Updated: April 4th, 2024 12:31

2023 journal article

A COMPUTATIONAL FRAMEWORK FOR EDGE-PRESERVING REGULARIZATION IN DYNAMIC INVERSE PROBLEMS

*ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS*, *58*, 486–516.

Sources: Web Of Science, NC State University Libraries

Added: November 27, 2023

2023 journal article

MONTE CARLO METHODS FOR ESTIMATING THE DIAGONAL OF A REAL SYMMETRIC MATRIX

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, *44*(1), 240–269.

Sources: Web Of Science, NC State University Libraries, ORCID

Added: March 10, 2023

2023 journal article

RANDOMIZED ALGORITHMS FOR ROUNDING IN THE TENSOR-TRAIN FORMAT

*SIAM JOURNAL ON SCIENTIFIC COMPUTING*, *45*(1), A74–A95.

author keywords: high-dimensional problems; randomized algorithms; tensor decompositions; tensortrain format

TL;DR:
Several randomized algorithms are proposed that are generalizations of randomized low-rank matrix approximation algorithms and provide significant reduction in computation compared to deterministic TT-rounding algorithms for rounding a sum of TT-tensors.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: August 28, 2023

2023 journal article

Randomized reduced basis methods for parameterized fractional elliptic PDEs

*FINITE ELEMENTS IN ANALYSIS AND DESIGN*, *227*.

Sources: Web Of Science, NC State University Libraries

Added: November 20, 2023

2023 journal article

Tensor-based flow reconstruction from optimally located sensor measurements

*JOURNAL OF FLUID MECHANICS*, *962*.

author keywords: low-dimensional models; big data; computational methods

TL;DR:
This work introduces a tensor-based sensor placement and flow reconstruction method which retains and exploits the inherent multidimensionality of the flow and is significantly more accurate than similar vectorized methods.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

14. Life Below Water
(OpenAlex)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 7, 2023

2022 journal article

Computationally efficient methods for large-scale atmospheric inverse modeling

*GEOSCIENTIFIC MODEL DEVELOPMENT*, *15*(14), 5547–5565.

UN Sustainable Development Goal Categories

13. Climate Action
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: August 1, 2022

2022 journal article

Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions

*ADVANCES IN COMPUTATIONAL MATHEMATICS*, *48*(5).

author keywords: Multivariate function approximation; Tucker format; Randomized algorithms; Low-rank approximations; Kernel methods

TL;DR:
This paper develops novel randomized techniques to accomplish the tensor compression, provides a detailed analysis of the computational costs, provides insight into the error of the resulting approximations, and discusses the benefits of the proposed approaches.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: October 17, 2022

2022 journal article

Kryging: geostatistical analysis of large-scale datasets using Krylov subspace methods

*STATISTICS AND COMPUTING*, *32*(5).

author keywords: Approximate inference; Profile likelihood; Block Toeplitz matrix; Fast Fourier transform; Krylov subspace methods; Golub-Kahan bidiagonalization

TL;DR:
A novel approximate inference methodology that uses profile likelihood and Krylov subspace methods to estimate the spatial covariance parameters and makes spatial predictions with uncertainty quantification for point-referenced spatial data is presented.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

2. Zero Hunger
(Web of Science)

15. Life on Land
(OpenAlex)

Sources: Web Of Science, NC State University Libraries

Added: September 19, 2022

2022 journal article

MONTE CARLO ESTIMATORS FOR THE SCHATTEN p-NORM OF SYMMETRIC POSITIVE SEMIDEFINITE MATRICES

*ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS*, *55*, 213–241.

author keywords: Schatten p-norm; Monte Carlo estimator; optimal experimental design; Chebyshev polynomials

TL;DR:
A matrix-free method to estimate the Schatten $p$-norm using a Monte Carlo estimator and derive convergence results and error estimates for the estimator is proposed and demonstrated.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: January 31, 2022

2022 journal article

STRUCTURED MATRIX APPROXIMATIONS VIA TENSOR DECOMPOSITIONS

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, *43*(4), 1599–1626.

author keywords: structured matrices; tensor decompositions; Kronecker products; system identifica-tion; image deblurring; covariance matrices

