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A flag is a nested sequence of vector spaces. The type of the flag encodes the sequence of dimensions of the vector spaces making up the flag. A flag manifold is a manifold whose points parameterize all flags of a fixed type in a fixed vector space. This paper provides the mathematical framework necessary for implementing self-organizing mappings on flag manifolds. Flags arise implicitly in many data analysis contexts including wavelet, Fourier, and singular value decompositions. The proposed geometric framework in this paper enables the computation of distances between flags, the computation of geodesics between flags, and the ability to move one flag a prescribed distance in the direction of another flag. Using these operations as building blocks, we implement the SOM algorithm on a flag manifold. The basic algorithm is applied to the problem of parameterizing a set of flags of a fixed type. 

Finding prototypes (e.g., mean and median) for a dataset is central to a number of common machine learning algorithms. Subspaces have been shown to provide useful, robust representations for datasets of images, videos and more. Since subspaces correspond to points on a Grassmann manifold, one is led to consider the idea of a subspace prototype for a Grassmann-valued dataset. While a number of different subspace prototypes have been described, the calculation of some of these prototypes has proven to be computationally expensive while other prototypes are affected by outliers and produce highly imperfect clustering on noisy data. This work proposes a new subspace prototype, the flag median, and introduces the FlagIRLS algorithm for its calculation. We provide evidence that the flag median is robust to outliers and can be used effectively in algorithms like Linde-Buzo-Grey (LBG) to produce improved clusterings on Grassmannians. Numerical experiments include a synthetic dataset, the MNIST handwritten digits dataset, the Mind's Eye video dataset and the UCF YouTube action dataset. The flag median is compared the other leading algorithms for computing prototypes on the Grassmannian, namely, the l_2-median and to the flag mean. We find that using FlagIRLS to compute the flag median converges in 4 iterations on a synthetic dataset. We also see that Grassmannian LBG with a codebook size of 20 and using the flag median produces at least a 10% improvement in cluster purity over Grassmannian LBG using the flag mean or l_2-median on the Mind's Eye dataset. 

Neutrino-nucleus cross section measurements are needed to improve interaction modeling to meet the precision needs of neutrino experiments in efforts to measure oscillation parameters and search for physics beyond the Standard Model. We review the difficulties associated with modeling neutrino-nucleus interactions that lead to a dependence on event generators in oscillation analyses and cross section measurements alike. We then describe data-driven model validation techniques intended to address this model dependence. The method relies on utilizing various goodness-of-fit tests and the correlations between different observables and channels to probe the model for defects in the phase space relevant for the desired analysis. These techniques shed light on relevant mismodeling, allowing it to be detected before it begins to bias the cross section results. We compare more commonly used model validation methods which directly validate the model against alternative ones to these data-driven techniques and show their efficacy with fake data studies. These studies demonstrate that employing data-driven model validation in cross section measurements represents a reliable strategy to produce robust results that will stimulate the desired improvements to interaction modeling. Published by the American Physical Society2025 

Large neutrino liquid argon time projection chamber (LArTPC) experiments can broaden their physics reach by reconstructing and interpreting MeV-scale energy depositions, or blips, present in their data. We demonstrate new calorimetric and particle discrimination capabilities at the MeV energy scale using reconstructed blips in data from the MicroBooNE LArTPC at Fermilab. We observe a concentration of low-energy ( $<3\mathrm{MeV}$) blips around fiberglass mechanical support struts along the time projection chamber edges with energy spectrum features consistent with the Compton edge of 2.614 MeV ${}^{208}\mathrm{Tl}$decay $\gamma$rays. These features are used to verify proper calibration of electron energy scales in MicroBooNE’s data to few percent precision and to measure the specific activity of ${}^{208}\mathrm{Tl}$in the fiberglass composing these struts, $(11.7\pm 0.2\left(\mathrm{stat}\right)\pm 3.1\left(\mathrm{syst}\right))\mathrm{Bq}/\mathrm{kg}$. Cosmogenically produced blips above 3 MeV in reconstructed energy are used to showcase the ability of large LArTPCs to distinguish between low-energy proton and electron energy depositions. An enriched sample of low-energy protons selected using this new particle discrimination technique is found to be smaller in data than in dedicated cosmic-ray simulations, suggesting either incorrect modeling of incident cosmic fluxes or particle transport modeling issues in eant4. Published by the American Physical Society2025 

