arXiv subjects

Anthony N. Burkitt

Publications and source records attributed to Anthony N. Burkitt.

7 recordsLinked to original sources

arXiv2025

Decoding Saccadic Eye Movements from Brain Signals Using an Endovascular Neural Interface

An Oculomotor Brain-Computer Interface (BCI) records neural activity from regions of the brain involved in planning eye movements and translates this activity into control commands. While previous successful oculomotor BCI studies primarily relied on invasive microelectrode implants in non-human primates, this study investigates the feasibility of an oculomotor BCI using a minimally invasive endovascular Stentrode device implanted near the supplementary motor area in a patient with amyotrophic lateral sclerosis (ALS). To achieve this, self-paced visually-guided and free-viewing saccade tasks were designed, in which the participant performed saccades in four directions (left, right, up, down), with simultaneous recording of endovascular EEG and eye gaze. The visually guided saccades were cued with visual stimuli, whereas the free-viewing saccades were self-directed without explicit cues. The results showed that while the neural responses of visually guided saccades overlapped with the cue-evoked potentials, the free-viewing saccades exhibited distinct saccade-related potentials that began shortly before eye movement, peaked approximately 50 ms after saccade onset, and persisted for around 200 ms. In the frequency domain, these responses appeared as a low-frequency synchronisation below 15 Hz. Classification of 'fixation vs. saccade' was robust, achieving mean area under the receiver operating characteristic curve (AUC) scores of 0.88 within sessions and 0.86 between sessions. In contrast, classifying saccade direction proved more challenging, yielding within-session AUC scores of 0.67 for four-class decoding and up to 0.75 for the best-performing binary comparisons (left vs. up and left vs. down). This proof-of-concept study demonstrates the feasibility of an endovascular oculomotor BCI in an ALS patient, establishing a foundation for future oculomotor BCI studies in human subjects.

eess.SP↗

arXiv2023

Path Signatures for Seizure Forecasting

Predicting future system behaviour from past observed behaviour (time series) is fundamental to science and engineering. In computational neuroscience, the prediction of future epileptic seizures from brain activity measurements, using EEG data, remains largely unresolved despite much dedicated research effort. Based on a longitudinal and state-of-the-art data set using intercranial EEG measurements from people with epilepsy, we consider the automated discovery of predictive features (or biomarkers) to forecast seizures in a patient-specific way. To this end, we use the path signature, a recent development in the analysis of data streams, to map from measured time series to seizure prediction. The predictor is based on linear classification, here augmented with sparsity constraints, to discern time series with and without an impending seizure. This approach may be seen as a step towards a generic pattern recognition pipeline where the main advantages are simplicity and ease of customisation, while maintaining forecasting performance on par with modern machine learning. Nevertheless, it turns out that although the path signature method has some powerful theoretical guarantees, appropriate time series statistics can achieve essentially the same results in our context of seizure prediction. This suggests that, due to their inherent complexity and non-stationarity, the brain's dynamics are not identifiable from the available EEG measurement data, and, more concretely, epileptic episode prediction is not reliably achieved using EEG measurement data alone.

stat.ML↗

arXiv2023

Autoregressive models for biomedical signal processing

Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity. Crucially, this data is subject to measurement errors as well as uncertainties in the underlying system model. As a result, standard signal processing using autoregressive model estimators may be biased. We present a framework for autoregressive modelling that incorporates these uncertainties explicitly via an overparameterised loss function. To optimise this loss, we derive an algorithm that alternates between state and parameter estimation. Our work shows that the procedure is able to successfully denoise time series and successfully reconstruct system parameters. This new paradigm can be used in a multitude of applications in neuroscience such as brain-computer interface data analysis and better understanding of brain dynamics in diseases such as epilepsy.

eess.SP↗

arXiv2023

On the benefit of overparameterisation in state reconstruction: An empirical study of the nonlinear case

The empirical success of machine learning models with many more parameters than measurements has generated an interest in the theory of overparameterisation, i.e., underdetermined models. This paradigm has recently been studied in domains such as deep learning, where one is interested in good (local) minima of complex, nonlinear loss functions. Optimisers, like gradient descent, perform well and consistently reach good solutions. Similarly, nonlinear optimisation problems are encountered in the field of system identification. Examples of such high-dimensional problems are optimisation tasks ensuing from the reconstruction of model states and parameters of an assumed known dynamical system from observed time series. In this work, we identify explicit parallels in the benefits of overparameterisation between what has been analysed in the deep learning context and system identification. We test multiple chaotic time series models, analysing the optimisation process for unknown model states and parameters in batch mode. We find that gradient descent reaches better solutions if we assume more parameters to be unknown. We hypothesise that, indeed, overparameterisation leads us towards better minima, and that more degrees of freedom in the optimisation are beneficial so long as the system is, in principle, observable.

math.OC↗

arXiv2021

On the benefit of overparameterization in state reconstruction

The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models. This work presents such a method, where we augment the system in such a way that there is no distinction between parameter and state reconstruction. We pose the resulting problem as a batch problem: given the model, reconstruct the state from a finite sequence of output measurements. In the case the model is linear, we derive an analytical expression for the state reconstruction given the model and the output measurements. Importantly, we estimate the state trajectory in its entirety and do not aim to estimate just an initial condition: that is, we use more degrees of freedom than strictly necessary in the optimization step. This particular approach can be reinterpreted as training of a neural network that estimates the state trajectory from available measurements. The technology associated with neural network optimization/training allows an easy extension to nonlinear models. The proposed framework is relatively easy to implement, does not depend on an informed initial guess, and provides an estimate for the state trajectory (which incorporates an estimate for the unknown parameters) over a given finite time horizon.

math.OC↗

arXiv2020

Emergence of radial orientation selectivity: Effect of cell density changes and eccentricity in a layered network

Previous work by Linsker revealed how simple cells can emerge in the absence of structured environmental input, via a self-organisation learning process. He empirically showed the development of spatial-opponent cells driven only by input noise, emerging as a result of structure in the initial synaptic connectivity distribution. To date, a complete set of radial eigenfunctions have not been provided for this multi-layer network. In this paper, the complete set of eigenfunctions and eigenvalues for a three-layered network is for the first time analytically derived. Initially a simplified learning equation is considered for which the homeostatic parameters are set to zero. To extend the eigenfunction analysis to the full learning equation, including non-zero homeostatic parameters, a perturbation analysis is used.

q-bio.NC↗

arXiv2018

A homotopic mapping between current-based and conductance-based synapses in a mesoscopic neural model of epilepsy

Changes in brain states, as found in many neurological diseases such as epilepsy, are often described as bifurcations in mesoscopic neural models. Nearly all of these models rely on a mathematically convenient, but biophysically inaccurate, description of the synaptic input to neurons called current-based synapses. We develop a novel analytical framework to analyze the effects of a more biophysically realistic description, known as conductance-based synapses. These are implemented in a mesoscopic neural model and compared to the standard approximation via a single parameter homotopic mapping. A bifurcation analysis using the homotopy parameter demonstrates that if a more realistic synaptic coupling mechanism is used in this class of models, then a bifurcation or transition to an abnormal brain state does not occur in the same parameter space. We show that the more realistic coupling has additional mathematical parameters that require a fundamentally different biophysical mechanism to undergo a state transition. These results demonstrate the importance of incorporating more realistic synapses in mesoscopic neural models and challenge the accuracy of previous models, especially those describing brain state transitions such as epilepsy.

q-bio.NC↗