TL;DR:
The approach has three steps: map the structured matrix to tensors, use tensor compression algorithms, and map the compressed tensors back to obtain two different matrix representations -- sum of Kronecker products and block low-rank format.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: January 30, 2023

2021 journal article

EFFICIENT ALGORITHMS FOR EIGENSYSTEM REALIZATION USING RANDOMIZED SVD

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, *42*(2), 1045–1072.

author keywords: eigensystem realization algorithm; system identification; singular value decomposition; randomized algorithms

TL;DR:
Computationally efficient algorithms for reducing the computational cost of the SVD step by using randomized subspace iteration and exploiting the block Hankel structure of the matrix are developed.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: August 16, 2021

2021 journal article

Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis

*NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS*, *28*(4).

author keywords: generalized singular value decomposition; iterative methods; randomized algorithms; sensitivity analysis

TL;DR:
New randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization are proposed, motivated by applications in hyper‐differential sensitivity analysis (HDSA).
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: March 22, 2021

2021 journal article

Randomized approaches to accelerate MCMC algorithms for Bayesian inverse problems

*JOURNAL OF COMPUTATIONAL PHYSICS*, *440*.

author keywords: Inverse problems; Randomized algorithms; Bayesian methods; Markov chain Monte Carlo

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: August 2, 2021

2020 journal article

Efficient Krylov subspace methods for uncertainty quantification in large Bayesian linear inverse problems

*NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS*, *27*(5).

author keywords: generalized Golub-Kahan; preconditioned iterative methods; Bayesian inverse problems; uncertainty measures; Krylov subspace samplers

TL;DR:
This work uses the generalized Golub‐Kahan bidiagonalization to derive an approximation of the posterior covariance matrix, and provides theoretical results that quantify the accuracy of the approximate posterior covance matrix and of the resulting posterior distribution.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: August 17, 2020

2020 journal article

Geostatistical inverse modeling with very large datasets: an example from the Orbiting Carbon Observatory 2 (OCO-2) satellite

*GEOSCIENTIFIC MODEL DEVELOPMENT*, *13*(3), 1771–1785.

UN Sustainable Development Goal Categories

13. Climate Action
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: April 20, 2020

2020 journal article

RANDOMIZATION AND REWEIGHTED l(1)-MINIMIZATION FOR A-OPTIMAL DESIGN OF LINEAR INVERSE PROBLEMS

*SIAM JOURNAL ON SCIENTIFIC COMPUTING*, *42*(3), A1714–A1740.

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: August 10, 2020

2020 journal article

Randomized Algorithms for Low-Rank Tensor Decompositions in the Tucker Format

*SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE*, *2*(1), 189–215.

author keywords: randomized algorithms; tensors; Tucker decompositions; low-rank; multilinear algebra; structure-preserving

TL;DR:
This work presents randomized versions of two well-known compression algorithms, namely, HOSVD and STHOSVD, and develops variants of these algorithms that tackle specific challenges posed by large-scale datasets.
(via Semantic Scholar)

Sources: ORCID, Web Of Science, NC State University Libraries

Added: May 30, 2020

2020 journal article

Randomized Discrete Empirical Interpolation Method for Nonlinear Model Reduction

*SIAM Journal on Scientific Computing*.

author keywords: model reduction; randomized algorithms; discrete empirical interpolation method; subset selection; subspace iteration

TL;DR:
This paper uses randomized range finding algorithms to efficiently find an approximate DEIM basis and develops randomized subset selection tools, based on leverage scores, to efficiently select the nonlinear components.
(via Semantic Scholar)

Source: ORCID

Added: May 30, 2020

2019 journal article

Efficient Marginalization-Based MCMC Methods for Hierarchical Bayesian Inverse Problems

*SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION*, *7*(3), 1105–1131.

author keywords: Markov chain Monte Carlo; hierarchical Bayesian approach; inverse problems; one-block algorithm; low-rank approximations

TL;DR:
This paper combines the low-rank techniques of Brown, Saibaba, and Vallelian (2018) with the marginalization approach of Rue and Held (2005), and considers two variants of this approach: delayed acceptance and pseudo-marginalization.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

10. Reduced Inequalities
(OpenAlex)

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: October 14, 2019

2019 journal article

Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

*JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS*, *28*(1), 36–47.

