Method and system for automatic identification and repair of bad segments of magnetoencephalography based on joint diagonalization

Abstract

The application discloses a method and system for automatic identification and repair of bad segments of magnetoencephalography based on joint diagonalization, wherein the method comprises the following steps: acquiring original multi-channel magnetoencephalography signals of a measured object; segmenting the multi-channel magnetoencephalography signals to obtain a plurality of segmented data; calculating a covariance matrix and an average covariance matrix of each segmented data; identifying bad segment data in the segmented data based on the covariance matrix and the average covariance matrix; and repairing the bad segment data by using a joint diagonalization method. In the method, the collected multi-channel magnetoencephalography signals are segmented, the covariance matrix and the Euclidean distance are used to identify the bad segments, automatic identification of the bad segments is realized, and the method can be effectively popularized to other time series signals. In addition, the joint diagonalization analysis method is applied to the repair of the bad segments, and the shortcoming of reducing data capacity of a traditional interpolation method is overcome. Furthermore, the method does not need manual marking or input of other parameters, and can effectively reduce the identification and marking process.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of magnetoencephalography signal denoising processing, in particular to a method and system for automatic identification and repair of bad segments of magnetoencephalography based on joint diagonalization. BACKGROUND

[0002] Magnetoencephalography (MEG) is a kind of magnetic source imaging technology that can measure brain neural activity in real time and completely non-invasively. It reflects specific physiological activities of the brain by measuring the magnetic field signals generated by brain neural current activity. Compared with other functional imaging technologies such as electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI), MEG is not affected by factors such as tissue conductivity and skull thickness, and has high temporal and spatial resolution.

[0003] In recent years, with the development of optically pumped magnetometers, not only has the sensitivity and portability made great breakthroughs, but also the cost and maintenance cost are relatively low, which makes up for the shortcomings of traditional superconducting quantum interference device-based MEG equipment, such as high operating cost and long distance between probe and measured object. It has broad prospects in brain science research and clinical medical applications.

[0004] However, due to the wearable characteristics, when collecting MEG data, it is inevitable to be affected by the head movement of the measured object, resulting in the existence of bad segments in the collected data. In addition, the instability of the optically pumped magnetometer during the measurement process and the interference of the external environment also easily lead to the generation of high-amplitude artifacts in some time periods. These high-amplitude artifacts are easy to affect the subsequent preprocessing steps, especially the subspace projection method commonly used in MEG, which is easy to be affected by high-amplitude bad segments and to spread bad segments to other channels. Therefore, before other preprocessing steps, it is necessary to visually inspect the data and remove the part of the data with bad segments, but this is a time-consuming and laborious work and is greatly affected by subjectivity.

[0005] Currently, the main strategies for handling bad segments are as follows: ①directly removing high-amplitude artifacts across multiple channels and repairing artifacts existing in a small number of channels through interpolation; ②projecting a certain channel into the subspace spanned by other channels. However, whether it is directly removing bad segments or interpolating through other channels, it will reduce the capacity of the data, especially when the number of channels is small, the interpolation method may have a large error; and the method of projecting into the subspace determined by other channels can only repair channel-specific noise, i.e. when other channels also have artifacts at the same time, this method does not work. And most of the above methods currently need manual marking or input parameters, and there are currently few fully automatic bad segment identification and repair methods, so a fast and automatic bad segment identification and repair method is needed to improve the data quality and processing efficiency of MEG signals. SUMMARY

[0006] To solve the technical problems in the above background, the present application aims to provide a method and system for automatic identification and repair of bad segments of magnetoencephalography based on joint diagonalization, which uses a time window to segment the data, identifies the bad segments through the Euclidean distance between the covariance matrix of the data segment and the average covariance matrix, realizes accurate identification of the bad segments according to the statistical threshold and the loop iteration, extracts the principal component artifact of the identified bad segments by using the joint diagonalization method, removes the artifact by regression, and realizes automatic repair of the bad segments.

