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Abstract We calculate the single-particle excitation spectrum and the Landau liquid parameters for the archetypal model of solids, the three-dimensional uniform electron gas, with the variational diagrammatic Monte Carlo method, which gives numerically controlled results without systematic error. In the metallic range of density, we establish benchmark values for the wave-function renormalization factor Z , the effective mass $$m^*/m$$ m ∗ / m , and the Landau parameters $$F_0^s$$ F 0 s and $$F_0^a$$ F 0 a with unprecedented accuracy, and we resolve the long-standing puzzle of non-monotonic dependence of mass on density. We also exclude the possibility that experimentally measured large reduction of bandwidth in Na metal can originate from the charge and spin fluctuations contained in the model of the uniform electron gas.

Compositional data reside in a simplex and measure fractions or proportions of parts to a whole. Most existing regression methods for such data rely on log‐ratio transformations that are inadequate or inappropriate in modeling high‐dimensional data with excessive zeros and hierarchical structures. Moreover, such models usually lack a straightforward interpretation due to the interrelation between parts of a composition. We develop a novelrelative‐shiftregression framework that directly uses proportions as predictors. The new framework provides a paradigm shift for regression analysis with compositional predictors and offers a superior interpretation of how shifting concentration between parts affects the response. New equi‐sparsity and tree‐guided regularization methods and an efficient smoothing proximal gradient algorithm are developed to facilitate feature aggregation and dimension reduction in regression. A unified finite‐sample prediction error bound is derived for the proposed regularized estimators. We demonstrate the efficacy of the proposed methods in extensive simulation studies and a real gut microbiome study. Guided by the taxonomy of the microbiome data, the framework identifies important taxa at different taxonomic levels associated with the neurodevelopment of preterm infants.

Macroions, as soluble ions with a size on the nanometer scale, show unique solution behavior different from those of simple ions and large colloidal suspensions. In macroionic solutions, the counterions are known to be important and wellexplored. However, the role of co-ions (ions carrying the same type of charge as the macroions) is often ignored. Here, through experimental and simulation studies, we demonstrate the role of coions as a function of co-ion size on their interaction with the macroions (using {Mo72Fe30} and {SrPd12} as models) and the related self-assembly into blackberry-type structures in dilute solutions. Several regimes of unique co-ion effects are clearly identified: small ions (halides, oxoacid ions), subnanometer-scaled bulky ions (lacunary Keggin and dodecaborate ions), and those with sizes comparable to the macroions. Small co-ions have no observable effect on the self-assembly of fully hydrophilic {Mo72Fe30}, while due to hydrophobic interaction and intermolecular hydrogen bonds, the small co-ions show influences on the self-assembly of hydrophobic {SrPd12}. Subnanometer ions, a.k.a. “superchaotropic ions”, are still too small to assemble into a blackberry by themselves, but they can coassemble with the macroions, showing a strong interaction with the macroionic system. When the co-ion size is comparable to that of the macroions,more »they assemble independently instead of assembling with the macroions, leading to the previously reported unique self-recognition phenomenon for macroions.« less