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Cadmium and Selenate Exposure Affects the Honey Bee Microbiome and Metabolome, and Bee-Associated Bacteria Show Potential for Bioaccumulation
Ridge Fusion in Statistical Learning
We propose a penalized likelihood method to jointly estimate multiple
precision matrices for use in quadratic discriminant analysis and model based
clustering. A ridge penalty and a ridge fusion penalty are used to introduce
shrinkage and promote similarity between precision matrix estimates. Block-wise
coordinate descent is used for optimization, and validation likelihood is used
for tuning parameter selection. Our method is applied in quadratic discriminant
analysis and semi-supervised model based clustering.Comment: 24 pages and 9 tables, 3 figure
Instability of Extremal Relativistic Charged Spheres
With the question, ``Can relativistic charged spheres form extremal black
holes?" in mind, we investigate the properties of such spheres from a classical
point of view. The investigation is carried out numerically by integrating the
Oppenheimer-Volkov equation for relativistic charged fluid spheres and finding
interior Reissner-Nordstr\"om solutions for these objects. We consider both
constant density and adiabatic equations of state, as well as several possible
charge distributions, and examine stability by both a normal mode and an energy
analysis. In all cases, the stability limit for these spheres lies between the
extremal () limit and the black hole limit (). That is, we find
that charged spheres undergo gravitational collapse before they reach ,
suggesting that extremal Reissner-Nordtr\"om black holes produced by collapse
are ruled out. A general proof of this statement would support a strong form of
the cosmic censorship hypothesis, excluding not only stable naked
singularities, but stable extremal black holes. The numerical results also
indicate that although the interior mass-energy obeys the usual stability limit for the Schwarzschild interior solution, the gravitational
mass does not. Indeed, the stability limit approaches as .
In the Appendix we also argue that Hawking radiation will not lead to an
extremal Reissner-Nordstr\"om black hole. All our results are consistent with
the third law of black hole dynamics, as currently understood
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