[0007] To achieve the above purpose, the present application provides a method for automatic identification and repair of bad segments of magnetoencephalography based on joint diagonalization, which comprises the following steps:

[0008] obtaining the original multi-channel magnetoencephalography signal of the measured object;

[0009] segmenting the multi-channel magnetoencephalography signal to obtain a plurality of segmented data;

[0010] calculating the covariance matrix and the average covariance matrix of each segmented data;

[0011] identifying the bad segment data in the segmented data based on the covariance matrix and the average covariance matrix;

[0012] repairing the bad segment data by using the joint diagonalization method.

[0013] Preferably, the multi-channel magnetoencephalography signal is obtained by using an optically pumped magnetometer; wherein,

[0014] The optically pumped magnetometer comprises a magnetic measurement sensor array with a very weak spin exchange relaxation effect for contacting a specified area of the measured object and a control device corresponding to each magnetometer;

[0015] The multi-channel magnetoencephalography signal comprises a multi-channel magnetoencephalography evoked signal obtained by stimulating the measured object with an experimental paradigm.

[0016] Preferably, the method for obtaining the segmented data comprises:

[0017] First, the multi-channel magnetoencephalography signal is band-pass filtered;

[0018] Then, the window method is used to segment the filtered multi-channel magnetoencephalography signal according to the fixed window length and the overlap length to obtain a plurality of segmented data.

[0019] Preferably, the method for calculating the covariance matrix and the average covariance matrix comprises:

[0020] The calculation formula of the covariance matrix of the i-th data segment is:

[0021] cov i =X i Xi T

[0022] The formula for calculating the average covariance matrix is:

[0023]

[0024] Among them, cov i X represents the covariance matrix of the i-th data segment; cov represents the average covariance matrix; X i Let represent the i-th segment of data; E represents the total number of data segments; and T represents the transpose matrix.

[0025] Preferably, the method for identifying the bad segment data includes:

[0026] First, calculate the Euclidean distance between the covariance matrix and the mean covariance matrix of each of the data segments:

[0027] d i =||cov i -cov|| F

[0028] Among them, || || F Denotes the F-norm;

[0029] Calculate the mean difference and standard deviation of Euclidean distance:

[0030]

[0031]

[0032] Where μ represents the mean deviation; σ represents the standard deviation; E represents the total number of data segments; d j This represents the distance between the covariance matrix and the mean covariance matrix of the j-th data segment;

[0033] The distance threshold is set as follows:

[0034] th=μ+4σ

[0035] Where th represents the selected threshold;

[0036] After identifying bad segments based on distance thresholds, the mean covariance matrix and statistical thresholds of other segments are recalculated, and the process of identifying bad segments is iteratively repeated until no bad segments are identified. The criteria for determining whether a segment is bad include:

[0037] d i >th

[0038] Where, d i This represents the distance between the covariance matrix and the average covariance matrix of the i-th data segment.

[0039] Preferably, the method for repairing the bad segment data comprises: using joint diagonalization to obtain an artifact component of the bad segment data according to the identified bad segment data, regarding the artifact component as a reference signal, and using reference regression to remove the artifact to obtain artifact-free data, and then repeating the process of identifying the bad segment data and repairing the bad segment data until no bad segment data is identified.

[0040] The application also provides a joint diagonalization-based automatic identification and repair system for bad segments of magnetoencephalography, which is used to implement the above method and comprises an acquisition module, a segmentation module, a calculation module, an identification module and a repair module.

[0041] The acquisition module is used to obtain original multi-channel magnetoencephalography signals of a measured object.

[0042] The segmentation module is used to segment the multi-channel magnetoencephalography signals to obtain a plurality of segmented data.

[0043] The calculation module is used to calculate a covariance matrix and an average covariance matrix of each segmented data.

[0044] The identification module is used to identify bad segment data in the segmented data based on the covariance matrix and the average covariance matrix.

[0045] The repair module is used to repair the bad segment data by using a joint diagonalization method.

[0046] Preferably, the working process of the acquisition module comprises: using an optically pumped magnetometer to obtain the multi-channel magnetoencephalography signals; wherein the optically pumped magnetometer comprises: a magnetic measurement sensor array with a very weak spin-exchange relaxation effect for contacting a specified region of a measured object and a control device corresponding to each magnetometer.

[0047] The multi-channel magnetoencephalography signals comprise multi-channel magnetoencephalography evoked signals obtained by stimulating a measured object by using an experimental paradigm.

