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Gaussian type densities estimated by representing unknown density in terms of convolution expansion of Gaussian probability density and arbitrary distribution, discussing convergence rates
Using both analytical and Monte Carlo techniques, beam-pointing errors of planar-phased arrays are analyzed. The obtained simple formulas for rms pointing errors are applicable to uniform planar arrays with both uniform and Gaussian uncorrelated phase-error distributions and for any arbitrary scan angle.
Data from the MIT X-ray experiment on the OSO-7 satellite were used to delineate the regions in B-L and geographic spaces where trapped radiation was encountered. The results pertain specifically to electrons with energies in a range of 10 keV centered on 55 keV which were encountered in an orbit between altitudes of 330 and 570 km and latitudes of 33.3 degrees. A typical pitch angle distribution is fitted by a Gaussian with a FWHM of 28 degrees.
Photometric and kinematic data from the literature are combined with new dynamical models to derive the intrinsic shape of the 'standard' elliptical galaxy NGC 3379. The parameters that are best constrained are the dynamical triaxiality T (essentially the triaxiality of the total mass distribution) and the short-to long axis ratio of the light distribution c(sub L). The inferred shape is given by a Bayesian probability distribution in the (T, c(sub L) plane. Assuming a uniform prior, the most probable shape is oblate with a flattening of c(sub L) = 87. The distribution is strongly non-Gaussian, however, and the expectation values, (T) = .31 (c(sub L) = .75, imply a flatter and more triaxial figure. The 68% highest posterior density region allows more triaxial shapes as long as they are fairly round, or flatter shapes as long as they are nearly oblate. These results are essentially unchanged if the galaxy is assumed to rotate about its short axis, or if it is modeled as an S0 with a negligible-mass disk rather than as an elliptical. The suggestion of Capaccioli et al. (ApJ, 371, 535 (1991)) that NGC 3379 is a rather flat, triaxial S0 galaxy is found to be improbable at the 98% level; this conclusion is largely independent of the bulge-to-disk ratio or the relative rotation speeds of the two components.
Low-frequency (less than 20 GHz) single-channel microwave retrievals of rain rate encounter the problem of beam-filling error. This error stems from the fact that the relationship between microwave brightness temperature and rain rate is nonlinear, coupled with the fact that the field of view is large or comparable to important scales of variability of the rain field. This means that one may not simply insert the area average of the brightness temperature into the formula for rain rate without incurring both bias and random error. The statistical heterogeneity of the rain-rate field in the footprint of the instrument is key to determining the nature of these errors. This paper makes use of a series of random rain-rate fields to study the size of the bias and random error associated with beam filling. A number of examples are analyzed in detail: the binomially distributed field, the gamma, the Gaussian, the mixed gamma, the lognormal, and the mixed lognormal ('mixed' here means there is a finite probability of no rain rate at a point of space-time). Of particular interest are the applicability of a simple error formula due to Chiu and collaborators and a formula that might hold in the large field of view limit. It is found that the simple formula holds for Gaussian rain-rate fields but begins to fail for highly skewed fields such as the mixed lognormal. While not conclusively demonstrated here, it is suggested that the notionof climatologically adjusting the retrievals to remove the beam-filling bias is a reasonable proposition.
Bit-wise arithmetic coding is data-compression scheme intended especially for use with uniformly quantized data from source with Gaussian, Laplacian, or similar probability distribution function. Code words of fixed length, and bits treated as being independent. Scheme serves as means of progressive transmission or of overcoming buffer-overflow or rate constraint limitations sometimes arising when data compression used.
We present a nonparametric Bayesian framework to infer radial distribution functions from experimental scattering measurements with uncertainty quantification using nonstationary Gaussian processes. The Gaussian process prior mean and kernel functions are designed to mitigate well-known numerical challenges with the Fourier transform, including discrete measurement binning and detector windowing, while encoding fundamental yet minimal physical knowledge of the liquid structure. We demonstrate uncertainty propagation of the Gaussian process posterior to unmeasured quantities of interest. Experimental radial distribution functions of liquid argon and water with uncertainty quantification are provided as both a proof of principle for the method and a benchmark for molecular models.
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The statistical distribution of fluctuations on various scales is analyzed in terms of the counts in cells of smoothed density fields, using volume-limited samples of galaxy redshift catalogs. It is shown that the distribution on large scales, with volume average of the two-point correlation function of the smoothed field less than about 0.05, is consistent with Gaussian. Statistics are shown to agree remarkably well with the negative binomial distribution, which has hierarchial correlations and a Gaussian behavior at large scales. If these observed properties correspond to the matter distribution, they suggest that our universe started with Gaussian fluctuations and evolved keeping hierarchial form.
This calculator outputs time-varying lower and upper bounds (matrices), called dispatch bounds, for the controllable portions of the power injections at each node in a distribution network to guarantee that the voltage magnitudes stay within prescribed bounds with at least a given probability for any set of power injections that are within their dispatch bounds. The calculator is meant to be a tool for a central controller of a distribution network to set dispatch bounds for each node that allows each node to independently decide their actual power injection within their dispatch bound. The user can choose whether to assume the forecast errors of the uncontrollable power injections are gaussian or are worst-case (distributionally robust). The user can choose whether the dispatch bounds include the controllable reactive power or just the active power under a constant power factor assumption.
