Leah Keating

About me

I am currently a Hedrick Assistant Adjunct Professor in the Dept. of Mathematics at UCLA. My mentor is Prof. Mason Porter.

I completed my PhD in the MACSI research group in the Dept. of Mathematics and Statistics at the University of Limerick, Ireland.

My PhD was funded by the SFI Centre for Research Training in Foundations of Data Science, this is a cohort-based PhD programme with strong industry links.

I was supervised by Prof. James Gleeson and Dr David O'Sullivan and my PhD focused on modelling social spreading processes on networks.

My PhD thesis is available here.

My Research

Multitype branching process method for modelling complex contagion on clustered networks (2022)
Leah A. Keating, James P. Gleeson and David J.P. O'Sullivan

This paper was an Editors' suggestion in Physical Review E.

Complex contagion adoption dynamics are characterised by a node being more likely to adopt after multiple network neighbours have adopted. We show how to construct multi-type branching processes to approximate complex contagion adoption dynamics on networks with clique-based clustering.  This involves tracking the evolution of a cascade via different classes of clique motifs that account for the different numbers of active, inactive and removed nodes. This discrete-time model assumes that active nodes become immediately and certainly removed in the next time step. This description allows for extensive Monte Carlo simulations (which are faster than network-based simulations), accurate analytical calculation of cascade sizes, determination of critical behaviour and other quantities of interest.

A generating-function approach to modelling complex contagion on clustered networks with multi-type branching processes  (Journal of Complex Networks, 2023)
Leah A. Keating, James P. Gleeson and David J.P. O'Sullivan

Understanding cascading processes on complex network topologies is paramount for modelling how diseases, information, fake news and other media spread. In this paper, we extend the multi-type branching process method developed in Keating et al., 2022, which relies on homogenous network properties, to a more general class of clustered networks. Using a model of socially-inspired complex contagion we obtain results, not just for the average behaviour of the cascades but for full distributions of the cascade properties. We introduce a new method for the inversion of probability generating functions to recover their underlying probability distributions; this derivation naturally extends to higher dimensions. This inversion technique is used along with the multi-type branching process to obtain univariate and bivariate distributions of cascade properties. Finally, using clique cover methods, we apply the methodology to synthetic and real-world networks and compare the theoretical distribution of cascade sizes with the results of extensive numerical simulations.

Distribution of cascade size for simulations on the power-grid network (purple points) compared to the multi-type branching process theory (black line).

Upcoming/Recent Presentations