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At least 379 records · Page 21

Fast HARDI Uncertainty Quantification and Visualization with Spherical Sampling

In this paper, we study uncertainty quantification and visualization of orientation distribution functions (ODF), which corresponds to the diffusion profile of high angular resolution diffusion imaging (HARDI) data. The shape inclusion probability (SIP) function is the state‐of‐the‐art method for capturing the uncertainty of ODF ensembles. The current method of computing the SIP function with a volumetric basis exhibits high computational and memory costs, which can be a bottleneck to integrating uncertainty into HARDI visualization techniques and tools. We propose a novel spherical sampling framework for faster computation of the SIP function with lower memory usage and increased accuracy. In particular, we propose direct extraction of SIP isosurfaces, which represent confidence intervals indicating spatial uncertainty of HARDI glyphs, by performing spherical sampling of ODFs. Our spherical sampling approach requires much less sampling than the state‐of‐the‐art volume sampling method, thus providing significantly enhanced performance, scalability, and the ability to perform implicit ray tracing. Our experiments demonstrate that the SIP isosurfaces extracted with our spherical sampling approach can achieve up to 8164× speedup, 37282× memory reduction, and 50.2% less SIP isosurface error compared to the classical volume sampling approach. We demonstrate the efficacy of our methods through experiments on synthetic and human‐brain HARDI datasets.

97 MATHEMATICS AND COMPUTING↗

A Multi-Armed Bayesian Ordinal Outcome Utility-Based Sequential Trial with a Pairwise Null Clustering Prior

A multi-armed trial based on ordinal outcomes is proposed that leverages a flexible non-proportional odds cumulative logit model and numerical utility scores for each outcome to determine treatment optimality. This trial design uses a Bayesian clustering prior on the treatment effects that encourages the pairwise null hypothesis of no differences between treatments. A group sequential design is proposed to determine which treatments are clinically different with an adaptive decision boundary that becomes more aggressive as the sample size or clinical significance grows, or the number of active treatments decreases. A simulation study is conducted for 3 and 5 treatment arms, which shows that the design has superior operating characteristics (family wise error rate, generalized power, average sample size) compared to utility designs that do not allow clustering, a frequentist proportional odds model, or a permutation test based on empirical mean utilities.

97 MATHEMATICS AND COMPUTING↗

Quantitative analysis of the reconstruction performance of interpolants

The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed.

Lansing, Donald L.↗

DESI and DECaLS (D&D): galaxy–galaxy lensing measurements with 1 per cent survey and its forecast

The shear measurement from the Dark Energy Camera Legacy Survey (DECaLS) provides an excellent opportunity for galaxy–galaxy lensing study with the Dark Energy Spectroscopic Instrument (DESI) galaxies, given the large (~9000 deg 2 ) sky overlap. We explore this potential by combining the DESI 1 per cent survey and DECaLS Data Release 8 (DR8). With ~106 deg 2 sky overlap, we achieve significant detection of galaxy–galaxy lensing for Bright Galaxy Survey (BGS) and luminous red galaxy (LRG) as lenses. Scaled to the full BGS sample, we expect the statistical errors to improve from 18(12)per cent to a promising level of 2(1.3)per cent at θ > 8arcmin(< 8 arcmin) ⁠. This brings stronger requirements for future systematics control. To fully realize such potential, we need to control the residual multiplicative shear bias |m| < 0.006 and the bias in the mean redshift |Δz| < 0.008, requiring the introduced bias in the measurement is <0.31σ. We also expect significant detection of galaxy–galaxy lensing with DESI LRG/emission line galaxy (ELG) full samples as lenses, and cosmic magnification of ELG through cross-correlation with low-redshift DECaLS shear. If such systematical error control can be achieved, we find the advantages of DECaLS, comparing with the Kilo Degree Survey (KiDS) and the Hyper Suprime-Cam (HSC), are at low redshift, large scale, and in measuring the shear ratio (to σ R ~ 0.04) and cosmic magnification.

