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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 selforganizing 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 »

Free, publiclyaccessible full text available March 1, 2023

Free, publiclyaccessible full text available March 1, 2023

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 pathconnected patch whose pointset 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 FrenetSerret frame for curves, and to what we call the RicciWeingarten principal directions for submanifolds. More importantly, the limit of differences and products of eigenvalues can be used to recover curvature informationmore »

Abstract This article presents the reconstruction of the electromagnetic activity from electrons and photons (showers) used in the MicroBooNE deep learningbased low energy electron search. The reconstruction algorithm uses a combination of traditional and deep learningbased 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 »Free, publiclyaccessible full text available December 1, 2022

Abstract—Given a collection of M experimentally measured subspaces, and a modelbased subspace, this paper addresses the problem of finding a subspace that approximates the collection, under the constraint that it intersects the modelbased subspace in a predetermined number of dimensions. This constrained subspace estimation (CSE) problem arises in applications such as beamforming, where the modelbased subspace encodes prior information about the directionofarrival 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 nonconvex problem. The performance of the proposed CSEmore »

A bstract The MicroBooNE liquid argon time projection chamber located at Fermilab is a neutrino experiment dedicated to the study of shortbaseline 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 nonuniform calorimetric reconstruction performance in the detector, showing dependence on the angle of the particle trajectory. Such nonuniform reconstruction directly affectsmore »Free, publiclyaccessible full text available December 1, 2022

Given a collection of M experimentally measured subspaces, and a modelbased subspace, this paper addresses the problem of finding a subspace that approximates the collection, under the constraint that it intersects the modelbased subspace in a predetermined number of dimensions. This constrained subspace estimation (CSE) problem arises in applications such as beamforming, where the modelbased subspace encodes prior information about the directionofarrival 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 nonconvex problem. The performance of the proposed CSEmore »

Free, publiclyaccessible full text available October 1, 2022