We construct all finite irreducible modules over Lie conformal superalgebras of type $W$ and $S$ .

We construct all finite irreducible modules over Lie conformal superalgebras of type $K$ .

In the clinical electrophysiological practice, reading and comparing electroencephalographic (EEG) recordings are sometimes insufficient and take too much time. Tools coming from the information theory or nonlinear systems theory such as entropy and complexity have been presented as an alternative to address this problem. In this work, we introduce a novel method—the permutation Lempel–Ziv Complexity vs. Permutation Entropy map. We apply this method to the EEGs of two patients with specific diagnosed pathologies during respective follow up processes of pharmacological changes in order to detect alterations that are not evident with the usual inspection method. The method allows for comparing between different states of the patients’ treatment, with a healthy control group, given global information about the signal, supplementing the traditional method of visual inspection of EEG.

We classify the irreducible quasifinite highest weight modules over the symplectic Lie subalgebra $W_{\infty },$ and realize them in terms of irreducible highest weight representations of classical Lie subalgebras of infinite matrices with finitely many nonzero diagonals.