Concept

Higher-dimensional gamma matrices

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RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

Daniel Kressner, Haoze He

Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...

Philadelphia2024

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

Duality and bicrystals on infinite binary matrices

Thomas Gerber

The set of finite binary matrices of a given size is known to carry a finite type AA bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and one-dimensional sums t ...

2023

Architecture-Controllable Single-Crystal Helical Self-assembly of Small-Molecule Disulfides with Dynamic Chirality

Lukas Pfeifer, Qixing Zhang

Beyond the common supramolecular helical polymers in solutions, controlling single-crystal helical self-assembly with precisely defined chirality and architectures has been challenging. Here, we report that simply merging static homochiral amino acids with ...

AMER CHEMICAL SOC2023

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

Bias Cancellation of MixColumns

Francesco Regazzoni, Andrea Felice Caforio, Subhadeep Banik

At COSADE'2020, Carre et al. established a novel biascancelling property of the AES MixColumns matrix that effectively corrects any skewed output distribution of a state byte due to a faulty substitution box. Consequently, any effected byte is rendered uni ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

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

Asymptotics of Cheeger constants and unitarisability of groups

Nicolas Monod, Maria Gerasimova

Given a group Gamma, we establish a connection between the unitarisability of its uniformly bounded representations and the asymptotic behaviour of the isoperimetric constants of Cayley graphs of Gamma for increasingly large generating sets. The connection ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Staggered flux state for rectangular-lattice spin-1/2 Heisenberg antiferromagnets

Henrik Moodysson Rønnow, Dmitri Ivanov, Bastien Dalla Piazza, Noore Elahi Shaik

We investigate the spin-1/2 Heisenberg model on a rectangular lattice, using the Gutzwiller projected variational wave function known as the staggered flux state. Using Monte Carlo techniques, the variational parameters and instantaneous spin-spin correlat ...

AMER PHYSICAL SOC2020