thus, when the matrix M30 has a column including such a change, the matrix M30 is decomposed into a 2-column chromatogram vector matrix (corresponding to the matrix M10) and a 2-row spectrum vector matrix (corresponding to the matrix M20).
[0110] By implementing the above-described deconvolution, one or more peaks are extracted from the chromatogram.
[0111] Further, the deconvolution method implemented in the chromatographic system 1 is not limited to the above-described method, and can be another method (for example, a method of peak fitting by Gaussian shape described in Japanese Patent No. 6260709).
[0112] In the above-described deconvolution, as an example of the analyzer 20, a mass spectrometer is used, as an example of the given analysis method, mass spectrometry is used, and as the "spectrum", a mass spectrum is used. Further, the given analysis method is not limited thereto, and for example, another analysis method such as absorbance analysis can be used. When the given analysis method is absorbance analysis, as an example of the analyzer 20, a fluorometer is used, and as the "spectrum", a fluorescence spectrum is used. In this case, in the above-described deconvolution, the "mass-to-charge ratio" is replaced with "wavelength". Figure 4 and Figure 5 In the above-described deconvolution, the "mass-to-charge ratio" is replaced with "wavelength".
[0113] [Correspondence of peaks]
[0114] In one implementation example, the correspondence of the peaks in the chromatogram G10 and the peaks in the chromatogram G20 uses the analysis results of the eluate of the portion corresponding to the peaks in the chromatogram G10 by the analyzer 20, and the analysis results of the eluate of the portion corresponding to the peaks in the chromatogram G20 by the analyzer 20. The analysis results of the eluate of the portion corresponding to the peaks by the analyzer 20 mean that when a certain portion of the eluate appears as a certain peak in the chromatogram, the portion is introduced into the analyzer 20, and the analysis results of the portion by the analyzer 20.
[0115] Figure 8 is a diagram for explaining the correspondence of the peaks. Figure 8 In the above-described deconvolution, the "mass-to-charge ratio" is replaced with "wavelength". In the above-described deconvolution, the "mass-to-charge ratio" is replaced with "wavelength".
[0116] The data processing apparatus 100 corresponds the certain peak within the chromatogram G10 with the peak within the chromatogram G20 which is in accordance with the analysis result of the peak.
[0117] For example, the data processing apparatus 100, in order to determine the peak within the chromatogram G20 which corresponds to the peak Pl l, searches the result in accordance with the analysis result Al l among the analysis results A21, A22, A23, A24, A25, A26, A27. When the analysis result Al l is in accordance with the analysis result A22, the data processing apparatus 100 corresponds the peak Pl l with the peak P22 which corresponds to the analysis result A22.
[0118] In Figure 8 , the analysis results in accordance with each other are connected with a dotted line. More specifically, each of the analysis results Al l, A12, A13, A14, A15, A16, A17 is in accordance with each of the analysis results A22, A23, A21, A25, A26, A24, A27, respectively. Thereby, the data processing apparatus 100 corresponds each of the peaks Pl l, P12, P13, P14, P15, P16, P17 with each of the peaks P22, P23, P21, P25, P26, P24, P27, respectively.
[0119] The kind of the value used as the analysis result depends on the kind of the apparatus used as the analyzer 20. When the analyzer 20 is a mass spectrometer, the value used as the analysis result is, for example, the value of the mass-to-charge ratio of the peak of the mass spectrum and / or the signal intensity. When the analyzer 20 is a fluorometer, the value used as the analysis result is, for example, the wavelength of the peak in the fluorescence spectrum, the peak width, the coefficient of symmetry of the peak, and / or the signal intensity.
[0120] [Processing flow]
[0121] Figure 9 is a flowchart of the processing which the data processing apparatus 100 implements in order to perform the correspondence of the peaks in the plurality of chromatograms. In one implementation example, in the data processing apparatus 100, the processing of Figure 9 is implemented by the operation apparatus 101 executing a given program. In one implementation example, the data processing apparatus 100 starts the processing of Figure 9 in response to receiving an instruction to start the correspondence via the input section 120.
