Publications related to The Truncated Tracial Moment Problem

Phase retrieval in high dimensions: Statistical and computational phase transitions

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, 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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Stefano Massei

Evaluating the action of a matrix function on a vector, that is

x=f(\mathcal M)v

, is an ubiquitous task in applications. When

\mathcal M

is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the pole ...

2019

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a

k\times k

submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix ...

MATHICSE2019

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

Hasse principles for multinorm equations

Eva Bayer Fluckiger, Ting-Yu Lee

A classical result of Hasse states that the norm principle holds for finite cyclic extensions of global fields, in other words local norms are global norms. We investigate the norm principle for finite dimensional commutative kale algebras over global fiel ...

2019

Revealing evolutionary constraints on proteins through sequence analysis

Anne-Florence Raphaëlle Bitbol

Statistical analysis of alignments of large numbers of protein sequences has revealed sectors of collectively coevolving amino acids in several protein families. Here, we show that selection acting on any functional property of a protein, represented by an ...

2019

Unlabeled Sensing with Random Linear Measurements

Martin Vetterli, Jayakrishnan Unnikrishnan, Saeid Haghighatshoar

We study the problem of solving a linear sensing system when the observations are unlabeled. Specifically we seek a solution to a linear system of equations y = Ax when the order of the observations in the vector y is unknown. Focusing on the setting in wh ...

Institute of Electrical and Electronics Engineers2018

Correspondence functors and finiteness conditions

Jacques Thévenaz, Serge Bouc

We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties wh ...

2018

The Truncated Tracial Moment Problem

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Phase retrieval in high dimensions: Statistical and computational phase transitions

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Global eigenvalue distribution of matrices defined by the skew-shift

Hasse principles for multinorm equations

Revealing evolutionary constraints on proteins through sequence analysis

Unlabeled Sensing with Random Linear Measurements

Correspondence functors and finiteness conditions

Hasse principles for multinorm equations

Revealing evolutionary constraints on proteins through sequence analysis

Phase retrieval in high dimensions: Statistical and computational phase transitions

Correspondence functors and finiteness conditions

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Unlabeled Sensing with Random Linear Measurements

Global eigenvalue distribution of matrices defined by the skew-shift