Testing Conditional Independence of Discrete Distributions

We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with probability at least $2/3$, between the case that $X$ and $Y$ are conditionally independent given $Z$ from the case that $(X, Y, Z)$ is $\epsilon$-far, in $\ell_1$-distance, from every distribution that has this property. Conditional independence is a concept of central importance in probability and statistics with a range of applications in various scientific domains. As such, the statistical task of testing conditional independence has been extensively studied in various forms within the statistics and econometrics communities for nearly a century. Perhaps surprisingly, this problem has not been previously considered in the framework of distribution property testing and in particular no tester with sublinear sample complexity is known, even for the important special case that the domains of $X$ and $Y$ are binary. The main algorithmic result of this work is the first conditional independence tester with {\em sublinear} sample complexity for discrete distributions over $[\ell_1]\times[\ell_2] \times [n]$. To complement our upper bounds, we prove information-theoretic lower bounds establishing that the sample complexity of our algorithm is optimal, up to constant factors, for a number of settings. Specifically, for the prototypical setting when $\ell_1, \ell_2 = O(1)$, we show that the sample complexity of testing conditional independence (upper bound and matching lower bound) is \[ \Theta\left({\max\left(n^{1/2}/\epsilon^2,\min\left(n^{7/8}/\epsilon,n^{6/7}/\epsilon^{8/7}\right)\right)}\right)\,. \

Mirror formation control in the vicinity of an asteroid

Two strategies are presented for the positioning and control of a spacecraft formation designed to focus sunlight onto a point on the surface of asteroid, thereby sublimating the material and ejecting debris creating thrust. In the first approach, the formation is located at artficial equilibrium points around the asteroid and controlled using the force from the solar radiation pressure. The second approach determines the optimal periodic formation orbits, subject to the gravitational perturbations from the asteroid, the solar radiation pressure and the control acceleration derived from a control law

Vortex annihilation in the ordering kinetics of the O(2) model

The vortex-vortex and vortex-antivortex correlation functions are determined for the two-dimensional O(2) model undergoing phase ordering. We find reasonably good agreement with simulation results for the vortex-vortex correlation function where there is a short-scaled distance depletion zone due to the repulsion of like-signed vortices. The vortex-antivortex correlation function agrees well with simulation results for intermediate and long-scaled distances. At short-scaled distances the simulations show a depletion zone not seen in the theory.Comment: 28 pages, REVTeX, submitted to Phys. Rev.

Fluctuations and defect-defect correlations in the ordering kinetics of the O(2) model

The theory of phase ordering kinetics for the O(2) model using the gaussian auxiliary field approach is reexamined from two points of view. The effects of fluctuations about the ordering field are included and we organize the theory such that the auxiliary field correlation function is analytic in the short-scaled distance (x) expansion. These two points are connected and we find in the refined theory that the divergence at the origin in the defect-defect correlation function $\tilde{g}(x)$ obtained in the original theory is removed. Modifications to the order-parameter autocorrelation exponent $\lambda$ are computed.Comment: 29 pages, REVTeX, to be published in Phys. Rev. E. Minor grammatical/syntax changes from the origina

Relationship between physiological measures of excitability and levels of glutamate and GABA in the human motor cortex

Magnetic resonance spectroscopy (MRS) allows measurement of neurotransmitter concentrations within a region of interest in the brain. Inter-individual variation in MRS-measured GABA levels have been related to variation in task performance in a number of regions. However, it is not clear how MRS-assessed measures of GABA relate to cortical excitability or GABAergic synaptic activity. We therefore performed two studies investigating the relationship between neurotransmitter levels as assessed by MRS and transcranial magnetic stimulation (TMS) measures of cortical excitability and GABA synaptic activity in the primary motor cortex. We present uncorrected correlations, where the P value should therefore be considered with caution. We demonstrated a correlation between cortical excitability, as assessed by the slope of the TMS input-output curve and MRS-assessed glutamate levels (r = 0.803, P = 0.015) but no clear relationship between MRS-assessed GABA levels and TMS-assessed synaptic GABA(A) activity (2.5 ms inter-stimulus interval (ISI) short-interval intracortical inhibition (SICI); Experiment 1: r = 0.33, P = 0.31; Experiment 2: r = -0.23, P = 0.46) or GABA(B) activity (long-interval intracortical inhibition (LICI); Experiment 1: r = -0.47, P = 0.51; Experiment 2: r = 0.23, P = 0.47). We demonstrated a significant correlation between MRS-assessed GABA levels and an inhibitory TMS protocol (1 ms ISI SICI) with distinct physiological underpinnings from the 2.5 ms ISI SICI (r = -0.79, P = 0.018). Interpretation of this finding is challenging as the mechanisms of 1 ms ISI SICI are not well understood, but we speculate that our results support the possibility that 1 ms ISI SICI reflects a distinct GABAergic inhibitory process, possibly that of extrasynaptic GABA tone

