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Abstract
Quadratic Phase Coupling (QPC) serves as an essential statistical instrument for evaluating nonlinear synchronization within multivariate time series data, especially in signal processing and neuroscience fields. This study explores the precision of QPC detection using numerical estimates derived from cross-bicoherence and bivariate Granger causality within a straightforward, yet noisy, instantaneous multiplier model. It further assesses the impact of accidental statistically significant bifrequency interactions, introducing new metrics such as the ratio of bispectral quadratic phase coupling and the ratio of bivariate Granger causality quadratic phase coupling. Ratios nearing 1 signify a high degree of accuracy in detecting QPC. The coupling strength between interacting channels is identified as a key element that introduces nonlinearities, influencing the signal-to-noise ratio in the output channel. The model is tested across 59 experimental conditions of simulated recordings, with each condition evaluated against six coupling strength values, covering a wide range of carrier frequencies to examine a broad spectrum of scenarios. The findings demonstrate that the bispectral method outperforms bivariate Granger causality, particularly in identifying specific QPC under conditions of very weak couplings and in the presence of noise. The detection of specific QPC is crucial for neuroscience applications aimed at better understanding the temporal and spatial coordination between different brain regions.
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1 Yamaguchi University, AI Systems Medicine Research and Training Center, Graduate School of Medicine and University Hospital, Yamaguchi, Japan (GRID:grid.268397.1) (ISNI:0000 0001 0660 7960); Yamaguchi University, Division of Systems Medicine and Informatics, Research Institute of Cell Design Medical Science, Yamaguchi, Japan (GRID:grid.268397.1) (ISNI:0000 0001 0660 7960)
2 Yamaguchi University, AI Systems Medicine Research and Training Center, Graduate School of Medicine and University Hospital, Yamaguchi, Japan (GRID:grid.268397.1) (ISNI:0000 0001 0660 7960); Yamaguchi University, Department of Systems Bioinformatics, Graduate School of Medicine, Yamaguchi, Japan (GRID:grid.268397.1) (ISNI:0000 0001 0660 7960); Yamaguchi University, Division of Systems Medicine and Informatics, Research Institute of Cell Design Medical Science, Yamaguchi, Japan (GRID:grid.268397.1) (ISNI:0000 0001 0660 7960)
3 University of Lausanne, HEC-LABEX, Lausanne, Switzerland (GRID:grid.9851.5) (ISNI:0000 0001 2165 4204); University of Lausanne, Neuroheuristic Research Group & Complexity Sciences Research Group, Lausanne, Switzerland (GRID:grid.9851.5) (ISNI:0000 0001 2165 4204)
4 University of Lausanne, Neuroheuristic Research Group & Complexity Sciences Research Group, Lausanne, Switzerland (GRID:grid.9851.5) (ISNI:0000 0001 2165 4204)