Factorial Structure and Measurement Invariance of the Acceptance and Action Questionnaire-Stigma (AAQ-S) in Spain

The objective of the present study was to validate and adapt the Acceptance and Action Questionnaire-Stigma (AAQ-S) to the Spanish context. Method: The study included the participation of 1212 subjects, with an average age of 17.12 years old. Results: The confirmatory factorial analysis revealed a number of adequate fit indices for the new version of the scale χ2/df = 3.24; Comparative Fit Index = 0.96; Incremental Fit Index = 0.96; Root Mean Square Error of Approximation = 0.060; Standardized Root Mean Square Residual = 0.035, in which the factorial structures displayed gender invariance. The two factors comprise the scale both exhibited high internal consistency (+0.90) and temporal stability. Conclusion: The Spanish version of the AAQ-S proved to be a robust and adequate psychometric instrument. In this sense, future lines of research focused on determining the role of psychological flexibility in stigma and the processes of change at the base of interventions could benefit substantially from the use of AAQ-S

Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case

We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index $H\in(1/2,1)$. We study the consistency and the asymptotic distributions of the least squares estimator $\hat{\theta}_t$ of $\theta$ based on the observation $\{X_s,\ s\in[0,t]\}$ as $t\rightarrow\infty$.Comment: 13 page

The Prediction value

We introduce the prediction value (PV) as a measure of players' informational importance in probabilistic TU games. The latter combine a standard TU game and a probability distribution over the set of coalitions. Player $i$'s prediction value equals the difference between the conditional expectations of $v(S)$ when $i$ cooperates or not. We characterize the prediction value as a special member of the class of (extended) values which satisfy anonymity, linearity and a consistency property. Every $n$-player binomial semivalue coincides with the PV for a particular family of probability distributions over coalitions. The PV can thus be regarded as a power index in specific cases. Conversely, some semivalues -- including the Banzhaf but not the Shapley value -- can be interpreted in terms of informational importance.Comment: 26 pages, 2 table

Synchrotron Cooling in Energetic Gamma-Ray Bursts Observed by the Fermi Gamma-Ray Burst Monitor

We study the time-resolved spectra of eight GRBs observed by Fermi GBM in its first five years of mission, with 1 keV - 1 MeV fluence $f>1.0\times10^{-4}$ erg cm$^{-2}$ and signal-to-noise level $\text{S/N}\geq10.0$ above 900 keV. We aim to constrain in detail the spectral properties of GRB prompt emission on a time-resolved basis and to discuss the theoretical implications of the fitting results in the context of various prompt emission models. We perform time-resolved spectral analysis using a variable temporal binning technique according to optimal S/N criteria, resulting in a total of 299 time-resolved spectra. We fit the Band function to all spectra and obtain the distributions for the low-energy power-law index $\alpha$, the high-energy power-law index $\beta$, the peak energy in the observed $\nu F_\nu$ spectrum $E_\text{p}$, and the difference between the low- and high-energy power-law indices $\Delta s=\alpha-\beta$. Using the distributions of $\Delta s$ and $\beta$, the electron population index $p$ is found to be consistent with the "moderately fast" scenario which fast- and slow-cooling scenarios cannot be distinguished. We also apply a physically motivated synchrotron model, which is a triple power-law with constrained power-law indices and a blackbody component, to test for consistency with a synchrotron origin for the prompt emission and obtain the distributions for the two break energies $E_\text{b,1}$ and $E_\text{b,2}$, the middle segment power-law index $\beta$, and the Planck function temperature $kT$. A synchrotron model is found consistent with the majority of time-resolved spectra for these eight energetic Fermi GBM bursts with good high-energy photon statistics, as long as both the cooling and injection break are included and the leftmost spectral slope is lifted either by inclusion of a thermal component or when an evolving magnetic field is accounted for.Comment: 20 pages, 7 figures, 8 tables, accepted for publication in A&

A Nonparametric Bayesian Approach to Copula Estimation

We propose a novel Dirichlet-based P\'olya tree (D-P tree) prior on the copula and based on the D-P tree prior, a nonparametric Bayesian inference procedure. Through theoretical analysis and simulations, we are able to show that the flexibility of the D-P tree prior ensures its consistency in copula estimation, thus able to detect more subtle and complex copula structures than earlier nonparametric Bayesian models, such as a Gaussian copula mixture. Further, the continuity of the imposed D-P tree prior leads to a more favorable smoothing effect in copula estimation over classic frequentist methods, especially with small sets of observations. We also apply our method to the copula prediction between the S\&P 500 index and the IBM stock prices during the 2007-08 financial crisis, finding that D-P tree-based methods enjoy strong robustness and flexibility over classic methods under such irregular market behaviors

