Algebraic topology bridging the gap between single neurons and networks

This research proposal aims to advance our understanding of neuronal networks through the integration of topological data analysis (TDA), computational modelling, and machine learning techniques. By combining these innovative approaches, I seek to create a comprehensive framework for the topological description of trees, leading to valuable insights into brain function and the development of computational models of disease brain regions.
The human brain is a complex network of billions of neurons connected by trillions of synapses. The shapes and connectivity patterns of neurons play a critical role in brain activity and are associated with various brain disorders. However, the precise mechanisms underlying the relationship between neuronal shape and network function remain elusive. This proposal addresses this knowledge gap by leveraging the power of TDA, which allows us to capture and analyze the intricate topology of neuronal structures.
To achieve these objectives, I will utilize well-studied organisms such as C. elegans and Fruit Fly, which provide fully reconstructed data, to develop and validate our methodology. These organisms offer an excellent opportunity to demonstrate the efficacy of TDA in understanding brain function. Furthermore, I will employ computational modelling to simulate artificial neuronal trees and investigate the rules governing neuronal growth and network formation. This approach will enable us to generate networks with specific topological properties and shed light on the fundamental mechanisms underlying neuronal connections.