Random and free observables saturate the Tsirelson bound for CHSH inequality

Maximal violation of the CHSH-Bell inequality is usually said to be a feature of anticommuting observables. In this work we show that even random observables exhibit near-maximal violations of the CHSH-Bell inequality. To do this, we use the tools of free probability theory to analyze the commutators of large random matrices. Along the way, we introduce the notion of "free observables" which can be thought of as infinite-dimensional operators that reproduce the statistics of random matrices as their dimension tends towards infinity. We also study the fine-grained uncertainty of a sequence of free or random observables, and use this to construct a steering inequality with a large violation

First record of phoresy of Dendrochernes cyrneus (L. Koch, 1873) (Pseudoscorpiones, Chernetidae) on Cerambyx cerdo Linnaeus, 1758 (Coleoptera, Cerambycidae) and their potential value as bioindicators

El primer registro de foresía de Dendrochernes cyrneus (L. Koch, 1873) (Pseudoscorpiones, Chernetidae) en Cerambyx cerdo Linnaeus, 1758 (Coleoptera, Cerambycidae) y su valor potencial como bioindicadores Se documenta la primera prueba de foresía de Dendrochernes cyrneus (L. Koch, 1873) en Cerambyx cerdo Linnaeus, 1758. También se presenta una revisión crítica de todos los informes científicos publicados sobre la foresía relacionados con D. cyrneus. Dos de estos informes guardan relación con la misma observación y son el resultado de la confusión sistemática existente en la familia Cerambycidae. Ambas especies se tratan como vestigios del bosque primigenio y sus aisladas poblaciones viven en las zonas residuales dispersas de los bosques antiguos que cubrían Europa en el pasado. Aportamos nueva información sobre las relaciones ecológicas de D. cyrneus con escarabajos saproxílicos y analizamos las preferencias ecológicas de las dos especies y su función como indicadores de la calidad del ambiente.El primer registro de foresía de Dendrochernes cyrneus (L. Koch, 1873) (Pseudoscorpiones, Chernetidae) en Cerambyx cerdo Linnaeus, 1758 (Coleoptera, Cerambycidae) y su valor potencial como bioindicadores Se documenta la primera prueba de foresía de Dendrochernes cyrneus (L. Koch, 1873) en Cerambyx cerdo Linnaeus, 1758. También se presenta una revisión crítica de todos los informes científicos publicados sobre la foresía relacionados con D. cyrneus. Dos de estos informes guardan relación con la misma observación y son el resultado de la confusión sistemática existente en la familia Cerambycidae. Ambas especies se tratan como vestigios del bosque primigenio y sus aisladas poblaciones viven en las zonas residuales dispersas de los bosques antiguos que cubrían Europa en el pasado. Aportamos nueva información sobre las relaciones ecológicas de D. cyrneus con escarabajos saproxílicos y analizamos las preferencias ecológicas de las dos especies y su función como indicadores de la calidad del ambiente.The first evidence of phoresy of Dendrochernes cyrneus (L. Koch, 1873) on Cerambyx cerdo Linnaeus, 1758 is documented. A critical review of all known literature reports of phoresy involving D. cyrneus is also presented. Two of these reports relate to the same observation and are the result of the systematic turmoil within the family Cerambycidae. Both species are treated as primeval forest relics and their isolated populations live in the scattered remains of the ancient forests that covered Europe in the past. We provide new information about the ecological relationships of D. cyrneus with saproxylic beetles, and discuss the ecological preferences of the two species and their role as indicators of the quality of the environment

How to reduce the number of rating scale items without predictability loss?

Rating scales are used to elicit data about qualitative entities (e.g., research collaboration). This study presents an innovative method for reducing the number of rating scale items without the predictability loss. The "area under the receiver operator curve method" (AUC ROC) is used. The presented method has reduced the number of rating scale items (variables) to 28.57\% (from 21 to 6) making over 70\% of collected data unnecessary. Results have been verified by two methods of analysis: Graded Response Model (GRM) and Confirmatory Factor Analysis (CFA). GRM revealed that the new method differentiates observations of high and middle scores. CFA proved that the reliability of the rating scale has not deteriorated by the scale item reduction. Both statistical analysis evidenced usefulness of the AUC ROC reduction method.Comment: 14 pages, 5 figure

Ultra-deep Large Binocular Camera U-band Imaging of the GOODS-North Field: Depth vs. Resolution