Massive Scattering Amplitudes in Six Dimensions

We show that a natural spinor-helicity formalism that can describe massive scattering amplitudes exists in $D=6$ dimensions. This is arranged by having helicity spinors carry an index in the Dirac spinor {\bf 4} of the massive little group, $SO(5) \sim Sp(4)$. In the high energy limit, two separate kinds of massless helicity spinors emerge as required for consistency with arXiv:0902.0981, with indices in the two $SU(2)$'s of the massless little group $SO(4)$. The tensors of ${\bf 4}$ lead to particles with arbitrary spin, and using these and demanding consistent factorization, we can fix $3-$ and $4-$point tree amplitudes of arbitrary masses and spins: we provide examples. We discuss the high energy limit of scattering amplitudes and the Higgs mechanism in this language, and make some preliminary observations about massive BCFW recursion.Comment: 37 pages; v2: minor improvements, JHEP versio

Swift XRT Observations of the Afterglow of XRF 050416A

Swift discovered XRF 050416A with the BAT and began observing it with its narrow field instruments only 64.5 s after the burst onset. Its very soft spectrum classifies this event as an X-ray flash. The afterglow X-ray emission was monitored up to 74 days after the burst. The X-ray light curve initially decays very fast, subsequently flattens and eventually steepens again, similar to many X-ray afterglows. The first and second phases end about 172 and 1450 s after the burst onset, respectively. We find evidence of spectral evolution from a softer emission with photon index Gamma ~ 3.0 during the initial steep decay, to a harder emission with Gamma ~ 2.0 during the following evolutionary phases. The spectra show intrinsic absorption in the host galaxy. The consistency of the initial photon index with the high energy BAT photon index suggests that the initial phase of the X-ray light curve may be the low-energy tail of the prompt emission. The lack of jet break signatures in the X-ray afterglow light curve is not consistent with empirical relations between the source rest-frame peak energy and the collimation-corrected energy of the burst. The standard uniform jet model can give a possible description of the XRF 050416A X-ray afterglow for an opening angle larger than a few tens of degrees, although numerical simulations show that the late time decay is slightly flatter than expected from on-axis viewing of a uniform jet. A structured Gaussian-type jet model with uniform Lorentz factor distribution and viewing angle outside the Gaussian core is another possibility, although a full agreement with data is not achieved with the numerical models explored.Comment: Accepted for publication on ApJ; replaced with revised version: part of the discussion moved in an appendix; 11 pages, 6 figures; abstract shortened for posting on astro-p

How well can we measure supermassive black hole spin?

Being one of only two fundamental properties black holes possess, the spin of supermassive black holes (SMBHs) is of great interest for understanding accretion processes and galaxy evolution. However, in these early days of spin measurements, consistency and reproducibility of spin constraints have been a challenge. Here we focus on X-ray spectral modelling of active galactic nuclei (AGN), examining how well we can truly return known reflection parameters such as spin under standard conditions. We have created and fit over 4000 simulated Seyfert 1 spectra each with 375$\pm$1k counts. We assess the fits with reflection fraction of $R$ = 1 as well as reflection-dominated AGN with $R$ = 5. We also examine the consequence of permitting fits to search for retrograde spin. In general, we discover that most parameters are over-estimated when spectroscopy is restricted to the 2.5 - 10.0 keV regime and that models are insensitive to inner emissivity index and ionization. When the bandpass is extended out to 70keV, parameters are more accurately estimated. Repeating the process for $R$ = 5 reduces our ability to measure photon index ($\sim$3 to 8 per cent error and overestimated), but increases precision in all other parameters -- most notably ionization, which becomes better constrained ($\pm$45 erg cm $\rm{s^{-1}}$) for low ionization parameters ($\xi$$<$200 erg cm $\rm{s^{-1}}$). In all cases, we find the spin parameter is only well measured for the most rapidly rotating supermassive black holes (i.e. $a$ $>$ 0.8 to about $\pm$0.10) and that inner emissivity index is never well constrained. Allowing our model to search for retrograde spin did not improve the results.Comment: Accepted for publication in MNRAS. 13 pages, 7 figure