[0048] Compared with the prior art, the application has the following beneficial effects:

[0049] (1) In the method of the application, the acquired multi-channel magnetoencephalography signals are segmented, and the covariance matrix and the Euclidean distance are used to identify bad segments, so that automatic identification of bad segments is realized, and the method can be effectively popularized to other time series signals.

[0050] (2) In addition, the joint diagonalization analysis method is applied to bad segment repair in the application, which overcomes the disadvantage of reducing data capacity of the traditional interpolation method. Furthermore, the application applies a cyclic iteration method to avoid input of related parameters, so that the bad channel identification and repair are completely automated, without the need for manual marking or input of other parameters, thereby replacing the time-consuming and laborious identification and marking process of researchers and clinical medical staff.

[0051] (3) The application excludes the bad segment data that has been identified before in the cycle iteration process, and renews the related parameters, thereby improving the stability and accuracy of the overall bad segment automatic identification. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed to be used in the embodiments, obviously, the drawings described in the following only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0053] Figure 1 The figure is a method flowchart of the embodiment of the present application.

[0054] Figure 2 The figure is a schematic diagram of repairing bad segment data using joint diagonalization of the embodiment of the present application.

[0055] Figure 3 The figure is a schematic diagram of bad segment data identification and repair of the embodiment of the present application.

[0056] Figure 4 The figure is a system structure schematic diagram of the embodiment of the present application. DETAILED DESCRIPTION

[0057] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings of the embodiments of the present application, obviously, the described embodiments only constitute some embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0058] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0059] Embodiment one

[0060] As shown in the figure, the figure is a method flowchart of the embodiment, and the steps include: Figure 1

[0061] S1. Obtain the original multi-channel brain magnetic signal of the measured object.

[0062] ​First, a multi-channel magnetoencephalogram (MEG) signal is acquired using an optically pumped magnetometer. In this embodiment, the optically pumped magnetometer includes: an array of extremely weak magnetic field measurement sensors with no spin exchange relaxation effect for contacting a designated area of ​​the test subject, and a control device corresponding to each magnetometer; the multi-channel MEG signal includes: multi-channel MEG evoked signals obtained by stimulating the test subject using an experimental paradigm.

[0063] S2. The multi-channel magnetoencephalogram (MEG) signal is segmented to obtain several segmented data.

[0064] First, bandpass filtering was performed on the multi-channel magnetoencephalography (MEG) signals. Then, using the windowing method, the filtered multi-channel MEG signals were segmented according to a fixed window length and overlap length, resulting in several segmented data X = [X1, X2, ..., X...]. E ], where E represents the total number of data segments.

[0065] S3. Calculate the covariance matrix and mean covariance matrix for each data segment.

[0066] The formula for calculating the covariance matrix of the i-th data segment is:

[0067] cov i =X i X i T

[0068] The formula for calculating the average covariance matrix is:

[0069]

[0070] Among them, cov i X represents the covariance matrix of the i-th data segment; cov represents the average covariance matrix; X i Let represent the i-th segment of data; E represents the total number of data segments; and T represents the transpose matrix.

[0071] S4. Identify bad segments in segmented data based on the covariance matrix and the average covariance matrix.

[0072] First, calculate the Euclidean distance between the covariance matrix and the mean covariance matrix of each of the data segments:

[0073] d i =||cov i -cov|| F

[0074] Among them, || || F Denotes the F-norm;

[0075] Calculate the mean difference and standard deviation of Euclidean distance:

[0076]

[0077] wherein μ represents the mean difference; σ represents the standard deviation; E represents the total number of data segments; d j represents the distance between the covariance matrix of the jth data segment and the mean covariance matrix;

[0078] The distance threshold is set as:

[0079] th = μ + 4σ

[0080] wherein th represents the selected threshold;

[0081] After identifying the bad segment according to the distance threshold, the mean covariance matrix and the statistical threshold of the other segmented data except the bad segment are recalculated, and the iterative cycle of identifying the bad segment is performed until no bad segment is identified; the basis for judging that the segmented data is a bad segment includes:

[0082] d i > th

[0083] wherein d i represents the distance between the covariance matrix of the ith data segment and the mean covariance matrix.

