Optimal Computation of Overabundant Words

The observed frequency of the longest proper prefix, the longest proper suffix, and the longest infix of a word w in a given sequence x can be used for classifying w as avoided or overabundant. The definitions used for the expectation and deviation of w in this statistical model were described and biologically justified by Brendel et al. (J Biomol Struct Dyn 1986). We have very recently introduced a time-optimal algorithm for computing all avoided words of a given sequence over an integer alphabet (Algorithms Mol Biol 2017). In this article, we extend this study by presenting an O(n)-time and O(n)-space algorithm for computing all overabundant words in a sequence x of length n over an integer alphabet. Our main result is based on a new non-trivial combinatorial property of the suffix tree T of x: the number of distinct factors of x whose longest infix is the label of an explicit node of T is no more than 3n-4. We further show that the presented algorithm is time-optimal by proving that O(n) is a tight upper bound for the number of overabundant words. Finally, we present experimental results, using both synthetic and real data, which justify the effectiveness and efficiency of our approach in practical terms

Determining the spectroscopic mass ratio in interacting binaries: Application to X-Ray Nova Sco 1994

We present a model for determining the mass ratio in interacting binaries by directly fitting the observed spectrum with synthetic spectra. We make direct use of NextGen model atmospheres intensities which are the most comprehensive and detailed models available for cool stars. We fully take into account the varying temperature and gravity across the secondary star's photosphere, by incorporating the synthetic spectra into the secondary star's Roche geometry. As a result, we determine the exact rotationally broadened spectrum of the secondary star and so eliminate the need for a limb-darkening law, and the uncertainties associated with it. As an example we determine the mass ratio for the well studied soft X-ray transient Nova Sco 1994. In order to obtain a more accurate determination of the mass ratio, which does not depend on assumptions about the rotation profile and limb-darkening coefficients, we use our model to compute the exact rotationally broadened model spectrum, which we compare directly with the observed intermediate resolution spectrum of Nova Sco 1994. We determine the mass ratio of Nova Sco 1994 to be 0.419+/-0.028 (90 percent confidence), which is the most accurate determination of the binary mass ratio in an X-ray binary. This result combined with the binary mass function and inclination angle gives a refined black hole mass of 5.99+\-0.42 Mo (90 percent confidence). We also perform simulations which show that, for an F-type secondary star, the standard rotation profile with zero and continuum value for the line limb-darkening coefficient gives a value for q that brackets the value found using the full geometrical treatment.Comment: 11 pages including 5 figures, accepted by MNRA

Optimal Computation of Avoided Words

The deviation of the observed frequency of a word $w$ from its expected frequency in a given sequence $x$ is used to determine whether or not the word is avoided. This concept is particularly useful in DNA linguistic analysis. The value of the standard deviation of $w$, denoted by $std(w)$, effectively characterises the extent of a word by its edge contrast in the context in which it occurs. A word $w$ of length $k>2$ is a $\rho$-avoided word in $x$ if $std(w) \leq \rho$, for a given threshold $\rho < 0$. Notice that such a word may be completely absent from $x$. Hence computing all such words na\"{\i}vely can be a very time-consuming procedure, in particular for large $k$. In this article, we propose an $O(n)$-time and $O(n)$-space algorithm to compute all $\rho$-avoided words of length $k$ in a given sequence $x$ of length $n$ over a fixed-sized alphabet. We also present a time-optimal $O(\sigma n)$-time and $O(\sigma n)$-space algorithm to compute all $\rho$-avoided words (of any length) in a sequence of length $n$ over an alphabet of size $\sigma$. Furthermore, we provide a tight asymptotic upper bound for the number of $\rho$-avoided words and the expected length of the longest one. We make available an open-source implementation of our algorithm. Experimental results, using both real and synthetic data, show the efficiency of our implementation

A Thousand and One Nova Outbursts

Multicycle nova evolution models have been calculated over the past twenty years, the number being limited by numerical constraints. Here we present a long-term evolution code that enables a continuous calculation through an unlimited number of nova cycles for an unlimited evolution time, even up to (or exceeding) a Hubble time. Starting with two sets of the three independent nova parameters -- the white dwarf mass, the temperature of its isothermal core, and the rate of mass transfer on to it -- we have followed the evolution of two models, with initial masses of 1 and 0.65 solar masses, accretion rates (constant throughout each calculation) of 1e-11 and 1e-9 solar-masses/yr, and relatively high initial temperatures (as they are likely to be at the onset of the outburst phase), through over 1000 and over 3000 cycles, respectively. The results show that although on the short-term consecutive outbursts are almost identical, on the long-term scale the characteristics change. This is mainly due to the changing core temperature, which decreases very similarly to that of a cooling white dwarf for a time, but at a slower rate thereafter. As the white dwarf's mass continually decreases, since both models lose more mass than they accrete, the central pressure decreases accordingly. The outbursts on the massive white dwarf change gradually from fast to moderately fast, and the other characteristics (velocity, abundance ratios, isotopic ratios) change, too. Very slowly, a steady state is reached, where all characteristics, both in quiescence and in outburst, remain almost constant. For the less massive white dwarf accreting at a high rate, outbursts are similar throughout the evolution.Comment: To be published in MNRA

