Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors

In this paper we study the existence of locally most powerful invariant tests (LMPIT) for the problem of testing the covariance structure of a set of Gaussian random vectors. The LMPIT is the optimal test for the case of close hypotheses, among those satisfying the invariances of the problem, and in practical scenarios can provide better performance than the typically used generalized likelihood ratio test (GLRT). The derivation of the LMPIT usually requires one to find the maximal invariant statistic for the detection problem and then derive its distribution under both hypotheses, which in general is a rather involved procedure. As an alternative, Wijsman's theorem provides the ratio of the maximal invariant densities without even finding an explicit expression for the maximal invariant. We first consider the problem of testing whether a set of $N$-dimensional Gaussian random vectors are uncorrelated or not, and show that the LMPIT is given by the Frobenius norm of the sample coherence matrix. Second, we study the case in which the vectors under the null hypothesis are uncorrelated and identically distributed, that is, the sphericity test for Gaussian vectors, for which we show that the LMPIT is given by the Frobenius norm of a normalized version of the sample covariance matrix. Finally, some numerical examples illustrate the performance of the proposed tests, which provide better results than their GLRT counterparts

Granulation in K-type Dwarf Stars. II. Hydrodynamic simulations and 3D spectrum synthesis

We construct a 3D radiative-hydrodynamic model atmosphere of parameters Teff = 4820 K, log g = 4.5, and solar chemical composition. The theoretical line profiles computed with this model are asymmetric, with their bisectors having a characteristic C-shape and their core wavelengths shifted with respect to their laboratory values. The line bisectors span from about 10 to 250 m/s, depending on line strength, with the stronger features showing larger span. The corresponding core wavelength shifts range from about -200 m/s for the weak Fe I lines to almost +100 m/s in the strong Fe I features. Based on observational results for the Sun, we argue that there should be no core wavelength shift for Fe I lines of EW > 100 mA. The cores of the strongest lines show contributions from the uncertain top layers of the model, where non-LTE effects and the presence of the chromosphere, which are important in real stars, are not accounted for. The comparison of model predictions to observed Fe I line bisectors and core wavelength shifts for a reference star, HIP86400, shows excellent agreement, with the exception of the core wavelength shifts of the strongest features, for which we suspect inaccurate theoretical values. Since this limitation does not affect the predicted line equivalent widths significantly, we consider our 3D model validated for photospheric abundance work.Comment: A&A, in pres

The temporal evolution of neutron-capture elements in the Galactic discs

Important insights into the formation and evolution of the Galactic disc(s) are contained in the chemical compositions of stars. We analysed high-resolution and high signal to noise HARPS spectra of 79 solar twin stars in order to obtain precise determinations of their atmospheric parameters, ages ($\sigma$$\sim$0.4 Gyr) and chemical abundances ($\sigma$$<$0.01~dex) of 12 neutron-capture elements (Sr, Y, Zr, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, and Dy). This valuable dataset allows us to study the [X/Fe]-age relations over a time interval of $\sim$10 Gyr and among stars belonging to the thin and thick discs. These relations show that i) the $s$-process has been the main channel of nucleosynthesis of $n$-capture elements during the evolution of the thin disc; ii) the thick disc is rich in $r$-process elements which suggests that its formation has been rapid and intensive. %; iii) a chemical continuity between the thin and thick discs is evident in the abundances of Ba. In addition, the heavy (Ba, La, Ce) and light (Sr, Y, Zr) $s$-process elements revealed details on the dependence between the yields of AGB stars and the stellar mass or metallicity. Finally, we confirmed that both [Y/Mg] and [Y/Al] ratios can be employed as stellar clocks, allowing ages of solar twin stars to be estimated with an average precision of $\sim$0.5~Gyr

Nonlinear Dynamics of Dipoles in Microtubules: Pseudo-Spin Model

We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of the classical pseudo-spin model. We derive the system of nonlinear dynamical ordinary differential equations of motion for interacting dipoles, and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.Comment: 14 pages, 15 figures. The high resolution figure files are available by reques

Masculinity and feminity measurement in physical education teachers

Esta investigación tuvo por objetivo analizar las mediciones de masculinidad, feminidad, machismo y sumisión, características asociadas a la personalidad, de un grupo de docentes de Educación Física. Participaron en el estudio 53 docentes de nivel básico que laboran en un programa implementado por una institución gubernamental en la Ciudad de México. El muestreo fue de tipo no probabilístico. Se empleó como instrumento el Inventario de Masculinidad y Feminidad (IMAFE), instrumento confiable y válido en México, sujeto a prueba en otros países, en él se incluyen aspectos de los papeles de género tradicionales: machismo y sumisión. El análisis de los datos se efectúo mediante la prueba “t-Student” y el análisis de varianza de una clasificación, así como la comparación de medias de los resultados arrojados. Se concluye que no hay diferencias estadísticamente significativas en las cuatro escalas propuestas por el IMAFE y las variables de trabajo, sexo, edad y estado civil, en el grupo de docentes de Educación Física, en lo que respecta a las características asociadas a la personalidadThis research aimed to analyze the measurements of masculinity, femininity, machismo and submission features associated with the personality characteristics of a group of physical education teachers. Participated in the study53 basic level teachers working in a program implemented by a government institution in Mexico City. The sampling was not probabilistic type. As a tool for data collection was used the Inventory of Masculinity and femininity (IMAFE), reliable and valid instrument in Mexico, subject to testing in other countries, there aspects of traditional gender roles: machismo and submission. Data analysis undertaken using the “t-student” test and analysis of variance classification and comparison of the results obtained. It is concluded that no statistically significant differences in the four scales proposed by IMAFE and work variables sex, age and marital status in the group of physical education teachers in regard to the characteristics associated with personalit

Changes in retinal OCT and their correlations with neurological disability in early ALS patients, a follow-up study

Background: To compare early visual changes in amyotrophic lateral sclerosis (ALS) patients with healthy controls in a baseline exploration, to follow-up the patients after 6 months, and to correlate these visual changes with neurological disability. Methods: All patients underwent a comprehensive neurological and ophthalmological examination. A linear mixed analysis and Bonferroni p-value correction were performed, testing four comparisons as follows: Control baseline vs. control follow-up, control baseline vs. ALS baseline, control follow-up vs. ALS follow-up, and ALS baseline vs. ALS follow-up. Results: The mean time from the diagnosis was 10.80 +/- 5.5 months. The analysis of the optical coherence tomography (OCT) showed: (1) In ALS baseline vs. control baseline, a macular significantly increased thickness of the inner macular ring temporal and inferior areas; (2) in ALS follow-up vs. ALS baseline, a significant macular thinning in the inner and outer macular ring inferior areas; (3) in ALS follow-up vs. ALS baseline, a significant peripapillary retinal nerve fiber layer (pRNFL) thinning in the superior and inferior quadrants; and (4) ALS patients showed a moderate correlation between some OCT pRNFL parameters and Amyotrophic Lateral Sclerosis Functional Rating Scale-Revised (ALSFRS-R) score. Conclusion: The OCT showed retinal changes in patients with motoneuron disease and could serve as a complementary tool for studying ALS

The VLT-FLAMES Tarantula Survey X: Evidence for a bimodal distribution of rotational velocities for the single early B-type stars

Aims: Projected rotational velocities (\vsini) have been estimated for 334 targets in the VLT-FLAMES Tarantula survey that do not manifest significant radial velocity variations and are not supergiants. They have spectral types from approximately O9.5 to B3. The estimates have been analysed to infer the underlying rotational velocity distribution, which is critical for understanding the evolution of massive stars. Methods: Projected rotational velocities were deduced from the Fourier transforms of spectral lines, with upper limits also being obtained from profile fitting. For the narrower lined stars, metal and non-diffuse helium lines were adopted, and for the broader lined stars, both non-diffuse and diffuse helium lines; the estimates obtained using the different sets of lines are in good agreement. The uncertainty in the mean estimates is typically 4% for most targets. The iterative deconvolution procedure of Lucy has been used to deduce the probability density distribution of the rotational velocities. Results: Projected rotational velocities range up to approximately 450 \kms and show a bi-modal structure. This is also present in the inferred rotational velocity distribution with 25% of the sample having $0\leq$\ve$\leq$100\,\kms and the high velocity component having \ve$\sim 250$\,\kms. There is no evidence from the spatial and radial velocity distributions of the two components that they represent either field and cluster populations or different episodes of star formation. Be-type stars have also been identified. Conclusions: The bi-modal rotational velocity distribution in our sample resembles that found for late-B and early-A type stars. While magnetic braking appears to be a possible mechanism for producing the low-velocity component, we can not rule out alternative explanations.Comment: to be publisged in A&