[0084] S5. Repairing the bad segment data by using the joint diagonalization method.

[0085] As shown in Figure 2 , according to the identified bad segment data, the artifact component of the bad segment data is obtained by using the joint diagonalization, the artifact component is regarded as a reference signal, the reference regression is used to remove the artifact, the non-artifact data is obtained, and then the process of identifying and repairing the bad segment data is repeated until no bad segment data is identified.

[0086] Specifically, the steps include:

[0087] S501. Calculating the covariance matrix of the non-bad segment segmented data and the covariance matrix of the nth bad segment data:

[0088] c s = X s X s T

[0089] c n = X n X n T

[0090] wherein c s represents the covariance matrix of all non-bad segment segmented data; c n represents the covariance matrix of the nth bad segment data; X s represents the non-artifact data of all non-bad segment data, X nBad segment data currently in need of repair is represented by X;

[0091] S502. Perform principal component analysis on the covariance matrix of the artifact-free data:

[0092] c s P = PD

[0093] where D is the eigenvalue and P is the eigenvector matrix corresponding to each eigenvalue;

[0094] Calculate the normalization matrix:

[0095] N = D -1 / 2

[0096] where N represents the normalization matrix.

[0097] S503. Perform principal component analysis on the covariance matrix of the current bad segment data:

[0098] c n Q = QD z

[0099] where D z is the eigenvalue and Q is the eigenvector matrix corresponding to each eigenvalue;

[0100] Obtain the analysis matrix:

[0101] W = PNQ;

[0102] S504. Obtain the first artifact component:

[0103] J1 = X n W1

[0104] where W1 represents the first column of the analysis matrix W;

[0105] S505. Take the first artifact component as the reference signal and remove the artifact by regression.

[0106] Calculate the cross-covariance matrix of the bad segment data and the artifact component:

[0107]

[0108] Calculate the covariance matrix of the artifact component:

[0109]

[0110] Perform principal component analysis on the covariance matrix of the artifact component and obtain the regression matrix r of the bad segment data on the artifact component:

[0111] c ref P = PD

[0112]

[0113] Projecting out the artifact and subtracting the artifact from the bad segment data to obtain noise-free data:

[0114] Y = X n -J1r

[0115] Wherein, Y is the repaired artifact-free data.

[0116] In order to illustrate the effect of the application in the aspect of brain magnetic bad segment identification and repair, Figure 3 A real brain magnetic signal containing a bad segment is given, and the result after the bad segment is identified and repaired by the method of the embodiment is given.

[0117] As Figure 4 shown, it is a system structure schematic diagram of the embodiment, including: a collection module, a segmentation module, a calculation module, an identification module and a repair module; the collection module is used to obtain the original multi-channel brain magnetic signal of the measured object; the segmentation module is used to segment the multi-channel brain magnetic signal to obtain a plurality of segmented data; the calculation module is used to calculate the covariance matrix and the average covariance matrix of each segmented data; the identification module is used to identify the bad segment data in the segmented data based on the covariance matrix and the average covariance matrix; the repair module is used to repair the bad segment data by using the joint diagonalization method.

[0118] The technical problems in actual work will be explained in detail below by combining the embodiment.

[0119] Firstly, the collection module uses the optically pumped magnetometer to obtain the multi-channel brain magnetic signal. In the embodiment, the optically pumped magnetometer includes: a weak magnetic measurement sensor array with a non-spin exchange relaxation effect for contacting the specified area of the measured object and a control device corresponding to each magnetometer; the multi-channel brain magnetic signal includes: a multi-channel brain magnetic evoked signal obtained by stimulating the measured object with an experimental paradigm.

[0120] Then the segmentation module segments the multi-channel brain magnetic signal to obtain a plurality of segmented data.

[0121] Firstly, the multi-channel brain magnetic signal is band-pass filtered; then the window method is adopted to segment the filtered multi-channel brain magnetic signal according to the fixed window length and the overlap length to obtain a plurality of segmented data X = [X1, X2,..., X E ], wherein E represents the total number of data segments.

[0122] The calculation module is used to calculate the covariance matrix and the average covariance matrix of each segmented data.

