Packing spheres in high dimensions with moderate computational effort.

We generate nonlattice packings of spheres in up to 22 dimensions using the geometrical constraint satisfaction algorithm RRR. Our aggregated data suggest that it is easy to double the density of Ball's lower bound and, more tentatively, that the exponential decay rate of the density can be improved relative to Minkowski's longstanding 1/2.

Learning grammar with a divide-and-concur neural network.

We implement a divide-and-concur iterative projection approach to context-free grammar inference. Unlike most state-of-the-art models of natural language processing, our method requires a relatively small number of discrete parameters, making the inferred grammar directly interpretable-one can read off from a solution how to construct grammatically valid sentences. Another advantage of our approach is the ability to infer meaningful grammatical rules from just a few sentences, compared to the hundreds of gigabytes of training data many other models employ.

Reconstructing cellular automata rules from observations at nonconsecutive times.

Recent experiments have shown that a deep neural network can be trained to predict the action of t steps of Conway's Game of Life automaton given millions of examples of this action on random initial states. However, training was never completely successful for t>1, and even when successful, a reconstruction of the elementary rule (t=1) from t>1 data is not within the scope of what the neural network can deliver. We describe an alternative network-like method, based on constraint projections, where this is possible.

Charge-order-enhanced capacitance in semiconductor moiré superlattices.

Van der Waals moiré materials have emerged as a highly controllable platform to study electronic correlation phenomena. Robust correlated insulating states have recently been discovered at both integer and fractional filling factors of semiconductor moiré systems. In this study we explored the thermodynamic properties of these states by measuring the gate capacitance of MoSe/WS moiré superlattices.

Correlated insulating states at fractional fillings of moiré superlattices.

Quantum particles on a lattice with competing long-range interactions are ubiquitous in physics; transition metal oxides, layered molecular crystals and trapped-ion arrays are a few examples. In the strongly interacting regime, these systems often show a rich variety of quantum many-body ground states that challenge theory. The emergence of transition metal dichalcogenide moiré superlattices provides a highly controllable platform in which to study long-range electronic correlations.