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  1. Free, publicly-accessible full text available January 1, 2023
  2. X-ray diffraction indicates that the structure of the recently discovered carbonaceous sulfur hydride (C-S-H) room temperature superconductor is derived from previously established van der Waals compounds found in the H2S-H2 and CH4-H2 systems. Crystals of the superconducting phase were produced by a photochemical synthesis technique leading to the superconducting critical temperature Tc of 288 K at 267 GPa. X-ray diffraction patterns measured from 124 to 178 GPa, within the pressure range of the superconducting phase, are consistent with an orthorhombic structure derived from the Al2Cu-type determined for (H2S)2H2 and (CH4)2H2 that differs from those predicted and observed for the S-H system to these pressures. The formation and stability of the C-S-H compound can be understood in terms of the close similarity in effective volumes of the H2S and CH4 components, and denser carbon-bearing S-H phases may form at higher pressures. The results are crucial for understanding the very high superconducting Tc found in the C-S-H system at megabar pressures.
  3. As machine learning has become more prevalent, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates over-representation in traditional clustering. In this paper we extend this notion to hierarchical clustering, where the goal is to recursively partition the data to optimize a specific objective. For various natural objectives, we obtain simple, efficient algorithms to find a provably good fair hierarchical clustering. Empirically, we show that our algorithms can find a fair hierarchical clustering, with only a negligible loss in the objective.