Research

My research is interdisciplinary, straddling branches of mathematics, neuroscience, network theory, and machine learning.

I am mostly occupied with studying neural networks and their structure-dynamics-function relationship in the context of reservoir computing and biological networks in the brain.

Key words:

Recurrent Neural Network	Reservoir Computing	Network Structure	Dynamics	Applied Topology	Heterosynaptic Plasticity	Biological Connectomes

• My main current PhD work (which had its inception with a visiting research collaboration) revolves around the structure-function relationship of recurrent neural networks in reservoir computing. The idea is to analyse reservoir architectures in performing computational tasks, finding optimal network structures and typifying their topological trademarks. This work includes using biological connectome-based inspiration for reservoir computing, in a "NeuroAI" sort of sense, helping us make machine learning better and more efficient, as well as shedding light on possible brain network mechanisms.
  We also want to ascertain if synaptic plasticity rules can produce similar architectures to those found in optimal reservoir networks.
• I am also interested in the mathematical and network properties of heterosynaptic plasticity learning rules using graph theory and topological analysis. This involves primarily studying synaptic plasticity's functional implications at the network and architectural level. Here and here are little insights into this work.
• I am involved in another collaboration with Bristol using mathematical modelling to analyse the dynamics of synaptic maturation and network formation.
• I have done work on how deficits in short term plasticity in individuals with psychosis may impact their decision making processes and capacities in working memory. This is mainly through attractor state dynamical systems. See a little flavour here.
• I am also interested in using topological data analysis with persistent homology on large datasets to better understand the structures and interconnectedness of neurocognitive performance, such as short-term and working memory, cognitive functions, and processing speed.
• I also have research interests in assessment theory, in a mathematics pedagogical context. See, for example, here.