arXiv subjects
Publications and source records attributed to Joey McCollum.
We examine Bourbaki's function, an easily-constructed continuous but nowhere-differentiable function, and explore properties including functional identities, the antiderivative, and the box and Hausdorff dimensions of the graph.
We examine a parameterized family of functions F_a, all of which are continuous and some of which are nowhere or almost nowhere differentiable, we explore the behavior of F'_a and F"_a almost everywhere for different values of a, focusing on specific questions regarding F_a's differentiability for certain a, and we calculate the Hausdorff dimension of the graphs of all F_a.
The text-critical practice of grouping witnesses into families or texttypes often faces two obstacles: Contamination in the manuscript tradition, and co-dependence in identifying characteristic readings and manuscripts. We introduce non-negative matrix factorization (NMF) as a simple, unsupervised, and efficient way to cluster large numbers of manuscripts and readings simultaneously while summarizing contamination using an easy-to-interpret mixture model. We apply this method to an extensive collation of the New Testament epistle of Jude and show that the resulting clusters correspond to human-identified textual families from existing research.