Abstract In this paper, we review scientific opportunities and challenges related to detection and reconstruction of low-energy (less than 100 MeV) signatures in liquid argon time-projection chamber (LArTPC) neutrino detectors. LArTPC neutrino detectors designed for performing precise long-baseline oscillation measurements with GeV-scale accelerator neutrino beams also have unique sensitivity to a range of physics and astrophysics signatures via detection of event features at and below the few tens of MeV range. In addition, low-energy signatures are an integral part of GeV-scale accelerator neutrino interaction final-states, and their reconstruction can enhance the oscillation physics sensitivities of LArTPC experiments. New physics signals from accelerator and natural sources also generate diverse signatures in the low-energy range, and reconstruction of these signatures can increase the breadth of Beyond the Standard Model scenarios accessible in LArTPC-based searches. A variety of experimental and theory-related challenges remain to realizing this full range of potential benefits. Neutrino interaction cross-sections and other nuclear physics processes in argon relevant to sub-hundred-MeV LArTPC signatures are poorly understood, and improved theory and experimental measurements are needed; pion decay-at-rest sources and charged particle and neutron test beams are ideal facilities for improving this understanding. There are specific calibration needs in the low-energy range, as well as specific needs for control and understanding of radiological and cosmogenic backgrounds. Low-energy signatures, whether steady-state or part of a supernova burst or larger GeV-scale event topology, have specific triggering, DAQ and reconstruction requirements that must be addressed outside the scope of conventional GeV-scale data collection and analysis pathways. Novel concepts for future LArTPC technology that enhance low-energy capabilities should also be explored to help address these challenges. 

A flag is a nested sequence of vector spaces. The type of the flag is determined by the sequence of dimensions of the vector spaces making up the flag. A flag manifold is a manifold whose points parameterize all flags of a particular type in a fixed vector space. This paper provides the mathematical framework necessary for implementing self-organizing mappings on flag manifolds. Flags arise implicitly in many data analysis techniques for instance in wavelet, Fourier, and singular value decompositions. The proposed geometric framework in this paper enables the computation of distances between flags, the computation of geodesics between flags, and the ability to move one flag a prescribed distance in the direction of another flag. Using these operations as building blocks, we implement the SOM algorithm on a flag manifold. The basic algorithm is applied to the problem of parameterizing a set of flags of a fixed type. 

We present a measurement of neutral pion production in charged-current interactions using data recorded with the MicroBooNE detector exposed to Fermilab’s booster neutrino beam. The signal comprises one muon, one neutral pion, any number of nucleons, and no charged pions. Studying neutral pion production in the MicroBooNE detector provides an opportunity to better understand neutrino-argon interactions, and is crucial for future accelerator-based neutrino oscillation experiments. Using a dataset corresponding to $6.86\times {10}^{20}$protons on target, we present single-differential cross sections in muon and neutral pion momenta, scattering angles with respect to the beam for the outgoing muon and neutral pion, as well as the opening angle between the muon and neutral pion. Data extracted cross sections are compared to generator predictions. We report good agreement between the data and the models for scattering angles, except for an over-prediction by generators at muon forward angles. Similarly, the agreement between data and the models as a function of momentum is good, except for an underprediction by generators in the medium momentum ranges, 200–400 MeV for muons and 100–200 MeV for pions. Published by the American Physical Society2024 

We present a deep learning-based method for estimating the neutrino energy of charged-current neutrino-argon interactions. We employ a recurrent neural network (RNN) architecture for neutrino energy estimation in the MicroBooNE experiment, utilizing liquid argon time projection chamber (LArTPC) detector technology. Traditional energy estimation approaches in LArTPCs, which largely rely on reconstructing and summing visible energies, often experience sizable biases and resolution smearing because of the complex nature of neutrino interactions and the detector response. The estimation of neutrino energy can be improved after considering the kinematics information of reconstructed final-state particles. Utilizing kinematic information of reconstructed particles, the deep learning-based approach shows improved resolution and reduced bias for the muon neutrino Monte Carlo simulation sample compared to the traditional approach. In order to address the common concern about the effectiveness of this method on experimental data, the RNN-based energy estimator is further examined and validated with dedicated data-simulation consistency tests using MicroBooNE data. We also assess its potential impact on a neutrino oscillation study after accounting for all statistical and systematic uncertainties and show that it enhances physics sensitivity. This method has good potential to improve the performance of other physics analyses. Published by the American Physical Society2024 

Abstract A significant challenge in measurements of neutrino oscillations is reconstructing the incoming neutrino energies. While modern fully-active tracking calorimeters such as liquid argon time projection chambers in principle allow the measurement of all final state particles above some detection threshold, undetected neutrons remain a considerable source of missing energy with little to no data constraining their production rates and kinematics. We present the first demonstration of tagging neutrino-induced neutrons in liquid argon time projection chambers using secondary protons emitted from neutron-argon interactions in the MicroBooNE detector. We describe the method developed to identify neutrino-induced neutrons and demonstrate its performance using neutrons produced in muon-neutrino charged current interactions. The method is validated using a small subset of MicroBooNE’s total dataset. The selection yields a sample with$$60\%$$ $60\%$of selected tracks corresponding to neutron-induced secondary protons. At this purity, the integrated efficiency is 8.4% for neutrons that produce a detectable proton.