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 $h_c(f) = A f^{-2/3}$ with $A = 10^{-15}$ yr$^{-2/3}$. Unless a sample of 20 super-stable millisecond pulsars can be found --- those with timing residuals from red-noise contributions $\sigma_r \lesssim 20$ ns --- a much larger timing program on $\gtrsim 50 - 100$ MSPs will be needed. For other values of $A$, the constraint is $\sigma_r \lesssim 20 {\rm ns} (A/10^{-15} {\rm yr}^{-2/3})$. 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 $z_{\rm s}=1$, more than $65\%$ peaks with $\text{SNR} \geq 3$ (signal to noise ratio) are related to more than one massive haloes with mass larger than $10^{13} {\rm M}_{\odot}$. Those massive haloes contribute $87.2\%$ to high peaks ($\text{SNR} \geq 5$) 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 $60\%$ high peaks ($\text{SNR} \geq 5$) are true peaks and the fraction decreases to $20\%$ for lower peaks ($3 \leq \text{SNR} < 5$). Furthermore, we find that high peaks ($\text{SNR} \geq 5$) are dominated by very massive haloes larger than $10^{14} {\rm M}_{\odot}$.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 $^{171}$Yb$^{+}$ ion as a qubit and inject engineered noise ($\propto \sigma^z$) 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 $\sigma^z$ 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 $\sigma^x$ or $\sigma^y$ 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