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DOE OSTI2021

Bayesian analysis for estimating statistical parameter distributions of elasto-viscoplastic material models

High temperature design methods rely on constitutive models for inelastic deformation and failure typically calibrated against the mean of experimental data without considering the associated scatter. Variability may arise from the experimental data acquisition process, from heat-to-heat material property variations, or both and need to be accurately captured to predict parameter bounds leading to efficient component design. Applying the Bayesian Markov Chain Monte Carlo (MCMC) method to produce statistical models capturing the underlying uncertainty in the experimental data is an area of ongoing research interest. This work varies aspects of the Bayesian MCMC method and explores their effect on the posterior parameter distributions for a uniaxial elasto-viscoplastic damage model using synthetically generated reference data. From our analysis with the uniaxial inelastic model we determine that an informed prior distribution including different types of test conditions results in more accurate posterior parameter distributions. The parameter posterior distributions, however, do not improve when increasing the number of similar experimental data. Additionally, changing the amount of scatter in the data affects the quality of the posterior distributions, especially for the less sensitive model parameters. Moreover, we perform a sensitivity study of the model parameters against the likelihood function prior to the Bayesian analysis. The results of the sensitivity analysis help to determine the reliability of the posterior distributions and reduce the dimensionality of the problem by fixing the insensitive parameters. The comprehensive study described in this work demonstrates how to efficiently apply the Bayesian MCMC methodology to capture parameter uncertainties in high temperature inelastic material models. Quantifying these uncertainties in inelastic models will improve high temperature engineering design practices and lead to safer, more effective component designs.

42 ENGINEERING↗

DOE OSTI2024

Biophysical and Structural Features of αβT ‐Cell Receptor Mechanosensing: A Paradigmatic Shift in Understanding T‐Cell Activation

ABSTRACT αβT cells protect vertebrates against many diseases, optimizing surveillance using mechanical force to distinguish between pathophysiologic cellular alterations and normal self‐constituents. The multi‐subunit αβT‐cell receptor (TCR) operates outside of thermal equilibrium, harvesting energy via physical forces generated by T‐cell motility and actin‐myosin machinery. When a peptide‐bound major histocompatibility complex molecule (pMHC) on an antigen presenting cell is ligated, the αβTCR on the T cell leverages force to form a catch bond, prolonging bond lifetime, and enhancing antigen discrimination. Under load, the αβTCR undergoes reversible structural transitions involving partial unfolding of its clonotypic immunoglobulin‐like (Ig) domains and coupled rearrangements of associated CD3 subunits and structural elements. We postulate that transitions provide critical energy to initiate the signaling cascade via induction of αβTCR quaternary structural rearrangements, associated membrane perturbations, exposure of CD3 ITAMs to phosphorylation by non‐receptor tyrosine kinases, and phase separation of signaling molecules. Understanding force‐mediated signaling by the αβTCR clarifies long‐standing questions regarding αβTCR antigen recognition, specificity and affinity, providing a basis for continued investigation. Future directions include examining atomistic mechanisms of αβTCR signal initiation, performance quality, tissue compliance adaptability, and T‐cell memory fate. The mechanotransduction paradigm will foster improved rational design of T‐cell based vaccines, CAR‐Ts, and adoptive therapies.

Immunology↗

DOE OSTI2021

Toho-1 β-lactamase: backbone chemical shift assignments and changes in dynamics upon binding with avibactam

Backbone chemical shift assignments for the Toho-1 β-lactamase (263 amino acids, 28.9 kDa) are reported based on triple resonance solution-state NMR experiments performed on a uniformly 2 H, 13 C, 15 N-labeled sample. These assignments allow for subsequent site-specific characterization at the chemical, structural, and dynamical levels. At the chemical level, titration with the non-β-lactam β-lactamase inhibitor avibactam is found to give chemical shift perturbations indicative of tight covalent binding that allow for mapping of the inhibitor binding site. At the structural level, protein secondary structure is predicted based on the backbone chemical shifts and protein residue sequence using TALOS-N and found to agree well with structural characterization from X-ray crystallography. At the dynamical level, model-free analysis of 15 N relaxation data at a single field of 16.4 T reveals well-ordered structures for the ligand-free and avibactam-bound enzymes with generalized order parameters of ~0.85. Complementary relaxation dispersion experiments indicate that there is an escalation in motions on the millisecond timescale in the vicinity of the active site upon substrate binding. The combination of high rigidity on short timescales and active site flexibility on longer timescales is consistent with hypotheses for achieving both high catalytic efficiency and broad substrate specificity: the induced active site dynamics allows variously sized substrates to be accommodated and increases the probability that the optimal conformation for catalysis will be sampled.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Heat Loss Effects on Emissions in an NH 3 RRQL Combustor

