Deriving the sampling errors of correlograms for general white noise

We derive the second-order sampling properties of certain autocovariance and autocorrelation estimators for sequences of independent and identically distributed samples. Specifically, the estimators we consider are the classic lag windowed correlogram, the correlogram with subtracted sample mean, and the fixed-length summation correlogram. For each correlogram we derive explicit formulas for the bias, covariance, mean square error and consistency for generalised higher-order white noise sequences. In particular, this class of sequences may have non-zero means, be complexed valued and also includes non-analytical noise signals. We find that these commonly used correlograms exhibit lag dependent covariance despite the fact that these processes are white and hence by definition do not depend on lag.Comment: Submitted to Biometrik

Scanning-electron-microscope used in real-time study of friction and wear

Small friction and wear apparatus built directly into scanning-electron-microscope provides both dynamic observation and microscopic view of wear process. Friction and wear tests conducted using this system have indicated that considerable information can readily be gained

Sampling errors of correlograms with and without sample mean removal for higher-order complex white noise with arbitrary mean

We derive the bias, variance, covariance, and mean square error of the standard lag windowed correlogram estimator both with and without sample mean removal for complex white noise with an arbitrary mean. We find that the arbitrary mean introduces lag dependent covariance between different lags of the correlogram estimates in spite of the lack of covariance in white noise for non-zeros lags. We provide a heuristic rule for when the sample mean should be, and when it should not be, removed if the true mean is not known. The sampling properties derived here are useful is assesing the general statistical performance of autocovariance and autocorrelation estimators in different parameter regimes. Alternatively, the sampling properties could be used as bounds on the detection of a weak signal in general white noise.Comment: 11 pages, 2 figures, To be published in Journal of Time Series Analysi

Discovery of spin modulated circular polarization from IGR J17014-4306, the remnant of Nova Scorpii 1437 A.D

Polarimetry of IGR J1401-4306, a long period (12.7 hours), eclipsing intermediate polar and remnant of Nova Scorpii 1437 A.D., reveals periodic variations of optical circular polarization, confirming the system as the longest period eclipsing intermediate polar known. This makes it an interesting system from an evolutionary perspective. The circular polarization is interpreted as optical cyclotron emission from an accreting magnetic white dwarf primary. Based on the polarimetry, we propose that it is a disc-fed intermediate polar. The detection of predominantly negative circular polarization is consistent with only one of the magnetic poles dominating the polarized emission, while the other is mostly obscured by the accretion disc.Comment: 7 pages, figures, accepted for publication in MNRA

Dynamic-scanning-electron-microscope study of friction and wear

A friction and wear apparatus was built into a real time scanning electron microscope (SEM). The apparatus and SEM comprise a system which provides the capability of performing dynamic friction and wear experiments in situ. When the system is used in conjunction with dispersive X-ray analysis, a wide range of information on the wearing process can be obtained. The type of wear and variation with speed, load, and time can be investigated. The source, size, and distribution of wear particles can be determined and metallic transferal observed. Some typical results obtained with aluminum, copper, and iron specimens are given

The N.A.C.A. Combustion Chamber Gas-sampling Valve and Some Preliminary Test Results

A gas sampling valve of the inertia-operated type was designed for procuring samples of the gases in the combustion chamber of internal combustion engines at identical points in successive cycles so that the analysis of the gas samples thus procured may aid in the study of the process of combustion. The operation of the valve is described. The valve was used to investigate the CO2 content of gases taken from the quiescent combustion chamber of a high speed compression-ignition engine when operating with two different multiple-orifice fuel injection nozzles. An analysis of the gas samples thus obtained shows that the state of quiescence in the combustion chamber is maintained during the combustion of the fuel

Dynamic SEM wear studies of tungsten carbide cermets

Dynamic friction and wear experiments were conducted in a scanning electron microscope. The wear behavior of pure tungsten carbide and composite with 6 and 15 weight percent cobalt binder was examined, and etching of the binder was done to selectively determine the role of the binder in the wear process. Dynamic experiments were conducted as the tungsten carbide (WC) and bonded WC cermet surfaces were transversed by a 50 micron radiused diamond stylus. These studies show that the predominant wear process in WC is fracture initiated by plastic deformation, and the wear of the etched cermets is similar to pure WC. The presence of the cobalt binder reduces both friction and wear. The cementing action of the cobalt reduces granular separation, and promotes a dense polished layer because of its low shear strength film-forming properties. The wear debris generated from unetched surface is approximately the same composition as the bulk

Optimisation in ‘Self-modelling’ Complex Adaptive Systems

When a dynamical system with multiple point attractors is released from an arbitrary initial condition it will relax into a configuration that locally resolves the constraints or opposing forces between interdependent state variables. However, when there are many conflicting interdependencies between variables, finding a configuration that globally optimises these constraints by this method is unlikely, or may take many attempts. Here we show that a simple distributed mechanism can incrementally alter a dynamical system such that it finds lower energy configurations, more reliably and more quickly. Specifically, when Hebbian learning is applied to the connections of a simple dynamical system undergoing repeated relaxation, the system will develop an associative memory that amplifies a subset of its own attractor states. This modifies the dynamics of the system such that its ability to find configurations that minimise total system energy, and globally resolve conflicts between interdependent variables, is enhanced. Moreover, we show that the system is not merely ‘recalling’ low energy states that have been previously visited but ‘predicting’ their location by generalising over local attractor states that have already been visited. This ‘self-modelling’ framework, i.e. a system that augments its behaviour with an associative memory of its own attractors, helps us better-understand the conditions under which a simple locally-mediated mechanism of self-organisation can promote significantly enhanced global resolution of conflicts between the components of a complex adaptive system. We illustrate this process in random and modular network constraint problems equivalent to graph colouring and distributed task allocation problems