Bayesian Hyperbolic Multidimensional Scaling

Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold representing similarity. We propose a Bayesian approach to multidimensional scaling when the low-dimensional manifold is hyperbolic. Using hyperbolic space facilitates representing tree-like structures common in many settings (e.g. text or genetic data with hierarchical structure). A Bayesian approach provides regularization that minimizes the impact of measurement error in the observed data and assesses uncertainty. We also propose a case-control likelihood approximation that allows for efficient sampling from the posterior distribution in larger data settings, reducing computational complexity from approximatelyO(n2)to O(n). We evaluate the proposed method against state-of-the-art alternatives using simulations, canonical reference datasets, Indian village network data, and human gene expression data. Code to reproduce the result in the paper is available athttps://github.com/peterliu599/BHMDS.</p

Fundamental Role of Oxygen Stoichiometry in Controlling the Band Gap and Reactivity of Cupric Oxide Nanosheets

CuO is a nonhazardous, earth-abundant material that has exciting potential for use in solar cells, photocatalysis, and other optoelectronic applications. While progress has been made on the characterization of properties and reactivity of CuO, there remains significant controversy on how to control the precise band gap by tuning conditions of synthetic methods. Here, we combine experimental and theoretical methods to address the origin of the wide distribution of reported band gaps for CuO nanosheets. We establish reaction conditions to control the band gap and reactivity via a high-temperature treatment in an oxygen-rich environment. SEM, TEM, XRD, and BET physisorption reveals little to no change in nanostructure, crystal structure, or surface area. In contrast, UV–vis spectroscopy shows a modulation in the material band gap over a range of 330 meV. A similar trend is found in H₂ temperature-programmed reduction where peak H₂ consumption temperature decreases with treatment. Calculations of the density of states show that increasing the oxygen to copper coverage ratio of the surface accounts for most of the observed changes in the band gap. An oxygen exchange mechanism, supported by ¹⁸O₂ temperature-programmed oxidation, is proposed to be responsible for changes in the CuO nanosheet oxygen to copper stoichiometry. The changes induced by oxygen depletion/deposition serve to explain discrepancies in the band gap of CuO, as reported in the literature, as well as dramatic differences in catalytic performance