Asymptotics of Bayesian Error Probability and 2D Pair Superresolution

This paper employs a recently developed asymptotic Bayesian multi-hypothesis testing (MHT) error analysis to treat the problem of superresolution imaging of a pair of closely spaced, equally bright point sources. The analysis exploits the notion of the minimum probability of error (MPE) in discriminating between two competing equi-probable hypotheses, a single point source of a certain brightness at the origin vs. a pair of point sources, each of half the brightness of the single source and located symmetrically about the origin, as the distance between the source pair is changed. For a Gaussian point-spread function (PSF), the analysis makes predictions on the scaling of the minimum source strength, expressed in units of photon number, required to disambiguate the pair as a function of their separation, in both the signal-dominated and background-dominated regimes. Certain logarithmic corrections to the quartic scaling of the minimum source strength with respect to the degree of superresolution characterize the signal-dominated regime, while the scaling is purely quadratic in the background-dominated regime. For the Gaussian PSF, general results for arbitrary strengths of the signal, background, and sensor noise levels are also presented.Comment: Submitted to Optics Express, March 18, 201

More Color More Pride: Addressing Structural Barriers to Interracial LGBTQ Loving

Through an examination of State-supported racial structures, this Essay illustrates that even after the legalization of interracial and same-sex marriages, the State’s control over housing, education, and employment prospects impedes the formation of interracial LGBTQ relationships. This Essay suggests that reducing residential segregation can be a first step in dismantling structural barriers to interracial LGBTQ loving, as truly integrated housing would increase cross-racial contact, lead to better educational and employment outcomes, and give LGBTQ people of color a chance to improve their social capital. This, together with altering how issues of race are framed within the LGBTQ community, will help dispel negative racial stereotypes and facilitate the formation of interracial LGBTQ relationships