Cross-Document Pattern Matching

We study a new variant of the string matching problem called cross-document string matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear-space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted level ancestor problem

Efficient Seeds Computation Revisited

The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover. The seed is a more complicated generalization of periodicity, it is a cover of a superstring of a given string, and the shortest seed problem is of much higher algorithmic difficulty. The problem is not well understood, no linear time algorithm is known. In the paper we give linear time algorithms for some of its versions --- computing shortest left-seed array, longest left-seed array and checking for seeds of a given length. The algorithm for the last problem is used to compute the seed array of a string (i.e., the shortest seeds for all the prefixes of the string) in $O(n^2)$ time. We describe also a simpler alternative algorithm computing efficiently the shortest seeds. As a by-product we obtain an $O(n\log{(n/m)})$ time algorithm checking if the shortest seed has length at least $m$ and finding the corresponding seed. We also correct some important details missing in the previously known shortest-seed algorithm (Iliopoulos et al., 1996).Comment: 14 pages, accepted to CPM 201

The spectroscopic evolution of the recurrent nova T Pyxidis during its 2011 outburst I. The optically thick phase and the origin of moving lines in novae

The nova T Pyx was observed with high resolution spectroscopy (R ~ 65000) spectroscopy, beginning 1 day after discovery of the outburst and continuing through the last visibility of the star at the end of May 2011. The interstellar absorption lines of Na I, Ca II, CH, CH$^+$, and archival H I 21 cm emission line observations have been used to determine a kinematic distance. Interstellar diffuse absorption features have been used to determine the extinction independent of previous assumptions. Sample Fe-peak line profiles show the optical depth and radial velocity evolution of the discrete components. We propose a distance to T Pyx $\geq$4.5kpc, with a strict lower limit of 3.5 kpc (the previously accepted distance). We derive an extinction, E(B-V)$\approx0.5\pm$0.1, that is higher than previous estimates. The first observation, Apr. 15, displayed He I, He II, C III, and N III emission lines and a maximum velocity on P Cyg profiles of the Balmer and He I lines of $\approx$2500 km s$^{-1}$ characteristic of the fireball stage. These ions were undetectable in the second spectrum, Apr. 23, and we use the recombination time to estimate the mass of the ejecta, $10^{-5}f$M$_\odot$ for a filling factor $f$. Numerous absorption line systems were detected on the Balmer, Fe-peak, Ca II, and Na I lines, mirrored in broader emission line components, that showed an "accelerated" displacement in velocity. We also show that the time sequence of these absorptions, which are common to all lines and arise only in the ejecta, can be described by recombination front moving outward in the expanding gas without either a stellar wind or circumstellar collisions.Comment: Accepted for publication in Astronomy & Astrophysics Letters (17/8/11

Subaru/HDS Abundances in Three Giant Stars in the Ursa Minor Dwarf Spheroidal Galaxy

With the HDS (High Dispersion Spectrograph) on the Subaru telescope, we obtained high resolution optical region spectra of three red giant stars (cos 4, cos 82, and cos 347) in the Ursa Minor dwarf spheriodal galaxy. Chemical abundances in these stars have been analysed for 26 elements including alpha-, iron-peak, and neutron capture elements. All three stars show low abundances of alpha-elements (Mg, Si, and Ca) and two stars (cos 82 and cos 347) show high abundance of Mn compared to Galactic halo stars of similar metallicity. One star (cos 4) has been confirmed to be very metal deficient ([Fe/H]=-2.7) and found to show anomalously low abundances of Mn, Cu, and Ba. In another star cos 82 ([Fe/H]=-1.5), we have found large excess of heavy neutron-capture elements with the general abundance pattern similar to the scaled solar system r-process abundance curve. These observational results are rather puzzling: low abundances of alpha-elements and high abundance of Mn seem to sugggest a significant contribution of SNe Ia at low metallicity, while there is no hint of s-process (i.e., AGB stars) contribution even at [Fe/H]=-1.5, suggesting a peculiar nucleosynthetic history of the UMi dSph galaxy.Comment: 26 pages with 12 figures, accepted to PAS

Cooler and bigger than thought? Planetary host stellar parameters from the InfraRed Flux Method

Effective temperatures and radii for 92 planet-hosting stars as determined from the InfraRed Flux Method (IRFM) are presented and compared with those given by other authors using different approaches. The IRFM temperatures we have derived are systematically lower than those determined from the spectroscopic condition of excitation equilibrium, the mean difference being as large as 110 K. They are, however, consistent with previous IRFM studies and with the colors derived from Kurucz and MARCS model atmospheres. Comparison with direct measurements of stellar diameters for 7 dwarf stars, which approximately cover the range of temperatures of the planet-hosting stars, suggest that the IRFM radii and temperatures are reliable in an absolute scale. A better understanding of the fundamental properties of the stars with planets will be achieved once this discrepancy between the IRFM and the spectroscopic temperature scales is resolved.Comment: 15 pages, 4 figures. Accepted for publication in Ap

