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At least 109 records · Page 6

Statistical-mechanical selection of the shapes of disk galaxies

A new method is proposed for selecting steady state shapes of disk galaxies as 'most probable states' of a large number of stars, given only the total energy and total angular momentum. A partial differential equation is derived for the mean gravitational potential; it is closely related to the 'sinh-Poisson' equation for the mean-field description of a line vortex system or electrostatic guiding-center plasma. A 'water bag' approximation to the distribution function for bound stars renders the equation analytically tractable, but accurate solution of it may require numerical integration, in view of its general nonlinearity.

Montgomery, David↗

Wave propagation in a random medium

A simple technique is used to derive statistical characterizations of the perturbations imposed upon a wave (plane, spherical or beamed) propagating through a random medium. The method is essentially physical rather than mathematical, and is probably equivalent to the Rytov method. The limitations of the method are discussed in some detail; in general they are restrictive only for optical paths longer than a few hundred meters, and for paths at the lower microwave frequencies. Situations treated include arbitrary path geometries, finite transmitting and receiving apertures, and anisotropic media. Results include, in addition to the usual statistical quantities, time-lagged functions, mixed functions involving amplitude and phase fluctuations, angle-of-arrival covariances, frequency covariances, and other higher-order quantities.

Lee, R. W.↗

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique signature of visual behavior. This is true even in a restricted domain, such as piloting an aircraft, where patterns of visual signatures might represent activities like communicating, navigating, and monitoring. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these activities based on their behavioral signatures. The method is in some respects similar to recurrence analysis, but here we compare not individual fixations, but groups of fixations aggregated over a fixed time interval. The duration of this interval is a parameter that we will refer to as τ. We assume that the environment has been divided into a set of N different areas-of-interest (AOIs). For a given interval of time of duration τ, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector. These proportions can be converted to counts by multiplying by τ divided by the average fixation duration (another parameter that we fix at 280 milliseconds). We compare different intervals by computing the chi-square statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. We have investigated the method using a set of 10 synthetic "activities," that sample 4 AOIs. Four of these activities visit 3 of the 4 AOIs, with equal probability; as there are four different ways to leave-one- out, there are four such activities. Similarly, there are six different activities that leave-two-out. Sequences of simulated behavior were generated by running each activity for 40 seconds, in sequence, for a total of 6.7 minutes. The figure to the right shows the matrix of chi-square statistics, using a value of 2.8 seconds for τ, corresponding to 10 fixations. Low values (dark) indicate poor evidence for activity differences, while high values (bright) indicate strong evidence. The dark squares along the main diagonal each correspond to the forty second intervals in which the activity was held constant; the 4x4 block at the lower left corresponds to the four leave-one-out activities, while the 6x6 block in the upper right corresponds to the leave-two-out activities. (The anti-diagonal pattern of white squares indicates those activity pairs that share no AOIs.) The chi-square values can be binarized by choosing a particular significance level; we are interested in grouping bins that represent the same activity, effectively accepting the null hypothesis. Therefore, we may adopt a relatively lax criterion; for example, choosing a p-value of 0.2 means that two behaviors that have only a 1-in-5 chance of being produced by a single activity might nevertheless be clustered together. We have explored several methods to perform clustering on the data and solving for the activity probabilities. Greedy methods begin by selecting the time bin that is similar to the most (or least) other bins, and then forming a cluster from it and all other non-discriminable bins. These methods show mediocre performance, as they do not take into account temporal contiguity. Preliminary results indicate that methods that "grow" clusters in time from seed points perform better.

activity analysis↗

Development of a Probabilistic Dynamic Synthesis Method for the Analysis of Nondeterministic Structures

