16,363 research outputs found
Macroscopic Resonant Tunneling in the Presence of Low Frequency Noise
We develop a theory of macroscopic resonant tunneling of flux in a
double-well potential in the presence of realistic flux noise with significant
low-frequency component. The rate of incoherent flux tunneling between the
wells exhibits resonant peaks, the shape and position of which reflect
qualitative features of the noise, and can thus serve as a diagnostic tool for
studying the low-frequency flux noise in SQUID qubits. We show, in particular,
that the noise-induced renormalization of the first resonant peak provides
direct information on the temperature of the noise source and the strength of
its quantum component.Comment: 4 pages, 1 figur
A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation
Approximate Bayesian computation (ABC) methods make use of comparisons
between simulated and observed summary statistics to overcome the problem of
computationally intractable likelihood functions. As the practical
implementation of ABC requires computations based on vectors of summary
statistics, rather than full data sets, a central question is how to derive
low-dimensional summary statistics from the observed data with minimal loss of
information. In this article we provide a comprehensive review and comparison
of the performance of the principal methods of dimension reduction proposed in
the ABC literature. The methods are split into three nonmutually exclusive
classes consisting of best subset selection methods, projection techniques and
regularization. In addition, we introduce two new methods of dimension
reduction. The first is a best subset selection method based on Akaike and
Bayesian information criteria, and the second uses ridge regression as a
regularization procedure. We illustrate the performance of these dimension
reduction techniques through the analysis of three challenging models and data
sets.Comment: Published in at http://dx.doi.org/10.1214/12-STS406 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Attack Detection in Sensor Network Target Localization Systems with Quantized Data
We consider a sensor network focused on target localization, where sensors
measure the signal strength emitted from the target. Each measurement is
quantized to one bit and sent to the fusion center. A general attack is
considered at some sensors that attempts to cause the fusion center to produce
an inaccurate estimation of the target location with a large mean-square-error.
The attack is a combination of man-in-the-middle, hacking, and spoofing attacks
that can effectively change both signals going into and coming out of the
sensor nodes in a realistic manner. We show that the essential effect of
attacks is to alter the estimated distance between the target and each attacked
sensor to a different extent, giving rise to a geometric inconsistency among
the attacked and unattacked sensors. Hence, with the help of two secure
sensors, a class of detectors are proposed to detect the attacked sensors by
scrutinizing the existence of the geometric inconsistency. We show that the
false alarm and miss probabilities of the proposed detectors decrease
exponentially as the number of measurement samples increases, which implies
that for sufficiently large number of samples, the proposed detectors can
identify the attacked and unattacked sensors with any required accuracy
Testing the Structure of a Gaussian Graphical Model with Reduced Transmissions in a Distributed Setting
Testing a covariance matrix following a Gaussian graphical model (GGM) is
considered in this paper based on observations made at a set of distributed
sensors grouped into clusters. Ordered transmissions are proposed to achieve
the same Bayes risk as the optimum centralized energy unconstrained approach
but with fewer transmissions and a completely distributed approach. In this
approach, we represent the Bayes optimum test statistic as a sum of local test
statistics which can be calculated by only utilizing the observations available
at one cluster. We select one sensor to be the cluster head (CH) to collect and
summarize the observed data in each cluster and intercluster communications are
assumed to be inexpensive. The CHs with more informative observations transmit
their data to the fusion center (FC) first. By halting before all transmissions
have taken place, transmissions can be saved without performance loss. It is
shown that this ordering approach can guarantee a lower bound on the average
number of transmissions saved for any given GGM and the lower bound can
approach approximately half the number of clusters when the minimum eigenvalue
of the covariance matrix under the alternative hypothesis in each cluster
becomes sufficiently large
Target Localization Accuracy Gain in MIMO Radar Based Systems
This paper presents an analysis of target localization accuracy, attainable
