Sums of kk-bonacci Numbers

We give a combinatorial proof of a formula giving the partial sums of the $k$-bonacci sequence as alternating sums of powers of two multiplied by binomial coefficients. As a corollary we obtain a formula for the $k$-bonacci numbers.Comment: 6 page

Stellar Diameters and Temperatures. I. Main-Sequence A, F, and G Stars

We have executed a survey of nearby, main-sequence A-, F-, and G-type stars with the CHARA Array, successfully measuring the angular diameters of forty-four stars with an average precision of ~1.5%. We present new measures of the bolometric flux, which in turn leads to an empirical determination of the effective temperature for the stars observed. In addition, these CHARA-determined temperatures, radii, and luminosities are fit to Yonsei-Yale model isochrones to constrain the masses and ages of the stars. These results are compared to indirect estimates of these quantities obtained by collecting photometry of the stars and applying them to model atmospheres and evolutionary isochrones. We find that for most cases, the models overestimate the effective temperature by ~1.5%-4% when compared to our directly measured values. The overestimated temperatures and underestimated radii in these works appear to cause an additional offset in the star's surface gravity measurements, which consequently yield higher masses and younger ages, in particular for stars with masses greater than ~1.3 M_☉. Additionally, we compare our measurements to a large sample of eclipsing binary stars, and excellent agreement is seen within both data sets. Finally, we present temperature relations with respect to (B – V) and (V – K) colors as well as spectral type, showing that calibration of effective temperatures with errors ~1% is now possible from interferometric angular diameters of stars

Stellar Diameters and Temperatures II. Main Sequence K & M Stars

We present interferometric diameter measurements of 21 K- and M- dwarfs made with the CHARA Array. This sample is enhanced by literature radii measurements to form a data set of 33 K-M dwarfs with diameters measured to better than 5%. For all 33 stars, we compute absolute luminosities, linear radii, and effective temperatures (Teff). We develop empirical relations for \simK0 to M4 main- sequence stars between the stellar Teff, radius, and luminosity to broad-band color indices and metallicity. These relations are valid for metallicities between [Fe/H] = -0.5 and +0.1 dex, and are accurate to ~2%, ~5%, and ~4% for Teff, radius, and luminosity, respectively. Our results show that it is necessary to use metallicity dependent transformations to convert colors into stellar Teffs, radii, and luminosities. We find no sensitivity to metallicity on relations between global stellar properties, e.g., Teff-radius and Teff-luminosity. Robust examinations of single star Teffs and radii compared to evolutionary model predictions on the luminosity-Teff and luminosity-radius planes reveals that models overestimate the Teffs of stars with Teff < 5000 K by ~3%, and underestimate the radii of stars with radii < 0.7 R\odot by ~5%. These conclusions additionally suggest that the models overestimate the effects that the stellar metallicity may have on the astrophysical properties of an object. By comparing the interferometrically measured radii for single stars to those of eclipsing binaries, we find that single and binary star radii are consistent. However, the literature Teffs for binary stars are systematically lower compared to Teffs of single stars by ~ 200 to 300 K. Lastly, we present a empirically determined HR diagram for a total of 74 nearby, main-sequence, A- to M-type stars, and define regions of habitability for the potential existence of sub-stellar mass companions in each system. [abridged]Comment: 73 pages, 12 Tables, 18 Figures. Accepted for publication in The Astrophysical Journa

Erratum: “stellar diameters and temperatures. II. main-sequence K- and M-stars” (2012, ApJ, 757, 112)

Published versio

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead