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)\,. \

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

Ancient climate change, antifreeze, and the evolutionary diversification of Antarctic fishes

The Southern Ocean around Antarctica is among the most rapidly warming regions on Earth, but has experienced episodic climate change during the past 40 million years. It remains unclear how ancient periods of climate change have shaped Antarctic bio-diversity. The origin of antifreeze glycoproteins (AFGPs) in Antarctic notothenioid fishes has become a classic example of how the evolution of a key innovation in response to climate change can drive adaptive radiation. By using a time-calibrated molecular phylogeny of notothenioids and reconstructed paleoclimate, we demonstrate that the origin of AFGP occurred between 42 and 22 Ma, which includes a period of global cooling approximately 35 Ma. However, the most species-rich lineages diversified and evolved significant ecological differences at least 10 million years after the origin of AFGPs, during a second cooling event in the Late Miocene (11.6-5.3 Ma). This pattern indicates that AFGP was not the sole trigger of the notothenioid adaptive radiation. Instead, the bulk of the species richness and ecological diversity originated during the Late Miocene and into the Early Pliocene, a time co-incident with the origin of polar conditions and increased ice activity in the Southern Ocean. Our results challenge the current understanding of the evolution of Antarctic notothenioids suggesting that the ecological opportunity that underlies this adaptive radiation is not linked to a single trait, but rather to a combination of freeze avoidance offered by AFGPs and subsequent exploitation of new habitats and open niches created by increased glacial and ice sheet activity.Fil: Near, Thomas. University of Yale; Estados UnidosFil: Dornburg, Alex. University of Yale; Estados UnidosFil: Kuhn, K.. University of Yale; Estados UnidosFil: Eastman,Joseph T.. Ohio State University; Estados UnidosFil: Pennington, Jillian N.. University of Yale; Estados UnidosFil: Patarnello, Tomaso. Università di Padova; ItaliaFil: Zane, Lorenzo. Università di Padova; ItaliaFil: Fernandez, Daniel Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Austral de Investigaciones Científicas; ArgentinaFil: Jones, Christopher D.. National Oceanic And Atmospheric Administration; Estados Unido

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.

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

Comparison of seven modelling algorithms for γ-aminobutyric acid–edited proton magnetic resonance spectroscopy

Edited MRS sequences are widely used for studying γ-aminobutyric acid (GABA) in the human brain. Several algorithms are available for modelling these data, deriving metabolite concentration estimates through peak fitting or a linear combination of basis spectra. The present study compares seven such algorithms, using data obtained in a large multisite study. GABA-edited (GABA+, TE = 68 ms MEGA-PRESS) data from 222 subjects at 20 sites were processed via a standardised pipeline, before modelling with FSL-MRS, Gannet, AMARES, QUEST, LCModel, Osprey and Tarquin, using standardised vendor-specific basis sets (for GE, Philips and Siemens) where appropriate. After referencing metabolite estimates (to water or creatine), systematic differences in scale were observed between datasets acquired on different vendors' hardware, presenting across algorithms. Scale differences across algorithms were also observed. Using the correlation between metabolite estimates and voxel tissue fraction as a benchmark, most algorithms were found to be similarly effective in detecting differences in GABA+. An interclass correlation across all algorithms showed single-rater consistency for GABA+ estimates of around 0.38, indicating moderate agreement. Upon inclusion of a basis set component explicitly modelling the macromolecule signal underlying the observed 3.0 ppm GABA peaks, single-rater consistency improved to 0.44. Correlation between discrete pairs of algorithms varied, and was concerningly weak in some cases. Our findings highlight the need for consensus on appropriate modelling parameters across different algorithms, and for detailed reporting of the parameters adopted in individual studies to ensure reproducibility and meaningful comparison of outcomes between different studies.publishedVersio

Globular-shaped variable lymphocyte receptors B antibody multimerized by a hydrophobic clustering in hagfish

In hagfish and lampreys, two representative jawless vertebrates, the humoral immunity is directly mediated by variable lymphocyte receptors B (VLRBs). Both monomeric VLRBs are structurally and functionally similar, but their C-terminal tails differ: lamprey VLRB has a Cys-rich tail that forms disulfide-linked pentamers of dimers, contributing to its multivalency, whereas hagfish VLRB has a superhydrophobic tail of unknown structure. Here, we reveal that VLRBs obtained from hagfish plasma have a globular-shaped multimerized form (approximately 0.6 to 1.7 MDa) that is generated by hydrophobic clustering instead of covalent linkage. Electron microscopy (EM) and single-particle analysis showed that the multimerized VLRBs form globular-shaped clusters with an average diameter of 28.7 ± 2.2 nm. The presence of VLRBs in the complex was confirmed by immune-EM analysis using an anti-VLRB antibody. Furthermore, the hydrophobic hagfish C-terminus (HC) was capable of triggering multimerization and directing the cellular surface localization via a glycophosphatidylinositol linkage. Our results strongly suggest that the hagfish VLRB forms a previously unknown globular-shaped antibody. This novel identification of a structurally unusual VLRB complex may suggest that the adaptive immune system of hagfish differs from that of lamprey

The motivations of external whistleblowers and their impact on the intention to blow the whistle again

The purpose of this study was to inquire into the relative importance of morality, cost‐benefit, and emotion as motivations for the decision to blow the whistle externally, and the effects of such factors as motivations, perceived negative consequences, and preferences for reform on the intention to blow the whistle again. Based on a literature review, we formulated some hypotheses and, to test them, we used the data collected from a survey of 127 external whistleblowers in South Korea. The results revealed that morality was the most important motivation, followed by emotion, and then cost‐benefit, which thus, seemed to be the least important for the whistleblowers. Morality as a motivation and the perceived negative consequences of whistleblowing had a significant effect on the intention to blow the whistle again. This study helps advance the understanding of the motivations behind whistleblowing and the factors that influence the intention to blow the whistle again