author keywords: Convex optimization; Degrees of freedom; Hutchinson estimator; Information criterion; Penalization; Sparse linear systems

TL;DR:
This work presents a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: May 13, 2019

2019 journal article

RANDOMIZED SUBSPACE ITERATION: ANALYSIS OF CANONICAL ANGLES AND UNITARILY INVARIANT NORMS

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, *40*(1), 23–48.

author keywords: singular value decomposition; randomized algorithms; canonical angles; low-rank approximation

TL;DR:
Three different kinds of bounds for the low-rank approximation in any unitarily invariant norm (including the Schatten-p norm) are derived, which generalizes the bounds for Spectral and Frobenius norms found in the literature.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: April 9, 2019

2018 journal article

A randomized tensor singular value decomposition based on the t-product

*NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS*, *25*(5).

author keywords: randomized SVD; singular value decomposition; t-product; tensor; truncated SVD

TL;DR:
This paper proposes a method that extends a well‐known randomized matrix method to the t‐SVD, which can produce a factorization with similar properties to the sVD, but it is more computationally efficient on very large data sets.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: November 12, 2018

2018 journal article

EFFICIENT D-OPTIMAL DESIGN OF EXPERIMENTS FOR INFINITE-DIMENSIONAL BAYESIAN LINEAR INVERSE PROBLEMS

*SIAM JOURNAL ON SCIENTIFIC COMPUTING*, *40*(5), A2956–A2985.

author keywords: Bayesian inversion; D-optimal experimental design; large-scale ill-posed inverse problems; randomized matrix methods; low-rank approximation; uncertainty quantification

TL;DR:
A computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters is developed, to use randomized estimators for computing the D-Optimal criterion, its derivative, as well as the Kullback--Leibler divergence from posterior to prior.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: November 19, 2018

2018 journal article

Efficient generalized Golub-Kahan based methods for dynamic inverse problems

*Inverse Problems*, *34*(2).

Contributors: J. Chung ^{*}, ^{ n} , M. Brown^{*} & E. Westman ^{*}

Sources: NC State University Libraries, ORCID, NC State University Libraries

Added: August 6, 2018

2018 journal article

Goal-oriented optimal design of experiments for large-scale Bayesian linear inverse problems

*INVERSE PROBLEMS*, *34*(9).

author keywords: design of experiments; inverse problems; sensor placement; data assimilation

TL;DR:
This work develops a framework for goal-oriented optimal design of experiments (GOODE) for large-scale Bayesian linear inverse problems governed by PDEs, and develops an efficient gradient-based optimization framework for solving the GOODE optimization problems.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: October 19, 2018

2018 journal article

Low-Rank Independence Samplers in Hierarchical Bayesian Inverse Problems

*SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION*, *6*(3), 1076–1100.

author keywords: computerized tomography; image deblurring; low-rank approximation; Metropolis-Hastings independence sampler; prior-preconditioned Hessian

TL;DR:
This work presents a computationally efficient scheme for sampling high-dimensional Gaussian distributions in ill-posed Bayesian linear inverse problems by using Metropolis--Hastings independence sampling with a proposal distribution based on a low-rank approximation of the prior-preconditioned Hessian.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, NC State University Libraries

Added: October 16, 2018

2018 journal article

THE DISCRETE EMPIRICAL INTERPOLATION METHOD: CANONICAL STRUCTURE AND FORMULATION IN WEIGHTED INNER PRODUCT SPACES

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, *39*(3), 1152–1180.

author keywords: empirical interpolation; Galerkin projection; generalized empirical interpolation; nonlinear model reduction; oblique projection; proper orthogonal decomposition; parametrized-background data-weak approach; rank revealing QR factorization; weighted inner product

TL;DR:
A special case of $W-DEIM is introduced, which is DGEIM, a discrete version of the Generalized Empirical Interpolation Method that allows generalization of the interpolation via a dictionary of linear functionals.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries

Added: January 7, 2019

2017 journal article

GENERALIZED HYBRID ITERATIVE METHODS FOR LARGE-SCALE BAYESIAN INVERSE PROBLEMS

*SIAM JOURNAL ON SCIENTIFIC COMPUTING*, *39*(5), S24–S46.

