Publications related to Optimal denoising of rotationally invariant rectangular matrices

Certified And Fast Computations With Shallow Covariance Kernels

Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random fields have gained ...

AMER INST MATHEMATICAL SCIENCES-AIMS2020

Nonlinear Finite Elements in Dynamics

This report focuses on the implementation of the finite element method for nonlinear dynamical problems arising in solid mechanics. The theory of continuum mechanics is extensively covered in the literature and it is assumed the reader is already familiar ...

2020

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

Marius Christopher Lemm

The Lyapunov exponent characterizes the asymptotic behavior of long matrix products. Recognizing scenarios where the Lyapunov exponent is strictly positive is a fundamental challenge that is relevant in many applications. In this work we establish a novel ...

2020

A Covariance Formula For Topological Events Of Smooth Gaussian Fields

Alejandro Rivera

We derive a covariance formula for the class of 'topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example, (i) crossing events for level or excursion sets, (ii ...

INST MATHEMATICAL STATISTICS2020

Global eigenvalue distribution of matrices defined by the skew-shift

Marius Christopher Lemm

We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift

\binom{j}{2} \omega+jy+x \mod 1

for irrational

\omega

. We prove that the eigenvalue distribution of these matrices conv ...

2019

Streaming Low-Rank Matrix Approximation With An Application To Scientific Simulation

Volkan Cevher, Alp Yurtsever

This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm for constructing ...

2019

Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its mutual information when the tensor is of even order. The proof uses the adaptive interpolation method, for which rank-on ...

IEEE2019

Multi-panel, on-single-chip Memristive Biosensing

Giovanni De Micheli, Sandro Carrara, Danilo Demarchi, Ioulia Tzouvadaki, Abuduwaili Tuoheti

Memristive biosensors have demonstrated excellent capabilities for ultrasensitive bio-detection. In the present work, memristive biosensing chips are designed, fabricated and implemented in a for the first time presented multi-panel on-chip detection for d ...

2019

Fast hierarchical solvers for symmetric eigenvalue problems

Ana Susnjara

In this thesis we address the computation of a spectral decomposition for symmetric banded matrices. In light of dealing with large-scale matrices, where classical dense linear algebra routines are not applicable, it is essential to design alternative tech ...

EPFL2018

Geometry-aware Tracking of Manipulability Ellipsoids

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

Body posture can greatly influence human performance when carrying out manipulation tasks. Adopting an appropriate pose helps us regulate our motion and strengthen our capability to achieve a given task. This effect is also observed in robotic manipulation ...

2018

Optimal denoising of rotationally invariant rectangular matrices

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Certified And Fast Computations With Shallow Covariance Kernels

Nonlinear Finite Elements in Dynamics

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

A Covariance Formula For Topological Events Of Smooth Gaussian Fields

Global eigenvalue distribution of matrices defined by the skew-shift

Streaming Low-Rank Matrix Approximation With An Application To Scientific Simulation

Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization

Multi-panel, on-single-chip Memristive Biosensing

Fast hierarchical solvers for symmetric eigenvalue problems

Geometry-aware Tracking of Manipulability Ellipsoids

A Covariance Formula For Topological Events Of Smooth Gaussian Fields

Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

Certified And Fast Computations With Shallow Covariance Kernels

Nonlinear Finite Elements in Dynamics

Global eigenvalue distribution of matrices defined by the skew-shift

Streaming Low-Rank Matrix Approximation With An Application To Scientific Simulation

Fast hierarchical solvers for symmetric eigenvalue problems

Geometry-aware Tracking of Manipulability Ellipsoids

Multi-panel, on-single-chip Memristive Biosensing

Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization