Linear algebra approach to geometric graphs

Linear Algebra Approach to Separable Bayesian Networks

Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node’s parents, instead of the joint distributions. We describe the connection between an arbitrary Conditional Probability Table (CPT) and separable systems using linear algebra. We give an a...

A Geometric Algebra Approach to Some Problems of Robot Vision

Geometric algebra has been proved to be a powerful mathematical language for robot vision. We give an overview of some research results in two different areas of robot vision. These are signal theory in the multidimensional case and knowledge based neural computing. In both areas a considerable extension of the modeling has been achieved by applying geometric algebra.

Linear Orderings of Random Geometric Graphs

In random geometric graphs, vertices are randomly distributed on [0, 1] and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cu...

Switched Linear Systems . Geometric Approach

We consider equivalence relation between switched linear systems and compute the dimension of equivalence classes, after proving they can be obtained as the orbits of the action of a Lie group on the differentiable manifold of matrices defining the subsystems the system consists of and deduce miniversal deformations.

Introduction to Pauli Geometric Algebra