Effects of Age-Related Cognitive Deficits on EEG Phase Coherence

Body and brain undergo several changes with aging. One of these changes is the loss of neuroplasticity, which leads to the decrease of cognitive abilities. Hence the necessity of stopping or reversing these changes is of utmost importance to contemporary society. In the present work, electroencephalogram (EEG) markers of cognitive decline are sought whilst the subjects perform the Wisconsin Card Sorting Test (WCST). Considering the expected age-related cognitive deficits, WCST was applied to young and elder participants. The results suggest that coherence on theta and alpha EEG rhythms decrease with aging and increase with performance. Additionally, theta phase coherence seems more sensitive to performance, while alpha synchronization appears as a potential ageing marker.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.