by the use of MIMO (Multiple-Input Multiple-Output) radar systems, configured
with multiple transmit and receive sensors, widely distributed over a given
area. The Cramer-Rao lower bound (CRLB) for target localization accuracy is
developed for both coherent and non-coherent processing. Coherent processing
requires a common phase reference for all transmit and receive sensors. The
CRLB is shown to be inversely proportional to the signal effective bandwidth in
the non-coherent case, but is approximately inversely proportional to the
carrier frequency in the coherent case. We further prove that optimization over
the sensors' positions lowers the CRLB by a factor equal to the product of the
number of transmitting and receiving sensors. The best linear unbiased
estimator (BLUE) is derived for the MIMO target localization problem. The
BLUE's utility is in providing a closed form localization estimate that
facilitates the analysis of the relations between sensors locations, target
location, and localization accuracy. Geometric dilution of precision (GDOP)
contours are used to map the relative performance accuracy for a given layout
of radars over a given geographic area.Comment: 36 pages, 5 figures, submitted to IEEE Transaction on Information
Theor
The Refractory-to-Ice Mass Ratio in Comets
We review the complex relationship between the dust-to-gas mass ratio usually estimated in the material lost by comets, and the Refractory-to-Ice mass ratio inside the nucleus, which constrains the origin of comets. Such a relationship is dominated by the mass transfer from the perihelion erosion to fallout over most of the nucleus surface. This makes the Refractory-to-Ice mass ratio inside the nucleus up to ten times larger than the dust-to-gas mass ratio in the lost material, because the lost material is missing most of the refractories which were inside the pristine nucleus before the erosion. We review the Refractory-to-Ice mass ratios available for the comet nuclei visited by space missions, and for the Kuiper Belt Objects with well defined bulk density, finding the 1-σ lower limit of 3. Therefore, comets and KBOs may have less water than CI-chondrites, as predicted by models of comet formation by the gravitational collapse of cm-sized pebbles driven by streaming instabilities in the protoplanetary disc
Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks
We present a lattice calculation of the hadronic vacuum polarization and the
lowest-order hadronic contribution to the muon anomalous magnetic moment, a_\mu
= (g-2)/2, using 2+1 flavors of improved staggered fermions. A precise fit to
the low-q^2 region of the vacuum polarization is necessary to accurately
extract the muon g-2. To obtain this fit, we use staggered chiral perturbation
theory, including the vector particles as resonances, and compare these to
polynomial fits to the lattice data. We discuss the fit results and associated
systematic uncertainties, paying particular attention to the relative
contributions of the pions and vector mesons. Using a single lattice spacing
ensemble (a=0.086 fm), light quark masses as small as roughly one-tenth the
strange quark mass, and volumes as large as (3.4 fm)^3, we find a_\mu^{HLO} =
(713 \pm 15) \times 10^{-10} and (748 \pm 21) \times 10^{-10} where the error
is statistical only and the two values correspond to linear and quadratic
extrapolations in the light quark mass, respectively. Considering systematic
uncertainties not eliminated in this study, we view this as agreement with the
current best calculations using the experimental cross section for e^+e^-
annihilation to hadrons, 692.4 (5.9) (2.4)\times 10^{-10}, and including the
experimental decay rate of the tau lepton to hadrons, 711.0 (5.0)
(0.8)(2.8)\times 10^{-10}. We discuss several ways to improve the current
lattice calculation.Comment: 44 pages, 4 tables, 17 figures, more discussion on matching the chpt
calculation to lattice calculation, typos corrected, refs added, version to
appear in PR
The Wandering Exponent of a One-Dimensional Directed Polymer in a Random Potential with Finite Correlation Radius
We consider a one-dimensional directed polymer in a random potential which is
characterized by the Gaussian statistics with the finite size local
correlations. It is shown that the well-known Kardar's solution obtained
originally for a directed polymer with delta-correlated random potential can be
applied for the description of the present system only in the high-temperature
limit. For the low temperature limit we have obtained the new solution which is
described by the one-step replica symmetry breaking. For the mean square
deviation of the directed polymer of the linear size L it provides the usual
scaling with the wandering exponent z = 2/3 and the
temperature-independent prefactor.Comment: 14 pages, Late
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