Continuous ground-based observations of ionospheric and magnetospheric regions are critical to the Geospace Environmental Modeling (GEM) program. It is therefore important to establish clear intercalibrations between different ground-based instruments and satellites in order to clearly place the ground-based observations in context with the corresponding in situ satellite measurements. HF-radars operating at high latitudes are capable of observing very large spatial regions of the ionosphere on a nearly continuous basis. In this paper we report on an intercalibration study made using the Polar Anglo-American Conjugate Radar Experiment radars located at Goose Bay, Labrador, and Halley Station, Antarctica, and the Defense Meteorological Satellite Program (DMSP) satellites. The DMSP satellite data are used to provide clear identifications of the ionospheric cusp and the low-latitude boundary layer (LLBL). The radar data for eight cusp events and eight LLBL events have been examined in order to determine a radar signature of these ionospheric regions. This intercalibraion indicates that the cusp is always characterized by wide, complex Doppler power spectra, whereas the LLBL is usually found to have spectra dominated by a single component. The distribution of spectral widths in the cusp is of a generally Gaussian form with a peak at about 220 m/s. The distribution of spectral widths in the LLBL is more like an exponential distribution, with the peak of the distribution occurring at about 50 m/s. There are a few cases in the LLBL where the Doppler power spectra are strikingly similar to those observed in the cusp.
We present statistical single-spacecraft observations of magnetic and electron velocity fluctuations in Earth's magnetosheath, likely in the vicinity of the magnetopause, downstream of a bow shock immersed in quasi-parallel interplanetary magnetic field conditions, a situation conducive to plasma turbulence in the downstream flow. These fluctuations exhibit scale-dependent behavior, wherein histograms of their Partial Variance of Increments (PVIB or PVIV(sub e)) demonstrate highly non-Gaussian forms at small scales and are reasonably well-described by kappa distributions, albeit with fitted values of the kappa parameter only slightly larger than 1.5, exemplifying their power law nature at large values of PVI. At larger scales, the PVI histograms lose their non-Gaussian nature and are well described by both Gaussian and kappa distributions with large values of the kappa parameter. The PVI histograms furthermore exhibit kurtosis that increases with decreasing scale, a characteristic that is much more prominent in the magnetic fluctuations than in the electron velocity fluctuations. This feature that is not yet explained. In both cases, the results are characteristic of turbulent intermittency.
This study characterized and modeled heterogeneous surface wettability in sandstone and investigated the role of spatial heterogeneity and correlation length of surface wettability on relative permeability in a supercritical CO 2 (scCO 2 )-brine-rock system. Understanding the role of wettability heterogeneity on relative permeability is essential to geological CO 2 sequestration, oil and gas recovery, and contaminated groundwater remediation. Although numerous studies have attempted to understand the influences of surface wettability, capillary number (Ca), and viscosity ratio, the role of the spatial variation and correlation length of surface wettability on two-phase flow in three-dimensional (3D) porous media has not been unraveled due to the challenges in the measurement and representation of realistic rock surface wettability. In this work, we conducted in-situ measurements of surface contact angle (CA) in a Bentheimer sandstone after CO 2 flooding using micro-computed tomography (micro-CT), and found that the pore-scale CA distribution on rock surfaces followed a log-normal distribution associated with a spatial correlation length. Based on the statistical information from CT scanning, a Gaussian random field was used to model CA distributions that had desired standard deviations and spatial correlation lengths, which were then adjusted within a certain range of values for sensitivity analyses to study their combined effects on the two-phase flow in the porous medium using the lattice Boltzmann (LB) method. The LB two-phase flow simulation was accelerated using hybrid, multicore parallel computing to overcome the challenges in simulating multiphase flow in a large 3D domain having 800 × 800 × 600 nodes. The simulation results showed that the surface wettability heterogeneity (i.e., standard deviation of CA) had a lesser effect on the relative permeability of the wetting fluid (water) but a more significant impact on the relative permeability of the non-wetting fluid (scCO 2 ). The Corey model was used to fit the LB-simulated relative permeability curves of water and scCO 2 and showed that the variations in the relative permeability curves for both water and scCO 2 increased as the standard deviation and spatial correlation length of CA increased. This study illustrated that the assumption of homogeneous surface wettability may cause errors in multiphase flow simulations. Furthermore, the impacts of both the standard deviation and spatial correlation length of CAs should be accounted for. This is the first study that explored the spatial correlation lengths associated with CA distributions on sandstone surfaces and comprehensively investigated the roles of both spatial variation and correlation length of CA on two-phase flow properties in 3D porous media. The optimized LB multiphase flow model was proved a powerful tool to study the interplays and combined effects of these statistical parameters, which had critical applications in numerous natural and engineering processes that involved multiphase flow in porous media.