Accounting for the statistical geometric and material variability of structures in analysis has been a topic of considerable research for the last 30 years. The determination of quantifiable measures of statistical probability of a desired response variable, such as natural frequency, maximum displacement, or stress, to replace experience-based "safety factors" has been a primary goal of these studies. There are, however, several problems associated with their satisfactory application to realistic structures, such as bladed disks in turbomachinery. These include the accurate definition of the input random variables (rv's), the large size of the finite element models frequently used to simulate these structures, which makes even a single deterministic analysis expensive, and accurate generation of the cumulative distribution function (CDF) necessary to obtain the probability of the desired response variables. The research presented here applies a methodology called probabilistic dynamic synthesis (PDS) to solve these problems. The PDS method uses dynamic characteristics of substructures measured from modal test as the input rv's, rather than "primitive" rv's such as material or geometric uncertainties. These dynamic characteristics, which are the free-free eigenvalues, eigenvectors, and residual flexibility (RF), are readily measured and for many substructures, a reasonable sample set of these measurements can be obtained. The statistics for these rv's accurately account for the entire random character of the substructure. Using the RF method of component mode synthesis, these dynamic characteristics are used to generate reduced-size sample models of the substructures, which are then coupled to form system models. These sample models are used to obtain the CDF of the response variable by either applying Monte Carlo simulation or by generating data points for use in the response surface reliability method, which can perform the probabilistic analysis with an order of magnitude less computational effort. Both free- and forced-response analyses have been performed, and the results indicate that, while there is considerable room for improvement, the method produces usable and more representative solutions for the design of realistic structures with a substantial savings in computer time.

Brown, A. M.↗

Magnetic Field-Vector Measurements in Quiescent Prominences via the Hanle Effect: Analysis of Prominences Observed at Pic-Du-Midi and at Sacramento Peak

The Hanle effect method for magnetic field vector diagnostics has now provided results on the magnetic field strength and direction in quiescent prominences, from linear polarization measurements in the He I E sub 3 line, performed at the Pic-du-Midi and at Sacramento Peak. However, there is an inescapable ambiguity in the field vector determination: each polarization measurement provides two field vector solutions symmetrical with respect to the line-of-sight. A statistical analysis capable of solving this ambiguity was applied to the large sample of prominences observed at the Pic-du-Midi (Leroy, et al., 1984); the same method of analysis applied to the prominences observed at Sacramento Peak (Athay, et al., 1983) provides results in agreement on the most probable magnetic structure of prominences; these results are detailed. The statistical results were confirmed on favorable individual cases: for 15 prominences observed at Pic-du-Midi, the two-field vectors are pointing on the same side of the prominence, and the alpha angles are large enough with respect to the measurements and interpretation inaccuracies, so that the field polarity is derived without any ambiguity.

Bommier, V.↗

On the Probabilistic Analysis of Neural Networks

Neural networks are powerful tools for automated decision-making,seeing increased application in safety-critical domains, such as autonomous driving. Due to their black-box nature and large scale,reasoning about their behavior is challenging. Statistical analysis is often used to infer probabilistic properties of a network, such as its robustness to noise and inaccurate inputs. While scalable, statistical methods can only provide probabilistic guarantees on the quality of their results and may underestimate the impact of low probability inputs leading to undesired behavior of the network.We investigate here the use of symbolic analysis and constraint solution space quantification to precisely quantify probabilistic properties in neural networks. We demonstrate the potential of the proposed technique in a case study involving the analysis of ACAS-Xu, a collision avoidance system for unmanned aircraft control.

neural nets↗

An expert system for reliability modeling

A method is presented for computing the probability of failure of a unit during the next usage or mission based on sound statistical techniques. With the use of logit regression embedded in Lotus 1-2-3 macros, this package computes the probability of unit failure based upon a historical data base. Using this computed probability of failure, the package then makes a replacement recommendation based upon the experts acceptable risk parameters.

Goss, Ernst↗

Probabilistic structural analysis methods and applications

An advanced algorithm for simulating the probabilistic distribution of structural responses due to statistical uncertainties in loads, geometry, material properties, and boundary conditions is reported. The method effectively combines an advanced algorithm for calculating probability levels for multivariate problems (fast probability integration) together with a general-purpose finite-element code for stress, vibration, and buckling analysis. Application is made to a space propulsion system turbine blade for which the geometry and material properties are treated as random variables.