Ammonia (NH 3 ) is a carbon-free energy carrier with an infrastructure for production, storage, and distribution. There is interest in direct NH 3 combustion, but managing pollutant emissions is a key challenge, particularly nitric oxides (NO x ) due to the fuel-bound nitrogen atom, nitrous oxide (N 2 O), which is a potent greenhouse gas, and unburned NH 3 , which is harmful to humans and the environment. Rich staged combustor concepts with extended primary residence times (τ res,primary ), like Rich-Relax- Quick-mix-Lean (RRQL), offer a viable pathway for direct NH 3 combustion with low levels of NO x formation. However, minimizing secondary emissions such as N 2 O and unburned NH 3 and hydrogen (H 2 ) remains a critical challenge. Prior atmospheric-pressure studies have demonstrated that RRQL operation with sufficiently long τ res,primary enables substantial NO x relaxation and promotes NH 3 cracking to H 2 , if heat losses from the relaxation stage are limited. However, the combined influence of elevated pressure and long residence time on RRQL performance has not been explored. The present work examines RRQL operation at pressures up to 5 bar and elevated τ res,primary . Exhaust measurements of NO x , NH 3 , and N 2 O are used to quantify the extent of NO x relaxation and NH 3 cracking under nonadiabatic conditions. To contextualize and quantify the effects of heat losses in the experimental data, chemical reactor networks (CRNs) incorporating prescribed heat loss rates are employed to assess the sensitivity of emissions to thermal losses in the relaxation stage. Collectively, the results demonstrate that management and quantification of heat losses are essential to preserve NO x relaxation and limit NH 3 and N 2 O emissions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Specific absorbed fractions for a revised series of the UF/NCI pediatric reference phantoms: internal photon sources

Assessment of radiation absorbed dose to internal organs of the body from the intake of radionuclides, or in the medical setting through the injection of radiopharmaceuticals, is generally performed based upon reference biokinetic models or patient imaging data, respectively. Biokinetic models estimate the time course of activity localized to source organs. The time-integration of these organ activity profiles are then scaled by the radionuclide S-value, which defines the absorbed dose to a target tissue per nuclear transformation in various source tissues. S-values are computed using established nuclear decay information (particle energies and yields), and a parameter termed the specific absorbed fraction (SAF). The SAF is the ratio of the absorbed fraction—fraction of particle energy emitted in the source tissue that is deposited in the target tissue—and the target organ mass. While values of the SAF may be computed using patient-specific or individual-specific anatomic models, they have been more widely available through the use of computational reference phantoms. In this study, we report on an extensive series of photon SAFs computed in a revised series of the University of Florida and the National Cancer Institute pediatric reference phantoms which have been modified to conform to the specifications embodied in the ICRP reference adult phantoms of Publication 110 (e.g. organs modeled, organ ID numbers, blood contribution to elemental compositions). Following phantom anatomical revisions, photon radiation transport simulations were performed using MCNPX v2.7 in each of the ten phantoms of the series—male and female newborn, 1 year old, 5 year old, 10 year old, and 15 year old—for 60 different tissues serving as source and/or target regions. A total of 25 photon energies were considered from 10 keV to 10 MeV along a logarithm energy grid. Detailed analyses were conducted of the relative statistical errors in the Monte Carlo target tissue energy deposition tallies at low photon energies and over all energies for source–target combinations at large intra-organ separation distances. Based on these analyses, various data smoothing algorithms were employed, including multi-point weighted data smoothing, and log–log interpolation at low energies (1 keV and 5 keV) using limiting SAF values based upon target organ mass to bound the interpolation interval. The final dataset is provided in a series of ten electronic supplemental files in MS Excel format. Finally, the results of this study were further used as the basis for assessing the radiative component of internal electron source SAFs as described in our companion paper (Schwarz et al 2021) for this same pediatric phantom series.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2021

Specific absorbed fractions for a revised series of the UF/NCI pediatric reference phantoms: internal electron sources

