Geometry optimization of atomic structures is a common and crucial task in computational chemistry and materials design. Following the learning to optimize paradigm, we propose a new multi-agent reinforcement learning method called Multi-Agent Crystal Structure optimization (MACS) to address the problem of periodic crystal structure optimization. MACS treats geometry optimization as a partially observable Markov game in which atoms are agents that adjust their positions to collectively discover a stable configuration. We train MACS across various compositions of reported crystalline materials to obtain a policy that successfully optimizes structures from the training compositions as well as structures of larger sizes and unseen compositions, confirming its excellent scalability and zero-shot transferability. We benchmark our approach against a broad range of state-of-the-art optimization methods and demonstrate that MACS optimizes periodic crystal structures significantly faster, with fewer energy calculations, and the lowest failure rate.

Establishing suitable in vitro culture conditions for microorganisms is crucial for dissecting their biology and empowering potential applications. However, a significant number of bacterial and fungal species, including Pneumocystis jirovecii, remain unculturable, hampering research efforts. P. jirovecii is a deadly pathogen of humans that causes life-threatening pneumonia in immunocompromised individuals and transplant patients. Despite the major impact of Pneumocystis on human health, limited progress has been made in dissecting the pathobiology of this fungus. This is largely due to the fact that its experimental dissection has been constrained by the inability to culture the organism in vitro. We present a comprehensive in silico genome-scale metabolic model of Pneumocystis growth and metabolism, to identify metabolic requirements and imbalances that hinder growth in vitro. We utilise recently published genome data and available information in the literature as well as bioinformatics and software tools to develop and validate the model. In addition, we employ relaxed Flux Balance Analysis and Reinforcement Learning approaches to make predictions regarding metabolic fluxes and to identify critical components of the Pneumocystis growth medium. Our findings offer insights into the biology of Pneumocystis and provide a novel strategy to overcome the longstanding challenge of culturing this pathogen in vitro.

A set S of Boolean points is a specifying set for a threshold function f if the only threshold function consistent with f on S is f itself. The minimal cardinality of a specifying set for f is the specification number of f and it is never smaller than n+1 for a function with n relevant variables. In the present paper, we develop an inductive approach to describing the set of Boolean threshold functions with minimum specification number by means of operations that allow us to extend functions of n variables in this set to functions of n+1 variables.

An extremal point of a positive threshold Boolean function $f$ is either a maximal zero or a minimal one. It is known that if $f$ depends on all its variables, then the set of its extremal points completely specifies $f$ within the universe of threshold functions. However, in some cases, $f$ can be specified by a smaller set. The minimum number of points in such a set is the specification number of $f$. Hu (1965) showed that the specification number of a threshold function of $n$ variables is at least $n+1$. Anthony et al. (1995) proved that this bound is attained for nested functions and conjectured that for all other threshold functions the specification number is strictly greater than $n+1$. In the present paper, we resolve this conjecture negatively by exhibiting threshold Boolean functions of $n$ variables, which are non-nested and for which the specification number is $n+1$. On the other hand, we show that the set of extremal points satisfies the statement of the conjecture, i.e.~a positive threshold Boolean function depending on all its $n$ variables has $n+1$ extremal points if and only if it is nested. To prove this, we reveal an underlying structure of the set of extremal points.