V39: an unusual object in the field of IC 1613

The variable star V39 in the field of IC 1613 is discussed in the light of the available photometric and new spectroscopic data. It has strong emission Balmer lines, and the observed characteristics could be explained by a W Vir pulsating star with a period of 14.341 d, located at more than 115 kpc, that is in the very outer halo of our Galaxy. It should have an apparent companion, a long period (1118d) red variable, belonging to IC 1613. The main uncertainty in this interpretation is an emission feature at 668.4 nm, which we tentatively identified as a He I line.Comment: 5 pages; accepted for publication in Astronomy & Astrophysic

The Cepheid Phase Lag Revisited

We compute the phase lags between the radial velocity curves and the light curves $\Delta \Phi_1= \phi^{V_r}_1 - \phi^{mag}_1$ for classical Cepheid model sequences both in the linear and the nonlinear regimes. The nonlinear phase lags generally fall below the linear ones except for high period models where they lie above, and of course for low pulsation amplitudes where the two merge. The calculated phase lags show good agreement with the available observational data of normal amplitude Galactic Cepheids. The metallicity has but a moderate effect on the phase lag, while the mass-luminosity relation and the parameters of the turbulent convective model (time-dependent mixing length) mainly influence the modal selection and the period, which is then reflected in the period -- $\Delta \Phi_1$ diagram. We discuss the potential application of this observable as a discriminant for pulsation modes and as a test for ultra-low amplitudes (ULA) pulsation.Comment: 11 pages, 8 figures, accepted for publication in ApJ, minor revisions in the text and figures, (black and white version available from 2nd author's website

Variable stars in nearby galaxies. VI. Frequency-period distribution of Cepheids in IC 1613 and other galaxies of the Local Group

The frequency--period distribution and other properties of Cepheids in IC 1613 are discussed and compared with those of stars in our Galaxy (Milky Way), LMC, SMC, M31 and M33. Taking into account the observational limitations and related incompleteness, it is concluded that the frequency-period distribution of Cepheids in IC 1613 is similar to that of SMC; we suspect that a much larger number of stars exist in IC 1613 with a period of less than 2 d that have not yet been detected. A discussion of the deficiency of fundamental mode Cepheids with periods in the range 8 - 10 d in the Milky Way, M31 and M33 is reported. The present data are not sufficient to verify if this is produced by a real bimodal frequency--period distribution or whether depends on the lack of pulsating stars in such a period range due to pulsational stability reasons. Some arguments are presented in favor of a bimodal distribution that is a function of the average metallicity. The Milky Way, M31 and M33 have the two maxima located at the same periods, about 5 and 13 d, respectively. A comment on very long period Cepheids is also given.Comment: 6 pages; accepted for publication in Astronomy and Astrophysic

On the use of Principal Component Analysis in analysing Cepheid light curves

We show how Principal Component Analysis can be used to analyse the structure of Cepheid light curves. This method is more efficient than Fourier analysis at bringing out changes in light curve shape as a function of period. Using this technique, we study the shape of fundamental and first overtone mode Cepheid light curves in the Galaxy, LMC and SMC over a wide period range. For fundamentals, we find evidence for structural changes at $\log P \approx 1.55, 2.1$. It is suggested that the feature at $\log P \approx 2.1$ is associated with a resonance in the Cepheid normal mode spectrum. For overtones, we recover the Z shape in the $R_{21}$ period plane and reproduce the metallicity dependence of this Z shape.Comment: Accepted for publication in MNRA

The Index Distribution of Gaussian Random Matrices

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N_{+}/N scales, for large N, as Prob(c,N)\simeq\exp[-\beta N^2 \Phi(c)] where the rate function \Phi(c), symmetric around c=1/2 and universal (independent of $\beta$), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at c=1/2 it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function.Comment: 4 pages Revtex, 4 .eps figures include