(cosmology:) large-scale structure of Universe↗

Improvements to photometry. Part 1: Better estimation of derivatives in extinction and transformation equations

Atmospheric extinction in wideband photometry is examined both analytically and through numerical simulations. If the derivatives that appear in the Stromgren-King theory are estimated carefully, it appears that wideband measurements can be transformed to outside the atmosphere with errors no greater than a millimagnitude. A numerical analysis approach is used to estimate derivatives of both the stellar and atmospheric extinction spectra, avoiding previous assumptions that the extinction follows a power law. However, it is essential to satify the requirements of the sampling theorem to keep aliasing errors small. Typically, this means that band separations cannot exceed half of the full width at half-peak response. Further work is needed to examine higher order effects, which may well be significant.

Young, Andrew T.↗

Verification of land cover maps from LANDSAT data

The application of cluster sampling to verifying the accuracy of maps derived from digital data is discussed. Variants of the cluster sampling technique were used in large scale assessments for areas in excess of one million hectares. Three types of classification errors are possible: commission errors, omission errors, and overall error classification. Commission errors for a particular cover type occur when pixels are classified as that cover type but are found to be some other cover type when the field is checked. Omission errors occur when pixels of fields already visited and known to be of a particular cover type, are classified as some other cover type. Overall error is the proportion of pixels incorrectly classified, without regard to omission or commission. Since the classified image represents the sampling frame, sampling for accuracy assessment was designed to estimate commission error. However, the sample can also provide useful estimates of omission and overall error. Assessment for Alaska, Arizona, and Oklahoma are presented.

Linden, D. S.↗

Designing an Optimal Ensemble Strategy for GMAO S2S Forecast System

GMAO Sub/Seasonal prediction system (S2S) is being readied for a major upgrade to GEOS-S2S Version 3. An important factor in successful extended range forecast is the definition of an ensemble For initialization of the ensemble we propose a combination of lagged and burst initial conditions. We plan to run a relatively large ensemble of 40 members for sub-seasonal forecast (up to 3 months), at which point we sub-sample the ensemble, and continue the forecast with 10 members (up to 12 months). Here we present the results of the extensive testing of various ways to generate the perturbations to the initial conditions and the validation of the stratified sampling strategy we chose.To generate perturbations for the burst ensemble members we used scaled differences of pairs of analysis states separated by 1-10 days, randomly chosen from a corresponding season. We considered perturbing separately only the atmospheric fields or only the ocean or both of the forecast initial conditions. Considering varying separation times between the analysis states, we were able to produce perturbations sampling various modes of variability. Focusing on the ENSO SST indices, we found that all types of perturbations are important for the ensemble spread.Our ensemble size for sub-seasonal forecasts was determined as to maximize the skill of predicting some of the leading modes of boreal winter atmospheric modes, NAO, PNA and AO. It is not feasible to run equally large ensemble for seasonal forecasts. Using a stratified sampling procedure we can identify the emerging directions of error growth. By comparing the stratified ensemble with randomly sampled ensemble of the same size, we were able to show that the former better estimates the mean of the original large ensemble.

Borovikov, Anna↗

Investigation of Error Patterns in Geographical Databases

The objective of the research conducted in this project is to develop a methodology to investigate the accuracy of Airport Safety Modeling Data (ASMD) using statistical, visualization, and Artificial Neural Network (ANN) techniques. Such a methodology can contribute to answering the following research questions: Over a representative sampling of ASMD databases, can statistical error analysis techniques be accurately learned and replicated by ANN modeling techniques? This representative ASMD sample should include numerous airports and a variety of terrain characterizations. Is it possible to identify and automate the recognition of patterns of error related to geographical features? Do such patterns of error relate to specific geographical features, such as elevation or terrain slope? Is it possible to combine the errors in small regions into an error prediction for a larger region? What are the data density reduction implications of this work? ASMD may be used as the source of terrain data for a synthetic visual system to be used in the cockpit of aircraft when visual reference to ground features is not possible during conditions of marginal weather or reduced visibility. In this research, United States Geologic Survey (USGS) digital elevation model (DEM) data has been selected as the benchmark. Artificial Neural Networks (ANNS) have been used and tested as alternate methods in place of the statistical methods in similar problems. They often perform better in pattern recognition, prediction and classification and categorization problems. Many studies show that when the data is complex and noisy, the accuracy of ANN models is generally higher than those of comparable traditional methods.

