241,258 research outputs found
Structured Matrix Completion with Applications to Genomic Data Integration
Matrix completion has attracted significant recent attention in many fields
including statistics, applied mathematics and electrical engineering. Current
literature on matrix completion focuses primarily on independent sampling
models under which the individual observed entries are sampled independently.
Motivated by applications in genomic data integration, we propose a new
framework of structured matrix completion (SMC) to treat structured missingness
by design. Specifically, our proposed method aims at efficient matrix recovery
when a subset of the rows and columns of an approximately low-rank matrix are
observed. We provide theoretical justification for the proposed SMC method and
derive lower bound for the estimation errors, which together establish the
optimal rate of recovery over certain classes of approximately low-rank
matrices. Simulation studies show that the method performs well in finite
sample under a variety of configurations. The method is applied to integrate
several ovarian cancer genomic studies with different extent of genomic
measurements, which enables us to construct more accurate prediction rules for
ovarian cancer survival.Comment: Accepted for publication in Journal of the American Statistical
Associatio
A Note on Thermodynamics of Black Holes in Lovelock Gravity
The Lovelock gravity consists of the dimensionally extended Euler densities.
The geometry and horizon structure of black hole solutions could be quite
complicated in this gravity, however, we find that some thermodynamic
quantities of the black holes like the mass, Hawking temperature and entropy,
have simple forms expressed in terms of horizon radius. The case with black
hole horizon being a Ricci flat hypersurface is particularly simple. In that
case the black holes are always thermodynamically stable with a positive heat
capacity and their entropy still obeys the area formula, which is no longer
valid for black holes with positive or negative constant curvature horizon
hypersurface. In addition, for black holes in the gravity theory of Ricci
scalar plus a -dimensional Euler density with a positive coefficient,
thermodynamically stable small black holes always exist in dimensions,
which are absent in the case without the Euler density term, while the
thermodynamic properties of the black hole solutions with the Euler density
term are qualitatively similar to those of black holes without the Euler
density term as .Comment: Latex, 10 pages, v2: typos corrected, references added, to appear in
PL
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