[0123] The calculation formula of the covariance matrix of the i-th data is:

[0124] covi =X i X i T

[0125] The formula for calculating the average covariance matrix is:

[0126]

[0127] Among them, cov i X represents the covariance matrix of the i-th data segment; cov represents the average covariance matrix; X i Let represent the i-th segment of data; E represents the total number of data segments; and T represents the transpose matrix.

[0128] The identification module uses the covariance matrix and the average covariance matrix to identify bad segments in segmented data.

[0129] First, calculate the Euclidean distance between the covariance matrix and the mean covariance matrix of each of the data segments:

[0130] d i =||cov i -cov|| F

[0131] Among them, || || F Denotes the F-norm;

[0132] Calculate the mean difference and standard deviation of Euclidean distance:

[0133]

[0134] Where μ represents the mean deviation; σ represents the standard deviation; E represents the total number of data segments; d j This represents the distance between the covariance matrix and the mean covariance matrix of the j-th data segment;

[0135] The distance threshold is set as follows:

[0136] th=μ+4σ

[0137] Where th represents the selected threshold;

[0138] After identifying bad segments based on distance thresholds, the mean covariance matrix and statistical thresholds of other segments are recalculated, and the process of identifying bad segments is iteratively repeated until no bad segments are identified. The criteria for determining whether a segment is bad include:

[0139] d i >th

[0140] Where, d i This represents the distance between the covariance matrix and the average covariance matrix of the i-th data segment.

[0141] Finally, the repair module uses joint diagonalization to repair the bad segment data.

[0142] According to the identified bad segment data, the artifact component of the bad segment data is obtained using joint diagonalization, the artifact component is regarded as a reference signal, and the reference regression is used to remove the artifact to obtain artifact-free data. Then, the process of identifying bad segment data and repairing bad segment data is repeated until no bad segment data is identified.

[0143] Specifically, the process includes:

[0144] S501. Calculate the covariance matrix of the non-bad segment data and the covariance matrix of the nth bad segment data:

[0145] c s =X s X s T

[0146] c n =X n X n T

[0147] wherein c s represents the covariance matrix of all non-bad segment data; c n represents the covariance matrix of the nth bad segment data; X s represents artifact-free data of all non-bad segment data, X n represents the bad segment data that needs to be repaired at present;

[0148] S502. Perform principal component analysis on the covariance matrix of the artifact-free data:

[0149] c s P=PD

[0150] wherein D is the eigenvalue, and P is the eigenvector matrix corresponding to each eigenvalue;

[0151] Calculate the normalization matrix:

[0152] N=D -1 / 2

[0153] wherein N represents the normalization matrix.

[0154] S503. Perform principal component analysis on the covariance matrix of the current bad segment data:

[0155] c n Q=QD z

[0156] wherein D z is the eigenvalue, and Q is the eigenvector matrix corresponding to each eigenvalue.

[0157] Obtain an analysis matrix:

[0158] W=PNQ;

[0159] S504. Obtain a first artifact component:

[0160] J1=X n W1

[0161] wherein W1 represents the first column of the analysis matrix W;

[0162] S505. Remove the artifact by regression using the first artifact component as a reference signal.

[0163] Calculate the cross-covariance matrix of the bad segment data and the artifact components:

[0164]

[0165] Calculate the covariance matrix of the artifact components:

[0166]

[0167] Perform principal component analysis on the covariance matrix of the artifact components and obtain the regression matrix r of the bad segment data on the artifact components:

[0168] c ref P=PD

[0169]

[0170] Project the artifact and subtract the artifact from the bad segment data to obtain noise-free data:

[0171] Y=X n -J1r

[0172] wherein Y is the repaired artifact-free data.

[0173] The above-described embodiments are merely descriptions of the preferred modes of the present application and are not intended to limit the scope of the present application. Various modifications and improvements to the technical solutions of the present application made by those of ordinary skill in the art without departing from the design spirit of the present application shall fall within the scope of protection of the present application as defined by the claims.

