Interest in the field of spectral geometry, the study of how analytic and geometric properties of manifolds are related, was sparked when Marc Kac in 1966 asked the question “can one hear the shape of a drum?”. One of ...

The thesis introduces an innovative way of decreasing the computational cost of approximate Bayesian computation (ABC) simulations when implemented via Markov chain Monte Carlo (MCMC). Bayesian inference has enjoyed ...

We investigate group invariance in unsupervised learning in the context of certain generative networks based on Boltzmann machines. Specifically, we introduce a generalization of restricted Boltzmann machines which is ...

The graph of the implied volatility of call options as a function of the strike price is called volatility curve. If the options market were perfectly described by the Black-Scholes model, the implied volatility would ...

Focused ion beam scanning electron microscopy (FIB-SEM) is a well-established microscopy technique for 3D imaging of porous materials. We investigate three porous samples of ethyl cellulose microporous films made from ...

A new pharmaceutical drug needs to be shown to be safe and effective before it can be used to treat patients. Adverse events (AEs) are potential side-effects that are recorded during clinical trials, in which a new drug ...

This thesis concerns distributions on Rn with the property of being positive-definite relative to a finite subgroup of the orthogonal group O(n). We construct examples of such distributions as the inverse Abel transform ...