Stratified Space Learning: Reconstructing Embedded Graphs

Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction of large volumes of data embedded in high dimensional spaces. The modelling of these underlying structures is also beneficial for the creation of simulated data that better represents real data. In particular, for systems testing in cases where the use of real data streams might prove impractical or otherwise undesirable. We seek to discover and model the structure by combining methods from topological data analysis with numerical modelling. As a first step in combining these two areas, we examine the recovery of the abstract graph $G$ structure, and model a linear embedding $|G|$ given only a noisy point cloud sample $X$ of $|G|$.Comment: 7 pages, 3 figures, accepted for MODSIM 2019 conferenc

Sacrifice of the Mass and the Sacrifice of Christ: Thomas Aquinas against Later Thomists

According to Aquinas, Christ’s body and blood are really present in the Eucharist, his historical sacrifice on the cross is not. The latter is said to be ‘represented’ in the Eucharist, but the expression does not mean that it is made present in the way Christ’s body and blood are. Christ’s passion and sacrifice are to be remembered by the faithful as a historical event of the past. This is in contrast with the reading of later 16th and 17th century Thomist commentators. It goes against the ‘hyper-realist’ interpretation of Bellarmine. But, unlike the more moderate theories of Cano and others, Aquinas also does not think that the act of Christ being immolated is ritually re-enacted in the mass by some specific ritual gestures

‘So the Sons are Free’: The Temple Tax in the Matthean Community

This paper assesses possible exegetical underpinnings of Jesus paying the Temple tax. It concludes that the Matthean tradition does not address exegetical concerns but social considerations to buttress his legal position, which marks Matthew's view as unique in first Century Judaism