[0122] In step S10, the data processing apparatus 100 acquires the result of the experiment performed according to each of a plurality of conditions different from each other with respect to a certain sample. In one implementation example, the result of each experiment is stored in the storage 102, and in step S10, the operation apparatus 101 reads out the result of the experiment stored in the storage 102.
[0123] The experimental results include chromatograms and analysis results. The experimental results according to the first condition include the measurement results of the chromatograph 10 (e.g., the chromatogram G10) and the analysis results of the analyzer 20 (e.g., the analysis results Al l to Al 7) under the first column condition. The experimental results according to the second condition include the measurement results of the chromatograph 10 (e.g., the chromatogram G20) and the analysis results of the analyzer 20 (e.g., the analysis results A21 to A27) under the second column condition. Figure 8 Figure 8 The column condition is, for example, the kind of mobile phase and / or the kind of stationary phase.
[0124] In step S20, the data processing apparatus 100 performs separation of peaks in the chromatogram of each experimental result.
[0125] In step S30, the data processing apparatus 100 performs correspondence of peaks in the chromatogram between a plurality of experimental results.
[0126] In step S40, the data processing apparatus 100 generates results of the correspondence performed in step S30. An example of the generated results is the chromatogram G30 (and the chromatograms G10, G20) shown in Figure 2 Another example is the table shown in Figure 3
[0127] In step S50, the data processing apparatus 100 displays the results generated in step S40 on the display portion 110. Thereafter, the data processing apparatus 100 ends the processing of Figure 9
[0128] [Example (1)]
[0129] Figure 10 is a graph showing the display of the results of the correspondence. Figure 10 The chromatograms 500, 510, 520 are shown in
[0130] The vertical axis of the chromatogram 510 and the horizontal axis of the chromatogram 520 represent the retention time. The horizontal axis of the chromatogram 510 and the vertical axis of the chromatogram 520 represent the signal intensity. The horizontal axis of the chromatogram 500 represents the vertical axis and the retention time of the chromatogram 520, and the vertical axis of the chromatogram 500 represents the retention time of the chromatogram 510.
[0131] A peak group (peaks 511, 512, 513, 514) is extracted from the chromatogram 510. A peak group (peaks 521, 522, 523, 524) is extracted from the chromatogram 520.
[0132] In Figure 10 In the example of FIG. 10, each of the peaks 512, 513, 514 of the chromatogram 510 corresponds to each of the peaks 522, 524, 523 of the chromatogram 520, respectively. The peak 511 of the chromatogram 510 does not correspond to a peak within the chromatogram 520. In addition, the peak 521 of the chromatogram 520 does not correspond to a peak within the chromatogram 510.
[0133] The chromatogram 500 includes three peaks 501, 502, 503. The peak 501 is constituted by the product of the signal intensity of the peak 512 of the chromatogram 510 and the signal intensity of the peak 522 of the chromatogram 520. The peak 502 is constituted by the product of the signal intensity of the peak 513 of the chromatogram 510 and the signal intensity of the peak 524 of the chromatogram 520. The peak 503 is constituted by the product of the signal intensity of the peak 514 of the chromatogram 510 and the signal intensity of the peak 523 of the chromatogram 520. The respective intensities of the three peaks 501, 502, 503 follow the respective product values by which they are constituted. More specifically, the greater the product value of each peak, the higher the concentration that is displayed.
[0134] [Example (2)]
[0135] Figure 11 FIG. 11 is a diagram showing a second specific example of a display of corresponding results. Figure 11 The chromatograms 600, 620, 640 are shown in FIG. 12. The chromatogram 620 is a chromatogram obtained from measurement according to a first condition. The chromatogram 640 is a chromatogram obtained from measurement according to a second condition. The chromatogram 600 is a chromatogram generated by combining the chromatogram 620 and the chromatogram 640.