Cruse, T. A.↗

Searches for Periodic Neutrino Emission from Binary Systems with 22 and 40 Strings of IceCube

Recent observations of GeV /TeV photon emission from several X-ray binaries have sparked a renewed interest in these objects as galactic particle accelerators. In spite of the available multi-wavelength data, their acceleration mechanisms are not determined, and the nature of the accelerated particles (hadrons or leptons) is unknown. While much evidence favors leptonic emission, it is very likely that a hadronic component is also accelerated in the jets of these binary systems. The observation of neutrino emission would be clear evidence for the presence of a hadronic component in the outflow of these sources. In this paper we look for periodic neutrino emission from binary systems. Such modulation, observed in the photon flux, would be caused by the geometry of these systems. The results of two searches are presented that differ in the treatment of the spectral shape and phase of the emission. The 'generic' search allows parameters to vary freely and best fit values, in a 'model-dependent' search, predictions are used to constrain these parameters. We use the IceCube data taken from May 31, 2007 to April 5, 2008 with its 22-string configuration, and from April 5, 2008 and May 20, 2009 with its 40-string configuration. For the generic search and the 40 string sample, we find that the most significant source in the catalog of 7 binary stars is Cygnus X-3 with a 1.8% probability after trials (2.10" sigma one-sided) of being produced by statistical fluctuations of the background. The model-dependent method tested a range of system geometries - the inclination and the massive star's disk size - for LS I+61 deg 303, no significant excess was found.

Abassi, R.↗

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique pattern of interaction with the visual environment. This is true even in a restricted domain, such as a piloting an aircraft, where activities with distinct visual signatures might be things like communicating, navigating, and monitoring. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these hypothetical activities. The method is in some respects similar to recurrence analysis, but here we compare not individual fixations, but groups of fixations aggregated over a fixed time interval. The duration of this interval is a parameter that we will refer to as delta. We assume that the environment has been divided into a set of N different areas-of-interest (AOIs). For a given interval of time of duration delta, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector. These proportions can be converted to integer counts by multiplying by delta divided by the average fixation duration (another parameter that we fix at 280 milliseconds). We compare different intervals by computing the chi-square statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. The method has been applied to approximately 100 hours of eye movement data collected from pilots in a high-fidelity B747 flight simulator, and the results have been compared to synthetic data in which the each activity is represented as first-order Markov process with random probabilities assigned to the AOIs. Randomly-generated synthetic activities can require thousands of fixations to be discriminated with statistical significance, while the human data can be clustered using averaging windows of some 10's of seconds, suggesting that the actual activities are much more narrowly focused than random Markov models.

activity analysis↗

Assessment of NDE Reliability Data

Twenty sets of relevant Nondestructive Evaluation (NDE) reliability data have been identified, collected, compiled, and categorized. A criterion for the selection of data for statistical analysis considerations has been formulated. A model to grade the quality and validity of the data sets has been developed. Data input formats, which record the pertinent parameters of the defect/specimen and inspection procedures, have been formulated for each NDE method. A comprehensive computer program has been written to calculate the probability of flaw detection at several confidence levels by the binomial distribution. This program also selects the desired data sets for pooling and tests the statistical pooling criteria before calculating the composite detection reliability. Probability of detection curves at 95 and 50 percent confidence levels have been plotted for individual sets of relevant data as well as for several sets of merged data with common sets of NDE parameters.

Yee, B. G. W.↗

Non-Gaussian statistical models of surface wave fields for remote sensing applications

Based on the complete Stokes wave model with the bias term and using a simple mapping approach and an iteration solution method, we established a formula for the joint probability density function of the surface slope elevation of a nonlinear random wave field. The formula requires three parameters to define the whole density function: the rms surface elevation and slope values and the significant slope. This model represents the dynamics of the wave in a more direct way than the Gram-Charlier approximation. Based on this new statistical model and laboratory experiments, formula and numerical values of EM bias and dynamics bias are derived. The results indicate that various biases should be considered seriously if accuracy of the altimeter measurement is required in centimeter range.

