Structural Decompositions for Problems with Global Constraints

A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed combinations of values, or implicitly, by special-purpose algorithms provided by a solver. Such implicitly represented constraints, known as global constraints, are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. In recent years, a variety of restrictions on the structure of CSP instances have been shown to yield tractable classes of CSPs. However, most such restrictions fail to guarantee tractability for CSPs with global constraints. We therefore study the applicability of structural restrictions to instances with such constraints. We show that when the number of solutions to a CSP instance is bounded in key parts of the problem, structural restrictions can be used to derive new tractable classes. Furthermore, we show that this result extends to combinations of instances drawn from known tractable classes, as well as to CSP instances where constraints assign costs to satisfying assignments.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s10601-015-9181-

Is FIRST J102347.6+003841 Really a Cataclysmic Binary?

The radio source FIRST J102347.6+003841 was presented as the first radio-selected cataclysmic. In the discovery paper, Bond et al. (2002) show a spectrum consistent with a magnetic AM Her-type system and a light curve with rapid, irregular flickering. In contrast, Woudt, Warner, and Pretorius (2004) found a smoothly-varying light curve with a period near 4.75 h and one minimum per orbit, indicating a dramatic change. We present time-resolved spectra showing a superficially normal, mid-G type photosphere, with no detectable emission lines. The absorption-line radial velocity varies sinusoidally, with semi-amplitude 268 +- 4 km/s, on the orbital period, which is refined to 0.198094(2) d. At this orbital period the secondary's spectral type is atypically early, suggesting an unusual evolutionary history. We also obtained BVI photometry around the orbit. The light curve resembles that given by Woudt et al., and the color modulation is consistent with a heating effect. A simple illumination model matches the observations strikingly well with a Roche-lobe filling secondary near 5650 kelvin being illuminated by a primary giving out around 2 solar luminosities. The modest amplitude of the observed modulation constrains the orbital inclination to be less than about 55 deg, unless the gravity darkening is artificially reduced. The resulting primary star mass is above the Chandrasekhar limit (assuming conventional gravity darkening). We examine the possibility that the compact object in this system is not a white dwarf, in which case this is not actually a cataclysmic variable. On close examination, FIRST J102347.6+003841 defies easy classification.Comment: 24 pages, 5 postscript and two JPG figures; Astronomical Journal, accepte

Spectroscopy and Photometry of Cataclysmic Variable Candidates from the Catalina Real Time Survey

The Catalina Real Time Survey (CRTS) has found over 500 cataclysmic variable (CV) candidates, most of which were previously unknown. We report here on followup spectroscopy of 36 of the brighter objects. Nearly all the spectra are typical of CVs at minimum light. One object appears to be a flare star, while another has a spectrum consistent with a CV but lies, intriguingly, at the center of a small nebulosity. We measured orbital periods for eight of the CVs, and estimated distances for two based on the spectra of their secondary stars. In addition to the spectra, we obtained direct imaging for an overlapping sample of 37 objects, for which we give magnitudes and colors. Most of our new orbital periods are shortward of the so-called period gap from roughly 2 to 3 hours. By considering the cross-identifications between the Catalina objects and other catalogs such as the Sloan Digital Sky Survey, we argue that a large number of cataclysmic variables remain uncatalogued. By comparing the CRTS sample to lists of previously-known CVs that CRTS does not recover, we find that the CRTS is biased toward large outburst amplitudes (and hence shorter orbital periods). We speculate that this is a consequence of the survey cadence.Comment: Accepted for publication in The Astronomical Journal. 35 pages, including 7 figure

Cataclysmic Variables in the SUPERBLINK Proper Motion Survey

We have discovered a new high proper motion cataclysmic variable (CV) in the SUPERBLINK proper motion survey, which is sensitive to stars with proper motions greater than 40 mas/yr. This CV was selected for follow-up observations as part of a larger search for CVs selected based on proper motions and their NUV-V and V-K$_{s}$ colors. We present spectroscopic observations from the 2.4m Hiltner Telescope at MDM Observatory. The new CV's orbital period is near 96 minutes, its spectrum shows the double-peaked Balmer emission lines characteristic of quiescent dwarf novae, and its V magnitude is near 18.2. Additionally, we present a full list of known CVs in the SUPERBLINK catalog.Comment: Accepted for publication in The Astronomical Journal, 22 pages, 6 figure

Spectroscopy of Four Cataclysmic Variables with Periods above 7 Hours

We present spectroscopy of four cataclysmic variables. Using radial velocity measurements, we find orbital periods for the first time. The stars and their periods are GY Hya, 0.347230(9) d; SDSS J204448-045929, 1.68(1) d; V392 Hya, 0.324952(5) d; and RX J1951.7+3716, 0.492(1) d. We also detect the spectra of the secondary stars, estimate their spectral types, and derive distances based on surface brightness and Roche lobe constraints.Comment: 22 pages, 3 figures, 5 tables, to be published in December 2006 PAS