author keywords: inverse problems; Bayesian methods; hybrid iterative methods; Tikhonov regularization; Golub-Kahan bidiagonalization; Matern covariance kernels

TL;DR:
A hybrid algorithm based on the generalized Golub-Kahan bidiagonalization for computing Tikhonov regularized solutions to problems where explicit computation of the square root and inverse of the covariance kernel for the prior covariance matrix is not feasible.
(via Semantic Scholar)

Sources: Web Of Science, ORCID, NC State University Libraries

Added: August 6, 2018

2017 journal article

MULTIPRECONDITIONED GMRES FOR SHIFTED SYSTEMS

*SIAM JOURNAL ON SCIENTIFIC COMPUTING*, *39*(5), S222–S247.

author keywords: shifted systems; Krylov solvers; GMRES

TL;DR:
An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditionsers, and the numerical results indicate the effectiveness of the proposed approach.
(via Semantic Scholar)

Sources: Web Of Science, ORCID, NC State University Libraries

Added: August 6, 2018

2017 journal article

Randomized matrix-free trace and log-determinant estimators

*NUMERISCHE MATHEMATIK*, *137*(2), 353–395.

Contributors: ^{ n} , A. Alexanderian^{ n} & I. Ipsen ^{ n}

Sources: Web Of Science, ORCID, NC State University Libraries

Added: August 6, 2018

2016 journal article

HOID: HIGHER ORDER INTERPOLATORY DECOMPOSITION FOR TENSORS BASED ON TUCKER REPRESENTATION

*SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS*, *37*(3), 1223–1249.

author keywords: tensors; interpolatory decomposition; CUR decomposition; Tucker decomposition

TL;DR:
The HOID provides a decomposition that preserves certain important features of the original tensor such as sparsity, non-negativity, integer values, etc.
(via Semantic Scholar)

Sources: Web Of Science, ORCID, NC State University Libraries

Added: August 6, 2018

2015 conference paper

3D parameter reconstruction in hyperspectral diffuse optical tomography

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE*, *9319*.

Contributors: ^{*} , N. Krishnamurthy ^{*}, P. Anderson ^{*}, J. Kainerstorfer ^{*}, A. Sassaroli ^{*}, E. Miller ^{*}, S. Fantini ^{*}, M. Kilmer^{*}

Source: ORCID

Added: May 14, 2019

2015 journal article

A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers

*Journal of Computational Physics*, *299*, 940–954.

author keywords: Inverse problems; Krylov solvers; Hydraulic tomography; Laplace transforms

TL;DR:
This work proposes an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently and speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time.
(via Semantic Scholar)

Source: ORCID

Added: May 14, 2019

2015 journal article

Fast Kalman filter using hierarchical matrices and a low-rank perturbative approach

*Inverse Problems*, *31*(1).

Contributors: ^{*} , E. Miller ^{*} & P. Kitanidis^{*}

author keywords: Kalman filter; hierarchical matrices; uncertainty quantification; random walk forecast model

TL;DR:
An efficient algorithm to update the weights of the preceding terms and the computation of eigenmodes of the generalized eigenvalue problem is described and shown how to efficiently compute measures of uncertainty and conditional realizations from the state distribution at each time step.
(via Semantic Scholar)

Source: ORCID

Added: May 14, 2019

2015 journal article

Fast algorithms for hyperspectral diffuse optical tomography

*SIAM Journal on Scientific Computing*, *37*(5), B712–B743.

author keywords: diffuse optical tomography; inverse problems; recycling Krylov subspaces; parametric level set; recursive SVD

TL;DR:
A novel recycling-based Krylov subspace approach that leverages certain system similarities across wavelengths and develops a fast algorithm for compressing the Born operator that locally compresses across wavelengths for a given source-detector set and then recursively combines the low-rank factors to provide a global low- rank approximation.
(via Semantic Scholar)

Source: ORCID

Added: May 14, 2019

2015 journal article

Fast computation of uncertainty quantification measures in the geostatistical approach to solve inverse problems

*Advances in Water Resources*, *82*, 124–138.

author keywords: Inverse problems; Geostatistical approach; Uncertainty quantification; Seismic tomography; Hydraulic tomography

TL;DR:
This work considers the computational challenges associated with uncertainty quantification involved in parameter estimation such as seismic slowness and hydraulic transmissivity fields and shows how to efficiently compute measures of uncertainty that are based on scalar functions of the posterior covariance matrix.
(via Semantic Scholar)

Source: ORCID

Added: May 14, 2019

2015 journal article

Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing Karhunen-Loève expansion

*Numerical Linear Algebra with Applications*, *23*(2), 314–339.

