Computationally efficient estimation of the extreme event probability of the mass loss of Greenland and Antarctic ice sheets.
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We present a novel stochastic optimal control framework that accounts for various types of uncertainties, with application to reentry trajectory planning. The formulation of the optimal trajectory control problem is presented in the context of an indirect method where a functional objective associated with the terminal vehicle speed is to be minimized. Uncertain input parameters in the optimal trajectory control model, including aerodynamic parameters and initial and terminal conditions, are modeled as aleatory random variables, while the statistical parameters of these aleatory distributions are themselves random variables. The parametric and model uncertainties are simultaneously propagated through an extended polynomial chaos expansion (EPCE) formalism. Several metrics are described to evaluate response statistics and presented as insightful tools for robust decision making. Specifically, the response probability density function (PDF) reflecting influence of both epistemic and aleatory uncertainties is obtained. By sampling over the random variables representing model error, an ensemble of response PDFs is generated and the associated failure probability is estimated as a random variable with its own polynomial chaos expansion. Besides, the sensitivity index functions of response PDF with respect to the statistical parameters are evaluated. Coupling parametric and model uncertainties within the EPCE framework leads to a robust and efficient paradigm for multilevel uncertainty propagation and PDF characterization in general optimal control problems.
X-ray free electron lasers, with their ultrashort highly coherent pulses, opened up the opportunity of probing ultrafast nano- and atomic-scale dynamics in amorphous and disordered material systems via speckle visibility spectroscopy. However, the anticipated count rate in a typical experiment is usually low. Therefore, visibility needs to be extracted via photon statistics analysis, i.e., by estimating the probabilities of multiple photons per pixel events using pixelated detectors. Considering the realistic X-ray detector responses including charge cloud sharing between pixels, pixel readout noise, and gain non-uniformity, speckle visibility extraction relying on photon assignment algorithms are often computationally demanding and suffer from systematic errors. In this paper, we present a systematic study of the commonly-used algorithms by applying them to an experimental data set containing small-angle coherent scattering with visibility levels ranging from below 1% to ∼60%. We also propose a contrast calibration protocol and show that a computationally lightweight algorithm can be implemented for high-speed correlation evaluation.
Molecular oxygen is a strong indicator of life on Earth and may indicate biological processes on exoplanets too. Recent studies proposed that Earth-like O 2 levels might be detectable on nearby exoplanets using high-resolution spectrographs on future extremely large telescopes (ELTs). However, these studies did not consider constraints like relative velocities, planet occurrence rates, and target observability. We expanded on past studies by creating a homogeneous catalog of 286,391 main-sequence stars within 120 pc using Gaia DR3 and used the Bioverse framework to simulate the likelihood of finding nearby transiting Earth analogs. We also simulated a survey of M dwarfs within 20 pc accounting for η ⊕ estimates, transit probabilities, relative velocities, and target observability to determine how long ELTs and theoretical 50–100 m ground-based telescopes need to observe to probe for Earth-like O 2 levels with an R = 100,000 spectrograph. This would only be possible within 50 yr for up to ~21% of nearby M-dwarf systems if a suitable transiting habitable-zone Earth analog was discovered, assuming signals from every observable partial transit from each ELT can be combined. If so, Earth-like O 2 levels could be detectable on TRAPPIST-1 d–g within 16–55 yr, respectively, and about half that time with an R = 500,000 spectrograph. These results have important implications for whether ELTs can survey nearby habitable-zone Earth analogs for O 2 via transmission spectroscopy. Our work provides the most comprehensive assessment to date of the ground-based capabilities to search for life beyond the solar system.
