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Here we deposit a MATLAB package – ierp_tools_d1 for performing the intrinsic event-related potential (iERP) analysis as well as two example EEG data set (in \data_iERPex1 and \data_iERPex2). The data sets and code package are primarily for demonstrating the iERP technique proposed in the paper - “*Event-related components are structurally represented by intrinsic event-related potentials*” (**Tsai and Liang, 2021, Scientific Reports**). In \data_iERPex1\ we simply shared a minimal EEG data set that only acquired channels EEG051 and EEG065 from its original data set (https://openneuro.org/datasets/ds000117/, Wakeman and Henson, 2015; Henson et al., 2019), where the data of EEG065 are used for producing result on Fig. 2B, D, and F in the manuscript. For the whole head topographical iERP analysis, we only provide the final iERP result that can be used for performing statistical tests (Fig. 3A and C). Similarly, in \data_iERPex2\ we only shared the minimal EEG data set that acquired the parietal electrodes [(PO7, PO5, P7, P5) vs. (PO8, PO6, P8, P6)] from its original data set (Tseng et al., 2012) to demonstrate the N2pc in iERP (Fig. 5B). For the entire head topographical iERP analysis, we offer the final iERP result that can be used for performing statistical tests (Fig. 5C). An installation procedure is required if it is the first time a user trying to run “ierp_tools_d1” in a MATLAB environment. To install the software tool, users should first download ierp_tools_d1 files to a user-specified folder, followed by changing the MATLAB current directory to this folder and running the installer: “install_ierp.m”. After completing the above procedures for installation, scripts for replicating iERP results in the manuscript can be executed. These scripts are in the subfolder: “\data_iERPex1\rep_scripts\” and “\data_iERPex2\rep_scripts\” for the first and second example, respectively. Using the first data set as example, the steps are as follows: 1. Change the matlab directory to D:\data_iERPex1 2. Run rep_CEEMD.m to perform the improved CEEMD for the data 3. Run rep_iERP_afterCEEMD.m to obtain the iERP modes. 4. Run rep_average_merge_baselinecorr_afteriERP.m to perform the averaging, merging, and baseline correcting steps for the iERP modes for further statistical analyses. 5. Run ierp_stats_fig2B_D_F.m and ierp_stats_fig3A_C.m to replicate the results of the first example in the manuscript. 6. Run tconn_clusterperm_corr.m to replicate main findings of HHCFPC between theta phase and beta AM in the manuscript. Please note that the above installation script will also include a special version of SPM12. Therefore, if there is already a previous version of SPM12 installed in your MATLAB environment, please remove their related paths so that the current iERP tool can be executed correctly. The package was well tested on MATLAB versions from 2017a to 2018b in WIN64 platform. The ierp_tools_d1 has been tested in MATLAB from version 2017a to 2018b on WIN64 platform. For users running ierp_tools_d1 in other platform, please recompile some key functions in the ept_TFCE toolbox (https://github.com/Mensen/ept_TFCE-matlab; see Mensen et al., 2017) by using the following commands: mex ept_mex_TFCE2D.c mex ept_mex_TFCE3D.c mex ept_mex_TFCE.c Wakeman, D.G., Henson, R.N., 2015. A multi-subject, multi-modal human neuroimaging dataset. Scientific data 2, 150001. Henson, R.N., Abdulrahman, H., Flandin, G., Litvak, V., 2019. Multimodal Integration of M/EEG and f/MRI Data in SPM12. Frontiers in neuroscience 13, 300. Mensen, A., Marshall, W., Tononi, G., 2017. EEG Differentiation analysis and stimulus set meaningfulness. Frontiers in psychology 8, 1748.
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