Browsing by Subject "Applied mathematics"

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    Investigation of brain ageing in HIV-positive individuals using convolutional neural networks
    (2024) Catzel, Rachel; Shock, Jonathan; Moodley, Deshendran
    Developments in the field of Deep Learning (DL) have provided new means of tracking healthy ageing, and have established DL-predicted brain age as an accurate and reliable biomarker for brain health. Deviations from a healthy brain ageing trajectory, indicated by an increased predicted brain age relative to chronological age, and thus positive brain age delta, have been associated with cognitive impairments. This thesis focuses on de veloping a robust brain age prediction model to investigate brain ageing in HIV-positive individuals. We utilise the UK Biobank, CamCAN, and ENIGMA-HIV datasets for this task and train a convolutional neural network in two stages. First, we pre-train the model on the large UK Biobank dataset (N=21366) which contains individuals in the age range of 45-82 years. To this end, we achieve a mean absolute error (MAE) of 2.57±1.94 years. Next, we fine-tune the pre-trained model on a smaller dataset, with a wider age range, aligned with that of our testing dataset from ENIGMA-HIV. We select the CamCAN dataset (N=484) for this, with individuals spanning the age range of 18-88 years. We obtain an MAE of 3.54 ± 2.59 years on the holdout CamCAN test set, substantially im proving upon the 6.38 ± 5.30 years MAE achieved without pre-training. We then apply the trained model to the multi-site ENIGMA-HIV testing dataset which we have har monised to remove inter-site variation. Following testing, we apply a fixed-effects model to analyse whether the brain age deltas are significantly higher in HIV-positive individu als compared to HIV-negative controls. Although no statistically significant difference is found in the brain age deltas due to HIV status, further analysis reveals significant cor relations between the brain age deltas and specific HIV clinical measures, in particular, nadir CD4 count and current CD4 count. This thesis's findings contribute to under standing the impact of HIV on brain ageing and associated factors of significance, and highlights the value of DL techniques in medical research.
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    Quantum states on spheres in the presence of magnetic fields
    (2019) Slayen, Ruach Pillay; Murugan, Jeffrey; Shock, Jonathan
    The study of quantum states on the surface of various two-dimensional geometries in the presence of strong magnetic fields has proven vital to the theoretical understanding of the quantum Hall effect. In particular, Haldane’s seminal study of quantum states on the surface of a compact geometry, the sphere, in the presence of a monopole magnetic field, was key to developing an early understanding of the fractional quantum Hall effect. Most of the numerous studies undertaken of similar systems since then have been limited to cases in which the magnetic fields are everywhere constant and perpendicular to the surface on which the charged particles are confined. In this thesis, we study two novel variations of Haldane’s spherical monopole system: the 'squashed sphere’ in the presence of a monopole-like magnetic field, and the sphere in the presence of a dipole magnetic field. In both cases the magnetic field is neither perpendicular nor constant with respect to the surface on which the charged particles are confined. Furthermore, the spherical dipole system has vanishing net magnetic flux. For the 'squashed sphere’ system we find the lowest Landau level single-particle Hilbert space, and it is shown that the effect of the squashing is to localise the particles around the equator. For the spherical dipole system we find the entire single-particle Hilbert space and energy spectrum. We show that in the strong-field limit the spectrum exhibits a Landau level structure, as in the spherical monopole case. Unlike in the spherical monopole case, each Landau level is shown to be infinitely degenerate. The emergence of this Landau level structure is explained by the tendency of a strong dipole field to localise particles at the poles of the sphere.