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  1. 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,more »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.« less
  2. Free, publicly-accessible full text available March 1, 2023
  3. Free, publicly-accessible full text available March 1, 2023
  4. Principal component analysis of cylindrical neighborhoods is proposed to study the local geometry of embedded Riemannian manifolds. At every generic point and scale, a highdimensional cylinder orthogonal to the tangent space at the point cuts out a path-connected patch whose point-set distribution in ambient space encodes the intrinsic and extrinsic curvature. The covariance matrix of the points from that neighborhood has eigenvectors whose scale limit tends to the Frenet-Serret frame for curves, and to what we call the Ricci-Weingarten principal directions for submanifolds. More importantly, the limit of differences and products of eigenvalues can be used to recover curvature informationmore »at the point. The formula for hypersurfaces in terms of principal curvatures is particularly simple and plays a crucial role in the study of higher-codimension cases.« less
  5. Abstract This article presents the reconstruction of the electromagnetic activity from electrons and photons (showers) used in the MicroBooNE deep learning-based low energy electron search. The reconstruction algorithm uses a combination of traditional and deep learning-based techniques to estimate shower energies. We validate these predictions using two ν μ -sourced data samples: charged/neutral current interactions with final state neutral pions and charged current interactions in which the muon stops and decays within the detector producing a Michel electron. Both the neutral pion sample and Michel electron sample demonstrate agreement between data and simulation. Further, the absolute shower energy scale ismore »shown to be consistent with the relevant physical constant of each sample: the neutral pion mass peak and the Michel energy cutoff.« less
    Free, publicly-accessible full text available December 1, 2022
  6. Abstract—Given a collection of M experimentally measured subspaces, and a model-based subspace, this paper addresses the problem of finding a subspace that approximates the collection, under the constraint that it intersects the model-based subspace in a predetermined number of dimensions. This constrained subspace estimation (CSE) problem arises in applications such as beamforming, where the model-based subspace encodes prior information about the direction-of-arrival of some sources impinging on the array. In this paper, we formulate the constrained subspace estimation (CSE) problem, and present an approximation based on a semidefinite relaxation (SDR) of this non-convex problem. The performance of the proposed CSEmore »algorithm is demonstrated via numerical simulation, and its application to beamforming is also discussed.« less
  7. A bstract The MicroBooNE liquid argon time projection chamber located at Fermilab is a neutrino experiment dedicated to the study of short-baseline oscillations, the measurements of neutrino cross sections in liquid argon, and to the research and development of this novel detector technology. Accurate and precise measurements of calorimetry are essential to the event reconstruction and are achieved by leveraging the TPC to measure deposited energy per unit length along the particle trajectory, with mm resolution. We describe the non-uniform calorimetric reconstruction performance in the detector, showing dependence on the angle of the particle trajectory. Such non-uniform reconstruction directly affectsmore »the performance of the particle identification algorithms which infer particle type from calorimetric measurements. This work presents a new particle identification method which accounts for and effectively addresses such non-uniformity. The newly developed method shows improved performance compared to previous algorithms, illustrated by a 93.7% proton selection efficiency and a 10% muon mis-identification rate, with a fairly loose selection of tracks performed on beam data. The performance is further demonstrated by identifying exclusive final states in ν μ CC interactions. While developed using MicroBooNE data and simulation, this method is easily applicable to future LArTPC experiments, such as SBND, ICARUS, and DUNE.« less
    Free, publicly-accessible full text available December 1, 2022
  8. Given a collection of M experimentally measured subspaces, and a model-based subspace, this paper addresses the problem of finding a subspace that approximates the collection, under the constraint that it intersects the model-based subspace in a predetermined number of dimensions. This constrained subspace estimation (CSE) problem arises in applications such as beamforming, where the model-based subspace encodes prior information about the direction-of-arrival of some sources impinging on the array. In this paper, we formulate the constrained subspace estimation (CSE) problem, and present an approximation based on a semidefinite relaxation (SDR) of this non-convex problem. The performance of the proposed CSEmore »algorithm is demonstrated via numerical simulation, and its application to beamforming is also discussed.« less
  9. Free, publicly-accessible full text available October 1, 2022