The velocity probability density of upper atmospheric turbulence.
Upper atmospheric turbulence velocity probability density investigated in 90 to 110 km region
ATMOSPHERIC TURBULENCE↗
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The radio-optical-X-ray spectral flux distributions of blazars
Ten confirmed and probable BL Lac objects were searched for X-ray emission using the Einstein Observatory. All 10 were detected. These data were combined with existing data to form a catalog of 99 confirmed (by measured, high, optical linear polarization) and probable blazars (BL Lac objects and highly polarized quasars). Radio, optical, and X-ray observations are available for 77 of these. One of the ten program objects was observed at four epochs during large radio and optical outbursts. The correlations of radio, optical, and X-ray luminosities are examined.
Ledden, J. E.↗
On the use of the noncentral chi-square density function for the distribution of helicopter spectral estimates
A probability density function for the variability of ensemble averaged spectral estimates from helicopter acoustic signals in Gaussian background noise was evaluated. Numerical methods for calculating the density function and for determining confidence limits were explored. Density functions were predicted for both synthesized and experimental data and compared with observed spectral estimate variability.
Garber, Donald P.↗
Computing the Instantaneous Collision Probability between Satellites using Characteristic Function Inversion
The probability that two satellites overlap in space at a specified instant of time is called their instantaneous collision probability. Assuming Gaussian uncertainties and spherical satellites, this probability is the integral of a Gaussian distribution over a sphere. This paper shows how to compute the probability using an established numerical procedure called characteristic function inversion. The collision probability in the short-term encounter scenario is also evaluated with this approach, where the instant at which the probability is computed is the time of closest approach between the objects. Python and R code is provided to evaluate the probability in practice. Overall, the approach has been established for over fifty years, is implemented in existing software, does not rely on analytical approximations, and can be used to evaluate two and three dimensional collision probabilities.
79 ASTRONOMY AND ASTROPHYSICS↗
Time analysis of volcanic activity on Io by means of plasma observations
A model of Io volcanism in which the probability of activity obeys a binomial distribution is presented. Observed values of the electron density obtained over a 3-year period by ground-based spectroscopy are fitted to such a distribution. The best fit is found for a total number of 15 volcanoes with a probability of individual activity at any time of 0.143. The Pioneer 10 ultraviolet observations are reinterpreted as emissions of sulfur and oxygen ions and are found to be consistent with a plasma much less dense than that observed by the Voyager spacecraft. Late 1978 and the first half of 1979 are shown to be periods of anomalous volcanicity. Rapid variations in electron density are related to enhanced radial diffusion.
Mekler, Y.↗
Crater Topography on Titan: Implications for Landscape Evolution
We present a comprehensive review of available crater topography measurements for Saturn's moon Titan. In general, the depths of Titan's craters are within the range of depths observed for similarly sized fresh craters on Ganymede, but several hundreds of meters shallower than Ganymede's average depth vs. diameter trend. Depth-to-diameter ratios are between 0.0012 +/- 0.0003 (for the largest crater studied, Menrva, D approximately 425 km) and 0.017 +/- 0.004 (for the smallest crater studied, Ksa, D approximately 39 km). When we evaluate the Anderson-Darling goodness-of-fit parameter, we find that there is less than a 10% probability that Titan's craters have a current depth distribution that is consistent with the depth distribution of fresh craters on Ganymede. There is, however, a much higher probability that the relative depths are uniformly distributed between 0 (fresh) and 1 (completely infilled). This distribution is consistent with an infilling process that is relatively constant with time, such as aeolian deposition. Assuming that Ganymede represents a close 'airless' analogue to Titan, the difference in depths represents the first quantitative measure of the amount of modification that has shaped Titan's surface, the only body in the outer Solar System with extensive surface-atmosphere exchange.
Implications↗
A Search Model for Imperfectly Detected Targets
Under the assumptions that 1) the search region can be divided up into N non-overlapping sub-regions that are searched sequentially, 2) the probability of detection is unity if a sub-region is selected, and 3) no information is available to guide the search, there are two extreme case models. The search can be done perfectly, leading to a uniform distribution over the number of searches required, or the search can be done with no memory, leading to a geometric distribution for the number of searches required with a success probability of 1/N. If the probability of detection P is less than unity, but the search is done otherwise perfectly, the searcher will have to search the N regions repeatedly until detection occurs. The number of searches is thus the sum two random variables. One is N times the number of full searches (a geometric distribution with success probability P) and the other is the uniform distribution over the integers 1 to N. The first three moments of this distribution were computed, giving the mean, standard deviation, and the kurtosis of the distribution as a function of the two parameters. The model was fit to the data presented last year (Ahumada, Billington, & Kaiwi, 2 required to find a single pixel target on a simulated horizon. The model gave a good fit to the three moments for all three observers.
