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Current Research

Understanding the complex dynamics of the brain is one of science’s greatest challenges. Consisting of millions of neurons, studying this complicated structure requires a multidisciplinary approach, involving mathematicians, statisticians and neuroscientists alike. Neuronal activity can be measured in a variety of ways. Some of which, such as Electroencephalography (EEG) or functional magnetic resonance imaging (fMRI), are non-invasive procedures. As such, they can be carried out in humans to diagnose certain conditions such as epilepsy, or brain tumours. However, these tools record the coordinated activity of thousands of neurons, rather than the activity of individual neurons themselves. 

To get a more microscopic view of the brain, our research considers measurements obtained from mice using multi electrode array (MEA) recordings. Using this technology, the activity of individual neurons can be measured via electrodes implanted directly into the brain. This allows for the analysis of neuronal behaviour in much greater detail, permitting the study of the brain’s processes at a much more refined level. 

My PhD is entitled ‘Understanding Neuronal Synchronisation in High Dimensions’. Below, I give information about the current projects I am working on and where I have presented this work.

Regularised Spectral Estimation for High Dimensional Point Processes

We have developed novel methodology for the estimation of neuronal connectivity in the brain network. In practice, this research can be used to infer networks of neuronal interactions. A tool of this nature is essential to our continued understanding of the brain and its intricate processes. This project is in collaboration with world-leading statisticians and neuroscientists at the University of Washington in Seattle.

Preprint and Abstract

C. Pinkney, C. Euan, A. Gibberd, A. Shojaie. Regularised Spectral Estimation for High-Dimensional Point Processes, ArXiV Preprint, 2024 (link)

“Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the spectral density matrix, a frequency domain equivalent of the covariance matrix. In the context of neuronal analysis, statistics based on the spectral density matrix can be used to infer connectivity in the brain network between individual neurons. However, the high-dimensional nature of spike train data mean that it is often difficult, or at times impossible, to compute these statistics. In this work, we discuss the importance of regularisation-based methods for spectral estimation, and propose novel methodology for use in the point process setting. We establish asymptotic properties for our proposed estimators and evaluate their performance on synthetic data simulated from multivariate Hawkes processes. Finally, we apply our methodology to neuroscience spike train data in order to illustrate its ability to infer connectivity in the brain network. “

Conferences and Workshops

  • Statistical Challenges for Complex Brain Signals and Images (2023) – The Casa Matemática Oaxaca (CMO), Mexico

“Sparse Partial Coherence Estimation for Neuroscience Spike Train Data” (Abstract available here).

  • Time Series Analysis of Noisy Data (2023) – Lancaster University 

   “Spectral Analysis for Neuroscience Spike Train Data” (Poster).

  • STOR-i Annual Conference (2024) – Lancaster University

   “Understanding Neuronal Synchronisation in High-Dimensions” (Abstract available here).

  • STEM for Britain Final (2024) – Houses of Parliament, London

   “Statistical Analysis of Brain Activity” (Poster available here).