NEOWISE Observations of Near-Earth Objects: Preliminary Results

With the NEOWISE portion of the \emph{Wide-field Infrared Survey Explorer} (WISE) project, we have carried out a highly uniform survey of the near-Earth object (NEO) population at thermal infrared wavelengths ranging from 3 to 22 $\mu$m, allowing us to refine estimates of their numbers, sizes, and albedos. The NEOWISE survey detected NEOs the same way whether they were previously known or not, subject to the availability of ground-based follow-up observations, resulting in the discovery of more than 130 new NEOs. The survey's uniformity in sensitivity, observing cadence, and image quality have permitted extrapolation of the 428 near-Earth asteroids (NEAs) detected by NEOWISE during the fully cryogenic portion of the WISE mission to the larger population. We find that there are 981$\pm$19 NEAs larger than 1 km and 20,500$\pm$3000 NEAs larger than 100 m. We show that the Spaceguard goal of detecting 90% of all 1 km NEAs has been met, and that the cumulative size distribution is best represented by a broken power law with a slope of 1.32$\pm$0.14 below 1.5 km. This power law slope produces $\sim13,200\pm$1,900 NEAs with $D>$140 m. Although previous studies predict another break in the cumulative size distribution below $D\sim$50-100 m, resulting in an increase in the number of NEOs in this size range and smaller, we did not detect enough objects to comment on this increase. The overall number for the NEA population between 100-1000 m are lower than previous estimates. The numbers of near-Earth comets will be the subject of future work.Comment: Accepted to Ap

Thermopower of the Correlated Narrow Gap Semiconductor FeSi and Comparison to RuSi

Iron based narrow gap semiconductors such as FeSi, FeSb2, or FeGa3 have received a lot of attention because they exhibit a large thermopower, as well as striking similarities to heavy fermion Kondo insulators. Many proposals have been advanced, however, lacking quantitative methodologies applied to this problem, a consensus remained elusive to date. Here, we employ realistic many-body calculations to elucidate the impact of electronic correlation effects on FeSi. Our methodology accounts for all substantial anomalies observed in FeSi: the metallization, the lack of conservation of spectral weight in optical spectroscopy, and the Curie susceptibility. In particular we find a very good agreement for the anomalous thermoelectric power. Validated by this congruence with experiment, we further discuss a new physical picture of the microscopic nature of the insulator-to-metal crossover. Indeed, we find the suppression of the Seebeck coefficient to be driven by correlation induced incoherence. Finally, we compare FeSi to its iso-structural and iso-electronic homologue RuSi, and predict that partially substituted Fe(1-x)Ru(x)Si will exhibit an increased thermopower at intermediate temperatures.Comment: 14 pages. Proceedings of the Hvar 2011 Workshop on 'New materials for thermoelectric applications: theory and experiment

Equilibrium configurations of two charged masses in General Relativity

An asymptotically flat static solution of Einstein-Maxwell equations which describes the field of two non-extreme Reissner - Nordstr\"om sources in equilibrium is presented. It is expressed in terms of physical parameters of the sources (their masses, charges and separating distance). Very simple analytical forms were found for the solution as well as for the equilibrium condition which guarantees the absence of any struts on the symmetry axis. This condition shows that the equilibrium is not possible for two black holes or for two naked singularities. However, in the case when one of the sources is a black hole and another one is a naked singularity, the equilibrium is possible at some distance separating the sources. It is interesting that for appropriately chosen parameters even a Schwarzschild black hole together with a naked singularity can be "suspended" freely in the superposition of their fields.Comment: 4 pages; accepted for publication in Phys. Rev.

Whistleblowing as a protracted process: a study of UK whistleblower journeys

This paper provides an exploration of whistleblowing as a protracted process, using secondary da-ta from 868 cases from a whistleblower advice line in the UK. Previous research on whistleblow-ing has mainly studied this phenomenon as a one-off decision by someone perceiving wrongdoing within an organisation to raise a concern or to remain silent. Earlier suggestions that whistleblowing is a process and that people find themselves inadvertently turned into whistleblowers by management responses, has not been followed up by a systematic study tracking the path of how a concern is repeatedly raised by whistleblowers. This paper provides a quantitative exploration of whistleblowing as a protracted process, rather than a one-off decision. Our research finds that the whistleblowing process generally entails two or even three internal at-tempts to raise a concern before an external attempt is made, if it is made at all. We also find that it is necessary to distinguish further between different internal (e.g. line manager, higher management, specialist channels) as well as external whistleblowing recipients (e.g. regulators, professional bodies, journalists). Our findings suggest that whistleblowing is a protracted process and that this process is internally more protracted than previously documented. The overall pattern is that whistleblowers tend to search for a more independent recipient at each successive attempt to raise their concern. Formal whistleblower power seems to determine which of the available recipients are perceived as viable, and also what the initial responses are in terms of retaliation and effectiveness

Shrinking-Hole Colloidal Lithography: Self-Aligned Nanofabrication of Complex Plasmonic Nanoantennas

Plasmonic nanoantennas create locally strongly enhanced electric fields in so-called hot spots. To place a relevant nanoobject with high accuracy in such a hot spot is crucial to fully capitalize on the potential of nanoantennas to control, detect, and enhance processes at the nanoscale. With state-of-the-art nanofabrication, in particular when several materials are to be used, small gaps between antenna elements are sought, and large surface areas are to be patterned, this is a grand challenge. Here we introduce self-aligned, bottom-up and self-assembly based Shrinking-Hole Colloidal Lithography, which provides (i) unique control of the size and position of subsequently deposited particles forming the nanoantenna itself, and (ii) allows delivery of nanoobjects consisting of a material of choice to the antenna hot spot, all in a single lithography step and, if desired, uniformly covering several square centimeters of surface. We illustrate the functionality of SHCL nanoantenna arrangements by (i) an optical hydrogen sensor exploiting the polarization dependent sensitivity of an Au-Pd nanoantenna ensemble; and (ii) single particle hydrogen sensing with an Au dimer nanoantenna with a small Pd nanoparticle in the hot spot