46,829 research outputs found
Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy
We present a class of exact analytic and static, spherically symmetric black
hole solutions in the semi-classical Einstein equations with Weyl anomaly. The
solutions have two branches, one is asymptotically flat and the other
asymptotically de Sitter. We study thermodynamic properties of the black hole
solutions and find that there exists a logarithmic correction to the well-known
Bekenstein-Hawking area entropy. The logarithmic term might come from non-local
terms in the effective action of gravity theories. The appearance of the
logarithmic term in the gravity side is quite important in the sense that with
this term one is able to compare black hole entropy up to the subleading order,
in the gravity side and in the microscopic statistical interpretation side.Comment: Revtex, 10 pages. v2: minor changes and to appear in JHE
Thermodynamic Geometry and Critical Behavior of Black Holes
Based on the observations that there exists an analogy between the
Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) black holes and the van der
Waals-Maxwell liquid-gas system, in which a correspondence of variables is
, we study the Ruppeiner geometry, defined as
Hessian matrix of black hole entropy with respect to the internal energy (not
the mass) of black hole and electric potential (angular velocity), for the RN,
Kerr and RN-AdS black holes. It is found that the geometry is curved and the
scalar curvature goes to negative infinity at the Davies' phase transition
point for the RN and Kerr black holes.
Our result for the RN-AdS black holes is also in good agreement with the one
about phase transition and its critical behavior in the literature.Comment: Revtex, 18 pages including 4 figure
On adaptive estimation of linear functionals
Adaptive estimation of linear functionals over a collection of parameter
spaces is considered. A between-class modulus of continuity, a geometric
quantity, is shown to be instrumental in characterizing the degree of
adaptability over two parameter spaces in the same way that the usual modulus
of continuity captures the minimax difficulty of estimation over a single
parameter space. A general construction of optimally adaptive estimators based
on an ordered modulus of continuity is given. The results are complemented by
several illustrative examples.Comment: Published at http://dx.doi.org/10.1214/009053605000000633 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Nonquadratic estimators of a quadratic functional
Estimation of a quadratic functional over parameter spaces that are not
quadratically convex is considered. It is shown, in contrast to the theory for
quadratically convex parameter spaces, that optimal quadratic rules are often
rate suboptimal. In such cases minimax rate optimal procedures are constructed
based on local thresholding. These nonquadratic procedures are sometimes fully
efficient even when optimal quadratic rules have slow rates of convergence.
Moreover, it is shown that when estimating a quadratic functional nonquadratic
procedures may exhibit different elbow phenomena than quadratic procedures.Comment: Published at http://dx.doi.org/10.1214/009053605000000147 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Adaptive confidence balls
Adaptive confidence balls are constructed for individual resolution levels as
well as the entire mean vector in a multiresolution framework. Finite sample
lower bounds are given for the minimum expected squared radius for confidence
balls with a prespecified confidence level. The confidence balls are centered
on adaptive estimators based on special local block thresholding rules. The
radius is derived from an analysis of the loss of this adaptive estimator. In
addition adaptive honest confidence balls are constructed which have guaranteed
coverage probability over all of and expected squared radius
adapting over a maximum range of Besov bodies.Comment: Published at http://dx.doi.org/10.1214/009053606000000146 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Nonparametric estimation over shrinking neighborhoods: Superefficiency and adaptation
A theory of superefficiency and adaptation is developed under flexible
performance measures which give a multiresolution view of risk and bridge the
gap between pointwise and global estimation. This theory provides a useful
benchmark for the evaluation of spatially adaptive estimators and shows that
the possible degree of superefficiency for minimax rate optimal estimators
critically depends on the size of the neighborhood over which the risk is
measured. Wavelet procedures are given which adapt rate optimally for given
shrinking neighborhoods including the extreme cases of mean squared error at a
point and mean integrated squared error over the whole interval. These adaptive
procedures are based on a new wavelet block thresholding scheme which combines
both the commonly used horizontal blocking of wavelet coefficients (at the same
resolution level) and vertical blocking of coefficients (across different
resolution levels).Comment: Published at http://dx.doi.org/10.1214/009053604000000832 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
An adaptation theory for nonparametric confidence intervals
A nonparametric adaptation theory is developed for the construction of
confidence intervals for linear functionals. A between class modulus of
continuity captures the expected length of adaptive confidence intervals. Sharp
lower bounds are given for the expected length and an ordered modulus of
continuity is used to construct adaptive confidence procedures which are within
a constant factor of the lower bounds. In addition, minimax theory over
nonconvex parameter spaces is developed.Comment: Published at http://dx.doi.org/10.1214/009053604000000049 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Optimal adaptive estimation of a quadratic functional
Adaptive estimation of a quadratic functional over both Besov and balls
is considered. A collection of nonquadratic estimators are developed which have
useful bias and variance properties over individual Besov and balls. An
adaptive procedure is then constructed based on penalized maximization over
this collection of nonquadratic estimators. This procedure is shown to be
optimally rate adaptive over the entire range of Besov and balls in the
sense that it attains certain constrained risk bounds.Comment: Published at http://dx.doi.org/10.1214/009053606000000849 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Using reflections to explore student learning during the project component of an advanced laboratory course
We redesigned an advanced physics laboratory course to include a project
component. The intention was to address learning outcomes such as modeling,
design of experiments, teamwork, and developing technical skills in using
apparatus and analyzing data. The course included experimental labs in
preparation for a six-week team project in which students designed and
implemented a research experiment. The final assignment given to students was a
reflective essay, which asked students to discuss their learning and
satisfaction in doing the project. Qualitative analysis of the students'
reflections showed that the majority of the students reported satisfaction and
achievement, functional team dynamics, learning outcomes unique to this
experience, practicing modeling skills, and potential future improvements. We
suggest that reflections are useful as support for student learning as well as
in guiding curricular improvements. Our findings may be useful for other course
redesign initiatives incorporating project-based learning and student
reflections.Comment: This work was presented at the Physics Education Research Conference
held in Washington DC. from August 1-2, 201
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