Complex Objects in the Polytopes of the Linear State-Space Process
Abstract
A simple object (one point in -dimensional space) is the resultant of the evolving matrix polynomial of walks in the irreducible aperiodic network structure of the first order DeGroot (weighted averaging) state-space process. This paper draws on a second order generalization the DeGroot model that allows complex object resultants, i.e, multiple points with distinct coordinates, in the convex hull of the initial state-space. It is shown that, holding network structure constant, a unique solution exists for the particular initial space that is a sufficient condition for the convergence of the process to a specified complex object. In addition, it is shown that, holding network structure constant, a solution exists for dampening values sufficient for the convergence of the process to a specified complex object. These dampening values, which modify the values of the walks in the network, control the system's outcomes, and any strongly connected typology is a sufficient condition of such control.
Cite
@article{arxiv.1401.5339,
title = {Complex Objects in the Polytopes of the Linear State-Space Process},
author = {Noah E. Friedkin},
journal= {arXiv preprint arXiv:1401.5339},
year = {2014}
}