Variable stars in nearby galaxies. V. Search for Cepheids in Field A of NGC 6822

The results of a CCD survey for variability of stars in the nearby galaxy NGC 6822 are presented. The goal of the survey was to obtain good light curves of Cepheids for Fourier decomposition and to detect shorter period Cepheids. Since the program was carried out with a relatively small telescope, the Dutch 0.9 m at ESO-La Silla, the observations were unfiltered (white light, or Wh-band). The analysis revealed the presence of more than 130 variable stars. 21 population I Cepheids are detected; 6 of them were already known from previous works (Kayser, 1967). For at least three Cepheids, however, the previous identification or period was wrong. Some probable population II (W Vir) stars are also identified. The dispersion of the fundamental mode Cepheid PL relation appears to be small.Comment: 5 pages; accepted for publication in Astronomy and Astrophysic

Parsimonious hidden Markov models for matrix-variate longitudinal data

Hidden Markov models (HMMs) have been extensively used in the univariate and multivariate literature. However, there has been an increased interest in the analysis of matrix-variate data over the recent years. In this manuscript we introduce HMMs for matrix-variate balanced longitudinal data, by assuming a matrix normal distribution in each hidden state. Such data are arranged in a four-way array. To address for possible overparameterization issues, we consider the eigen decomposition of the covariance matrices, leading to a total of 98 HMMs. An expectation-conditional maximization algorithm is discussed for parameter estimation. The proposed models are firstly investigated on simulated data, in terms of parameter recovery, computational times and model selection. Then, they are fitted to a four-way real data set concerning the unemployment rates of the Italian provinces, evaluated by gender and age classes, over the last 16 years.publishedVersio

A nutrition mathematical model to account for dietary supply and requirements of energy and nutrients for domesticated small ruminants: the development and evaluation of the Small Ruminant Nutrition System

A mechanistic model that predicts nutrient requirements and biological values of feeds for sheep (Cornell Net Carbohydrate and Protein System; CNCPS-S) was expanded to include goats and the name was changed to the Small Ruminant Nutrition System (SRNS). The SRNS uses animal and environmental factors to predict metabolizable energy (ME) and protein, and Ca and P requirements. Requirements for goats in the SRNS are predicted based on the equations developed for CNCPS-S, modified to account for specific requirements of goats, including maintenance, lactation, and pregnancy requirements, and body reserves. Feed biological values are predicted based on carbohydrate and protein fractions and their ruminal fermentation rates, forage, concentrate and liquid passage rates, and microbial growth. The evaluation of the SRNS for sheep using published papers (19 treatment means) indicated no mean bias (MB; 1.1 g/100 g) and low root mean square prediction error (RMSPE; 3.6 g/100g) when predicting dietary organic matter digestibility for diets not deficient in ruminal nitrogen. The SRNS accurately predicted gains and losses of shrunk body weight (SBW) of adult sheep (15 treatment means; MB = 5.8 g/d and RMSPE = 30 g/d) when diets were not deficient in ruminal nitrogen. The SRNS for sheep had MB varying from -34 to 1 g/d and RSME varying from 37 to 56 g/d when predicting average daily gain (ADG) of growing lambs (42 treatment means). The evaluation of the SRNS for goats based on literature data showed accurate predictions for ADG of kids (31 treatment means; RMSEP = 32.5 g/d; r2= 0.85; concordance correlation coefficient, CCC, = 0.91), daily ME intake (21 treatment means; RMSEP = 0.24 Mcal/d g/d; r2 = 0.99; CCC = 0.99), and energy balance (21 treatment means; RMSEP = 0.20 Mcal/d g/d; r2 = 0.87; CCC = 0.90) of goats. In conclusion, the SRNS for sheep can accurately predict dietary organic matter digestibility, ADG of growing lambs and changes in SBW of mature sheep. The SRNS for goats is suitable for predicting ME intake and the energy balance of lactating and non-lactating adult goats and the ADG of kids of dairy, meat, and indigenous breeds. The SRNS model is available at http://nutritionmodels.tamu.edu