113,919 research outputs found
The Effect of Focusing and Caustics on Exit Phenomena in Systems Lacking Detailed Balance
We study the trajectories followed by a particle subjected to weak noise when
escaping from the domain of attraction of a stable fixed point. If detailed
balance is absent, a _focus_ may occur along the most probable exit path,
leading to a breakdown of symmetry (if present). The exit trajectory
bifurcates, and the exit location distribution may become `skewed'
(non-Gaussian). The weak-noise asymptotics of the mean escape time are strongly
affected. Our methods extend to the study of skewed exit location distributions
in stochastic models without symmetry.Comment: REVTEX macros (latest version). Two accompanying PS figures, one of
which is large (over 600K unpacked
Robust Inference for State-Space Models with Skewed Measurement Noise
Filtering and smoothing algorithms for linear discrete-time state-space
models with skewed and heavy-tailed measurement noise are presented. The
algorithms use a variational Bayes approximation of the posterior distribution
of models that have normal prior and skew-t-distributed measurement noise. The
proposed filter and smoother are compared with conventional low-complexity
alternatives in a simulated pseudorange positioning scenario. In the
simulations the proposed methods achieve better accuracy than the alternative
methods, the computational complexity of the filter being roughly 5 to 10 times
that of the Kalman filter.Comment: 5 pages, 7 figures. Accepted for publication in IEEE Signal
Processing Letter
Expectile Matrix Factorization for Skewed Data Analysis
Matrix factorization is a popular approach to solving matrix estimation
problems based on partial observations. Existing matrix factorization is based
on least squares and aims to yield a low-rank matrix to interpret the
conditional sample means given the observations. However, in many real
applications with skewed and extreme data, least squares cannot explain their
central tendency or tail distributions, yielding undesired estimates. In this
paper, we propose \emph{expectile matrix factorization} by introducing
asymmetric least squares, a key concept in expectile regression analysis, into
the matrix factorization framework. We propose an efficient algorithm to solve
the new problem based on alternating minimization and quadratic programming. We
prove that our algorithm converges to a global optimum and exactly recovers the
true underlying low-rank matrices when noise is zero. For synthetic data with
skewed noise and a real-world dataset containing web service response times,
the proposed scheme achieves lower recovery errors than the existing matrix
factorization method based on least squares in a wide range of settings.Comment: 8 page main text with 5 page supplementary documents, published in
AAAI 201
2001 WisDOT Specifications - Construction Note
For the past several years, Marquette University has been conducting a research study for WisDOT on tining patterns to reduce the objectionable tire/pavement whine. During the research study, WisDOT issued Construction Notes to implement the interim results of the research rather than tine the pavement according to Subsection 415.5.9.6.3 of the Standard Specifications.
In the completed study, Marquette University has determined that a skewed, randomly spaced, transversely tined surface results in the lowest levels of pavement whine while retaining the favorable friction characteristics achieved under the current specifications. The overall noise level is not reduced by skewed randomly tined surfaces.
The research study wasn’t completed in time to include the recommended tining requirements in the bidding documents for 2001 construction projects. However, Wisconsin Concrete Pavement Association (WCPA) members are aware of the findings of the research study. All WCPA member contractors are intending to use the randomly spaced tining rake, meeting the study recommendations, during the 2001 construction season.
Therefore, WisDOT is implementing the research study recommendations on randomly spaced rake for the 2001 construction season with this Construction Note
Minimum Requirements for Detecting a Stochastic Gravitational Wave Background Using Pulsars
We assess the detectability of a nanohertz gravitational wave (GW) background
with respect to additive red and white noise in the timing of millisecond
pulsars. We develop detection criteria based on the cross-correlation function
summed over pulsar pairs in a pulsar timing array. The distribution of
correlation amplitudes is found to be non-Gaussian and highly skewed, which
significantly influences detection and false-alarm probabilities. When only
white noise and GWs contribute, our detection results are consistent with those
found by others. Red noise, however, drastically alters the results. We discuss
methods to meet the challenge of GW detection ("climbing mount significance")
by distinguishing between GW-dominated and red or white-noise limited regimes.
