A Determinantal Identity for the Permanent of a Rank 2 Matrix

Related publications (29)

About
Privacy
Disclaimer

Graph Chatbot

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

Harmonic decomposition of the trace of 1D transfer matrices in layered media

Antonio Joaquin Garcia Suarez

The Transfer Matrix formalism is ubiquitous when it comes to study wave propagation in various stratified media, applications ranging from Seismology to Quantum Mechanics. A relation between variables at two points in two different layers can be establishe ...

2022

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

Alice Cortinovis

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building ...

EPFL2022

Leveraging topology, geometry, and symmetries for efficient Machine Learning

Michaël Defferrard

When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...

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

A Theory of Value for Service Ecosystems

Blagovesta Hristova Kostova

In this thesis, we present a theory of value for the design and analysis of service ecosystems. The theory is based on general systems thinking. The concept of a system is used for relating knowledge from different disciplines (such as software engineering ...

EPFL2022

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Daniel Kressner, Alice Cortinovis, Marcel Schweitzer

This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified conve ...

SIAM PUBLICATIONS2021

Construction of optimal spectral methods in phase retrieval

Florent Gérard Krzakala, Lenka Zdeborová

We consider the phase retrieval problem, in which the observer wishes to recover a n-dimensional real or complex signal X⋆ from the (possibly noisy) observation of |ΦX⋆|, in which Φ is a matrix of size m×n. We consider a \emph{high-dimensional} setting whe ...

2021

The Dimension of the Body in Higher Education: Matrix of Meanings in Students’ Diaries

Simon Nessim Henein, Ramiro Tau

In this paper, we attempt to show some consequences of bringing the body back into higher education, through the use of performing arts in the curricular context of scientific programs. We start by arguing that dominant traditions in higher education repro ...

2022

Reversible and Broad-Range Oxygen Sensing Based on Purely Organic Long-Lived Photoemitters

Esther Amstad, René M. Rossi, Efe Armagan

The detection of oxygen (O-2) by optical sensors is of growing importance, for example, in biology, life science, environmental science, and aerodynamics, where the composition of gases is crucial for many applications. Purely organic optical O-2 sensors a ...

2021

Page 2 of 3