The atomic cluster expansion (ACE) was proposed recently as a new class of data-driven interatomic potentials with formally complete basis set. Since the development any potential requires careful selection training data and thorough validation, an automation construction dataset well indication model's uncertainty are highly desirable. In this work, we compare performance two approaches for AC...

We present a new implementation of the cluster expansion formalism. The new code, UNiversal CLuster Expansion (UNCLE), consolidates recent advances in the methodology and leverages one new development in the formalism itself. As a core goal, the package reduces the need for user intervention, automating the method to reduce human error and judgment. The package extends standard cluster expansio...

We have seen the Lovász Local Lemma and its stronger variant, Shearer’s Lemma, which is unfortunately quite unwieldy in applications. Quite recently, researchers in mathematical physics discovered an intermediate form of the lemma, which seems to give results close to Shearer’s Lemma but it is much more easily applicable. First let us review a connection between Shearer’s Lemma and statistical ...

The boxdot conjecture asserts that every normal modal logic that faithfully interprets T by the well-known boxdot translation is in fact included in T. We confirm that the conjecture is true. More generally, we present a simple semantic condition on modal logics L0 which ensures that the largest logic where L0 embeds faithfully by the boxdot translation is L0 itself. In particular, this natural...

The Glimm-Jaffe-Spencer cluster expansion from constructive quantum field theory is adapted to treat quantum statistical mechanical systems of particles interacting by finite range potentials. The Hamiltonian H 0 + Vneed be stable in the extended sense that Ho +4V+BN>O for some B. In this situation, with a mild technical condition on the potentials, the cluster expansion converges and the infin...

The observed properties of young star clusters, such as the core radius and luminosity profile, change rapidly during the early evolution of the clusters. Here we present observations of 6 young clusters in M51 where we derive their sizes using HST imaging and ages using deep Gemini-North spectroscopy. We find evidence for a rapid expansion of the cluster cores during the first 20 Myr of their ...