Ahumada, Albert↗
The Error Distribution of BATSE Gamma-Ray Burst Locations
Empirical probability models for BATSE gamma-ray burst (GRB) location errors are developed via a Bayesian analysis of the separations between BATSE GRB locations and locations obtained with the Interplanetary Network (IPN). Models are compared and their parameters estimated using 392 GRBs with single IPN annuli and 19 GRBs with intersecting IPN annuli. Most of the analysis is for the 4Br BATSE catalog; earlier catalogs are also analyzed. The simplest model that provides a good representation of the error distribution has 78% of the probability in a "core" term with a systematic error of 1.85 deg and the remainder in an extended tail with a systematic error of 5.1 deg, which implies a 68% confidence radius for bursts with negligible statistical uncertainties of 2.2 deg. There is evidence for a more complicated model in which the error distribution depends on the BATSE data type that was used to obtain the location. Bright bursts are typically located using the CONT data type, and according to the more complicated model, the 68% confidence radius for CONT-located bursts with negligible statistical uncertainties is 2.0 deg.
Briggs, Michael S.↗
Surface sticking probabilities for sputtered atoms of Nb-93 and Rh-103
The capture coefficient probabilities for sputtered atoms of Nb-93 and Rh-103 incident on Al2O3 surfaces were measured using the backscattering of MeV heavy ions. In the circumstance where the collecting surface is thickly covered, the sticking probabilities integrated over the energy distribution of sputtered atoms are 0.97 plus or minus 0.01 for Nb-93 and 0.95 plus or minus 0.01 for Rh-103 respectively. In the limit of negligible areal coverage of the collector, the accuracy is less; in this case the sticking probabilities are 0.97 + 0.03 or -0.08 and 0.95 + 0.05 or -0.08.
Weller, M. R.↗
Statistics of the geomagnetic secular variation for the past 5Ma
A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.
Constable, C. G.↗
Statistics of the geomagnetic secular variation for the past 5 m.y
A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.
Constable, C. G.↗
The Attraction Indian Buffet Distribution
We propose the attraction Indian buffet distribution (AIBD), a distribution for binary feature matrices influenced by pairwise similarity information. Binary feature matrices are used in Bayesian models to uncover latent variables (i.e., features) that explain observed data. The Indian buffet process (IBP) is a popular exchangeable prior distribution for latent feature matrices. In the presence of additional information, however, the exchangeability assumption is not reasonable or desirable. The AIBD can incorporate pairwise similarity information, yet it preserves many properties of the IBP, including the distribution of the total number of features. Thus, much of the interpretation and intuition that one has for the IBP directly carries over to the AIBD. A temperature parameter controls the degree to which the similarity information affects feature-sharing between observations. Unlike other nonexchangeable distributions for feature allocations, the probability mass function of the AIBD has a tractable normalizing constant, making posterior inference on hyperparameters straight-forward using standard MCMC methods. A novel posterior sampling algorithm is proposed for the IBP and the AIBD. We demonstrate the feasibility of the AIBD as a prior distribution in feature allocation models and compare the performance of competing methods in simulations and an application.
97 MATHEMATICS AND COMPUTING↗
Non-gaussian statistics of pencil beam surveys
We study the effect of the non-Gaussian clustering of galaxies on the statistics of pencil beam surveys. We derive the probability from the power spectrum peaks by means of Edgeworth expansion and find that the higher order moments of the galaxy distribution play a dominant role. The probability of obtaining the 128 Mpc/h periodicity found in pencil beam surveys is raised by more than one order of magnitude, up to 1%. Further data are needed to decide if non-Gaussian distribution alone is sufficient to explain the 128 Mpc/h periodicity, or if extra large-scale power is necessary.