[0136] The vertical axis of the chromatogram 620 and the horizontal axis of the chromatogram 640 represent retention times. The horizontal axis of the chromatogram 620 and the vertical axis of the chromatogram 640 represent signal intensities. The horizontal axis of the chromatogram 600 represents the vertical axis as well as the retention times of the chromatogram 640, and the vertical axis of the chromatogram 600 represents the retention times of the chromatogram 620.
[0137] A group of peaks (peaks 621 to 631) is extracted from the chromatogram 620. A group of peaks (peaks 641 to 652) is extracted from the chromatogram 640.
[0138] Figure 12 FIG. 13 is a diagram showing the correspondence of peaks in the chromatogram 620 to peaks in the chromatogram 640. In Figure 12 In FIG. 14, as shown by "peaks of the chromatogram 620" and "peaks of the chromatogram 640", in Figure 12In the example, each of the peaks 622, 628, 626, 625, 627, 630, 621, 629, and 623 in chromatogram 620 corresponds to each of the peaks 642, 644, 645, 646, 627, 648, 650, 651, and 652 in chromatogram 640.
[0139] Chromatogram 600 contains peaks 601–609. Figure 12 The diagram shows the peaks in chromatograms 620 and 640 that constitute each of peaks 601 to 609. For example, peak 601 is composed of peak 622 in chromatogram 620 and peak 642 in chromatogram 640.
[0140] The concentration of each peak 601 to 609 is determined by the product of the signal intensity of the peak in chromatogram 620 and the signal intensity of the peak in chromatogram 640. For example, the concentration of the image shown as peak 601 is determined by the product of the signal intensity of peak 622 in chromatogram 620 and the signal intensity of peak 642 in chromatogram 640.
[0141] exist Figure 11 In the example, the extracted peaks are adjacent to each other in both chromatograms 620 and 640. For instance, in chromatogram 620, the three peaks 627, 628, and 629 are adjacent to each other. Furthermore, in chromatogram 640, the three peaks 650, 651, and 652 are adjacent to each other.
[0142] According to this embodiment, a virtual two-dimensional chromatogram (chromatogram 600) is obtained by multiplying the signal intensities between corresponding peaks in two chromatograms 620 and 640 obtained under different conditions. In the virtual two-dimensional chromatogram (chromatogram 600), each peak is represented only by the product of the signal intensities between corresponding peaks in chromatograms 620 and 640, and does not include information on the signal intensities of other peaks in chromatograms 620 and 640. Thus, the adjacent peaks 627, 628, and 629, as well as peaks 650, 651, and 652 in the original two chromatograms 620 and 640, are appropriately separated in chromatogram 600.
[0143] According to this embodiment, only two measurements by the chromatograph 10 under different conditions (and analysis by the analyzer 20) are required to obtain a chromatogram 600, which can separate the adjacent peaks in the two chromatograms 620 and 640.
[0144] [Way]
[0145] Those skilled in the art will understand that the above-described exemplary embodiments are specific examples of the following approaches.
[0146] (1) According to an aspect, there is provided a data processing apparatus for processing data, including: an interface; and a computing apparatus that acquires, via the interface, a first chromatogram according to a first condition of a sample and a second chromatogram according to a second condition of the sample, separates the first chromatogram into a first peak group and separates the second chromatogram into a second peak group, performs correspondence of each of a plurality of peaks included in the first peak group with each of a plurality of peaks included in the second peak group, and displays a result of the correspondence.
[0147] According to the data processing apparatus according to the aspect (1), it is possible to provide information that enables detailed investigation of a sample to a user, and to reduce a burden on the user.
[0148] (2) In the data processing apparatus according to the aspect (1), the computing apparatus can use, in the correspondence, analysis results of a portion of the sample corresponding to each of the peaks included in the first peak group, by an analysis method other than the first chromatogram, and a portion of the sample corresponding to each of the peaks included in the second peak group, by an analysis method other than the second chromatogram.
[0149] According to the data processing apparatus according to the aspect (2), the correspondence of the peaks included in the first chromatogram and the peaks included in the second chromatogram is based on analysis results of the portions of the sample corresponding to the peaks themselves, which are used to obtain the respective chromatograms. Thus, the correspondence between the peaks can be accurately performed.
[0150] (3) In the data processing apparatus according to the aspect (2), the analysis method other than the first chromatogram and the analysis method other than the second chromatogram can be mass spectrometry or absorbance analysis.
[0151] According to the data processing apparatus according to the aspect (3), the correspondence between the peaks can be easily and accurately performed.
[0152] (4) In the data processing apparatus according to any one of the aspects (1) to (3), the result can include correspondence of peak information of each of the peaks included in the first peak group with peak information of each of the peaks included in the second peak group.
[0153] According to the data processing apparatus according to the aspect (4), a user can easily understand the correspondence of the peaks extracted in each of the plurality of chromatograms.
[0154] (5) In the data processing apparatus according to the aspect (4), the peak information can indicate an order with respect to a retention time in a chromatogram.
[0155] According to the data processing apparatus according to the item 5, the user can more easily understand the correspondence of the peaks extracted in each of the plurality of chromatograms.
[0156] (6) In the data processing apparatus according to any one of the items 1 to 5, the result includes a three-dimensional representation in which a first dimension is a retention time of the first chromatogram, a second dimension is a retention time of the second chromatogram, and a third dimension is a value based on intensity information indicating a signal intensity common to the first chromatogram and the second chromatogram.
[0157] According to the data processing apparatus according to the item 6, the user can not only understand the correspondence of the peaks of the first chromatogram and the peaks of the second chromatogram, but also obtain an insight into the signal intensities of the two peaks.
[0158] (7) In the data processing apparatus according to the item 6, the first peak group includes a first peak, the second peak group includes a second peak, the correspondence corresponds the first peak to the second peak, and the three-dimensional representation, in a plane constituted by a first axis indicating a retention time of the first chromatogram and a second axis indicating a retention time of the second chromatogram, indicates a value based on intensity information indicating a signal intensity of the first peak and a signal intensity of the second peak at an intersection of a retention time of the first peak on the first axis and a retention time of the second peak on the second axis.
[0159] According to the data processing apparatus according to the item 7, the user can intuitively understand the relationship of the peak of the first chromatogram and the peak of the second chromatogram corresponding to the peak.
[0160] (8) In the data processing apparatus according to the item 7, the intensity information can indicate a product of the signal intensity of the first peak and the signal intensity of the second peak.
[0161] According to the data processing apparatus according to the item 8, the user can emphasize the signal intensities of the peaks of the first chromatogram and the peaks of the second chromatogram in the intensity information.
[0162] (9) According to an aspect, there is provided a data processing method including: a step of separating a first chromatogram according to a first condition of a sample into a first peak group and separating a second chromatogram according to a second condition of the sample into a second peak group; a step of performing correspondence of each of a plurality of peaks included in the first peak group to each of a plurality of peaks included in the second peak group; and a step of displaying a result of the correspondence.
[0163] According to the data processing method according to the item 9, there is provided a technique that can provide the user with information that can be used for detailed study of the sample and can reduce the burden on the user.
[0164] Item 10. A program that is executed by an arithmetic device of a computer, thereby causing the computer to implement the method according to item 9.
[0165] According to the program according to item 10, a technology is provided that can provide information that enables detailed study of a sample to a user while reducing the burden on the user.
[0166] Item 11. According to an aspect, there is provided a chromatographic system including: a data processing device; and a chromatograph, the data processing device including an arithmetic device that acquires a first chromatogram according to a first condition of a sample and a second chromatogram according to a second condition of the sample from the chromatograph, separates the first chromatogram into a first peak group and separates the second chromatogram into a second peak group, implements correspondence of each of a plurality of peaks included in the first peak group and each of a plurality of peaks included in the second peak group, and displays a result of the correspondence.
[0167] According to the chromatographic system according to item 11, a technology is provided that can provide information that enables detailed study of a sample to a user while reducing the burden on the user.
