546 research outputs found
Optimal query complexity for estimating the trace of a matrix
Given an implicit matrix with oracle access for any
, we study the query complexity of randomized algorithms for
estimating the trace of the matrix. This problem has many applications in
quantum physics, machine learning, and pattern matching. Two metrics are
commonly used for evaluating the estimators: i) variance; ii) a high
probability multiplicative-approximation guarantee. Almost all the known
estimators are of the form for being i.i.d. for some special distribution.
Our main results are summarized as follows. We give an exact characterization
of the minimum variance unbiased estimator in the broad class of linear
nonadaptive estimators (which subsumes all the existing known estimators). We
also consider the query complexity lower bounds for any (possibly nonlinear and
adaptive) estimators: (1) We show that any estimator requires
queries to have a guarantee of variance at most
. (2) We show that any estimator requires
queries to achieve a
-multiplicative approximation guarantee with probability at
least . Both above lower bounds are asymptotically tight.
As a corollary, we also resolve a conjecture in the seminal work of Avron and
Toledo (Journal of the ACM 2011) regarding the sample complexity of the
Gaussian Estimator.Comment: full version of the paper in ICALP 201
Observations of central toroidal rotation in ICRF heated Alcator C-Mod plasmas
AC02-78ET51013. Reproduction, translation, publication, use and disposal, in whole or in part by or for the United States government is permitted
Change in MRI synovitis correlates with change in pain following intra-articular steroid injection
Damped Bogoliubov excitations of a condensate interacting with a static thermal cloud
We calculate the damping of condensate collective excitations at finite
temperatures arising from the lack of equilibrium between the condensate and
thermal atoms. We neglect the non-condensate dynamics by fixing the thermal
cloud in static equilibrium. We derive a set of generalized Bogoliubov
equations for finite temperatures that contain an explicit damping term due to
collisional exchange of atoms between the two components. We have numerically
solved these Bogoliubov equations to obtain the temperature dependence of the
damping of the condensate modes in a harmonic trap. We compare these results
with our recent work based on the Thomas-Fermi approximation.Comment: 9 pages, 3 figures included. Submitted to PR
Theory of coherent Bragg spectroscopy of a trapped Bose-Einstein condensate
We present a detailed theoretical analysis of Bragg spectroscopy from a
Bose-Einstein condensate at T=0K. We demonstrate that within the linear
response regime, both a quantum field theory treatment and a meanfield
Gross-Pitaevskii treatment lead to the same value for the mean evolution of the
quasiparticle operators. The observable for Bragg spectroscopy experiments,
which is the spectral response function of the momentum transferred to the
condensate, can therefore be calculated in a meanfield formalism. We analyse
the behaviour of this observable by carrying out numerical simulations in
axially symmetric three-dimensional cases and in two dimensions. An approximate
analytic expression for the observable is obtained and provides a means for
identifying the relative importance of three broadening and shift mechanisms
(meanfield, Doppler, and finite pulse duration) in different regimes. We show
that the suppression of scattering at small values of q observed by
Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the
meanfield treatment, and can be interpreted in terms of the interference of the
u and v quasiparticle amplitudes. We also show that, contrary to the
assumptions of previous analyses, there is no regime for trapped condensates
for which the spectral response function and the dynamic structure factor are
equivalent. Our numerical calculations can also be performed outside the linear
response regime, and show that at large laser intensities a significant
decrease in the shift of the spectral response function can occur due to
depletion of the initial condensate.Comment: RevTeX4 format, 16 pages plus 7 eps figures; Update to published
version: minors changes and an additional figure. (To appear in Phys. Rev. A
Comparison of case note review methods for evaluating quality and safety in health care
Objectives: To determine which of two methods of case note review – holistic (implicit) and criterion-based (explicit) – provides the most useful and reliable information for quality and safety of care, and the level of agreement within and between groups of health-care professionals when they use the two methods to review the same record. To explore the process–outcome relationship between holistic and criterion-based quality-of-care measures and hospital-level outcome indicators. © 2010 Crown Copyrigh
Finite temperature effects on the collapse of trapped Bose-Fermi mixtures
By using the self-consistent Hartree-Fock-Bogoliubov-Popov theory, we present
a detailed study of the mean-field stability of spherically trapped Bose-Fermi
mixtures at finite temperature. We find that, by increasing the temperature,
the critical particle number of bosons (or fermions) and the critical
attractive Bose-Fermi scattering length increase, leading to a significant
stabilization of the mixture.Comment: 5 pages, 4 figures; minor changes, proof version, to appear in Phys.
Rev. A (Nov. 1, 2003
Thermodynamics of an interacting trapped Bose-Einstein gas in the classical field approximation
We present a convenient technique describing the condensate in dynamical
equilibrium with the thermal cloud, at temperatures close to the critical one.
We show that the whole isolated system may be viewed as a single classical
field undergoing nonlinear dynamics leading to a steady state. In our procedure
it is the observation process and the finite detection time that allow for
splitting the system into the condensate and the thermal cloud.Comment: 4 pages, 4 eps figures, final versio
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