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Material Identification From Radiographs Without Energy Resolution

We propose a method for performing material identification from radiographs without energy-resolved measurements. Material identification has a wide variety of applications, including in biomedical imaging, nondestructive testing, and security. While existing techniques for radiographic material identification make use of dual energy sources, energy-resolving detectors, or additional (e.g., neutron) measurements, such setups are not always practical— requiring additional hardware and complicating imaging. We tackle material identification without energy resolution, allowing standard X-ray systems to provide material identification information without requiring additional hardware. Assuming a setting where the geometry of each object in the scene is known and the materials come from a known set of possible materials, we pose the problem as a combinatorial optimization with a loss function that accounts for the presence of scatter and an unknown gain and propose a branch and bound algorithm to efficiently solve it. We present experiments on both synthetic data and real, experimental data with relevance to security applications— thick, dense objects imaged with MeV X-rays. We show that material identification can be efficient and accurate, for example, in a scene with three shells (two copper, one aluminum), our algorithm ran in six minutes on a consumer-level laptop and identified the correct materials as being among the top 10 best matches out of 8,000 possibilities.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Performance of the A-01 Constructed Wetland over 20 Years

The A-01 wetland treatment system (WTS) was designed to remove metals from the effluent at the A-01 National Pollution Discharge Elimination System (NPDES) outfall at the Savannah River Site, Aiken, SC. The A-01 effluent flows from a retention basin to a splitter box, where it is distributed to four pairs of cells in series before discharge to a stream. Each treatment cell is a one-acre wetland that contains Schoenoplectus californicus (giant bulrush) and has a nominal 24-hour retention time. The purpose of this research was to investigate metal removal, distribution and retention in the A-01 WTS over a period of 20 years. During 20 years of operation, systematic water and sediment sampling validated the wetlands' performance. After passage through the treatment cells, Cu concentrations were well below permit limits (22 pg L -1 ) during all years of operation, often falling below 10 pg L -1 . Cu removal has been consistent over time, averaging about 80% despite large changes in influent Cu concentrations. Most divalent metals were rapidly removed from the water and held in the sediments shortly after the water entered the treatment wetlands. Average removal of Pb from water by the wetland system was 67 and 74%, respectively, in 2004, and 2020. Comparable values for Zn were 52 and 65%, respectively. Generally, the highest concentrations of Cu, Pb, and Zn were found in the sediment from the first cell in each pair of cells suggesting that most of the Cu, Pb, and Zn in the A-01 effluent was bound to the sediment quickly. Diffusive gradients in thin films (DGT) measurements of Cu and Zn in the sediments were much lower than bulk sediment concentrations. These results suggest that most of the Cu and Zn in the A-01 WTS sediments was not bioavailable, hence not toxic to aquatic organisms, as a likely consequence of adsorption to sediment particles and complexation with organic and inorganic substances.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Toward Revealing Microcystin Distribution in Mouse Liver Tissue Using MALDI-MS Imaging

Cyanotoxins can be found in water and air during cyanobacterial harmful algal blooms (cHABs) in lakes and rivers. Therefore, it is very important to monitor their potential uptake by animals and humans as well as their health effects and distribution in affected organs. Herein, the distribution of hepatotoxic peptide microcystin-LR (MC-LR) is investigated in liver tissues of mice gavaged with this most common MC congener. Preliminary matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) imaging experiments performed using a non-automated MALDI matrix deposition device and a MALDI-time-of-flight (TOF) mass spectrometer yielded ambiguous results in terms of MC-LR distribution in liver samples obtained from MC-LR-gavaged mice. The tissue preparation for MALDI-MS imaging was improved by using an automated sprayer for matrix deposition, and liver sections were imaged using an Nd:YAG MALDI laser coupled to a 15 Tesla Fourier-transform ion cyclotron resonance (FT-ICR)-mass spectrometer. MALDI-FT-ICR-MS imaging provided unambiguous detection of protonated MC-LR (calculated m/z 995.5560, z = +1) and the sodium adduct of MC-LR (m/z 1017.5380, z = +1) in liver sections from gavaged mice with great mass accuracy and ultra-high mass resolution. Since both covalently bound and free MC-LR can be found in liver of mice exposed to this toxin, the present results indicate that the distribution of free microcystins in tissue sections from affected organs, such as liver, can be monitored with high-resolution MALDI-MS imaging.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Wave-function-based emulation for nucleon-nucleon scattering in momentum space

