Our main contribution will be to develop analysis tools that will allow a geometric interpretation of information flow as a causal inference indicated by positive transfer entropy.
The Portrait Divergence reveals important characteristics of multilayer and temporal networks extracted from data.
Social and Information Networks Information Theory Information Theory Data Analysis, Statistics and Probability Physics and Society
Herein, we propose a framework for nonlinear dimensionality reduction that generates a manifold in terms of smooth geodesics that is designed to treat problems in which manifold measurements are either sparse or corrupted by noise.
We describe an image processing perspective inference of coherent sets from a fluidic system directly from image data, without attempting to first model underlying flow fields, related to a concept in image processing called motion tracking.
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure.
Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates.
In a topological sense, we describe these changes as switching between low-dimensional embedding manifolds underlying a group of evolving agents.