10,785 research outputs found
Number-resolved master equation approach to quantum measurement and quantum transport
In addition to the well-known Landauer-Buttiker scattering theory and the
nonequilibrium Green's function technique for mesoscopic transports, an
alternative (and very useful) scheme is quantum master equation approach. In
this article, we review the particle-number (n)-resolved master equation (n-ME)
approach and its systematic applications in quantum measurement and quantum
transport problems. The n-ME contains rich dynamical information, allowing
efficient study of topics such as shot noise and full counting statistics
analysis. Moreover, we also review a newly developed master equation approach
(and its n-resolved version) under self-consistent Born approximation. The
application potential of this new approach is critically examined via its
ability to recover the exact results for noninteracting systems under arbitrary
voltage and in presence of strong quantum interference, and the challenging
non-equilibrium Kondo effect.Comment: 24 pages, 16 figures; review article to appear in Frontiers of
Physic
Masses of doubly heavy baryons in the Bethe-Salpeter equation approach
A doubly heavy baryon can be regarded as composed of a heavy diquark and a
light quark. In this picture, we study the masses of the doubly heavy diquarkes
in the Bethe-Salpeter (BS) formalism first, which are then used as one of the
inputs in studying the masses of the doubly heavy baryons in the quark-diquark
model. We establish the BS equations for both the heavy diquarks and the heavy
baryons with and without taking the heavy quark limit, respectively. These
equations are solved numerically with the kernel containing the scalar
confinement and one-gluon-exchange terms. The mass of the doubly charmed baryon
is obtained in both approaches,
() under the heavy quark limit, for
and for without taking the
heavy quark limit. The masses of , ,
, , ,
and are also predicted in the
same way. We find that the corrections to the results in the heavy quark limit
are about for the masses of the doubly heavy
baryons
An Orthogonal Discrete Auditory Transform
An orthogonal discrete auditory transform (ODAT) from sound signal to
spectrum is constructed by combining the auditory spreading matrix of Schroeder
et al and the time one map of a discrete nonlocal Schr\"odinger equation.
Thanks to the dispersive smoothing property of the Schr\"odinger evolution,
ODAT spectrum is smoother than that of the discrete Fourier transform (DFT)
consistent with human audition. ODAT and DFT are compared in signal denoising
tests with spectral thresholding method. The signals are noisy speech segments.
ODAT outperforms DFT in signal to noise ratio (SNR) when the noise level is
relatively high.Comment: 11 pages, 4 figure
Global well-posedness and multi-tone solutions of a class of nonlinear nonlocal cochlear models in hearing
We study a class of nonlinear nonlocal cochlear models of the transmission
line type, describing the motion of basilar membrane (BM) in the cochlea. They
are damped dispersive partial differential equations (PDEs) driven by time
dependent boundary forcing due to the input sounds. The global well-posedness
in time follows from energy estimates. Uniform bounds of solutions hold in case
of bounded nonlinear damping. When the input sounds are multi-frequency tones,
and the nonlinearity in the PDEs is cubic, we construct smooth quasi-periodic
solutions (multi-tone solutions) in the weakly nonlinear regime, where new
frequencies are generated due to nonlinear interaction. When the input is two
tones at frequencies , (), and high enough intensities,
numerical results illustrate the formation of combination tones at
and , in agreement with hearing experiments. We visualize the
frequency content of solutions through the FFT power spectral density of
displacement at selected spatial locations on BM.Comment: 23 pages,4 figure
Signal extraction approach for sparse multivariate response regression
In this paper, we consider multivariate response regression models with high
dimensional predictor variables. One way to model the correlation among the
response variables is through the low rank decomposition of the coefficient
matrix, which has been considered by several papers for the high dimensional
predictors. However, all these papers focus on the singular value decomposition
of the coefficient matrix. Our target is the decomposition of the coefficient
matrix which leads to the best lower rank approximation to the regression
function, the signal part in the response. Given any rank, this decomposition
has nearly the smallest expected prediction error among all approximations to
the the coefficient matrix with the same rank. To estimate the decomposition,
we formulate a penalized generalized eigenvalue problem to obtain the first
matrix in the decomposition and then obtain the second one by a least squares
method. In the high-dimensional setting, we establish the oracle inequalities
for the estimates. Compared to the existing theoretical results, we have less
