A deep, wide-field search for substellar members in NGC 2264

We report the first results of our ongoing campaign to discover the first brown dwarfs (BD) in NGC 2264, a young (3 Myr), populous star forming region for which our optical studies have revealed a very high density of potential candidates - 236 in $<$ 1 deg$^2$ - from the substellar limit down to at least $\sim$ 20 M$_{\rm Jup}$ for zero reddening. Candidate BD were first selected using wide field ($I,z$) band imaging with CFH12K, by reference to current theoretical isochrones. Subsequently, 79 (33%) of the $I,z$ sample were found to have near-infrared 2MASS photometry ($JHK_s$ $\pm$ 0.3 mag. or better), yielding dereddened magnitudes and allowing further investigation by comparison with the location of NextGen and DUSTY isochrones in colour-colour and colour-magnitude diagrams involving various combinations of $I$,$J$,$H$ and $K_s$. We discuss the status and potential substellarity of a number of relatively unreddened (A$_{\rm v}$ $<$ 5) likely low-mass members in our sample, but in spite of the depth of our observations in $I,z$, we are as yet unable to unambiguously identify substellar candidates using only 2MASS data. Nevertheless, there are excellent arguments for considering two faint (observed $I$ $\sim$ 18.4 and 21.2) objects as cluster candidates with masses respectively at or rather below the hydrogen burning limit. More current candidates could be proven to be cluster members with masses around 0.1 M$_{\odot}$ {\it via} gravity-sensitive spectroscopy, and deeper near-infrared imaging will surely reveal a hitherto unknown population of young brown dwarfs in this region, accessible to the next generation of deep near-infrared surveys.Comment: 10 pages, 12 figures, accepted by A&

Optical measurements of phase steps in segmented mirrors - fundamental precision limits

Phase steps are an important type of wavefront aberrations generated by large telescopes with segmented mirrors. In a closed-loop correction cycle these phase steps have to be measured with the highest possible precision using natural reference stars, that is with a small number of photons. In this paper the classical Fisher information of statistics is used for calculating the Cramer-Rao bound, which determines the limit to the precision with which the height of the steps can be estimated in an unbiased fashion with a given number of photons and a given measuring device. Four types of measurement devices are discussed: a Shack-Hartmann sensor with one small cylindrical lenslet covering a sub-aperture centred over a border, a modified Mach-Zehnder interferometer, a Foucault test, and a curvature sensor. The Cramer-Rao bound is calculated for all sensors under ideal conditions, that is narrowband measurements without additional noise or disturbances apart from the photon shot noise. This limit is compared with the ultimate quantum statistical limit for the estimate of such a step which is independent of the measuring device. For the Shack-Hartmann sensor, the effects on the Cramer-Rao bound of broadband measurements, finite sampling, and disturbances such as atmospheric seeing and detector readout noise are also investigated. The methods presented here can be used to compare the precision limits of various devices for measuring phase steps and for optimising the parameters of the devices. Under ideal conditions the Shack-Hartmann and the Foucault devices nearly attain the ultimate quantum statistical limits, whereas the Mach-Zehnder and the curvature devices each require approximately twenty times as many photons in order to reach the same precision.Comment: 23 pages, 19 figures, to be submitted to Journal of Modern Optic

Free-stream noise and transition measurements on a cone in a Mach 3.5 pilot low-disturbance tunnel

A small scale Mach 3.5 wind tunnel incorporating certain novel design features and intended for boundary-layer-transition research has been tested. The free stream noise intensities and spectral distributions were determined throughout the test section for several values of unit Reynolds number and for nozzle boundary layer bleed on and off. The boundary layer transition location on a slender cone and the response of this to changes in the noise environment were determined. Root mean square free stream noise levels ranged from less than one tenth up to values approaching those for conventional nozzles, with the lowest values prevailing at upstream locations within the nozzle. For low noise conditions, cone transition Reynolds numbers were in the range of those for free flight; whereas for high noise conditions, they were in the range of those in conventional tunnels

On Minimum Violations Ranking in Paired Comparisons

Ranking a set of objects from the most dominant one to the least, based on the results of paired comparisons, proves to be useful in many contexts. Using the rankings of teams or individuals players in sports to seed tournaments is an example. The quality of a ranking is often evaluated by the number of violations, cases in which an object is ranked lower than another that it has dominated in a comparison, that it contains. A minimum violations ranking (MVR) method, as its name suggests, searches specifically for rankings that have the minimum possible number of violations which may or may not be zero. In this paper, we present a method based on statistical physics that overcomes conceptual and practical difficulties faced by earlier studies of the problem.Comment: 10 pages, 10 figures; typos corrected (v2

Branching processes, the max-plus algebra and network calculus

Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory

The Hudson Bay Lithospheric Experiment (HuBLE) : Insights into Precambrian Plate Tectonics and the Development of Mantle Keels

The UK component of HuBLE was supported by Natural Environment Research Council (NERC) grant NE/F007337/1, with financial and logistical support from the Geological Survey of Canada, Canada–Nunavut Geoscience Office, SEIS-UK (the seismic node of NERC), and First Nations communities of Nunavut. J. Beauchesne and J. Kendall provided invaluable assistance in the field. Discussions with M. St-Onge, T. Skulski, D. Corrigan and M. Sanborne-Barrie were helpful for interpretation of the data. D. Eaton and F. A. Darbyshire acknowledge the Natural Sciences and Engineering Research Council. Four stations on the Belcher Islands and northern Quebec were installed by the University of Western Ontario and funded through a grant to D. Eaton (UWO Academic Development Fund). I. Bastow is funded by the Leverhulme Trust. This is Natural Resources Canada Contribution 20130084 to its Geomapping for Energy and Minerals Program. This work has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no. 240473 ‘CoMITAC’.Peer reviewedPublisher PD

On the Reliability of Cross Correlation Function Lag Determinations in Active Galactic Nuclei

Many AGN exhibit a highly variable luminosity. Some AGN also show a pronounced time delay between variations seen in their optical continuum and in their emission lines. In effect, the emission lines are light echoes of the continuum. This light travel-time delay provides a characteristic radius of the region producing the emission lines. The cross correlation function (CCF) is the standard tool used to measure the time lag between the continuum and line variations. For the few well-sampled AGN, the lag ranges from 1-100 days, depending upon which line is used and the luminosity of the AGN. In the best sampled AGN, NGC 5548, the H_beta lag shows year-to-year changes, ranging from about 8.7 days to about 22.9 days over a span of 8 years. In this paper it is demonstrated that, in the context of AGN variability studies, the lag estimate using the CCF is biased too low and subject to a large variance. Thus the year-to-year changes of the measured lag in NGC 5548 do not necessarily imply changes in the AGN structure. The bias and large variance are consequences of finite duration sampling and the dominance of long timescale trends in the light curves, not due to noise or irregular sampling. Lag estimates can be substantially improved by removing low frequency power from the light curves prior to computing the CCF.Comment: To appear in the PASP, vol 111, 1999 Nov; 37 pages; 10 figure

Measuring degree-degree association in networks

The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the applicability of different association measures to heavy-tailed degree distributions. Theoretical arguments together with our numerical study indicate that Pearson's coefficient often depends on the size of networks with equal association structure, impeding a systematic comparison of real-world networks. In contrast, Kendall-Gibbons' $\tau_{b}$ is a considerably more robust measure of the degree-degree association