Publications related to Pauli matrices

Spectral Estimators for High-Dimensional Matrix Inference

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

Tool Developments in the OpenMC Code: Correlated Sampling and Transient Fission Matrix Approach Coupled to OpenFOAM

Thomas Jean-François Ligonnet, Axel Guy Marie Laureau, Elsa Merle

This article outlines the advancements made in broadening the application scope of the OpenMC neutron transport code to include thermohydraulic coupling and nuclear data uncertainty propagation. These developments primarily involve the incorporation of the ...

Taylor & Francis Inc2024

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 ...

Siam Publications2024

Isogeny Problems with Level Structure

Tako Boris Fouotsa

Given two elliptic curves and the degree of an isogeny between them, finding the isogeny is believed to be a difficult problem—upon which rests the security of nearly any isogeny-based scheme. If, however, to the data above we add information about the beh ...

2024

Holography and localization of information in quantum gravity

Kyriakos Papadodimas, Alexandre Mathieu Frédéric Belin

Within the AdS/CFT correspondence, we identify a class of CFT operators which represent diff-invariant and approximately local observables in the gravitational dual. Provided that the bulk state breaks all asymptotic symmetries, we show that these operator ...

Springer Nature2024

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

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

STREAMING TENSOR TRAIN APPROXIMATION

Daniel Kressner

Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor ' in the tensor train fo ...

Siam Publications2023

Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms

Xiang Zhao

The boundary correlation functions for a quantum field theory (QFT) in a fixed anti-de Sitter (AdS) background should reduce to S-matrix elements in the flat-space limit. We consider this procedure in detail for four-point functions. With minimal assumptio ...

AMER PHYSICAL SOC2023

Spin, Charge, and ?-Spin Separation in One-Dimensional Photodoped Mott Insulators

Philipp Georg Werner Seeberger

We show that effectively cold metastable states in one-dimensional photodoped Mott insulators described by the extended Hubbard model exhibit spin, charge, and q-spin separation. Their wave functions in the large on-site Coulomb interaction limit can be ex ...

AMER PHYSICAL SOC2023

Bias Cancellation of MixColumns

Francesco Regazzoni, Subhadeep Banik, Andrea Felice Caforio

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

Virtual Capacitor Concept for Partitioning of Large Converter Systems for RT-HIL Simulations

Drazen Dujic, Stefan Milovanovic, Philippe Alexandre Bontemps

In this paper, the real-time simulation model of the modular multilevel matrix converter was split into three independent instances using the concept of virtual capacitance. In doing so, the number of state space matrices that define the system has been re ...

2022

The double exponential runtime is tight for 2-stage stochastic ILPs

Kim-Manuel Klein, Klaus Jansen, Alexandra Anna Lassota

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

SPRINGER HEIDELBERG2022

A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis

Annalisa Buffa, Espen Sande, Yannis Dirk Voet

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the li ...

2023

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

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

Virtual Capacitor Concept for Effective Real-Time MMC Simulations

Drazen Dujic, Stefan Milovanovic, Min Luo

In this paper, the real-time simulation model of the modular multilevel converter was split into several independent parts through the use of the virtual capacitor concept. As a result, the number of state-space matrices the real-time solver needs to take ...

2021

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

Virtual Capacitor Concept for Computationally Efficient and Flexible Real-Time MMC Model

Drazen Dujic, Stefan Milovanovic, Min Luo

This paper demonstrates the splitting of the modular multilevel converter real-time simulation model into several independent parts through the use of the virtual capacitor concept. As a result, the number of state-space matrices the real-time solver needs ...

2021

A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

WILEY2021