Horoball Packing Density Lower Bounds in Higher Dimensional Hyperbolic nn-space for 6≤n≤96 \leq n \leq 9

Koszul type Coxeter Simplex tilings exist in hyperbolic space $\mathbb{H}^n$ for $2 \leq n \leq 9$, and their horoball packings have the highest known regular ball packing densities for $3 \leq n \leq 5$. In this paper we determine the optimal horoball packings of Koszul type Coxeter simplex tilings of $n$-dimensional hyperbolic space for $6 \leq n \leq 9$, which give new lower bounds for packing density in each dimension. The symmetries of the packings are given by Coxeter simplex groups.Comment: 16 Pages, 6 Tables, 1 Figure. arXiv admin note: substantial text overlap with arXiv:1809.05411, arXiv:1401.608

Bessel Functions in Mass Action. Modeling of Memories and Remembrances

Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which provide time dependent representation of Bessel equation. The root loci of poles and zeros conform to solutions of K-sets. Some light is shed on the problem of filling the gap between the cellular level dynamics and the brain functional activity. Breakdown of time-reversal symmetry is related with the cortex thermodynamic features. This provides a possible mechanism to deduce lifetime of recorded memory.Comment: 16 pages, 9 figures, Physics Letters A, 2015 in pres