We develop and analyze a stage-progression compartmental model to study the emerging invasive nontyphoidal Salmonella (iNTS) epidemic in sub-Saharan Africa. iNTS bloodstream infections are often fatal, and the diverse and non-specific clinical features of iNTS make it difficult to diagnose. We focus our study on identifying approaches that can reduce the incidence of new infections. In sub-Saharan Africa, transmission and mortality are correlated with the ongoing HIV epidemic and severe malnutrition. We use our model to quantify the impact that increasing antiretroviral therapy (ART) for HIV infected adults and reducing malnutrition in children would have on mortality from iNTS in the population. We consider immunocompromised subpopulations in the region with major risk factors for mortality, such as malaria and malnutrition among children and HIV infection and ART coverage in both children and adults. We parameterize the progression rates between infection stages using the branching probabilities and estimated time spent at each stage. We interpret the basic reproduction number R 0 as the total contribution from an infinite infection loop produced by the asymptomatic carriers in the infection chain. The results indicate that the asymptomatic HIV+ adults without ART serve as the driving force of infection for the iNTS epidemic. We conclude that the worst disease outcome is among the pediatric population, which has the highest infection rates and death counts. Our sensitivity analysis indicates that the most effective strategies to reduce iNTS mortality in the studied population are to improve the ART coverage among high-risk HIV+ adults and reduce malnutrition among children.
Like all operations in which fluids are injected into the subsurface, geologic carbon storage (GCS) presents inherit risks that must be assessed and mitigated to successfully deploy such technology in the field. For example, alterations to pore pressure and the stress state due to fluid injection may trigger certain geohazards, such as potential fault activation and induced seismicity or unintentional hydraulic fracturing. Here we present capabilities for assessing these potential risks using the State of Stress Analysis Tool (SOSAT): a Python library and web-based application capable of probabilistically estimating the subsurface state of stress informed by various field observations. Using posterior distributions of principal stress components, SOSAT can assess the risk of fault activation within the injection formation for either a critically oriented fault or a fault with a user-prescribed orientation. Additionally, SOSAT can estimate the probability of unintentional hydraulic fracturing of the intact reservoir rock. Here, we demonstrate these SOSAT capabilities using a hypothetical GCS site. This type of risk assessment can assist with the effective deployment of GCS technology in the field by informing safe design and management practices.
Problem solving - nonparametric estimate of probability density function
Canonical expansion and output event techniques for estimating component probability of failure in simple and complex systems
Microbial exposure probabilities and estimated loads from fractured materials of lunar probes
Nonlinear adaptive and recursive algorithm to estimate unknown probability density from independent sample sequence
Perceived and responded to discriminative stimuli identification in probability learning, using parameter free model of event pattern association strength
Research completed in the Earth Resources Data Analysis Program is discussed along with recommendations for future study. Projects discussed include use of the Cholesky decomposition in feature selection and classification algorithms; optimal feature selection and extraction, probability density estimation and nonparametric classifiers; use of spatial information in classification; and model for crop row reflectance. The installation of LARSYS on the ICSA's IBM 370/155 is discussed, and a list of technical reports is included.
A method for extracting surface-slope frequency distributions from bistatic-radar data has been developed and applied to the lunar surface. Telemetry transmissions from orbiting Apollo spacecraft were received on the earth after reflection from the lunar surface. The echo-frequency spectrum was related analytically to the probability distribution of lunar slopes. Standard regression techniques were used to solve the inverse problem of finding slope distributions from observed echo-frequency spectra. Data taken simultaneously at two wavelengths, 13 and 116 cm, have yielded diverse slope statistics.
Approach is first to cluster and then to compute spatial boundaries for resulting clusters. Next step is to compute, from set of Monte Carlo samples obtained from scrambled data, estimates of probabilities of obtaining at least as many points within boundaries as were actually observed in original data.
The efforts and findings of the Earth Resources Data Analysis Program are summarized. Results of a detailed study of the needs of EOD with respect to an applications development system (ADS) for the analysis of remotely sensed data, including an evaluation of four existing systems with respect to these needs are described. Recommendations as to possible courses for EOD to follow to obtain a viable ADS are presented. Algorithmic development comprised of several subtasks is discussed. These subtasks include the following: (1) two algorithms for multivariate density estimation; (2) a data smoothing algorithm; (3) a method for optimally estimating prior probabilities of unclassified data; and (4) further applications of the modified Cholesky decomposition in various calculations. Little effort was expended on task 3, however, two reports were reviewed.
The Poisson arrival model was used to determine the effects of limiting the number of channels for a disaster warning satellite. State probabilities and delay probabilities were estimated for several values of the number of channels (C) for arrival and service rates obtained from disaster warnings issued by the National Weather Service. The results predicted by the queueing model were compared with the results of a digital computer simulation.