We present a study of the trade-off between depth and resolution using a large number of U-band imaging observations in the GOODS-North field (Giavalisco et al. 2004) from the Large Binocular Camera (LBC) on the Large Binocular Telescope (LBT). Having acquired over 30 hours of data (315 images with 5-6 mins exposures), we generated multiple image mosaics, starting with the best atmospheric seeing images (FWHM $\lesssim$0.8"), which constitute $\sim$10% of the total data set. For subsequent mosaics, we added in data with larger seeing values until the final, deepest mosaic included all images with FWHM $\lesssim$1.8" ($\sim$94% of the total data set). From the mosaics, we made object catalogs to compare the optimal-resolution, yet shallower image to the lower-resolution but deeper image. We show that the number counts for both images are $\sim$90% complete to $U_{AB}$ $\lesssim26$. Fainter than $U_{AB}$$\sim$ 27, the object counts from the optimal-resolution image start to drop-off dramatically (90% between $U_{AB}$ = 27 and 28 mag), while the deepest image with better surface-brightness sensitivity ($\mu^{AB}_{U}$$\lesssim$ 32 mag arcsec$^{-2}$) show a more gradual drop (10% between $U_{AB}$ $\simeq$ 27 and 28 mag). For the brightest galaxies within the GOODS-N field, structure and clumpy features within the galaxies are more prominent in the optimal-resolution image compared to the deeper mosaics. Finally, we find - for 220 brighter galaxies with $U_{AB}$$\lesssim$ 24 mag - only marginal differences in total flux between the optimal-resolution and lower-resolution light-profiles to $\mu^{AB}_{U}$$\lesssim$ 32 mag arcsec$^{-2}$. In only 10% of the cases are the total-flux differences larger than 0.5 mag. This helps constrain how much flux can be missed from galaxy outskirts, which is important for studies of the Extragalactic Background Light.Comment: 24 pages, 14 figures, submitted to PASP, comments welcom

Predicting the redshift 2 Halpha luminosity function using [OIII] emission line galaxies

Upcoming space-based surveys such as Euclid and WFIRST-AFTA plan to measure Baryonic Acoustic Oscillations (BAOs) in order to study dark energy. These surveys will use IR slitless grism spectroscopy to measure redshifts of a large number of galaxies over a significant redshift range. In this paper, we use the WFC3 Infrared Spectroscopic Parallel Survey (WISP) to estimate the expected number of Halpha (Ha) emitters observable by these future surveys. WISP is an ongoing HST slitless spectroscopic survey, covering the 0.8-1.65micron wavelength range and allowing the detection of Ha emitters up to z~1.5 and [OIII] emitters to z~2.3. We derive the Ha-[OIII] bivariate line luminosity function for WISP galaxies at z~1 using a maximum likelihood estimator that properly accounts for uncertainties in line luminosity measurement, and demonstrate how it can be used to derive the Ha luminosity function from exclusively fitting [OIII] data. Using the z~2 [OIII] line luminosity function, and assuming that the relation between Ha and [OIII] luminosity does not change significantly over the redshift range, we predict the Ha number counts at z~2 - the upper end of the redshift range of interest for the future surveys. For the redshift range 0.7<z<2, we expect ~3000 galaxies/deg^2 for a flux limit of 3x10^{-16} ergs/s/cm^2 (the proposed depth of Euclid galaxy redshift survey) and ~20,000 galaxies/deg^2 for a flux limit of ~10^{-16} ergs/s/cm^2 (the baseline depth of WFIRST galaxy redshift survey).Comment: Minor revisions to match accepted ApJ versio

Recurrence and differential relations for spherical spinors

We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor spherical harmonics) $\Omega_{\kappa\mu}(\mathbf{n})$ used in relativistic atomic, molecular, and solid state physics, as well as in relativistic quantum chemistry. First, we list finite expansions in the spherical spinor basis of the expressions $\mathbf{A}\cdot\mathbf{B}\,\Omega_{\kappa\mu}(\mathbf{n})$ and {$\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})\, \Omega_{\kappa\mu}(\mathbf{n})$}, where $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{C}$ are either of the following vectors or vector operators: $\mathbf{n}=\mathbf{r}/r$ (the radial unit vector), $\mathbf{e}_{0}$, $\mathbf{e}_{\pm1}$ (the spherical, or cyclic, versors), $\boldsymbol{\sigma}$ (the $2\times2$ Pauli matrix vector), $\hat{\mathbf{L}}=-i\mathbf{r}\times\boldsymbol{\nabla}I$ (the dimensionless orbital angular momentum operator; $I$ is the $2\times2$ unit matrix), $\hat{\mathbf{J}}=\hat{\mathbf{L}}+1/2\boldsymbol{\sigma}$ (the dimensionless total angular momentum operator). Then, we list finite expansions in the spherical spinor basis of the expressions $\mathbf{A}\cdot\mathbf{B}\,F(r)\Omega_{\kappa\mu}(\mathbf{n})$ and $\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})\, F(r)\Omega_{\kappa\mu}(\mathbf{n})$, where at least one of the objects $\mathbf{A}$, $\mathbf{B}$, $\mathbf{C}$ is the nabla operator $\boldsymbol{\nabla}$, while the remaining ones are chosen from the set $\mathbf{n}$, $\mathbf{e}_{0}$, $\mathbf{e}_{\pm1}$, $\boldsymbol{\sigma}$, $\hat{\mathbf{L}}$, $\hat{\mathbf{J}}$.Comment: LaTeX, 12 page