restrictions on the distribution of the noise vector in each observation and
allow correlations among its coordinates. Our theoretical results do not depend
on the dimension of the multivariate response. Therefore, the dimension is
arbitrary and can be larger than the sample size and the dimension of the
predictor. Simulation studies and application to real data show that the
proposed method has good prediction performance and is efficient in dimension
reduction for various reduced rank models.Comment: 28 pages, 4 figure
Sparse Fisher's discriminant analysis with thresholded linear constraints
Various regularized linear discriminant analysis (LDA) methods have been
proposed to address the problems of the classic methods in high-dimensional
settings. Asymptotic optimality has been established for some of these methods
in high dimension when there are only two classes. A major difficulty in
proving asymptotic optimality for multiclass classification is that the
classification boundary is typically complicated and no explicit formula for
classification error generally exists when the number of classes is greater
than two. For the Fisher's LDA, one additional difficulty is that the
covariance matrix is also involved in the linear constraints. The main purpose
of this paper is to establish asymptotic consistency and asymptotic optimality
for our sparse Fisher's LDA with thresholded linear constraints in the
high-dimensional settings for arbitrary number of classes. To address the first
difficulty above, we provide asymptotic optimality and the corresponding
convergence rates in high-dimensional settings for a large family of linear
classification rules with arbitrary number of classes, and apply them to our
method. To overcome the second difficulty, we propose a thresholding approach
to avoid the estimate of the covariance matrix. We apply the method to the
classification problems for multivariate functional data through the wavelet
transformations
An Invertible Discrete Auditory Transform
A discrete auditory transform (DAT) from sound signal to spectrum is
presented and shown to be invertible in closed form. The transform preserves
energy, and its spectrum is smoother than that of the discrete Fourier
transform (DFT) consistent with human audition. DAT and DFT are compared in
signal denoising tests with spectral thresholding method. The signals are noisy
speech segments. It is found that DAT can gain 5 to 7 decibel (dB) in signal to
noise ratio (SNR) over DFT except when the noise level is relatively low.Comment: 13 pages, 5 figure
A Many to One Discrete Auditory Transform
A many to one discrete auditory transform is presented to map a sound signal
to a perceptually meaningful spectrum on the scale of human auditory filter
band widths (critical bands). A generalized inverse is constructed in closed
analytical form, preserving the band energy and band signal to noise ratio of
the input sound signal. The forward and inverse transforms can be implemented
in real time. Experiments on speech and music segments show that the inversion
gives a perceptually equivalent though mathematically different sound from the
input.Comment: 23 pages, 7 figures, 2 table
Asymptotic optimality of sparse linear discriminant analysis with arbitrary number of classes
Many sparse linear discriminant analysis (LDA) methods have been proposed to
overcome the major problems of the classic LDA in high-dimensional settings.
However, the asymptotic optimality results are limited to the case that there
are only two classes, which is due to the fact that the classification boundary
of LDA is a hyperplane and explicit formulas exist for the classification error
in this case. In the situation where there are more than two classes, the
classification boundary is usually complicated and no explicit formulas for the
classification errors exist. In this paper, we consider the asymptotic
optimality in the high-dimensional settings for a large family of linear
classification rules with arbitrary number of classes under the situation of
multivariate normal distribution. Our main theorem provides easy-to-check
criteria for the asymptotic optimality of a general classification rule in this
family as dimensionality and sample size both go to infinity and the number of
classes is arbitrary. We establish the corresponding convergence rates. The
general theory is applied to the classic LDA and the extensions of two recently
proposed sparse LDA methods to obtain the asymptotic optimality. We conduct
simulation studies on the extended methods in various settings
Volume growth, eigenvalue and compactness for self-shrinkers
In this paper, we show an optimal volume growth for self-shrinkers, and
estimate a lower bound of the first eigenvalue of operator on
self-shrinkers, inspired by the first eigenvalue conjecture on minimal
hypersurfaces in the unit sphere by Yau \cite{SY}. By the eigenvalue estimates,
we can prove a compactness theorem on a class of compact self-shrinkers in
\ir{3} obtained by Colding-Minicozzi under weaker conditions.Comment: 17 page
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