We characterize detection regimes by evaluating the number of millisecond
pulsars that must be monitored in a high-cadence, 5-year timing program for a
GW background spectrum with yr.
Unless a sample of 20 super-stable millisecond pulsars can be found --- those
with timing residuals from red-noise contributions ns
--- a much larger timing program on MSPs will be needed. For
other values of , the constraint is . Identification of suitable MSPs itself requires
an aggressive survey campaign followed by characterization of the level of spin
noise in the timing residuals of each object. The search and timing programs
will likely require substantial fractions of time on new array telescopes in
the southern hemisphere as well as on existing ones.Comment: Submitted to the Astrophysical Journa
The Correspondence between Convergence Peaks from Weak Lensing and Massive Dark Matter Haloes
The convergence peaks, constructed from galaxy shape measurement in weak
lensing, is a powerful probe of cosmology as the peaks can be connected with
the underlined dark matter haloes. However the capability of convergence peak
statistic is affected by the noise in galaxy shape measurement, signal to noise
ratio as well as the contribution from the projected mass distribution from the
large-scale structures along the line of sight (LOS). In this paper we use the
ray-tracing simulation on a curved sky to investigate the correspondence
between the convergence peak and the dark matter haloes at the LOS. We find
that, in case of no noise and for source galaxies at , more than
peaks with (signal to noise ratio) are related to
more than one massive haloes with mass larger than .
Those massive haloes contribute to high peaks ()
with the remaining contributions are from the large-scale structures. On the
other hand, the peaks distribution is skewed by the noise in galaxy shape
measurement, especially for lower SNR peaks. In the noisy field where the shape
noise is modelled as a Gaussian distribution, about high peaks
() are true peaks and the fraction decreases to for
lower peaks (). Furthermore, we find that high peaks
() are dominated by very massive haloes larger than .Comment: 13 pages, 11 figures, 4 tables, accepted for publication in MNRAS.
Our mock galaxy catalog is available upon request by email to the author
([email protected]
Experimental quantum verification in the presence of temporally correlated noise
Growth in the complexity and capabilities of quantum information hardware
mandates access to practical techniques for performance verification that
function under realistic laboratory conditions. Here we experimentally
characterise the impact of common temporally correlated noise processes on both
randomised benchmarking (RB) and gate-set tomography (GST). We study these
using an analytic toolkit based on a formalism mapping noise to errors for
arbitrary sequences of unitary operations. This analysis highlights the role of
sequence structure in enhancing or suppressing the sensitivity of quantum
verification protocols to either slowly or rapidly varying noise, which we
treat in the limiting cases of quasi-DC miscalibration and white noise power
spectra. We perform experiments with a single trapped Yb ion as a
qubit and inject engineered noise () to probe protocol
performance. Experiments on RB validate predictions that the distribution of
measured fidelities over sequences is described by a gamma distribution varying
between approximately Gaussian for rapidly varying noise, and a broad, highly
skewed distribution for the slowly varying case. Similarly we find a strong
gate set dependence of GST in the presence of correlated errors, leading to
significant deviations between estimated and calculated diamond distances in
the presence of correlated errors. Numerical simulations demonstrate
that expansion of the gate set to include negative rotations can suppress these
discrepancies and increase reported diamond distances by orders of magnitude
for the same error processes. Similar effects do not occur for correlated
or errors or rapidly varying noise processes,
highlighting the critical interplay of selected gate set and the gauge
optimisation process on the meaning of the reported diamond norm in correlated
noise environments.Comment: Expanded and updated analysis of GST, including detailed examination
of the role of gauge optimization in GST. Full GST data sets and
supplementary information available on request from the authors. Related
results available from
http://www.physics.usyd.edu.au/~mbiercuk/Publications.htm
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