Finding octonionic eigenvectors using Mathematica

Finding community structure in networks using the eigenvectors of matrices.

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the ei...

Object recognition using eigenvectors

A method for object recognition and pose estimation for robotic bin picking is presented. The approach discussed is a variant on current approaches to eigenimage analysis. Compared to traditional approaches which use object geometry only (shape invariants), the implementation described uses the eigenspace determined by processing the eigenvalues and eigenvectors of the image set. The image set ...

An Octonionic Gauge Theory

The nonassociativity of the octonion algebra necessitates a bimodule representation, in which each element is represented by a left and a right multiplier. This representation can then be used to generate gauge transformations for the purpose of constructing a field theory symmetric under a gauged octonion algebra, the nonassociativity of which appears as a failure of the representation to clos...

Octonionic Aspects of Supergravity

Octonionic Gravitational Instantons

We construct eight-dimensional gravitational instantons by solving appropriate selfduality equations for the spin-connection. The particular gravitational instanton we present has Spin(7) holonomy and, in a sense, it is the eight-dimensional analog of the Eguchi-Hanson 4D space. It has a removable bolt singularity which is topologically S4 and its boundary at infinity is the squashed S7. We als...