Amendola, Luca↗
The impact cratering record on Triton
Impact craters on Triton are scarce owing to the relatively recent resurfacing by icy melts. The most heavily cratered surface has a crater density about the same as the lunar maria. The transition diameter from simple to complex craters occurs at a diameter of about 11 kilometers, and the depth-diameter relationship is similar to that of other icy satellites when gravity is taken into account. The crater size-frequency distribution has a differential -3 slope (cumulative -2 slope) and is the same as that for the fresh crater population on Miranda. The most heavily cratered region is on the leading hemisphere in Triton's orbit. Triton may have a leading-trailing asymmetry in its crater population. Based primarily on the similarity of size distributions on Triton and Miranda and the relatively young surface on Triton, the source of Triton's craters is probably comets. The very peculiar size distribution of sharp craters on the 'cantaloupe' terrain and other evidence suggests thay are volcanic explosion craters.
Strom, Robert G.↗
Boosting with Averaged Weight Vectors
AdaBoost is a well-known ensemble learning algorithm that constructs its constituent or base models in sequence. A key step in AdaBoost is constructing a distribution over the training examples to create each base model. This distribution, represented as a vector, is constructed to be orthogonal to the vector of mistakes made by the previous base model in the sequence. The idea is to make the next base model's errors uncorrelated with those of the previous model. Some researchers have pointed out the intuition that it is probably better to construct a distribution that is orthogonal to the mistake vectors of all the previous base models, but that this is not always possible. We present an algorithm that attempts to come as close as possible to this goal in an efficient manner. We present experimental results demonstrating significant improvement over AdaBoost and the Totally Corrective boosting algorithm, which also attempts to satisfy this goal.
Oza, Nikunj C.↗
Probability of cell hits in selected organs and tissues by high-LET particles at the ISS orbit
The fluence of high-LET particles (HLP) with LET infinity H2O greater than 15 keV micrometers-1 in selected organs and tissues were measured with plastic nuclear track detectors using a life-size human phantom on the 9th Shuttle-Mir Mission (STS-91). The planar-track fluence of HLP during the 9.8-day mission ranged from 1.9 x 10(3) n cm-2 (bladder) to 5.1 x 10(3) n cm-2 (brain) by a factor of 2.7. Based on these data, a probability of HLP hits to a matured cell of each organ or tissue was roughly estimated for a 90-day ISS mission. In the calculation, all cells were assumed to be spheres with a geometric cross-sectional area of 500 micrometers2 and the cell-hit frequency from isotropic space radiation can be described by the Poisson-distribution function. As results, the probability of one or more than 1 hit to a single cell by HLP for 90 days ranged from 17% to 38%; that of two or more than 2 hits was estimated to be 1.3-8.2%. c2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.
NASA Discipline Radiation Health↗
Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models
Here, we propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple “snapshots.” Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates “fake” sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space, which is induced from the inferred particle dynamics. We employ different metrics to quantify the differences between distributions, e.g., the sliced Wasserstein distances and the adversarial losses in generative adversarial networks. We refer to this method as generative “ensemble-regression” (GER), in analogy to the classic “point-regression,” where we infer the dynamics by performing regression in the Euclidean space. We illustrate the GER by learning the drift and diffusion terms of particle ensembles governed by SODEs with Brownian motions and Lévy processes up to 100 dimensions. We also discuss how to treat cases with noisy or truncated observations. Apart from systems consisting of independent particles, we also tackle nonlocal interacting particle systems with unknown interaction potential parameters by constructing a physics-informed loss function. Finally, we investigate scenarios of paired observations and discuss how to reduce the dimensionality in such cases by proving a convergence theorem that provides theoretical support.
97 MATHEMATICS AND COMPUTING↗
Statistical structural analysis of rotor impact ice shedding
The statistical characteristics of impact ice shear strength are analyzed, with emphasis placed on the most probable shear strength and statistical distribution of an ice deposit. Several distribution types are considered: the Weibull, two-parameter Weibull, and exponential distributions, as well as the Gumbell distribution of the smallest extreme and the Gumbell distribution of the largest extreme. It is concluded that the Weibull distribution yields the best results; however, the expected life, shape parameter, and scale parameter should be determined separately for each case of varying wind speed and droplet size. The theoretical predictions of shear stresses in a specific rotating ice shape are compared, and it is noted that when the effects of lift are added to the theoretical model and the interference is calculated with a new mean and standard deviation, the probability of ice shed is computed as 36.64 pct.
Kellacky, C. J.↗