Real root finding for equivariant semi-algebraic systems

Let $R$ be a real closed field. We consider basic semi-algebraic sets defined by $n$-variate equations/inequalities of $s$ symmetric polynomials and an equivariant family of polynomials, all of them of degree bounded by $2d < n$. Such a semi-algebraic set is invariant by the action of the symmetric group. We show that such a set is either empty or it contains a point with at most $2d-1$ distinct coordinates. Combining this geometric result with efficient algorithms for real root finding (based on the critical point method), one can decide the emptiness of basic semi-algebraic sets defined by $s$ polynomials of degree $d$ in time $(sn)^{O(d)}$. This improves the state-of-the-art which is exponential in $n$. When the variables $x_1, \ldots, x_n$ are quantified and the coefficients of the input system depend on parameters $y_1, \ldots, y_t$, one also demonstrates that the corresponding one-block quantifier elimination problem can be solved in time $(sn)^{O(dt)}$

Research with Collaborative Unmanned Aircraft Systems

We provide an overview of ongoing research which targets development of a principled framework for mixed-initiative interaction with unmanned aircraft systems (UAS). UASs are now becoming technologically mature enough to be integrated into civil society. Principled interaction between UASs and human resources is an essential component in their future uses in complex emergency services or bluelight scenarios. In our current research, we have targeted a triad of fundamental, interdependent conceptual issues: delegation, mixed- initiative interaction and adjustable autonomy, that is being used as a basis for developing a principled and well-defined framework for interaction. This can be used to clarify, validate and verify different types of interaction between human operators and UAS systems both theoretically and practically in UAS experimentation with our deployed platforms

The High Angular Resolution Multiplicity of Massive Stars

We present the results of a speckle interferometric survey of Galactic massive stars that complements and expands upon a similar survey made over a decade ago. The speckle observations were made with the KPNO and CTIO 4 m telescopes and USNO speckle camera, and they are sensitive to the detection of binaries in the angular separation regime between 0.03" and 5" with relatively bright companions (Delta V < 3). We report on the discovery of companions to 14 OB stars. In total we resolved companions of 41 of 385 O-stars (11%), 4 of 37 Wolf-Rayet stars (11%), and 89 of 139 B-stars (64%; an enriched visual binary sample that we selected for future orbital determinations). We made a statistical analysis of the binary frequency among the subsample that are listed in the Galactic O Star Catalog by compiling published data on other visual companions detected through adaptive optics studies and/or noted in the Washington Double Star Catalog and by collecting published information on radial velocities and spectroscopic binaries. We find that the binary frequency is much higher among O-stars in clusters and associations compared to the numbers for field and runaway O-stars, consistent with predictions for the ejection processes for runaway stars. We present a first orbit for the O-star Delta Orionis, a linear solution of the close, apparently optical, companion of the O-star Iota Orionis, and an improved orbit of the Be star Delta Scorpii. Finally, we list astrometric data for another 249 resolved and 221 unresolved targets that are lower mass stars that we observed for various other science programs.Comment: 76 pages, 6 figures, 11 table

Epistemic Vigilance

Humans massively depend on communication with others, but this leaves them open to the risk of being accidentally or intentionally misinformed. To ensure that, despite this risk, communication remains advantageous, humans have, we claim, a suite of cognitive mechanisms for epistemic vigilance. Here we outline this claim and consider some of the ways in which epistemic vigilance works in mental and social life by surveying issues, research and theories in different domains of philosophy, linguistics, cognitive psychology and the social sciences

Color-Induced Displacement double stars in SDSS

We report the first successful application of the astrometric color-induced displacement technique (CID, the displacement of the photocenter between different bandpasses due to a varying contribution of differently colored components to the total light), originally proposed by Wielen (1996) for discovering unresolved binary stars. Using the Sloan Digital Sky Survey (SDSS) Data Release 1 with 2.5 million stars brighter than 21m in the u and g bands, we select 419 candidate binary stars with CID greater than 0.5 arcsec. The SDSS colors of the majority of these candidates are consistent with binary systems including a white dwarf and any main sequence star with spectral type later than ~K7. The astrometric CID method discussed here is complementary to the photometric selection of binary stars in SDSS discussed by Smolcic et al. (2004), but there is considerable overlap (15%) between the two samples of selected candidates. This overlap testifies both to the physical soundness of both methods, as well as to the astrometric and photometric quality of SDSS data.Comment: submitted to A&A, 13 pages, 6 figure