Supernova type Ia luminosities, their dependence on second parameters, and the value of H_0

A sample of 35 SNe Ia with good to excellent photometry in B and V, minimum internal absorption, and 1200 < v < \approx 30000 km/s is compiled from the literature. As far as their spectra are known they are all Branch-normal. For 29 of the SNe Ia also peak magnitudes in I are known. The SNe Ia have uniform colors at maximum, i.e. =-0.012 mag (sigma=0.051) and =-0.276 mag (sigma=0.078). In the Hubble diagram they define a Hubble line with a scatter of $\sigma_M$=0.21-0.16 mag, decreasing with wavelength. The scatter is further reduced if the SNe Ia are corrected for differences in decline rate Delta_m_15 or color (B-V). A combined correction reduces the scatter to sigma<=0.13 mag. After the correction no significant dependence remains on Hubble type or galactocentric distance. The Hubble line suggests some curvature which can be differently interpreted. A consistent solution is obtained for a cosmological model with Omega_M=0.3, Omega_Lambda=0.7, which is indicated also by much more distant SNe Ia. Absolute magnitudes are available for eight equally blue (Branch-normal) SNe Ia in spirals, whose Cepheid distances are known. If their well defined mean values of M_B, M_V, and M_I are used to fit the Hubble line to the above sample of SNe Ia one obtains H_0=58.3 km/s/Mpc, or, after adjusting all SNe Ia to the average values of Delta_m_15 and (B-V), H_0=60.9 km/s/Mpc. Various systematic errors are discussed whose elimination tends to decrease H_0. The finally adopted value at the 90-percent level, including random and systematic errors, is H_0=58.5 +/- 6.3 km/s/Mpc. Several higher values of H_0 from SNe Ia, as suggested in the literature, are found to depend on large corrections for variations of the light curve parameter and/or on an unwarranted reduction of the Cepheid distances of the calibrating SNe Ia.Comment: 42 pages, including 9 figures; submitted to Ap

Five-Year Optical and Near Infrared Observations of the Extremely Slow Nova V1280 Scorpii

We present optical ($B$, $V$, $R_{\rm c}$, $I_{\rm c}$ and $y$) and near infrared ($J$, $H$ and $K_{\rm s}$) photometric and spectroscopic observations of a classical nova V1280 Scorpii for five years from 2007 to 2011. Our photometric observations show a declining event in optical bands shortly after the maximum light which continues $\sim$ 250 days. The event is most probably caused by a dust formation. The event is accompanied by a short ($\sim$ 30 days) re-brightening episode ($\sim$ 2.5 mag in $V$), which suggests a re-ignition of the surface nuclear burning. After 2008, the $y$ band observations show a very long plateau at around $y$ = 10.5 for more than 1000 days until April 2011 ($\sim$ 1500 days after the maximum light). The nova had taken a very long time ($\sim$ 50 months) before entering the nebular phase (clear detection of both [\ion{O}{iii}] 4959 and 5007) and is still continuing to generate the wind caused by H-burning. The finding suggests that V1280 Sco is going through the historically slowest evolution. The interval from the maximum light (2007 February 16) to the beginning of the nebular phase is longer than any previously known slow novae: V723 Cas (18 months), RR Pic (10 months), or HR Del (8 months). It suggests that the mass of a white dwarf in the V1280 Sco system might be 0.6 M_\mathrm{\sun} or smaller. The distance, based on our measurements of the expansion velocity combined with the directly measured size of the dust shell, is estimated to be 1.1 $\pm$ 0.5 kpc.Comment: 17 pages, 14 figures, accepted for publication in A&

Comparative Direct Analysis of Type Ia Supernova Spectra. IV. Postmaximum

A comparative study of optical spectra of Type Ia supernovae (SNe Ia) obtained near 1 week, 3 weeks, and 3 months after maximum light is presented. Most members of the four groups that were defined on the basis of maximum light spectra in Paper II (core normal, broad line, cool, and shallow silicon) develop highly homogeneous postmaximum spectra, although there are interesting exceptions. Comparisons with SYNOW synthetic spectra show that most of the spectral features can be accounted for in a plausible way. The fits show that 3 months after maximum light, when SN Ia spectra are often said to be in the nebular phase and to consist of forbidden emission lines, the spectra actually remain dominated by resonance scattering features of permitted lines, primarily those of Fe II. Even in SN 1991bg, which is said to have made a very early transition to the nebular phase, there is no need to appeal to forbidden lines at 3 weeks postmaximum, and at 3 months postmaximum the only clear identification of a forbidden line is [Ca II] 7291, 7324. Recent studies of SN Ia rates indicate that most of the SNe Ia that have ever occurred have been "prompt" SNe Ia, produced by young (100,000,000 yr) stellar populations, while most of the SNe Ia that occur at low redshift today are "tardy", produced by an older (several Gyrs) population. We suggest that the shallow silicon SNe Ia tend to be the prompt ones.Comment: Accepted by PAS