Efficient detection of a CW signal with a linear frequency drift

An efficient method is presented for the detection of a continuous wave (CW) signal with a frequency drift that is linear in time. Signals of this type occur in transmissions between any two locations that are accelerating relative to one another, e.g., transmissions from the Voyager spacecraft. We assume that both the frequency and the drift are unknown. We also assume that the signal is weak compared to the Gaussian noise. The signal is partitioned into subsequences whose discrete Fourier transforms provide a sequence of instantaneous spectra at equal time intervals. These spectra are then accumulated with a shift that is proportional to time. When the shift is equal to the frequency drift, the signal to noise ratio increases and detection occurs. Here, we show how to compute these accumulations for many shifts in an efficient manner using a variety of Fast Fourier Transformations (FFT). Computing time is proportional to L log L where L is the length of the time series

Semi-direct tree reconstruction using terrestrial LiDAR point cloud data

A new method was developed for reconstructing the geometric structure of large plants such as trees at the leaf-scale by utilizing terrestrial LiDAR data. The primary goal of the work was to develop a feasible means for accurately and rapidly reconstructing or “digitizing” entire trees in order to specify the position, orientation, and size of every leaf in digital tree models that provide geometric inputs for high-resolution biophysical models or analyses. As with any optical measurement technique, a primary challenge is accurately accounting for plant matter that is occluded from view of the sensor. The present method is termed “semi-direct” because it uses a triangulation procedure to approximately directly reconstruct as many leaves as possible that are in view of the scanner. For plant matter obstructed from view, a statistical backfilling procedure was used to add additional leaves such that the three-dimensional distribution of leaf area and orientation of the reconstructed plant matched that of the actual plant on average. In a best case scenario such as when leaf density is low, nearly all leaf area is directly reconstructed from the scan and the branch and clumping structure is preserved within the reconstruction. In the worst case scenario such as when the leaf density is very high and nearly all leaves are occluded from view of the scanner, only a small fraction of leaves can be directly reconstructed, but at a minimum the distribution of leaf area and the leaf angle distribution across the reconstructed plant will be consistent with that of the actual plant. Unlike many other approaches, the present method does not rely on the woody matter of the plant to provide a skeleton for reconstruction, and can be used in dense plants where little woody matter is visible from the scanner

A multiple testing approach to the regularisation of large sample correlation matrices

This paper proposes a novel regularisation method for the estimation of large covariance matrices, which makes use of insights from the multiple testing literature. The method tests the statistical significance of individual pair-wise correlations and sets to zero those elements that are not statistically significant, taking account of the multiple testing nature of the problem. The procedure is straightforward to implement, and does not require cross validation. By using the inverse of the normal distribution at a predetermined significance level, it circumvents the challenge of evaluating the theoretical constant arising in the rate of convergence of existing thresholding estimators. We compare the performance of our multiple testing (MT) estimator to a number of thresholding and shrinkage estimators in the literature in a detailed Monte Carlo simulation study. Results show that our MT estimator performs well in a number of different settings and tends to outperform other estimators, particularly when the cross-sectional dimension, N, is larger than the time series dimension, T IF the inverse covariance matrix is of interest then we recommend a shrinkage version of the MT estimator that ensures positive definitenes

Exponent of Cross-sectional Dependence: Estimation and Inference

An important issue in the analysis of cross-sectional dependence which has received renewed interest in the past few years is the need for a better understanding of the extent and nature of such cross dependencies. In this paper we focus on measures of cross-sectional dependence and how such measures are related to the behaviour of the aggregates defined as cross-sectional averages. We endeavour to determine the rate at which the cross-sectional weighted average of a set of variables appropriately demeaned, tends to zero. One parameterisation sets this to be , for . Given the fashion in which it arises, we refer to as the exponent of cross-sectional dependence. We derive an estimator of from the estimated variance of the cross-sectional average of the variables under consideration. We propose bias corrected estimators, derive their asymptotic properties and consider a number of extensions. We include a detailed Monte Carlo study supporting the theoretical results. Finally, we undertake an empirical investigation of using the S&P 500 data-set, and a large number of macroeconomic variables across and within countries

Pressurization of Liquid Oxygen Containers Progress Report No. 7, Nov. 1963 - Nov. 1964

Pressurization of liquid oxygen containers - cryogenic fluid boiling under high and low gravity, liquid hydrogen boiling, injection cooling, and two-dimensional heat transfe

A multiple testing approach to the regularisation of large sample correlation matrices

This paper proposes a novel regularisation method for the estimation of large covariance matrices, which makes use of insights from the multiple testing literature. The method tests the statistical significance of individual pair-wise correlations and sets to zero those elements that are not statistically significant, taking account of the multiple testing nature of the problem. The procedure is straightforward to implement, and does not require cross validation. By using the inverse of the normal distribution at a predetermined significance level, it circumvents the challenge of evaluating the theoretical constant arising in the rate of convergence of existing thresholding estimators. We compare the performance of our multiple testing (MT) estimator to a number of thresholding and shrinkage estimators in the literature in a detailed Monte Carlo simulation study. Results show that our MT estimator performs well in a number of different settings and tends to outperform other estimators, particularly when the cross-sectional dimension, N, is larger than the time series dimension, T IF the inverse covariance matrix is of interest then we recommend a shrinkage version of the MT estimator that ensures positive definitenes

A Two Stage Approach to Spatiotemporal Analysis with Strong and weak cross Sectional Dependence

An understanding of the spatial dimension of economic and social activity requires methods that can separate out the relationship between spatial units that is due to the effect of common factors from that which is purely spatial even in an abstract sense. The same applies to the empirical analysis of networks in general. We are able to distinguish between cross sectional strong dependence and weak dependence. Strong dependence in turn suggests that there are common factors. we use cross unit averages to extract common factors and contrast this to a principal components approach widely used in the literature. We then use a multiple testing procedure to determine significant bilateral correlations (signifying connections) between spatial units and compare this to an approach that just uses distance to determine units that are neighbours. We apply these methods to real house price changes at the level of Metropolitan statistical Areas in the USA, and estimate a heterogeneous spatiotemporal model for the de-factored real house price changes and obtain significant evidence of spatial connections, both positive and negative

Effect of possible rotor deformation on the probability of face contact for a liquid film bearing

The possibility of face contact is examined for a coaxial rotor-stator bearing in dynamic motion constrained by a highly rotating very thin liquid film. A modified Reynolds equation for pressurised flow is coupled to the bearing structure leading to determination of the bearing gap from solving a nonlinear second-order non-autonomous ordinary differential equation. Periodic solutions are found via a mapping solver. Rotor deformation is parametrised by a coning angle and considered a random variable. The method of derived distributions is used to quantify variation in coning angle and examine the probability of rotor-stator contact. Additionally, effects of possible destabilising random aspects on the axial rotor oscillations are investigated. Exact solutions for probability of contact are obtained for various bearing configurations.</p