Revisiting the relationship between composite multiscale entropy and THz optical parameters with exterior product

With the framework of exterior product, we investigate the relationship between composite multiscale entropy (CMSE) and refractive index and absorption coefficient by reanalyzing six concentrations of bovine serum albumin aqueous solutions from the published work. Two bivectors are constructed by CMSE and its square by the refractive index and absorption coefficient under vectorization. The desirable linear behaviors can be captured, not only between the defined two bivectors in normalized magnitudes, but also between the normalized magnitude of bivectors pertinent to CMSE and the magnitude of a single vector on the refractive index or absorption coefficient, with the processing of optimum selection. Besides that, the relationship between the coefficients of two bivectors is also considered. The results reveal that plenty of sound linear behaviors can be found and also suggest the scale of 15, 16 and frequency of 0.2, 0.21 THz are prominent for those linear behaviors. This work provides a new insight into the correlation between terahertz (THz) time and frequency domain information.