Temporal higher-order interactions in neural dynamics

Networks and graphs have been fundamental in modelling complex systems, yet their focus on pairwise interactions limits their ability to fully capture the dynamics of systems like the brain, where coordinated activity among multiple neurons is essential for functioning. Higher-order interactions (HOIs), which represent the collective interplay of groups of nodes, have become increasingly recognised as crucial for understanding both brain function and other complex systems. However, while HOIs have shown promise at the mesoscopic level, their relationship to microscale neural mechanisms remains largely unexplored.This project aims to address this gap by introducing a mathematical framework designed to characterise the temporal dynamics of HOIs in neuronal activity. By reconstructing higher-order networks from simulated neuronal dynamics, the project will model these interactions to offer a novel perspective on how the brain processes information over time. Validation of the framework will be carried out using high-resolution neuronal recordings, such as Neuropixels data, which provide unparalleled accuracy in observing ""genuine"" higher-order interactions within neural circuits.Given the challenges associated with direct neuronal data, we will also develop methods to infer HOIs from indirect data sources, such as calcium imaging. This approach will be fine-tuned to ensure that the inferred interactions closely align with the statistical patterns observed in Neuropixels recordings. This dual strategy enhances the robustness and generalisability of the framework, making it applicable across various data types.By offering a comprehensive characterisation of HOIs in brain dynamics, this project will not only deepen our understanding of neural processing but also open new avenues for cross-disciplinary research. Upon completion, an open-source software package will be released, ensuring the methods and tools developed are accessible to the broader scientific community.""