Emulators for low-energy nuclear physics can provide fast and accurate predictions of bound-state and scattering observables for applications that require repeated calculations with different parameters, such as Bayesian uncertainty quantification. In this paper, we extend a scattering emulator based on the Kohn variational principle (KVP) to momentum space (including coupled channels) with arbitrary boundary conditions, which enable the mitigation of spurious singularities known as Kohn anomalies. We test it on a modern chiral nucleon-nucleon (N N) interaction, including emulation of the coupled channels. We provide comparisons between a Lippmann-Schwinger equation emulator and our KVP momentum-space emulator for a representative set of neutron-proton (n p) scattering observables, and also introduce a quasi-spline-based approach for the KVP-based emulator. Furthermore, our findings show that while there are some trade-offs between accuracy and speed, all three emulators perform well. Self-contained Jupyter notebooks that generate the results and figures in this paper are publicly available.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Dynamic Power Network State Estimation with Asynchronous Measurements

The operation of distribution networks is becoming increasingly volatile, due to fast variations of renewables and, hence, net-loading conditions. To perform a reliable state estimation under these conditions, this paper considers the case where measurements from meters, phasor measurement units, and distributed energy resources are collected and processed in real time to produce estimates of the state at a fast time scale. Streams of measurements collected in real time and at heterogenous rates render the underlying processing asynchronous, and poses severe strains on workhorse state estimation algorithms. In this work, a real-time state estimation algorithm is proposed, where data are processed on the fly. Starting from a regularized least-squares model, and leveraging appropriate linear models, the proposed scheme boils down to a linear dynamical system where the state is updated based on the previous estimate and on the measurement gathered from a few available sensors. The estimation error is shown to be always bounded under mild condition. Numerical simulations are provided to corroborate the analytical findings.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Influences of lidar scanning parameters on wind turbine wake retrievals in complex terrain

Abstract. Scanning lidars enable the collection of spatially distributed measurements of turbine wakes and the estimation of wake properties such as magnitude, extent, and trajectory. Lidar-based characterizations, however, may be subject to distortions due to the observational system. Distortions can arise from the resolution of the measurement points across the wake, the projection of the winds onto the beam, averaging along the beam probe volume, and intervening evolution of the flow over the scan duration. Using a large-eddy simulation and simulated measurements with a virtual lidar model, we assess how scanning lidar systems may influence the properties of the retrieved wake using a case study from the Perdigão campaign. We consider three lidars performing range-height indicator sweeps in complex terrain, based on the deployments of lidars from the Danish Technical University (DTU) and German Aerospace Center (DLR) at the Perdigão site. The unwaked flow, measured by the DTU lidar, is well-captured by the lidar, even without combining data into a multi-lidar retrieval. The two DLR lidars measure a waked transect from different downwind vantage points. In the region of the wake, the observation system reacts to the smaller spatial and temporal variations of the winds, allowing more significant observation distortions to arise. While the measurements largely capture the wake structure and trajectory over its 4–5 D extent, limited spatial resolution of measurement points and volume averaging lead to a quicker loss of the two lobes in the near wake, smearing of the vertical bounds of the wake (< 30 m), wake center displacements up to 10 m, and dampening of the maximum velocity deficit by up to a third. The virtual lidar tool, coupled with simulations, provides a means for assessing measurement capabilities in advance of measurement campaigns.

17 WIND ENERGY↗

DOE OSTI2022

Neutron scattering maps the higher-order assembly of NADPH-dependent assimilatory sulfite reductase