Nucleosynthetic history of elements in the Galactic disk [X/Fe]-age relations from high-precision spectroscopy

Context. The chemical composition of stars is intimately linked to the formation and evolution of the Galaxy. Aims. We aim to trace the chemical evolution of the Galactic disk through the inspection of the [X/Fe]–age relations of 24 species from C to Eu. Methods. Using high-resolution and high signal-to-noise UVES spectra of nine solar twins, we obtained precise estimates of stellar ages and chemical abundances. These determinations have been integrated with additional accurate age and abundance determinations from recent spectroscopic studies of solar twins existing in the literature, comprising superb abundances with 0.01 dex precision. Based on this data set, we outlined the [X/Fe]–age relations over a time interval of 10 Gyr. Results. We present the [X/Fe] – age relations for 24 elements (C, O, Na, Mg, Al, Si, S, K, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Zn, Y, Ba, La, Ce, Nd, and Eu). Each different class of elements showed a distinct evolution with time that relies on the different characteristics, rates, and timescales of the nucleosynthesis sites from which they are produced. The α-elements are characterized by a [X/Fe] decrease with time. Strikingly, the opposite behavior is observed for Ca. The iron-peak elements show an early [X/Fe] increase followed by a decrease towards the youngest stars. The [X/Fe] for the n-capture elements decrease with age. We also found that both [Mg/Y] and [Al/Y] are precise stellar clocks, with [Al/Y] showing the steepest dependence on age. Conclusions. Knowledge of the [X/Fe]-age relations is a gold mine from which we can achieve a great understanding of the processes that governed the formation and evolution of the Milky Way. Through the reverse engineering of these relations we will be able to put strong constraints on the nature of the stellar formation history, the SNe rates, the stellar yields, and the variety of the SNe progenitors

Tomographic findings and mortality in patients with severe and critical pneumonia with COVID-19 diagnosis

Introduction: A high percentage of patients with non-severe (17.9%) and severe (2.9%) atypical pneumonia do not display pulmonary tomographic findings upon hospital admission; furthermore, lesion associated with COVI-19 are peripherally distributed in a multifocal ground-glass pattern, as well as displaying an irregular consolidation pattern, with a posterior or lower lobe predilection. The main objective of this study was to identify the pulmonary radiological patterns in patients diagnosed with SARS-CoV-2 pneumonia, the factors associated with the need for mechanical ventilation, as well as their survival rates at 30 days. Methods: We report the pulmonary tomographic findings of 490 consecutive patients with severe and critical pneumonia due to SARS-CoV-2. The patients were classified according to the tomography and demographic findings, sepsis severity prognostic scales, Charlson comorbidity index (CCI), the Sequential Organ Failure Assessment (SOFA), and the Acute Physiology and Chronic Health Evaluation (APACHE IV). The Kaplan-Meier method was used to calculate survival distributions. Results: 89.80% of patients had ground-glass opacities, 81.63% radiologic consolidation sign, 42.45% vascular thickening pattern, 37.55% lymphadenopathies, 14.90% pleural effusion, and 2.65% pulmonary thrombosis; meanwhile, 91.02% had bilateral lesions, 85.51% had peripheral lesions, and 75.92% had basal lobe lesions. APACHE IV (HR, 1.191, 95% CI [1.126, 1.260]), SOFA (HR, 5.178, 95%CI [3.103, 8.641]), and CCI (HR, 0.673, 95%CI [0.510, 0.889]), as well as the pulmonary damage severity index (HR, 1.282, 95%CI [1.151, 1.428]), predict the need for invasive mechanical ventilation. Only moderate ARDS patients with mild and severe lung disease showed different 30-day mortality distributions (χ2 = 7.00, p = 0.008). Discussion: Although the survival distributions did not vary significantly, an overwhelming majority of patients (i.e., 84.35%) with a higher pulmonary damage severity index (i.e., 23>) died within 30 days of hospital admission, while only 25.91% with moderate lung damage and 2.42% with mild lung damage