[0168] The embodiments disclosed herein are to be considered in all respects as illustrative and not restrictive. The scope of the disclosure is indicated not by the foregoing description but by the claims, and is intended to include all equivalents, and all changes in the meaning and range of equivalency that are encompassed thereby. Furthermore, it is intended that each of the technologies in the embodiments can be implemented alone or in combination with other technologies in the embodiments as needed.
[0169] [Explanation of Symbols]
[0170] 1: Chromatographic system
[0171] 10: Chromatograph
[0172] 14: Chromatographic column
[0173] 15: Assay device
[0174] 20: Analyzer
[0175] 100: Data processing device
[0176] 101: Arithmetic device
[0177] 500, 510, 520, 600, 620, 640, G10, G11, G20, G21, G30, GG21: Chromatogram
[0178] M10, M20, M30: Matrix
Claims
1. A data processing apparatus for processing data, characterized by comprises: an interface; and an arithmetic device, via the interface, acquires a first chromatogram according to a first condition of a sample and a second chromatogram according to a second condition of the sample, the arithmetic device, separates the first chromatogram into a first peak group, separates the second chromatogram into a second peak group, performs correspondence of each of a plurality of peaks included in the first peak group and each of a plurality of peaks included in the second peak group, and displays a result of the correspondence.
2. The data processing apparatus according to claim 1, characterized in that, In the correspondence, the arithmetic device uses an analysis result of a portion of the sample corresponding to each of the plurality of peaks included in the first peak group, which is obtained by an analysis method other than the first chromatogram, and an analysis result of a portion of the sample corresponding to each of the plurality of peaks included in the second peak group, which is obtained by an analysis method other than the second chromatogram.
3. The data processing apparatus according to claim 2, characterized in that, The analysis method other than the first chromatogram and the analysis method other than the second chromatogram are mass spectrometry or absorbance analysis.
4. The data processing apparatus according to claim 1 or claim 2, characterized by, The result includes correspondence of peak information of each of the plurality of peaks included in the first peak group and peak information of each of the plurality of peaks included in the second peak group.
5. The data processing apparatus according to claim 4, characterized in that, The peak information indicates an order with respect to retention time in a chromatogram.
6. The data processing apparatus according to claim 1 or claim 2, wherein, The result includes a three-dimensional representation, in which a first dimension is a retention time of the first chromatogram, a second dimension is a retention time of the second chromatogram, and a third dimension is a value based on intensity information of a signal intensity commonly used in the first chromatogram and the second chromatogram.
7. The data processing device according to claim 6, wherein the first peak group includes a first peak, the second peak group includes a second peak, the correspondence corresponds the first peak to the second peak, and the three-dimensional representation, in a plane constituted by a first axis indicating a retention time of the first chromatogram and a second axis indicating a retention time of the second chromatogram, at an intersection of a retention time of the first peak on the first axis and a retention time of the second peak on the second axis, indicates a value based on intensity information of a signal intensity of the first peak and a signal intensity of the second peak.
8. The data processing apparatus according to claim 7, characterized in that, The value based on the intensity information is a product of the signal intensity of the first peak and the signal intensity of the second peak.
9. A data processing method, characterized by, comprises the steps of: separating a first chromatogram according to a first condition of a sample into a first peak group and separating a second chromatogram according to a second condition of the sample into a second peak group; performing correspondence of each of a plurality of peaks included in the first peak group and each of a plurality of peaks included in the second peak group; and displaying a result of the correspondence.
10. A program, characterized by, The method of claim 9 is performed by an arithmetic device of a computer, whereby the computer performs the method.
11. A chromatography system characterized by, comprises: a data processing device; and a chromatograph, the data processing device includes an arithmetic device, the arithmetic device, acquires a first chromatogram according to a first condition of a sample and a second chromatogram according to a second condition of the sample from the chromatograph, separates the first chromatogram into a first peak group, separates the second chromatogram into a second peak group, implementing a correspondence of each of the plurality of peaks comprised in the first peak group with each of the plurality of peaks comprised in the second peak group, displaying a result of the correspondence.
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