You can never truly empty a box. Suppose you want to empty a box. You remove all its visible contents, pump out any gases, and--applying some science-fiction technology--evacuate any unseeable material such as dark matter. According to quantum mechanics, what's left inside? It sounds like a trick question.

To accurately compute data-based prediction of Hamiltonian systems, especially the long-term evolution of such systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a case that is particularly challenging for data-based methods: systems with interacting parts that do not reduce to pure momentum evolution. Such systems are essential in scientific computations. For example, any discretization of a continuum elastic rod can be viewed as interacting elements that can move and rotate in space, with each discrete element moving on the group of rotations and translations $SE(3)$. We develop a novel method of data-based computation and complete phase space learning of such systems. We follow the original framework of \emph{SympNets} (Jin et al, 2020) building the neural network from canonical phase space mappings, and transformations that preserve the Lie-Poisson structure (\emph{LPNets}) as in (Eldred et al, 2024). We derive a novel system of mappings that are built into neural networks for coupled systems. We call such networks Coupled Lie-Poisson Neural Networks, or \emph{CLPNets}. We consider increasingly complex examples for the applications of CLPNets: rotation of two rigid bodies about a common axis, the free rotation of two rigid bodies, and finally the evolution of two connected and interacting $SE(3)$ components. Our method preserves all Casimir invariants of each system to machine precision, irrespective of the quality of the training data, and preserves energy to high accuracy. Our method also shows good resistance to the curse of dimensionality, requiring only a few thousand data points for all cases studied, with the effective dimension varying from three to eighteen. Additionally, the method is highly economical in memory requirements, requiring only about 200 parameters for the most complex case considered.

Writing a scientific article is a challenging task as it is a highly codified and specific genre, consequently proficiency in written communication is essential for effectively conveying research findings and ideas. In this article, we propose an original textual resource on the revision step of the writing process of scientific articles. This new dataset, called CASIMIR, contains the multiple revised versions of 15,646 scientific articles from OpenReview, along with their peer reviews. Pairs of consecutive versions of an article are aligned at sentence-level while keeping paragraph location information as metadata for supporting future revision studies at the discourse level. Each pair of revised sentences is enriched with automatically extracted edits and associated revision intention. To assess the initial quality on the dataset, we conducted a qualitative study of several state-of-the-art text revision approaches and compared various evaluation metrics. Our experiments led us to question the relevance of the current evaluation methods for the text revision task.

A survey of early work exploring how AI can be used in medicine, with somewhat more technical expositions than in the complementary volume "Artificial Intelligence in Medicine." Each chapter is preceded by a brief introduction that outlines our view of its contribution to the field, the reason it was selected for inclusion in this volume, an overview of its content, and a discussion of how the work evolved after the article appeared and how it relates to other chapters in the book.