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

Unsupervised Learning with Self-Organizing Spiking Neural Networks

We present a system comprising a hybridization of self-organized map (SOM) properties with spiking neural networks (SNNs) that retain many of the features of SOMs. Networks are trained in an unsupervised manner to learn a self-organized lattice of filters via excitatory-inhibitory interactions among populations of neurons. We develop and test various inhibition strategies, such as growing with inter-neuron distance and two distinct levels of inhibition. The quality of the unsupervised learning algorithm is evaluated using examples with known labels. Several biologically-inspired classification tools are proposed and compared, including population-level confidence rating, and n-grams using spike motif algorithm. Using the optimal choice of parameters, our approach produces improvements over state-of-art spiking neural networks