Precursor molecules for biomass incorporation must be imported into cells and made available to the molecular machines that build the cell. Sulfur-containing macromolecules require that sulfur be in its S2- oxidation state before assimilation into amino acids, cofactors, and vitamins that are essential to organisms throughout the biosphere. In α-proteobacteria, NADPH-dependent assimilatory sulfite reductase (SiR) performs the final six-electron reduction of sulfur. SiR is a dodecameric oxidoreductase composed of an octameric flavoprotein reductase (SiRFP) and four hemoprotein metalloenzyme oxidases (SiRHPs). SiR performs the electron transfer reduction reaction to produce sulfide from sulfite through coordinated domain movements and subunit interactions without release of partially reduced intermediates. Efforts to understand the electron transfer mechanism responsible for SiR’s efficiency are confounded by structural heterogeneity arising from intrinsically disordered regions throughout its complex, including the flexible linker joining SiRFP’s flavin-binding domains. As a result, high-resolution structures of SiR dodecamer and its subcomplexes are unknown, leaving a gap in the fundamental understanding of how SiR performs this uniquely large-volume electron transfer reaction. In this work, we use deuterium labeling, in vitro reconstitution, analytical ultracentrifugation (AUC), small-angle neutron scattering (SANS), and neutron contrast variation (NCV) to observe the relative subunit positions within SiR’s higher-order assembly. AUC and SANS reveal SiR to be a flexible dodecamer and confirm the mismatched SiRFP and SiRHP subunit stoichiometry. NCV shows that the complex is asymmetric, with SiRHP on the periphery of the complex and the centers of mass between SiRFP and SiRHP components over 100 Å apart. SiRFP undergoes compaction upon assembly into SiR’s dodecamer and SiRHP adopts multiple positions in the complex. The resulting map of SiR’s higher-order structure supports a cis/trans mechanism for electron transfer between domains of reductase subunits as well as between tightly bound or transiently interacting reductase and oxidase subunits.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries

This paper introduces the scaled boundary cubature (SBC) scheme for accurate and efficient integration of functions over polygons and two-dimensional regions bounded by parametric curves. Over two-dimensional domains, the SBC method reduces integration over a region bounded by m curves to integration over m regions (referred to as curved triangular regions), where each region is bounded by two line segments and a curve. With proper (counterclockwise) orientation of the boundary curves, the scheme is applicable to convex and nonconvex domains. Additionally, for star-convex domains, a tensor-product cubature rule with positive weights and integration points in the interior of the domain is obtained. If the integrand is homogeneous, we show that this new method reduces to the homogeneous numerical integration scheme; however, the SBC scheme is more versatile since it is equally applicable to both homogeneous and non-homogeneous functions. This paper also introduces several methods for smoothing integrands with point singularities and near-singularities. When these methods are used, highly efficient integration of weakly singular functions is realized. Finally, the SBC method is applied to a number of benchmark problems, which reveal its broad applicability and superior performance (in terms of time to generate a rule and accuracy per cubature point) when compared to existing methods for integration.

42 ENGINEERING↗

DOE OSTI2020

Transformation of Ferrihydrite to Goethite and the Fate of Plutonium

Understanding the interactions between plutonium and iron (oxy)hydroxide minerals is necessary to gain a predictive understanding of plutonium environmental mobility and to evaluate long-term performance of nuclear waste repositories. We investigated the fate of plutonium during the formation of ferrihydrite and its subsequent transformation into goethite. Ferrihydrite was synthesized with varying quantities of Pu(IV) following either a sorption or coprecipitation process; the ferrihydrite was then aged hydrothermally to yield goethite. Additionally, the synthesized materials were characterized via extended X-ray absorption fine structure spectroscopy, transmission electron microscopy, and acid leaching to elucidate the nature of plutonium association with ferrihydrite and goethite. In samples prepared following the sorption method, plutonium was identified in two different forms: a PuO 2 precipitate and a surface-sorbed plutonium complex. For the samples prepared via coprecipitation, no PuO 2 formation occurs in the ferrihydrite precursor and in the goethite experiments where plutonium concentration is ≤1000 ppm (mg kg –1 ). In these coprecipitation products, plutonium is strongly bound to the minerals either via formation of an inner sphere complex, or via an incorporation process. In the coprecipitation experiments, PuO 2 formation only occurs at the highest plutonium concentration (3000 ppm), suggesting that during ferrihydrite transformation into goethite, part of the plutonium can be remobilized to form PuO 2 nanoparticles. Collectively, our results demonstrate that the nature of plutonium associated with the precursor ferrihydrite (adsorbed vs coprecipitated) will have a direct impact on the association of plutonium with its alteration product (goethite). Furthermore, the data illustrate that some properties of plutonium association with the precursor ferrihydrite are retained through the transformation into goethite. These findings show that plutonium strongly associates with iron (oxy)hydroxides formed through coprecipitation processes and in these materials, plutonium can be strongly retained by the iron minerals.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Carrier recombination dynamics and temperature dependent optical properties of InAs–GaSb heterostructures