Claims

1. A method for automatic identification and repair of brain magnetic resonance lesions based on joint diagonalization, characterized by the following steps: include: Acquire the raw multi-channel magnetoencephalogram (MEG) signals of the subject; The multi-channel magnetoencephalogram (MEG) signal was segmented to obtain several segmented data. Calculate the covariance matrix and mean covariance matrix for each of the data segments; Based on the covariance matrix and the average covariance matrix, bad segments of data in the segmented data are identified; The method for identifying the bad segment data includes: First, calculate the Euclidean distance between the covariance matrix and the mean covariance matrix of each of the data segments: in, Denotes the F-norm; Calculate the mean difference and standard deviation of Euclidean distance: in, Indicates the average difference; Indicates standard deviation; E represents the total number of data segments; d j This represents the distance between the covariance matrix and the mean covariance matrix of the j-th data segment; The distance threshold is set as follows: Where th represents the selected threshold; After identifying bad segments based on distance thresholds, the mean covariance matrix and statistical thresholds of other segments are recalculated, and the process of identifying bad segments is iteratively repeated until no bad segments are identified. The criteria for determining whether a segment is bad include: Where, d i This represents the distance between the covariance matrix and the mean covariance matrix of the i-th data segment; The bad segment data is repaired using a joint diagonalization method. The method for repairing the bad segment data includes: obtaining the artifact components of the bad segment data using joint diagonalization based on the identified bad segment data, treating the artifact components as reference signals, and removing artifacts using reference regression to obtain artifact-free data. Then, the process of identifying and repairing bad segment data is repeated until no bad segment data can be identified.

2. The method for automatic identification and repair of brain magnetic resonance lesions based on joint diagonalization according to claim 1, characterized in that, The multi-channel magnetoencephalogram (MEG) signals were acquired using an optically pumped magnetometer; wherein... The optically pumped magnetometer includes: an array of extremely weak magnetic field measurement sensors with no spin exchange relaxation effect for contacting a designated area of ​​the object being measured, and a control device corresponding to each magnetometer. The multi-channel magnetoencephalogram (MEG) signals include: multi-channel MEG evoked signals obtained by stimulating the test subject using experimental paradigms.

3. The method for automatic identification and repair of brain magnetic resonance lesions based on joint diagonalization according to claim 1, characterized in that, The methods for obtaining the segmented data include: First, the multi-channel magnetoencephalogram (MEG) signals are bandpass filtered. Then, the window method was used to segment the filtered multichannel magnetoencephalogram (MEG) signal according to a fixed window length and overlap length, resulting in several segmented data.

4. The method for automatic identification and repair of brain magnetic resonance lesions based on joint diagonalization according to claim 1, characterized in that, Methods for calculating the covariance matrix and the mean covariance matrix include: The formula for calculating the covariance matrix of the i-th data segment is: The formula for calculating the average covariance matrix is: Among them, cov i X represents the covariance matrix of the i-th data segment; cov represents the average covariance matrix; X i Let represent the i-th segment of data; E represents the total number of data segments; and T represents the transpose matrix.

5. An automatic identification and repair system for brain magnetic resonance lesions based on joint diagonalization, the system being used to implement the method according to any one of claims 1-4, characterized in that, include: The module includes a data acquisition module, a segmentation module, a calculation module, an identification module, and a repair module. The acquisition module is used to acquire the original multi-channel magnetic brain signals of the tested object; The segmentation module is used to segment the multi-channel magnetoencephalogram (MEG) signal to obtain several segmented data. The calculation module is used to calculate the covariance matrix and the average covariance matrix of each segment of data; The identification module is used to identify bad segments in the segmented data based on the covariance matrix and the average covariance matrix. The repair module is used to repair the bad segment data using a joint diagonalization method.

6. The automatic identification and repair system for brain magnetic resonance lesions based on joint diagonalization according to claim 5, characterized in that, The workflow of the acquisition module includes: acquiring the multi-channel magnetoencephalogram (MEG) signal using an optically pumped magnetometer; wherein, the optically pumped magnetometer includes: an array of extremely weak magnetic measurement sensors with no spin exchange relaxation effect for contacting a designated area of ​​the test object, and a control device corresponding to each magnetometer. The multi-channel magnetoencephalogram (MEG) signals include: multi-channel MEG evoked signals obtained by stimulating the test subject using experimental paradigms.

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