Comparison of two-dimensional binned data distributions using the energy test

For the purposes of monitoring HEP experiments, comparison is often made between regularly acquired histograms of data and reference histograms which represent the ideal state of the equipment. With the larger experiments now starting up, there is a need for automation of this task since the volume of comparisons would overwhelm human operators. However, the two-dimensional histogram comparison tools currently available in ROOT have noticeable shortcomings. We present a new comparison test for 2D histograms, based on the Energy Test of Aslan and Zech, which provides more decisive discrimination between histograms of data coming from different distributions

The Clustering of Luminous Red Galaxies in the Sloan Digital Sky Survey Imaging Data

We present the 3D real space clustering power spectrum of a sample of \~600,000 luminous red galaxies (LRGs) measured by the Sloan Digital Sky Survey (SDSS), using photometric redshifts. This sample of galaxies ranges from redshift z=0.2 to 0.6 over 3,528 deg^2 of the sky, probing a volume of 1.5 (Gpc/h)^3, making it the largest volume ever used for galaxy clustering measurements. We measure the angular clustering power spectrum in eight redshift slices and combine these into a high precision 3D real space power spectrum from k=0.005 (h/Mpc) to k=1 (h/Mpc). We detect power on gigaparsec scales, beyond the turnover in the matter power spectrum, on scales significantly larger than those accessible to current spectroscopic redshift surveys. We also find evidence for baryonic oscillations, both in the power spectrum, as well as in fits to the baryon density, at a 2.5 sigma confidence level. The statistical power of these data to constrain cosmology is ~1.7 times better than previous clustering analyses. Varying the matter density and baryon fraction, we find \Omega_M = 0.30 \pm 0.03, and \Omega_b/\Omega_M = 0.18 \pm 0.04, The detection of baryonic oscillations also allows us to measure the comoving distance to z=0.5; we find a best fit distance of 1.73 \pm 0.12 Gpc, corresponding to a 6.5% error on the distance. These results demonstrate the ability to make precise clustering measurements with photometric surveys (abridged).Comment: 23 pages, 27 figures, submitted to MNRA

3D Object Class Detection in the Wild

Object class detection has been a synonym for 2D bounding box localization for the longest time, fueled by the success of powerful statistical learning techniques, combined with robust image representations. Only recently, there has been a growing interest in revisiting the promise of computer vision from the early days: to precisely delineate the contents of a visual scene, object by object, in 3D. In this paper, we draw from recent advances in object detection and 2D-3D object lifting in order to design an object class detector that is particularly tailored towards 3D object class detection. Our 3D object class detection method consists of several stages gradually enriching the object detection output with object viewpoint, keypoints and 3D shape estimates. Following careful design, in each stage it constantly improves the performance and achieves state-ofthe-art performance in simultaneous 2D bounding box and viewpoint estimation on the challenging Pascal3D+ dataset

Testing the Hubble Law with the IRAS 1.2 Jy Redshift Survey

We test and reject the claim of Segal et al. (1993) that the correlation of redshifts and flux densities in a complete sample of IRAS galaxies favors a quadratic redshift-distance relation over the linear Hubble law. This is done, in effect, by treating the entire galaxy luminosity function as derived from the 60 micron 1.2 Jy IRAS redshift survey of Fisher et al. (1995) as a distance indicator; equivalently, we compare the flux density distribution of galaxies as a function of redshift with predictions under different redshift-distance cosmologies, under the assumption of a universal luminosity function. This method does not assume a uniform distribution of galaxies in space. We find that this test has rather weak discriminatory power, as argued by Petrosian (1993), and the differences between models are not as stark as one might expect a priori. Even so, we find that the Hubble law is indeed more strongly supported by the analysis than is the quadratic redshift-distance relation. We identify a bias in the the Segal et al. determination of the luminosity function, which could lead one to mistakenly favor the quadratic redshift-distance law. We also present several complementary analyses of the density field of the sample; the galaxy density field is found to be close to homogeneous on large scales if the Hubble law is assumed, while this is not the case with the quadratic redshift-distance relation.Comment: 27 pages Latex (w/figures), ApJ, in press. Uses AAS macros, postscript also available at http://www.astro.princeton.edu/~library/preprints/pop682.ps.g

Probing physics students' conceptual knowledge structures through term association

Traditional tests are not effective tools for diagnosing the content and structure of students' knowledge of physics. As a possible alternative, a set of term-association tasks (the "ConMap" tasks) was developed to probe the interconnections within students' store of conceptual knowledge. The tasks have students respond spontaneously to a term or problem or topic area with a sequence of associated terms; the response terms and timeof- entry data are captured. The tasks were tried on introductory physics students, and preliminary investigations show that the tasks are capable of eliciting information about the stucture of their knowledge. Specifically, data gathered through the tasks is similar to that produced by a hand-drawn concept map task, has measures that correlate with inclass exam performance, and is sensitive to learning produced by topic coverage in class. Although the results are preliminary and only suggestive, the tasks warrant further study as student-knowledge assessment instruments and sources of experimental data for cognitive modeling efforts.Comment: 31 pages plus 2 tables and 8 figure

Steady-state simulations using weighted ensemble path sampling

We extend the weighted ensemble (WE) path sampling method to perform rigorous statistical sampling for systems at steady state. The straightforward steady-state implementation of WE is directly practical for simple landscapes, but not when significant metastable intermediates states are present. We therefore develop an enhanced WE scheme, building on existing ideas, which accelerates attainment of steady state in complex systems. We apply both WE approaches to several model systems confirming their correctness and efficiency by comparison with brute-force results. The enhanced version is significantly faster than the brute force and straightforward WE for systems with WE bins that accurately reflect the reaction coordinate(s). The new WE methods can also be applied to equilibrium sampling, since equilibrium is a steady state

Computationally efficient algorithms for the two-dimensional Kolmogorov-Smirnov test

Goodness-of-fit statistics measure the compatibility of random samples against some theoretical or reference probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2^d-1 independent ways of ordering a cumulative distribution function in d dimensions. We discuss Peacock's version of the Kolmogorov-Smirnov test for two-dimensional data sets which computes the differences between cumulative distribution functions in 4n^2 quadrants. We also examine Fasano and Franceschini's variation of Peacock's test, Cooke's algorithm for Peacock's test, and ROOT's version of the two-dimensional Kolmogorov-Smirnov test. We establish a lower-bound limit on the work for computing Peacock's test of Omega(n^2.lg(n)), introducing optimal algorithms for both this and Fasano and Franceschini's test, and show that Cooke's algorithm is not a faithful implementation of Peacock's test. We also discuss and evaluate parallel algorithms for Peacock's test