Parity-expanded variational analysis for non-zero momentum

In recent years, the use of variational analysis techniques in lattice QCD has been demonstrated to be successful in the investigation of the rest-mass spectrum of many hadrons. However, due to parity-mixing, more care must be taken for investigations of boosted states to ensure that the projected correlation functions provided by the variational analysis correspond to the same states at zero momentum. In this paper we present the Parity-Expanded Variational Analysis (PEVA) technique, a novel method for ensuring the successful and consistent isolation of boosted baryons through a parity expansion of the operator basis used to construct the correlation matrix.Comment: 9 pages, 3 figures, 1 tabl

Variational Analysis of Constrained M-Estimators

We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the framework addresses situations where the class of functions is complex involving information and assumptions about shape, pointwise bounds, location of modes, height at modes, location of level-sets, values of moments, size of subgradients, continuity, distance to a "prior" function, multivariate total positivity, and any combination of the above. The class might be engineered to perform well in a specific setting even in the presence of little data. The framework views the class of functions as a subset of a particular metric space of upper semicontinuous functions under the Attouch-Wets distance. In addition to allowing a systematic treatment of numerous M-estimators, the framework yields consistency of plug-in estimators of modes of densities, maximizers of regression functions, level-sets of classifiers, and related quantities, and also enables computation by means of approximating parametric classes. We establish consistency through a one-sided law of large numbers, here extended to sieves, that relaxes assumptions of uniform laws, while ensuring global approximations even under model misspecification