This article applies multiple machine learning methods to strongly suggest that Chief Justice John Marshall behaved unethically in an important 19th Century case of American constitutional law: Martin v. Hunter's Lessee. He wrote large swathes of the opinion even though he had a large financial stake in the outcome of the case and even though he had formally recused himself. We establish this through multiple machine learning methods, including a character-sequence-to-image method known as the frequency chaos game representation (FCGR), sentence embeddings using BERT, and the reknowned Delta method involving bags of words. All these methods of stylometry reach the same conclusions.

BACKGROUND: Alignment-free methods of genomic comparison offer the possibility of scaling to large data sets of nucleotide sequences comprised of several thousand or more base pairs. Such methods can be used for purposes of deducing "nearby" species in a reference data set, or for constructing phylogenetic trees. RESULTS: We describe one such method that gives quite strong results. We use the Frequency Chaos Game Representation (FCGR) to create images from such sequences, We then reduce dimension, first using a Fourier trig transform, followed by a Singular Values Decomposition (SVD). This gives vectors of modest length. These in turn are used for fast sequence lookup, construction of phylogenetic trees, and classification of virus genomic data. We illustrate the accuracy and scalability of this approach on several benchmark test sets. CONCLUSIONS: The tandem of FCGR and dimension reductions using Fourier-type transforms and SVD provides a powerful approach for alignment-free genomic comparison. Results compare favorably and often surpass best results reported in prior literature. Good scalability is also observed.

Over the past few decades several variations on a half GCD algorithm for obtaining the pair of terms in the middle of a Euclidean sequence have been proposed. In the integer case algorithm design and proof of correctness are complicated by the effect of carries. This paper will demonstrate a variant with a relatively simple proof of correctness. We then apply this to the task of rational recovery for a linear algebra solver.