I present results obtained in four very distinct areas. In Chapter 1, I investigate vector based embedding models for text as applied to a corpus of scientific articles from the ar[chi]iv . I report on the utility of the learned word representations, and experiment with several techniques for learning vector representations for articles. I go on to discuss extensions to categories, authors, and readers, and the utility these would provide for enhancing the experience of ar[chi]iv users. Chapter 2 reviews work in the field of text segmentation, in particular the segmentation of long sequences of text into coherent topical sections. I introduce a novel segmentation algorithm that achieves state of the art results on a standard test set. Chapter 3 investigates a model of the fictional disease: zombies. I use zombism as an entertaining platform for investigating and exploring techniques in epidemiology modelling and critical phenomena. Chapter 4 summarizes work done towards building a group theoretic framework for creating generalized free energy expansions for elasticity. I found the first 50 terms in the expansion and show that these can be reliably fit to simulated data.