Geometric constraints on the dynamics of networks
Year: 2015
Type: preprint
Abstract: The functional and computational power of a network emerges as a property of the system operating as a coherent whole at a global scale, not at the scale of individual nodes. A natural question to ask is what are the physical principles that allow a collection of nodes to interact in such a way that they produce emergent global network dynamics? There is in general a lack of sufficient theory capable of providing insights into universal physical principles that bridge individual node dynamics to the behavior of the network as a whole in a deterministic way. Here, we show that in any physically constructible geometric network, the geometry of the network constrains and bounds signaling and the flow of information through the network, and develop a theory derived from foundational principles of neural signaling that can both describe and predict the dynamics of geometric networks from considerations of node dynamics. We provide empirical evidence that at least some important examples of widely different naturally occurring and engineered networks, specifically, the prevalence of the small world network topology, axonal branching of pyramidal neurons in the visual cortex, and the internet router network, are capable of approaching a state of optimal dynamical efficiency, a concept that is derived from the theory. The framework we develop has a wide range of (non-biological) engineering and neurophysiological applications.
Source: arXiv (Cornell University)
Author: Gabriel A. Silva
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2256757851