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  3. Uniformity testing is one of the most well-studied problems in property testing, with many known test statistics, including ones based on counting collisions, singletons, and the empirical TV distance. It is known that the optimal sample complexity to distinguish the uniform distribution on m elements from any ϵ-far distribution with 1−δ probability is n=Θ(mlog(1/δ)√ϵ2+log(1/δ)ϵ2), which is achieved by the empirical TV tester. Yet in simulation, these theoretical analyses are misleading: in many cases, they do not correctly rank order the performance of existing testers, even in an asymptotic regime of all parameters tending to 0 or ∞. We explain thismore »discrepancy by studying the \emph{constant factors} required by the algorithms. We show that the collisions tester achieves a sharp maximal constant in the number of standard deviations of separation between uniform and non-uniform inputs. We then introduce a new tester based on the Huber loss, and show that it not only matches this separation, but also has tails corresponding to a Gaussian with this separation. This leads to a sample complexity of (1+o(1))mlog(1/δ)√ϵ2 in the regime where this term is dominant, unlike all other existing testers.« less
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  5. Bukiya, A. N. ; Dopico, A. M. (Ed.)
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  9. Abstract Nuclear reactions heat and cool the crust of accreting neutron stars and need to be understood to interpret observations of X-ray bursts and long-term cooling in transiently accreting systems. It was recently suggested that previously ignored neutron transfer reactions may play a significant role in the nuclear processes. We present results from full nuclear network calculations that now include these reactions and determine their impact on crust composition, crust impurity, heating, and cooling. We find that a large number of neutron transfer reactions indeed occur and impact crust models. In particular, we identify a new type of reaction cyclemore »that brings a pair of nuclei across the nuclear chart into equilibrium via alternating neutron capture and neutron release, interspersed with a neutron transfer. While neutron transfer reactions lead to changes in crust model predictions and need to be considered in future studies, previous conclusions concerning heating, cooling, and compositional evolution are remarkably robust.« less
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