arXiv subjects

Athena Xiourouppa

Publications and source records attributed to Athena Xiourouppa.

3 recordsLinked to original sources

arXiv2026

Asymptotic analysis of parameterised univariate Gaussian splitting

This document provides in-depth details for the derivation of the univariate splitting algorithm developed in arXiv:2606.01530. The algorithm approximates the standard, 1-D Gaussian distribution with a mixture of uniformly spaced homoscedastic Gaussian components. The solution is found by minimising the squared $L^2$ norm of the mismatch between the approximation and the original Gaussian. This text presents asymptotic analyses of the proposed splitting in the limit of small step $h$ between the mixand means and in the limit of large number of mixands $M$.

math.ST↗

arXiv2026

A flexible and robust approach to univariate Gaussian splitting using parameterised Gaussian mixtures

We consider approximation of a Gaussian distribution with a mixture of homoscedastic Gaussians of smaller variance. The solution is obtained by minimising the $L^2$ norm between the original Gaussian and the mixture, which is parameterised to reduce the complexity of the optimisation problem. The developed technique is straightforward, sufficiently robust and yields Gaussian Mixtures that rapidly approach the original function as the number of mixands is increased. The proposed solution is examined for multiple special cases of input parameters resulting in further simplifications. Extension of the proposed method for approximating non-Gaussian distributions is discussed.

math.ST↗

arXiv2021

Investigating the Impact of 9/11 on The Simpsons through Natural Language Processing

The impact of real world events on fictional media is particularly apparent in the American cartoon series The Simpsons. While there are often very direct pop culture references evident in the dialogue and visual gags of the show, subtle changes in tone or sentiment may not be so obvious. Our aim was to use Natural Language Processing to attempt to search for changes in word frequency, topic, and sentiment before and after the September 11 terrorist attacks in New York. No clear trend change was seen, there was a slight decrease in the average sentiment over time around the relevant period between 2000 and 2002, but the scripts still maintained an overall positive value, indicating that the comedic nature of The Simpsons did not wane particularly significantly. The exploration of other social issues and even specific character statistics is needed to bolster the findings here.

cs.CL↗