No abstract

Electroencephalography (EEG) oscillations reflect the superposition of different cortical sources with potentially different frequencies. Various blind source separation (BSS) approaches have been developed and implemented in order to decompose these oscillations, and a subset of approaches have been developed for decomposition of multi-subject data. Group independent component analysis (Group ICA) is one such approach, revealing spatiospectral maps at the group level with distinct frequency and spatial characteristics. The reproducibility of these distinct maps across subjects and paradigms is relatively unexplored domain, and the topic of the present study. To address this, we conducted separate group ICA decompositions of EEG spatiospectral patterns on data collected during three different paradigms or tasks (resting-state, semantic decision task and visual oddball task). K-means clustering analysis of back-reconstructed individual subject maps demonstrates that fourteen different independent spatiospectral maps are present across the different paradigms/tasks, i.e. they are generally stable.

No abstract

A nonlinear delay differential equation with quadratic nonlinearity,is considered, where α k and β are positive constants, h k : [0, ∞) → R are continuous functions such that t -τ ≤ h k (t) ≤ t, τ = const, τ > 0, for any t > 0 the inequality h k (t) < t holds for at least one k, and r : [0, ∞) → (0, ∞) is a continuous function satisfying the inequality r(t) ≥ r 0 = const for an r 0 > 0. It is proved that the positive equilibrium is globally asymptotically stable without any further limitations on the parameters of this equation.

A linear(k+1)th-order discrete delayed equationΔx(n)=−p(n)x(n−k)wherep(n)a positive sequence is considered forn→∞. This equation is known to have a positive solution if the sequencep(n)satisfies an inequality. Our aim is to show that, in the case of the opposite inequality forp(n), all solutions of the equation considered are oscillating forn→∞.