The human brain has been described as a complex system. Its study by means of neurophysiological signals has revealed the presence of linear and nonlinear interactions. In this context, entropy metrics have been used to uncover brain behavior in the presence and absence of neurological disturbances. Entropy mapping is of great interest for the study of progressive neurodegenerative diseases such as Alzheimer’s disease. The aim of this study was to characterize the dynamics of brain oscillations in such disease by means of entropy and amplitude of low frequency oscillations from Bold signals of the default network and the executive control network in Alzheimer’s patients and healthy individuals, using a database extracted from the Open Access Imaging Studies series. The results revealed higher discriminative power of entropy by permutations compared to low-frequency fluctuation amplitude and fractional amplitude of low-frequency fluctuations. Increased entropy by permutations was obtained in regions of the default network and the executive control network in patients. The posterior cingulate cortex and the precuneus showed differential characteristics when assessing entropy by permutations in both groups. There were no findings when correlating metrics with clinical scales. The results demonstrated that entropy by permutations allows characterizing brain function in Alzheimer’s patients, and also reveals information about nonlinear interactions complementary to the characteristics obtained by calculating the amplitude of low frequency oscillations.

Based on the characteristics of liquid lens sparse aperture imaging, a radiative multiplet array structure is proposed; a simplified model of sparse aperture imaging is given, and the analytical expression of the modulation transfer function is derived from the optical pupil function of the multiplet array structure; the specific distribution form of this multiplet array structure is given, and the structure parameters are approximated by the dimensionless method; the two types of radiative multiplet array structures are discussed, and the filling factor, redundancy, modulation transfer function and other characteristic parameters are calculated. The physical phenomena exhibited by the parametric scan are discussed, and the structural features and imaging characteristics of these two arrays are compared. The results show that the type-II structure with larger actual equivalent aperture and actual cutoff frequency and lower redundancy is selected when the average modulation transfer function and the IF characteristics of the modulation transfer function of the two structures are close to each other; the type-II structure has certain advantages in imaging; the conclusion is suitable for arbitrary enclosing circle size because the liquid lens-based multiplet array structure adopts dimensionless approximation parameters; compared with the composite toroidal structure, the radiative multiplet mirror structure has a larger actual cut-off frequency and actual equivalent aperture when the filling factor is the same.