43 research outputs found
Morlet wavelets in quantum mechanics
Wavelets offer significant advantages for the analysis of problems in quantum
mechanics. Because wavelets are localized in both time and frequency they avoid
certain subtle but potentially fatal conceptual errors that can result from the
use of plane wave or delta function decomposition. Morlet wavelets are
particularly well-suited for this work: as Gaussians, they have a simple
analytic form and they work well with Feynman path integrals. To take full
advantage of Morlet wavelets we need an explicit form for the inverse Morlet
transform and a manifestly covariant form for the four-dimensional Morlet
wavelet. We supply both here.Comment: 17 pages, 2 figure
Bayesian and Frequentist Semantics for Common Variations of Differential Privacy: Applications to the 2020 Census
The purpose of this paper is to guide interpretation of the semantic privacy
guarantees for some of the major variations of differential privacy, which
include pure, approximate, R\'enyi, zero-concentrated, and differential
privacy. We interpret privacy-loss accounting parameters, frequentist
semantics, and Bayesian semantics (including new results). The driving
application is the interpretation of the confidentiality protections for the
2020 Census Public Law 94-171 Redistricting Data Summary File released August
12, 2021, which, for the first time, were produced with formal privacy
guarantees