We show that the universal Gröbner basis and the Graver basis of a binomial edge ideal coincide. We provide a description for this basis set in terms of certain paths in the underlying graph. We conjecture a similar result for a parity binomial edge ideal and prove this conjecture for the case when the underlying graph is the complete graph.

There exist a variety of distance measures which operate on time series kernels. The objective of this article is to compare those distance measures in a support vector machine setting. A support vector machine is a state-of-the-art classifier for static (non-time series) datasets and usually outperforms k-Nearest Neighbour, however it is often noted that that 1-NN DTW is a robust baseline for time-series classification. Through a collection of experiments we determine that the most effective distance measure is Dynamic Time Warping and the most effective classifier is kNN. However, a surprising result is that the pairing of kNN and DTW is not the most effective model. Instead we have discovered via experimentation that Dynamic Time Warping paired with the Gaussian Support Vector Machine is the most accurate time series classifier. Finally, with good reason we recommend a slightly inferior (in terms of accuracy) model Time Warp Edit Distance paired with the Gaussian Support Vector Machine as it has a better theoretical basis. We also discuss the reduction in computational cost achieved by using a Support Vector Machine, finding that the Negative Kernel paired with the Dynamic Time Warping distance produces the greatest reduction in computational cost.