Network modeling of complex systems: criticality, robustness, and computation

Complex and adaptive networks are ubiquitous in many felds of scientifc study,
ranging from biological to social and communication networks, and can produce
interesting and vital emerging phenomena, such as self-organized criticality. In this
thesis, we study complex and adaptive networks in four diferent applications.
Our frst feld of study regards neural science, specifcally brain criticality, which is
hypothesized to be vital for the functioning of brains. In three papers, we study the
presence of criticality in high-degree threshold networks and fnd a new critical point
with dynamics more similar to real brain dynamics than previous high-degree critical
points in such networks. Additionally, we develop algorithms that can tune networks
towards such criticality, providing ideas for how criticality might be maintained in
real brain networks.
Our second feld of interest is epidemiology. Here, networks can be used to model
contact between members of society and the spread of infectious diseases. We study
the efcacy of a recursive contact tracing algorithm that attempts to predict the
spread of a disease and quarantine possibly infectious people accordingly to combat
a disease with a fnite asymptomatic infection rate. We develop analytical calcula tions, supported by simulations, for the reduction of a disease’s infections using this
algorithm and fnd that recursive contact tracing can combat diseases that could
not be controlled with classical tracing of only frst contacts.
The third feld is epigenetics, in which genetic networks are often modeled as
simple Boolean networks. We hypothesize that genetic networks must be robust to
noise, due to the environment in which they must function to facilitate life, and test
this hypothesis by comparing the robustness of a number of real genetic networks
to random networks. We fnd a higher robustness of the real networks compared to
randomized variants and further trace the origins of this robustness to a combination
of the networks’ attractors themselves as well as the underlying network topology.
Finally, to spark ideas for amorphous computing, we develop a computing scheme
using collision-based computing in an irregular, two-dimensional threshold network.
We show that interactions of gliders of activity traversing the network can be used
to create a universal set of Boolean gates that can be used to facilitate universal
computing.