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 $L^{2z}$ with the wandering exponent z = 2/3 and the temperature-independent prefactor.Comment: 14 pages, Late