Dryer, David↗

Optical and X-ray GRB Fundamental Planes as cosmological distance indicators

ABSTRACT Gamma-ray bursts (GRBs), can be employed as standardized candles, extending the distance ladder beyond Type Ia supernovae (SNe Ia, z = 2.26). We standardize GRBs using the three-dimensional (3D) Fundamental Plane relation (the Dainotti relation) among the rest-frame end time of the X-ray plateau emission, its corresponding luminosity, and the peak prompt luminosity. Combining SNe Ia and GRBs, we constrain ΩM = 0.299 ± 0.009 assuming a flat Λ cold dark matter (ΛCDM) cosmology with and without correcting GRBs for selection biases and redshift evolution. Using a 3D optical Dainotti correlation, we find this sample is as efficacious in the determination of ΩM as the X-ray sample. We trimmed our GRB samples to achieve tighter planes to simulate additional GRBs. We determined how many GRBs are needed as stand-alone probes to achieve a comparable precision on ΩM to the one obtained by SNe Ia only. We reach the same error measurements derived using SNe Ia in 2011 and 2014 with 142 and 284 simulated optical GRBs, respectively, considering the error bars on the variables halved. These error limits will be reached in 2038 and in 2047, respectively. Using a doubled sample (obtained by future machine learning approaches allowing a light-curve reconstruction and the estimates of GRB redshifts when z is unknown) compared to the current sample, with error bars halved we will reach the same precision as SNe Ia in 2011 and 2014, now and in 2026, respectively. If we consider the current SNe precision, this will be reached with 390 optical GRBs by 2054.

Dainotti, M. G.↗

Private Tabular Survey Data Products through Synthetic Microdata Generation

We propose two synthetic microdata approaches to generate private tabular survey data products for public release. We adapt a pseudo posterior mechanism that downweights by-record likelihood contributions with weights ∈[0,1] based on their identification disclosure risks to producing tabular products for survey data. Our method applied to an observed survey database achieves an asymptotic global probabilistic differential privacy guarantee. Our two approaches synthesize the observed sample distribution of the outcome and survey weights, jointly, such that both quantities together possess a privacy guarantee. The privacy-protected outcome and survey weights are used to construct tabular cell estimates (where the cell inclusion indicators are treated as known and public) and associated standard errors to correct for survey sampling bias. Through a real data application to the Survey of Doctorate Recipients public use file and simulation studies motivated by the application, we demonstrate that our two microdata synthesis approaches to construct tabular products provide superior utility preservation as compared to the additive noise approach of the Laplace Mechanism. Moreover, our approaches allow the release of microdata to the public, enabling additional analyses at no extra privacy cost.

Mathematical Methods In Social Sciences↗

Problems in determining the surface density of the Galactic disk

A new method is presented for determining the local surface density of the Galactic disk from distance and velocity measurements of stars toward the Galactic poles. The procedure is fully three-dimensional, approximating the Galactic potential by a potential of Staeckel form and using the analytic third integral to treat the tilt and the change of shape of the velocity ellipsoid consistently. Applying the procedure to artificial data superficially resembling the K dwarf sample of Kuijken and Gilmore (1988, 1989), it is shown that the current best estimates of local disk surface density are uncertain by at least 30 percent. Of this, about 25 percent is due to the size of the velocity sample, about 15 percent comes from uncertainties in the rotation curve and the solar galactocentric distance, and about 10 percent from ignorance of the shape of the velocity distribution above z = 1 kpc, the errors adding in quadrature. Increasing the sample size by a factor of 3 will reduce the error to 20 percent. To achieve 10 percent accuracy, observations will be needed along other lines of sight to constrain the shape of the velocity ellipsoid.

