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Concept

Singular value

Related publications (26)

Spectral Estimators for High-Dimensional Matrix Inference

Farzad Pourkamali

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

EPFL2024

Randomized flexible GMRES with deflated restarting

Laura Grigori

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

Springer2024

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Alfio Quarteroni, Francesco Regazzoni

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

Elsevier Science Sa2023

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Daniel Kressner, Ivana Sain Glibic

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

SPRINGER2023

Academic boredom(s): a person-centered investigation

Alexandra Corina Niculescu

Should we refer to boredom or boredoms? Research on the emotion of boredom sets itself apart from studies on other emotions by posing the question: is boredom a singular concept or does it have multiple facets? In this manuscript presenting empirical resea ...

2023

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS

Xavier Fernandez-Real Girona, Riccardo Tione

In this note, we prove that if a subharmonic function Delta u >= 0 has pure second derivatives partial derivative(ii)u that are signed measures, then their negative part (partial derivative(ii)u)- belongs to L-1 (in particular, it is not singular). We then ...

American Mathematical Society (AMS)2023

Quand les artistes font forme en habitant ensemble. Usages, présences, imaginaires

Mathilde Coline Chénin

Taking root within a historical and transversal perspective of communities of artists at work, and of the relationship that they nourish with the places that host their creative activity, the present research intends to bring to light the grammars of "the ...

EPFL2022

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Nicolas Macris, Jean François Emmanuel Barbier

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

AMER PHYSICAL SOC2022

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Eva Vidlicková

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

EPFL2022

Value of T-2 Mapping MRI for Prostate Cancer Detection and Classification

Tom Hilbert

Background Currently, multi-parametric prostate MRI (mpMRI) consists of a qualitative T-2, diffusion weighted, and dynamic contrast enhanced imaging. Quantification of T-2 imaging might further standardize PCa detection and support artificial intelligence ...

WILEY2022

T2 mapping for the characterization of prostate lesions

Tom Hilbert

Purpose Purpose of this study is to evaluate the diagnostic accuracy of quantitative T2/ADC values in differentiating between PCa and lesions showing non-specific inflammatory infiltrates and atrophy, features of chronic prostatitis, as the most common his ...

SPRINGER2022

Local invertibility and sensitivity of atomic structure-feature mappings

Michele Ceriotti, Sergey Pozdnyakov

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...

2021

Phase retrieval in high dimensions: Statistical and computational phase transitions

Lenka Zdeborová, Florent Gérard Krzakala, Bruno Loureiro

We consider the phase retrieval problem of reconstructing a n -dimensional real or complex signal X ⋆ from m (possibly noisy) observations Y μ = | ∑ n i = 1 Φ μ i X ⋆ i / √ n | , for a large class of correlated real and complex random sensing matrices Φ , ...

Curran Associates, Inc.2020

Clinical implementation of accelerated T-2 mapping: Quantitative magnetic resonance imaging as a biomarker for annular tear and lumbar disc herniation

Tobias Kober, Tom Hilbert

Objectives This study evaluates GRAPPATINI, an accelerated T-2 mapping sequence combining undersampling and model-based reconstruction to facilitate the clinical implementation of T-2 mapping of the lumbar intervertebral disc. Methods Fifty-eight individua ...

SPRINGER2021

Magnetization transfer in magnetic resonance fingerprinting

Tobias Kober, Tom Hilbert

Purpose To study the effects of magnetization transfer (MT, in which a semi-solid spin pool interacts with the free pool), in the context of magnetic resonance fingerprinting (MRF). Methods Simulations and phantom experiments were performed to study the im ...

WILEY2020

Protostructure, archéologie et hypothèse d'une architecture-support

Agathe Claire Estelle Mignon

« How do we pile up dwellings without sacrificing their independence ? » Nicolas John Habraken asks the question in those terms in the book he first published in Dutch in 1961 then in English in 1972, Supports: An Alternative to Mass Housing, as an introd ...

EPFL2019

Patient respiratory-triggered quantitative T-2 mapping in the pancreas

Tobias Kober, Reto Meuli, Josefina Adriana Maria Bastiaansen, Tom Hilbert

Background Long acquisition times and motion sensitivity limit T-2 mapping in the abdomen. Accelerated mapping at 3 T may allow for quantitative assessment of diffuse pancreatic disease in patients during free-breathing. Purpose To test the feasibility of ...

2019

Model-based super-resolution reconstruction of T-2 maps

Jean-Philippe Thiran, Reto Meuli, Tobias Kober, Tom Hilbert, Mohammad Golbabaee, Gian Franco Piredda

Purpose High-resolution isotropic T-2 mapping of the human brain with multi-echo spin-echo (MESE) acquisitions is challenging. When using a 2D sequence, the resolution is limited by the slice thickness. If used as a 3D acquisition, specific absorption rate ...

Wiley2020

Fast model-based T-2 mapping using SAR-reduced simultaneous multislice excitation

Jean-Philippe Thiran, Tobias Kober, José Pedro Rebelo Ferreira Marques, Gunnar Krüger, Tom Hilbert

Purpose To obtain whole-brain high-resolution T-2 maps in 2 minutes by combining simultaneous multislice excitation and low-power PINS (power independent of number of slices) refocusing pulses with undersampling and a model-based reconstruction. Methods A ...

WILEY2019

A reduced basis approach to large-scale pseudospectra computation

Petar Sirkovic

For studying spectral properties of a nonnormal matrix A is an element of Cnxn, information about its spectrum sigma(A) alone is usually not enough. Effects of perturbations on sigma(A) can be studied by computing epsilon-pseudospectra, i.e. the level sets ...

WILEY2019