ORCID

https://orcid.org/0000-0001-6675-0355

Date of Award

Fall 2024

Language

English

Embargo Period

9-5-2024

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Physics

Program

Physics

First Advisor

Ariel Caticha

Second Advisor

Luis Rocha

Committee Members

Daniel Robbins, Jesse Ernst, Hiroki Sayama

Keywords

Biomolecular Networks, Directed Networks, Redundancy, Canalization, Dynamics on Networks, Dynamics of Networks

Subject Categories

Bioinformatics | Data Science | Dynamical Systems | Non-linear Dynamics | Statistical, Nonlinear, and Soft Matter Physics | Systems Biology | Systems Science

Abstract

A constant quest in network science has been in the development of methods to identify the most relevant components in a dynamical system solely via the interaction structure amongst its subsystems. This information allows the development of control and intervention strategies in biochemical signaling and epidemic spreading. We highlight the relevant components in heterogeneous dynamical system by their patterns of redundancy, which can connect how dynamics affect network topology and which pathways are necessary to spreading phenomena on networks. In order to measure the redundancies in a large class of empirical systems, we develop the backbone of directed networks methodology, which finds the interactions needed to compute the shortest paths in a directed graph and removes others which are deemed topologically redundant. We show that this methodology is not only able to quantify, but also qualify the interactions according to their relevance for spreading processes on empirical networks. In terms of biochemical regulation networks, spreading processes can happen as the response of those systems to local perturbations. Studying empirical networks, we show that the effect of local perturbations are minor at the attractor regime in comparison to quick transients. Nevertheless, accounting for the redundancy in the collective dynamics featured in each of those networks is shown here to be a good predictor of the quick transient and attractor response to perturbations. Those are measured by the topology of the effective graph and shortest path propagation in this network representation. Ultimately, we can define the backbone of the effective graph, which is a reduced graph representation that preserves the spreading dynamics approximation in the effective graph. This subgraph combines the topological and dynamical redundancy from biochemical regulation networks, in doing so it provides a recipe to link the dynamics on and of networks.

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