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Concept

Orthogonal matrix

Related publications (29)

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

First-principles thermodynamics of precipitation in aluminum-containing refractory alloys

Anirudh Raju Natarajan

Materials for high -temperature environments are actively being investigated for deployment in aerospace and nuclear applications. This study uses computational approaches to unravel the crystallography and thermodynamics of a promising class of refractory ...

Pergamon-Elsevier Science Ltd2024

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Nicolas Boumal

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

Siam Publications2024

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

Random matrix methods for high-dimensional machine learning models

Antoine Philippe Michel Bodin

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

EPFL2024

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Volkan Cevher, Grigorios Chrysos, Fanghui Liu

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

2024

K3 surfaces, cyclotomic polynomials and orthogonal groups

Eva Bayer Fluckiger

Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...

Springer Int Publ Ag2024

DARE-GRAM : Unsupervised Domain Adaptation Regression by Aligning Inverse Gram Matrices

Olga Fink, Ismail Nejjar

Unsupervised Domain Adaptation Regression (DAR) aims to bridge the domain gap between a labeled source dataset and an unlabelled target dataset for regression problems. Recent works mostly focus on learning a deep feature encoder by minimizing the discrepa ...

IEEE2023

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Yannis Dirk Voet

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

ELSEVIER SCIENCE INC2023

Spectral representation of EEG data using learned graphs with application to motor imagery decoding

Dimitri Nestor Alice Van De Ville, Hamid Behjat, Maliheh Miri

Electroencephalography (EEG) data entail a complex spatiotemporal structure that reflects ongoing organi-zation of brain activity. Characterization of the spatial patterns is an indispensable step in numerous EEG processing pipelines. We present a novel me ...

Elsevier Sci Ltd2023

Optimal denoising of rotationally invariant rectangular matrices

Lenka Zdeborová, Florent Gérard Krzakala, 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

Exceptional points at bound states in the continuum in photonic integrated circuits

Haoye Qin

We propose the realization of exceptional points (EP) at bound states in the continuum (BIC), with two coupled strips, made of an electron-beam resist and patterned on the thin film photonic integrated platform, which makes possible etchless photonics inte ...

WALTER DE GRUYTER GMBH2022

Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (Or: How to Prove Kabashima’s Replica Formula)

Florent Gérard Krzakala, Alia Abbara

There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal matrices. Here, we g ...

2022

Numerical Studies of Brillouin-induced Polarization Pulling of Probe and Pump in Weakly-Birefringent Optical fibers with Applications to BOTDA

Luc Thévenaz, Marcelo Alfonso Soto Hernandez

Numerical solution of the involved governing equations confirm that the commonly used two orthogonal sets of gain- and loss-probes in BOTDA, differently affect the evolution of the pump state-of- polarization, thereby potentially compromising the minimizat ...

Optica Publishing Group2022

Linearization and Identification of Multiple-Attractor Dynamical Systems through Laplacian Eigenmaps

Aude Billard, Bernardo Fichera

Dynamical Systems (DS) are fundamental to the modeling and understanding time evolving phenomena, and have application in physics, biology and control. As determining an analytical description of the dynamics is often difficult, data-driven approaches are ...

Microtome Publishing2022

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

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Dimitrios Gourzoulidis

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

EPFL2021

Topological Linear System Identification via Moderate Deviations Theory

Daniel Kuhn, Wouter Jongeneel, Tobias Sutter

Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such as stability or ...

2022

Sublinear Algorithms for Spectral Graph Clustering

Aidasadat Mousavifar

This thesis focuses on designing spectral tools for graph clustering in sublinear time. With the emergence of big data, many traditional polynomial time, and even linear time algorithms have become prohibitively expensive. Processing modern datasets requir ...

EPFL2021