30,290 research outputs found
A nonparametric empirical Bayes approach to covariance matrix estimation
We propose an empirical Bayes method to estimate high-dimensional covariance
matrices. Our procedure centers on vectorizing the covariance matrix and
treating matrix estimation as a vector estimation problem. Drawing from the
compound decision theory literature, we introduce a new class of decision rules
that generalizes several existing procedures. We then use a nonparametric
empirical Bayes g-modeling approach to estimate the oracle optimal rule in that
class. This allows us to let the data itself determine how best to shrink the
estimator, rather than shrinking in a pre-determined direction such as toward a
diagonal matrix. Simulation results and a gene expression network analysis
shows that our approach can outperform a number of state-of-the-art proposals
in a wide range of settings, sometimes substantially.Comment: 20 pages, 4 figure
Coupling of pion condensate, chiral condensate and Polyakov loop in an extended NJL model
The Nambu Jona-Lasinio model with a Polyakov loop is extended to finite
isospin chemical potential case, which is characterized by simultaneous
coupling of pion condensate, chiral condensate and Polyakov loop. The pion
condensate, chiral condensate and the Polyakov loop as functions of temperature
and isospin chemical potential are investigated by minimizing the thermodynamic
potential of the system. The resulting phase diagram is studied
with emphasis on the critical point and Polyakov loop dynamics. The tricritical
point for the pion superfluidity phase transition is confirmed and the phase
transition for isospin symmetry restoration in high isospin chemical potential
region perfectly coincides with the crossover phase transition for Polyakov
loop. These results are in agreement with the Lattice QCD data.Comment: 15pages, 8 figure
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