Heterostructures with two dissimilar materials could offer unprecedented properties if one can carefully synthesize these heterostructures with atomically smooth interfaces and reduced number of recombination centers. InAs/GaSb-based heterostructures have technological importance for long wavelength infrared photodetectors if one can synthesize these materials with high-optical quality and high-carrier lifetime. In this work, the InAs/GaSb heterostructures with a different number of heterointerfaces and growth conditions were grown by solid source molecular beam epitaxy using valved cracker sources for both arsenic and antimony. Precise control of growth parameters and shutter sequences enabled abrupt InAs/GaSb heterointerfaces, as supported by a high-resolution transmission electron microscopic study. The temperature and power-dependent optical properties by photoluminescence (PL) spectroscopic analysis of InAs/GaSb heterostructures with 4 and 28 heterointerfaces displayed donor to the acceptor and the exciton bound to complex defects (V Ga Ga Sb ) 0 . Since the optical transition in PL measurements serves to determine the quality of the material, and the observed excitonic transitions from these InAs/GaSb heterostructures is an indication of high-quality materials. The high-carrier lifetimes of 139 ns to 185 ns from InAs/GaSb heterostructures were measured using microwave photoconductivity decay (μ-PCD) technique at room temperature. The observed increase in carrier lifetime is due to the decreasing number of Ga-related carrier recombination centers or defect complexes. This is further supported by the PL spectroscopic study. In addition, the carrier lifetime with different injection levels is supported by Shockley–Read–Hall recombination. We report these InAs/GaSb heterostructures with high-optical quality and high-carrier lifetimes would offer a path for the development of high-performance infrared photodetectors.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Majorana bound states with chiral magnetic textures

The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of “spinless” fermions and show how two “half” fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how “spinless” fermions can be realized in more physical systems, e.g., by employing the spin-momentum locking. Next, we demonstrate how magnetic textures can be used to induce synthetic or fictitious spin–orbit interactions, and, thus, stabilize MBS. We describe a general approach that works for arbitrary textures and apply it to skyrmions. We show how MBS can be stabilized by elongated skyrmions, certain higher order skyrmions, and chains of skyrmions. We also discuss how braiding operations can be performed with MBS stabilized on magnetic skyrmions. Furthermore, this Tutorial is aimed at students at the graduate level.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Characterization of Partially Observed Epidemics - Application to COVID-19

This report documents a statistical method for the "real-time" characterization of partially observed epidemics. Observations consist of daily counts of symptomatic patients, diagnosed with the disease. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information for the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and is predicated on a model for the distribution of the incubation period. The model parameters are estimated as distributions using a Markov Chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. The method is applied to the COVID-19 pandemic of 2020, using data at the country, provincial (e.g., states) and regional (e.g. county) levels. The epidemiological model includes a stochastic component due to uncertainties in the incubation period. This model-form uncertainty is accommodated by a pseudo-marginal Metropolis-Hastings MCMC sampler, which produces posterior distributions that reflect this uncertainty. We approximate the discrepancy between the data and the epidemiological model using Gaussian and negative binomial error models; the latter was motivated by the over-dispersed count data. For small daily counts we find the performance of the calibrated models to be similar for the two error models. For large daily counts the negative-binomial approximation is numerically unstable unlike the Gaussian error model. Application of the model at the country level (for the United States, Germany, Italy, etc.) generally provided accurate forecasts, as the data consisted of large counts which suppressed the day-to-day variations in the observations. Further, the bulk of the data is sourced over the duration before the relaxation of the curbs on population mixing, and is not confounded by any discernible country-wide second wave of infections. At the state-level, where reporting was poor or which evinced few infections (e.g., New Mexico), the variance in the data posed some, though not insurmountable, difficulties, and forecasts were able to capture the data with large uncertainty bounds. The method was found to be sufficiently sensitive to discern the flattening of the infection and epidemic curve due to shelter-in-place orders after around 90% quantile for the incubation distribution (about 10 days for COVID-19). The proposed model was also used at a regional level to compare the forecasts for the central and north-west regions of New Mexico. Modeling the data for these regions illustrated different disease spread dynamics captured by the model. While in the central region the daily counts peaked in the late April, in the north-west region the ramp-up continued for approximately three more weeks.

59 BASIC BIOLOGICAL SCIENCES↗