Huang, N. E.↗

Chemical Compositions and Abundance Anomalies in Stellar Coronae ADP99

We have been investigating different statistical methods for analysing the metal abundances of sources with low S/N. A Bayesian technique has been developed that determines the most probable line-to-continuum ratio in the source, thereby leading to the metallicity. This method is a promising approach with which to mine the ASCA archive. Some of this work has now been published in conference proceedings. The flavour of the project has changed very slightly in the last year owing to the increasing availability of several good quality Chandra HETG and LETG spectra for stars for which we had reduced and analysed ASCA data. The Chandra grating spectra in principle provide a means of calibrating the results from the low resolution ASCA spectra and we have started some work toward that goal. One paper concerning abundance ratios in active stars is appearing shortly in conference proceedings and is being readied for publication in a main-stream astrophysical journal. This paper demonstrates for the first time that abundance anomalies cannot be categorized simply in terms of First Ionization Potential (FIP) or inverse-FIP based effects. Different Ne enhancements are found in different star types but a link between enhancement factors and stellar properties is not obvious. The publication noted as in preparation in an earlier report, finding strong Ne enhancements in active stars, is now published. These results will again be used to "calibrate" low resolution results for which line ratio techniques cannot be employed.

Drake, Jeremy↗

A Prognostic Launch Vehicle Probability of Failure Assessment Methodology for Conceptual Systems Predicated on Human Causal Factors

Lessons learned from past failures of launch vehicle developments and operations were used to create a new method to predict the probability of failure of conceptual systems. Existing methods such as Probabilistic Risk Assessments and Human Risk Assessments were considered but found to be too cumbersome for this type of system-wide application for yet-to-be-flown vehicles. The basis for this methodology were historic databases of past failures, where it was determined that various faulty human-interactions were the predominant root causes of failure rather than deficient component reliabilities evaluated through statistical analysis. This methodology contains an expert scoring part which can be used in either a qualitative or a quantitative mode. The method produces two products: a numerical score of the probability of failure and guidance to program management on critical areas in need of increased focus to improve the probability of success. In order to evaluate the effectiveness of this new method, data from a concluded vehicle program (USAF's Titan IV with the Centaur G-Prime upper stage) was used as a test case. The theoretical vs. actual probability of failure was found to be 4.46% vs. 6.67% respectively. Recommendations are made for future applications of this method to ongoing launch vehicle development programs.

Launch Vehicle↗

Prognostic Launch Vehicle Probability of Failure Assessment Methodology for Conceptual Systems Predicated on Human Causal Factors

Lessons learned from past failures of launch vehicle developments and operations were used to create a new method to predict the probability of failure of conceptual systems. Existing methods such as Probabilistic Risk Assessments and Human Risk Assessments were considered but found to be too cumbersome for this type of system-wide application for yet-to-be-flown vehicles. The basis for this methodology were historic databases of past failures, where it was determined that various faulty human-interactions were the predominant root causes of failure rather than deficient component reliabilities evaluated through statistical analysis. This methodology contains an expert scoring part which can be used in either a qualitative or a quantitative mode. The method produces two products: a numerical score of the probability of failure or guidance to program management on critical areas in need of increased focus to improve the probability of success. In order to evaluate the effectiveness of this new method, data from a concluded vehicle program (USAF's Titan IV with the Centaur G-Prime upper stage) was used as a test case. Although the theoretical vs. actual probability of failure was found to be in reasonable agreement (4.46% vs. 6.67% respectively) the underlying sub-root cause scoring had significant disparities attributable to significant organizational changes and acquisitions. Recommendations are made for future applications of this method to ongoing launch vehicle development programs.

Craig H Williams↗

A statistical model for telecommunication link design

An evaluation is conducted of the current telecommunication link design technique and a description is presented of an alternative method, called the probability distribution method (PDM), which is free of the disadvantages of the current technique while retaining its advantages. The PDM preserves the simplicity of the design control table (DCT) format. The use of the DCT as a management design control tool is continued. The telecommunication link margin probability density function used presents the probability of achieving any particular value of link performance. It is, therefore, possible to assess the performance risk and other tradeoffs.

Yuen, J. H.↗