Knowledge on geographical location and distribution of crops at global, national and regional scales is an extremely valuable source of information applications. Traditional approaches to crop mapping using remote sensing data rely heavily on reference or ground truth data in order to train/calibrate classification models. As a rule, such models are only applicable to a single vegetation season and should be recalibrated to be applicable for other seasons. This paper addresses the problem of early season large-area winter crop mapping using Moderate Resolution Imaging Spectroradiometer (MODIS) derived Normalized Difference Vegetation Index (NDVI) time-series and growing degree days (GDD) information derived from the Modern-Era Retrospective analysis for Research and Applications (MERRA-2) product. The model is based on the assumption that winter crops have developed biomass during early spring while other crops (spring and summer) have no biomass. As winter crop development is temporally and spatially non-uniform due to the presence of different agro-climatic zones, we use GDD to account for such discrepancies. A Gaussian mixture model (GMM) is applied to discriminate winter crops from other crops (spring and summer). The proposed method has the following advantages: low input data requirements, robustness, applicability to global scale application and can provide winter crop maps 1.5-2 months before harvest. The model is applied to two study regions, the State of Kansas in the US and Ukraine, and for multiple seasons (2001-2014). Validation using the US Department of Agriculture (USDA) Crop Data Layer (CDL) for Kansas and ground measurements for Ukraine shows that accuracies of greater than 90% can be achieved in mapping winter crops 1.5-2 months before harvest. Results also show good correspondence to official statistics with average coefficients of determination R(exp. 2) greater than 0.85.
Probability distribution functions (PDFs) are very used in modeling random processes and physics simulations. Improving the performance of algorithms that generate many random numbers under complex PDFs is often a very challenging task when methods as direct functions are not available. In this work we present general strategies on how to vectorize some PDFs using VecCore library. We show the results for the Exponential, Gaussian, discrete Poisson and Gamma probability distributions.
The dwarf irregular galaxy GR8, which is at the extreme faint end of the luminosity and mass functions, is studied using optical photometry and 21 cm H I line observations. It is shown that rotation is only important to the gravitational support of the system in the inner parts (r less than 250 pc). GR8 is one of the very few non-elliptical systems known (with M81dwA) where the random motions provide essentially all the support in the outer parts (4 greater than or equal to 500 pc). The Gaussian nature of the H I distribution and the isothermal distribution of the H I velocity dispersion implies M is directly proportional to R(exp 3) in the outer regions of GR8 (i.e., the stellar disk and the H I lie in the approximately uniform density core of the dark halo).
Stimulated-emission tomography (SET) is an excellent tool for characterizing the process of spontaneous parametric down conversion (SPDC), which is commonly used to create pairs of entangled photons for use in quantum information protocols. The use of stimulated emission increases the average number of detected photons by several orders of magnitude compared to the spontaneous process. In a SET measurement, the parametric down conversion is seeded by an intense signal field prepared with specified mode properties rather than by broadband multimodal vacuum fluctuations, as is the case for the spontaneous process. The SET process generates an intense idler field in a mode that is the complex conjugate to the signal mode. In this work we use SET to estimate the joint spatial mode distribution (JSMD) in the Laguerre-Gaussian (LG) basis of the two photons of an entangled photon pair. The pair is produced by parametric down conversion in a beta barium borate (BBO) crystal with type-II phase matching pumped at a wavelength of 405 nm along with a 780 nm seed signal beam prepared in a variety of LG modes to generate an 842 nm idler beam of which the spatial mode distribution is measured. We observe strong idler production and good agreement with the theoretical prediction of its spatial mode distribution. Our experimental procedure should enable the efficient determination of the photon-pair wavefunctions produced by low-brightness SPDC sources and the characterization of high-dimensional entangled-photon pairs. Published by the American Physical Society 2024
We propose a complete framework for Bayesian image reconstruction and uncertainty quantification based on a Gaussian process prior (GPP) to overcome limitations of maximum likelihood expectation maximization (ML-EM) image reconstruction algorithm. The prior distribution is constructed with a zero-mean Gaussian process (GP) with a choice of a covariance function, and a link function is used to map the Gaussian process to an image. Unlike many other maximum a posteriori approaches, our method offers highly interpretable hyperparamters that are selected automatically with the empirical Bayes method. Furthermore, the GP covariance function can be modified to incorporate a priori structural priors, enabling multi-modality imaging or contextual data fusion. Lastly, we illustrate that our approach lends itself to Bayesian uncertainty quantification techniques, such as the preconditioned Crank–Nicolson method and the Laplace approximation. The proposed framework is general and can be employed in most radiation image reconstruction problems, and we demonstrate it with simulated free-moving single detector radiation source imaging scenarios. We compare the reconstruction results from GPP and ML-EM, and show that the proposed method can significantly improve the image quality over ML-EM, all the while providing greater understanding of the source distribution via the uncertainty quantification capability. Furthermore, significant improvement of the image quality by incorporating a structural prior is illustrated.