Contributors: ^{*} , J. Lee ^{*} & P. Kitanidis^{*}

author keywords: randomized algorithms; generalized Hermitian eigenvalue problems; Karhunen-Loeve expansion

TL;DR:
The error analysis shows that the randomized algorithm is most accurate when the generalized singular values of B−1A decay rapidly, and the performance of the algorithm on computing an approximation to the Karhunen–Loève expansion is demonstrated.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Sources: Web Of Science, ORCID, NC State University Libraries, Crossref

Added: August 6, 2018

2014 conference paper

A fast Kalman filter for time-lapse electrical resistivity tomography

*International Geoscience and Remote Sensing Symposium (IGARSS)*, 3152–3155.

Contributors: ^{*} , E. Miller ^{*} & P. Kitandis^{*}

author keywords: Extended Kalman Filter; Electrical Resistivity Tomography; Fast algorithms

TL;DR:
A reduced complexity algorithm for time-lapse Electrical Resistivity Tomography (ERT) based on an extended Kalman filter with efficient representation of state covariance matrix at each step as a weighted combination of the system noise covariance Matrix and a low-rank perturbation term.
(via Semantic Scholar)

Source: ORCID

Added: May 14, 2019

2013 journal article

A flexible krylov solver for shifted systemswith application to oscillatory hydraulic tomography

*SIAM Journal on Scientific Computing*, *35*(6).

author keywords: Krylov solvers; shifted systems; hydraulic tomography; inverse problems

TL;DR:
The reconstruction of hydrogeological parameters such as hydraulic conductivity and specific storage using limited discrete measurements of pressure (head) obtained from sequential oscillatory pumping tests, leads to a nonlinear inverse problem.
(via Semantic Scholar)

Source: ORCID

Added: May 14, 2019

2013 article

Fast Algorithms for Bayesian Inversion

*Computational Challenges in the Geosciences*, pp. 101–142.

author keywords: Bayesian stochastic inverse modeling; Large-scale problems; Geostatistical estimation; Numerical linear algebra; Fast Fourier transform; Ast multipole method; Hierarchical matrices

TL;DR:
This article presents a few fast algorithms applicable to large-scale Bayesian inversion techniques, applicable to applications arising from geostatistics, and presents the algorithmic ideas and theoretical results.
(via Semantic Scholar)

Source: ORCID

Added: May 14, 2019

2012 journal article

Application of hierarchical matrices to linear inverse problems in geostatistics | Application des matrices hiérarchiques aux problèmes d'inversion linéaire en géostatistique

*Oil and Gas Science and Technology*, *67*(5), 857–875.

Source: ORCID

Added: May 14, 2019

2012 journal article

Efficient methods for large-scale linear inversion using a geostatistical approach

*Water Resources Research*, *48*(5).

Source: ORCID

Added: May 14, 2019

Updated: October 30th, 2020 16:09

2020 - present

2015 - 2020

2013 - 2015

Updated: February 14th, 2018 12:03

2008 - 2013

2007 - 2010

2003 - 2007

Funding history based on the linked ORCID record. Updated: October 15th, 2019 14:35

grant
September 1, 2019 - August 31, 2024

CAREER: Fast and Accurate Algorithms for Uncertainty Quantification in Large-Scale Inverse Problems

Directorate for Mathematical & Physical Sciences

grant
August 15, 2018 - July 31, 2021

Collaborative Research: A Tensor-Based Computational Framework for Model Reduction and Structured Matrices

Directorate for Mathematical & Physical Sciences

grant
September 1, 2017 - August 31, 2020

OP: Collaborative Research: Novel Feature-Based, Randomized Methods for Large-Scale Inversion

Directorate for Mathematical & Physical Sciences

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