Oscillation of linear ordinary differential equations: on a theorem by A. Grigoriev

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients.Comment: 16 page

Ages for illustrative field stars using gyrochronology: viability, limitations and errors

We here develop an improved way of using a rotating star as a clock, set it using the Sun, and demonstrate that it keeps time well. This technique, called gyrochronology, permits the derivation of ages for solar- and late-type main sequence stars using only their rotation periods and colors. The technique is clarified and developed here, and used to derive ages for illustrative groups of nearby, late-type field stars with measured rotation periods. We first demonstrate the reality of the interface sequence, the unifying feature of the rotational observations of cluster and field stars that makes the technique possible, and extends it beyond the proposal of Skumanich by specifying the mass dependence of rotation for these stars. We delineate which stars it cannot currently be used on. We then calibrate the age dependence using the Sun. The errors are propagated to understand their dependence on color and period. Representative age errors associated with the technique are estimated at ~15% (plus possible systematic errors) for late-F, G, K, & early-M stars. Ages derived via gyrochronology for the Mt. Wilson stars are shown to be in good agreement with chromospheric ages for all but the bluest stars, and probably superior. Gyro ages are then calculated for each of the active main sequence field stars studied by Strassmeier and collaborators where other ages are not available. These are shown to be mostly younger than 1Gyr, with a median age of 365Myr. The sample of single, late-type main sequence field stars assembled by Pizzolato and collaborators is then assessed, and shown to have gyro ages ranging from under 100Myr to several Gyr, and a median age of 1.2Gyr. Finally, we demonstrate that the individual components of the three wide binaries XiBooAB, 61CygAB, & AlphaCenAB yield substantially the same gyro ages.Comment: 58 pages, 18 color figures, accepted for publication in The Astrophysical Journal; Age uncertainties slightly modified upon correcting an algebraic error in Section

The orbit of the brown dwarf binary Gl 569B

We present photometric, astrometric and spectroscopic observations of the nearby (9.8 pc) low-mass binary Gl 569Bab (in turn being a companion to the early-M star Gl 569A), made with the Keck adaptive optics facility. Having observed Gl 569Bab since August 1999, we are able to see orbital motion and to determine the orbital parameters of the pair. We find the orbital period to be 892 +/- 25 days, the semi-major axis to be 0.90 +/- 0.02 AU, the eccentricity to be 0.32 +/- 0.02 and the inclination of the system to be 34+/- 3 degrees (1-sigma). The total mass is found to be 0.123 (-0.022/+0.027) Msun (3-sigma). In addition, we have obtained low resolution (R=1500-1700) near-infrared spectra of each of the components in the J- and K-bands. We determine the spectral types of the objects to be M8.5V (Gl 569Ba) and M9V (Gl 569Bb) with an uncertainty of half a subclass. We also present new J- and K-band photometry which allows us to accurately place the objects in the HR diagram. Most likely the binary system is comprised of two brown dwarfs with a mass ratio of 0.89 and with an age of approximately 300 Myr.Comment: Accepted for publication in ApJ, 28 pages, figures include

Orbital parameters, masses and distance to Beta Centauri determined with the Sydney University Stellar Interferometer and high resolution spectroscopy

The bright southern binary star beta Centauri (HR 5267) has been observed with the Sydney University Stellar Interferometer (SUSI) and spectroscopically with the ESO CAT and Swiss Euler telescopes at La Silla. The interferometric observations have confirmed the binary nature of the primary component and have enabled the determination of the orbital parameters of the system. At the observing wavelength of 442 nm the two components of the binary system have a magnitude difference of 0.15. The combination of interferometric and spectroscopic data gives the following results: orbital period 357 days, semi-major axis 25.30 mas, inclination 67.4 degrees, eccentricity 0.821, distance 102.3 pc, primary and secondary masses M1 = M2 = 9.1 solar masses and absolute visual magnitudes of the primary and secondary M1V = -3.85 and M2V = -3.70. The high accuracy of the results offers a fruitful starting point for future asteroseismic modelling of the pulsating binary components.Comment: 10 pages, 4 figures. Accepted for publication in MNRA