Chemical stratification in the atmosphere of Ap star HD 133792. Regularized solution of the vertical inversion problem

High spectral resolution studies of cool Ap stars reveal conspicuous anomalies of the shape and strength of many absorption lines. This is a signature of large atmospheric chemical gradients produced by the selective radiative levitation and gravitational settling of chemical species. Here we present a new approach to mapping the vertical chemical structures in stellar atmospheres. We have developed a regularized chemical inversion procedure that uses all information available in high-resolution stellar spectra. The new technique for the first time allowed us to recover chemical profiles without making a priori assumptions about the shape of chemical distributions. We have derived average abundances and applied the vertical inversion procedure to the high-resolution VLT UVES spectra of the weakly magnetic, cool Ap star HD 133792. Our analysis yielded improved estimates of the atmospheric parameters of HD 133792. We show that this star has negligible vsini and the mean magnetic field modulus =1.1+/-0.1 kG. We have derived average abundances for 43 ions and obtained vertical distributions of Ca, Si, Mg, Fe, Cr, and Sr. All these elements except Mg show high overabundance in the deep layers and solar or sub-solar composition in the upper atmosphere of HD 133792. In contrast, the Mg abundance increases with height. We find that transition from the metal-enhanced to metal-depleted zones typically occurs in a rather narrow range of depths in the atmosphere of HD 133792. Based on the derived photospheric abundances, we conclude that HD 133792 belongs to the rare group of evolved cool Ap stars, which possesses very large Fe-peak enhancement, but lacks a prominent overabundance of the rare-earth elements.Comment: Accepted by A&A; 12 pages, 9 figure

Late stages of the evolution of A-type stars on the main sequence: comparison between observed chemical abundances and diffusion models for 8 Am stars of the Praesepe cluster

Aims. We aim to provide observational constraints on diffusion models that predict peculiar chemical abundances in the atmospheres of Am stars. We also intend to check if chemical peculiarities and slow rotation can be explained by the presence of a weak magnetic field. Methods. We have obtained high resolution, high signal-to-noise ratio spectra of eight previously-classified Am stars, two normal A-type stars and one Blue Straggler, considered to be members of the Praesepe cluster. For all of these stars we have determined fundamental parameters and photospheric abundances for a large number of chemical elements, with a higher precision than was ever obtained before for this cluster. For seven of these stars we also obtained spectra in circular polarization and applied the LSD technique to constrain the longitudinal magnetic field. Results. No magnetic field was detected in any of the analysed stars. HD 73666, a Blue Straggler previously considered as an Ap (Si) star, turns out to have the abundances of a normal A-type star. Am classification is not confirmed for HD 72942. For HD 73709 we have also calculated synthetic Delta-a photometry that is in good agreement with the observations. There is a generally good agreement between abundance predictions of diffusion models and values that we have obtained for the remaining Am stars. However, the observed Na and S abundances deviate from the predictions by 0.6 dex and >0.25 dex respectively. Li appears to be overabundant in three stars of our sample.Comment: Accepted for publication on A&

Constraining the solutions of an inverse method of stellar population synthesis

In three previous papers (Pelat 1997, 1998 and Moultaka & Pelat 2000), we set out an inverse stellar population synthesis method which uses a database of stellar spectra. Unlike other methods, this one provides a full knowledge of all possible solutions as well as a good estimation of their stability; moreover, it provides the unique approximate solution, when the problem is overdetermined, using a rigorous minimization procedure. In Boisson et al. (2000), this method has been applied to 10 active and 2 normal galaxies. In this paper we analyse the results of the method after constraining the solutions. Adding {\it a priori} physical conditions on the solutions constitutes a good way to regularize the synthesis problem. As an illustration we introduce physical constraints on the relative number of stars taking into account our present knowledge of the initial mass function in galaxies. In order to avoid biases on the solutions due to such constraints, we use constraints involving only inequalities between the number of stars, after dividing the H-R diagram into various groups of stellar masses. We discuss the results for a well-known globular cluster of the galaxy M31 and discuss some of the galaxies studied in Boisson et al. (2000). We find that, given the spectral resolution and the spectral domain, the method is very stable according to such constraints (i.e. the constrained solutions are almost the same as the unconstrained one). However, an additional information can be derived about the evolutionary stage of the last burst of star formation, but the precise age of this particular burst seems to be questionable.Comment: Accepted in A&A. 15 pages, 5 figures and 6 table