Browsing by Author "Krometis, Justin"

Now showing 1 - 5 of 5
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    Approximating Community Water System Service Areas to Explore the Demographics of SDWA Compliance in Virginia
    Marcillo, Cristina; Krometis, Leigh-Anne H.; Krometis, Justin (MDPI, 2021-12-16)
    Although the United States Safe Drinking Water Act (SDWA) theoretically ensures drinking water quality, recent studies have questioned the reliability and equity associated with community water system (CWS) service. This study aimed to identify SDWA violation differences (i.e., monitoring and reporting (MR) and health-based (HB)) between Virginia CWSs given associated service demographics, rurality, and system characteristics. A novel geospatial methodology delineated CWS service areas at the zip code scale to connect 2000 US Census demographics with 2006–2016 SDWA violations, with significant associations determined via negative binomial regression. The proportion of Black Americans within a service area was positively associated with the likelihood of HB violations. This effort supports the need for further investigation of racial and socioeconomic disparities in access to safe drinking water within the United States in particular and offers a geospatial strategy to explore demographics in other settings where data on infrastructure extents are limited. Further interdisciplinary efforts at multiple scales are necessary to identify the entwined causes for differential risks in adverse drinking water quality exposures and would be substantially strengthened by the mapping of official CWS service boundaries.
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    A Bayesian Approach to Estimating Background Flows from a Passive Scalar
    Krometis, Justin (Virginia Tech, 2018-06-26)
    We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a pollutant). Here the unknown is a vector field that is specified by large or infinite number of degrees of freedom. We show that the inverse problem is ill-posed, i.e., there may be many or no background flows that match a given set of observations. We therefore adopt a Bayesian approach, incorporating prior knowledge of background flows and models of the observation error to develop probabilistic estimates of the fluid flow. In doing so, we leverage frameworks developed in recent years for infinite-dimensional Bayesian inference. We provide conditions under which the inference is consistent, i.e., the posterior measure converges to a Dirac measure on the true background flow as the number of observations of the solute concentration grows large. We also define several computationally-efficient algorithms adapted to the problem. One is an adjoint method for computation of the gradient of the log likelihood, a key ingredient in many numerical methods. A second is a particle method that allows direct computation of point observations of the solute concentration, leveraging the structure of the inverse problem to avoid approximation of the full infinite-dimensional scalar field. Finally, we identify two interesting example problems with very different posterior structures, which we use to conduct a large-scale benchmark of the convergence of several Markov Chain Monte Carlo methods that have been developed in recent years for infinite-dimensional settings.
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    Improving Deep Learning for Maritime Remote Sensing through Data Augmentation and Latent Space
    Sobien, Daniel; Higgins, Erik; Krometis, Justin; Kauffman, Justin; Freeman, Laura J. (MDPI, 2022-07-07)
    Training deep learning models requires having the right data for the problem and understanding both your data and the models’ performance on that data. Training deep learning models is difficult when data are limited, so in this paper, we seek to answer the following question: how can we train a deep learning model to increase its performance on a targeted area with limited data? We do this by applying rotation data augmentations to a simulated synthetic aperture radar (SAR) image dataset. We use the Uniform Manifold Approximation and Projection (UMAP) dimensionality reduction technique to understand the effects of augmentations on the data in latent space. Using this latent space representation, we can understand the data and choose specific training samples aimed at boosting model performance in targeted under-performing regions without the need to increase training set sizes. Results show that using latent space to choose training data significantly improves model performance in some cases; however, there are other cases where no improvements are made. We show that linking patterns in latent space is a possible predictor of model performance, but results require some experimentation and domain knowledge to determine the best options.
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    Lane Preference in a Simple Traffic Model
    Krometis, Justin (Virginia Tech, 2004-04-23)
    We examine the effect of lane preference on a quasi one-dimensional three-state driven lattice gas, consisting of holes and positive and negative particles, and periodic boundary conditions in the longitudinal direction. Particles move via particle-hole and, with a lesser rate, particle-particle exchanges; the species are driven in opposite directions along the lattice, each preferring one of the lanes with a given probability, p. The model can be interpreted as traffic flow on a two-lane beltway, with fast cars preferring the left lane and slow cars preferring the right, viewed in a comoving frame. In steady-sate, the system typically exhibits a macroscopic cluster containing a majority of the particles. At very high values of p, a first order transition takes the system to a spatially disordered state. Using Monte Carlo simulations to analyze the system, we find that the size of the cluster increases with lane preference. We also observe a region of negative response, where increasing the lane preference decreases the number of particles in their favored lane, against all expectations. In addition, simulations show an intriguing sequence of density profiles for the two species. We apply mean-field theory, continuity equations, and symmetries to derive relationships between observables to make a number of predictions verified by the Monte Carlo data.
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    A statistical framework for domain shape estimation in Stokes flows
    Borggaard, Jeffrey T.; Glatt-Holtz, Nathan E.; Krometis, Justin (IOP, 2023-08-01)
    We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct observations of the flow field as well as the measurement of concentrations of a solute passively advected by and diffusing within the flow. Adopting a statistical approach provides estimates of uncertainty in the shape due both to the non-invertibility of the forward map and to error in the measurements. When the shape represents a design problem of attempting to match desired target outcomes, this ‘uncertainty’ can be interpreted as identifying remaining degrees of freedom available to the designer. We demonstrate the viability of our framework on three concrete test problems. These problems illustrate the promise of our framework for applications while providing a collection of test cases for recently developed Markov chain Monte Carlo algorithms designed to resolve infinite-dimensional statistical quantities.