1,931 research outputs found
Mesoscopic threshold detectors: Telegraphing the size of a fluctuation
We propose a two-terminal method to measure shot noise in mesoscopic systems
based on an instability in the current-voltage characteristic of an on-chip
detector. The microscopic noise drives the instability, which leads to random
switching of the current between two values, the telegraph process. In the
Gaussian regime, the shot noise power driving the instability may be extracted
from the I-V curve, with the noise power as a fitting parameter. In the
threshold regime, the extreme value statistics of the mesoscopic conductor can
be extracted from the switching rates, which reorganize the complete
information about the current statistics in an indirect way, "telegraphing" the
size of a fluctuation. We propose the use of a quantum double dot as a
mesoscopic threshold detector.Comment: 9 pages, 7 figures, published versio
Modeling association between DNA copy number and gene expression with constrained piecewise linear regression splines
DNA copy number and mRNA expression are widely used data types in cancer
studies, which combined provide more insight than separately. Whereas in
existing literature the form of the relationship between these two types of
markers is fixed a priori, in this paper we model their association. We employ
piecewise linear regression splines (PLRS), which combine good interpretation
with sufficient flexibility to identify any plausible type of relationship. The
specification of the model leads to estimation and model selection in a
constrained, nonstandard setting. We provide methodology for testing the effect
of DNA on mRNA and choosing the appropriate model. Furthermore, we present a
novel approach to obtain reliable confidence bands for constrained PLRS, which
incorporates model uncertainty. The procedures are applied to colorectal and
breast cancer data. Common assumptions are found to be potentially misleading
for biologically relevant genes. More flexible models may bring more insight in
the interaction between the two markers.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS605 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Phonon Rabi-assisted tunneling in diatomic molecules
We study electronic transport in diatomic molecules connected to metallic
contacts in the regime where both electron-electron and electron-phonon
interactions are important. We find that the competition between these
interactions results in unique resonant conditions for interlevel transitions
and polaron formation: the Coulomb repulsion requires additional energy when
electrons attempt phonon-assisted interlevel jumps between fully or partially
occupied levels. We apply the equations of motion approach to calculate the
electronic Green's functions. The density of states and conductance through the
system are shown to exhibit interesting Rabi-like splitting of Coulomb blockade
peaks and strong temperature dependence under the it interacting resonant
conditions.Comment: Updated version, 5 pages, 4 figures, to be published in Phys. Rev. B
on 9/1
Discovering Active Subspaces for High-Dimensional Computer Models
Dimension reduction techniques have long been an important topic in
statistics, and active subspaces (AS) have received much attention this past
decade in the computer experiments literature. The most common approach towards
estimating the AS is to use Monte Carlo with numerical gradient evaluation.
While sensible in some settings, this approach has obvious drawbacks. Recent
research has demonstrated that active subspace calculations can be obtained in
closed form, conditional on a Gaussian process (GP) surrogate, which can be
limiting in high-dimensional settings for computational reasons. In this paper,
we produce the relevant calculations for a more general case when the model of
interest is a linear combination of tensor products. These general equations
can be applied to the GP, recovering previous results as a special case, or
applied to the models constructed by other regression techniques including
multivariate adaptive regression splines (MARS). Using a MARS surrogate has
many advantages including improved scaling, better estimation of active
subspaces in high dimensions and the ability to handle a large number of prior
distributions in closed form. In one real-world example, we obtain the active
subspace of a radiation-transport code with 240 inputs and 9,372 model runs in
under half an hour
Normalized, Segmented or Called aCGH Data?
Array comparative genomic hybridization (aCGH) is a high-throughput lab technique to measure genome-wide chromosomal copy numbers. Data from aCGH experiments require extensive pre-processing, which consists of three steps: normalization, segmentation and calling. Each of these pre-processing steps yields a different data set: normalized data, segmented data, and called data. Publications using aCGH base their findings on data from all stages of the pre-processing. Hence, there is no consensus on which should be used for further down-stream analysis. This consensus is however important for correct reporting of findings, and comparison of results from different studies. We discuss several issues that should be taken into account when deciding on which data are to be used. We express the believe that called data are best used, but would welcome opposing views
A nonparametric control chart based on the Mann-Whitney statistic
Nonparametric or distribution-free charts can be useful in statistical
process control problems when there is limited or lack of knowledge about the
underlying process distribution. In this paper, a phase II Shewhart-type chart
is considered for location, based on reference data from phase I analysis and
the well-known Mann-Whitney statistic. Control limits are computed using
Lugannani-Rice-saddlepoint, Edgeworth, and other approximations along with
Monte Carlo estimation. The derivations take account of estimation and the
dependence from the use of a reference sample. An illustrative numerical
example is presented. The in-control performance of the proposed chart is shown
to be much superior to the classical Shewhart chart. Further
comparisons on the basis of some percentiles of the out-of-control conditional
run length distribution and the unconditional out-of-control ARL show that the
proposed chart is almost as good as the Shewhart chart for the normal
distribution, but is more powerful for a heavy-tailed distribution such as the
Laplace, or for a skewed distribution such as the Gamma. Interactive software,
enabling a complete implementation of the chart, is made available on a
website.Comment: Published in at http://dx.doi.org/10.1214/193940307000000112 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
The spectral condition number plot for regularization parameter evaluation
Abstract: Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that employs regularization to cope with the subsequent singularity of the sample covariance matrix. These estimators depend on a penalty parameter and choosing its value can be hard, in terms of being computationally unfeasible or tenable only for a restricted set of ridge-type estimators. Here we introduce a simple graphical tool, the spectral condition number plot, for informed heuristic penalty parameter assessment. The proposed tool is computationally friendly and can be employed for the full class of ridge-type covariance (precision) estimators
Resonant electron transmission through a finite quantum spin chain
Electron transport in a finite one dimensional quantum spin chain (with
ferromagnetic exchange) is studied within an exchange Hamiltonian. Spin
transfer coefficients strongly depend on the sign of the exchange
constant. For a ferromagnetic coupling, they exhibit a novel resonant pattern,
reflecting the salient features of the combined electron-spin system. Spin-flip
processes are inelastic and feasible at finite voltage or at finite
temperature.Comment: 4 pages including 4 .eps figure
Spin relaxation in a GaAs quantum dot embedded inside a suspended phonon cavity
The phonon-induced spin relaxation in a two-dimensional quantum dot embedded
inside a semiconductor slab is investigated theoretically. An enhanced
relaxation rate is found due to the phonon van Hove singularities. Oppositely,
a vanishing deformation potential may also result in a suppression of the spin
relaxation rate. For larger quantum dots, the interplay between the spin orbit
interaction and Zeeman levels causes the suppression of the relaxation at
several points. Furthermore, a crossover from confined to bulk-like systems is
obtained by varying the width of the slab.Comment: 5 pages, 4 figures, to apper in Phys. Rev. B (2006
- ā¦