Statler, Thomas S.↗

Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme

The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector. *************************************** AUTHOR = Slater, Bethany University of Liverpool b.slater2@liverpool.ac.uk TITLE = Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme PAGES = 218 NOTE = Ph.D. University of Liverpool March 2026 ABSTRACT = The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector.

Slater, Bethany [Liverpool U.]↗

Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme

The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector. *************************************** AUTHOR = Slater, Bethany University of Liverpool b.slater2@liverpool.ac.uk TITLE = Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme PAGES = 218 NOTE = Ph.D. University of Liverpool March 2026 ABSTRACT = The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector.

Slater, Bethany [Liverpool U.]↗

Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme

The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector. *************************************** AUTHOR = Slater, Bethany University of Liverpool b.slater2@liverpool.ac.uk TITLE = Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme PAGES = 218 NOTE = Ph.D. University of Liverpool March 2026 ABSTRACT = The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector.

Slater, Bethany [Liverpool U.]↗

Use of Whatman-41 filters in air quality sampling networks (with applications to elemental analysis)

The operation of a 16-site parallel high volume air sampling network with glass fiber filters on one unit and Whatman-41 filters on the other is reported. The network data and data from several other experiments indicate that (1) Sampler-to-sampler and filter-to-filter variabilities are small; (2) hygroscopic affinity of Whatman-41 filters need not introduce errors; and (3) suspended particulate samples from glass fiber filters averaged slightly, but not statistically significantly, higher than from Whatman-41-filters. The results obtained demonstrate the practicability of Whatman-41 filters for air quality monitoring and elemental analysis.

Neustadter, H. E.↗

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗

Calibration of TOPEX/POSEIDON at Platform Harvest

We present estimates for the mean bias of the TOPEX/POSEIDON NASA altimeter (ALT) and the Centre National d'Etudes Spatiales altimeter (SSALT) using in-situ data gathered at Platform Harvest during the first 36 cycles of the mission. Data for 21 overflights of the ALT and six overflights of the SSALT have been analyzed. The analysis includes an independent assessment of in-situ measurements of sea level, the radial component of the orbit, wet tropospheric path delay, and ionospheric path delay. (The sign convention used is such that, to correct the geophysical data record values for sea level, add the bias algebraically. Unless otherwise stated, the uncertainty in a given parameter is depicted by +/- sigma(sub x), where sigma(sub x) is the sample standard deviation of x about the mean.) Tide gauges at Harvest provide estimates of sea level with an uncertainty of +/- 1.5 cm. The uncertainty in the radial component of the orbit is estimated to be +/- 1.3 cm. In-situ measurements of tropopsheric path delay at Harvest compare to within +/- 1.3 cm of the TOPEX/POSEIDON microwave radiometer, and in-situ measurements of the ionospheric path delay compare to within -0.4 +/- 0.7 cm of the dual-frequency ALT and 1.1 +/- 0.6 cm of Doppler orbitography and radiopositioning integrated by satellite. We obtain mean bias estimates of -14.5 +/- 2.9 cm for the ALT and +0.9 +/- 3.1 cm for the SSALT (where the uncertainties are based on the standard deviation of the estimated mean (sigma(sub bar x/y), which is derived from sample statistics and estimates for errors that cannot be observed). These results are consistent with independent estimates for the relative bias between the two altimeters. A linear regression applied to the complete set of data shows that there is a discernable secular trend in the time series for the ALT bias estimates. A preliminary analysis of data obtained through cycle 48 suggests that the apparent secular drift may be the result of a poorly sampled annual signal.

Christensen, E. J.↗

Weak Simulation v.0.1

The SPARSIFY algorithm implemented by the code allows for classical simulation of universal quantum computer sample outcomes. The code sparsifies the stabilizer decomposition of a qubit t-tensored T gate magic state to some additive error. This is accomplished by either independent L1 sampling or with correlated L1 sampling to supplement an independent subset, which offers a more efficient decomposition: for a given t, a sparser decomposition is sufficient with correlated L1 sampling to satisfy a given additive error. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2021-8296 O

SciDAC↗