Publications associées à Tenseur symétrique

Low-Rank Tensor Methods for High-Dimensional Problems

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

Rank-Adaptive Time Integration Of Tree Tensor Networks

Gianluca Ceruti

A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves connection tenso ...

SIAM PUBLICATIONS2023

Slice Estimation in Diffusion MRI of Neonatal and Fetal Brains in Image and Spherical Harmonics Domains Using Autoencoders

Meritxell Bach Cuadra, Erick Jorge Canales Rodriguez, Gabriel Girard, Thomas Yu, Hamza Kebiri

Diffusion MRI (dMRI) of the developing brain can provide valuable insights into the white matter development. However, slice thickness in fetal dMRI is typically high (i.e., 3-5 mm) to freeze the in-plane motion, which reduces the sensitivity of the dMRI s ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Bootstrapping Heisenberg magnets and their cubic instability

Alessandro Vichi, Ning Su

We study the critical O(3) model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of conformal field theory data from correlators involving the leading O( ...

American Physical Society2021

Complements to Mugge and Friedel's Theory of Twinning

Cyril Cayron

The crystallography of twinning is based on the concepts of simple shear and obliquity introduced by Mugge, Mallard and Friedel at the turn of the last century, with tensor mathematics later developed by Bilby, Bevis and Crocker in the 1960s. We propose a ...

2020

Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary Timescales

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations for wave propagation in periodic media for arbitrary timescales O(epsilon-alpha), where epsilon MUCH LESS-THAN1 is the period of the tensor describing the medium, is proposed. The well-posedness of the effective equations of ...

SPRINGER2020

Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its mutual information when the tensor is of even order. The proof uses the adaptive interpolation method, for which rank-on ...

IEEE2019

Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic

Mikko Tapani Korhonen

Let

G

be a classical group with natural module

V

over an algebraically closed field of good characteristic. For every unipotent element

u

of

G

, we describe the Jordan block sizes of

u

on the irreducible

G

-modules which occur as compositio ...

2019

Modeling spatially dependent functional data via regression with differential regularization

Fabio Nobile, Eleonora Arnone

We propose a method for modelling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of phenomenon under study ...

2019

Structure-Preserving Low Multilinear Rank Approximation Of Antisymmetric Tensors

Daniel Kressner

This paper is concerned with low multilinear rank approximations to antisymmetric tensors, that is, multivariate arrays for which the entries change sign when permuting pairs of indices. We show which ranks can be attained by an antisymmetric tensor and di ...

Siam Publications2017

Multilinear Low-Rank Tensors on Graphs & Applications

Pierre Vandergheynst, Nauman Shahid, Francesco Grassi

We propose a new framework for the analysis of low- rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank S ...

2016

Exterior Convexity And Classical Calculus Of Variations

Saugata Bandyopadhyay, Swarnendu Sil

We study the relation between various notions of exterior convexity introduced in [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009-1039.] with the classical notions of rank one convexity, quasiconvexity and polyconvexity. To th ...

Edp Sciences S A2016

Charge transport in superionic and melted AgI under a magnetic field studied via molecular dynamics

Sara Bonella, Luca Gagliardi

Charge transport in AgI subject to an external magnetic field is studied via computer simulations. We demonstrate that a recently developed algorithm can effectively complement problematic experiments to detect the ionic Hall effect, and identify previousl ...

Amer Physical Soc2016

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

Siam Publications2016

Trace maps for Mackey algebras

Baptiste Thierry Pierre Rognerud

Let G be a finite group and R be a commutative ring. The Mackey algebra μR(G) shares a lot of properties with the group algebra RG however, there are some differences. For example, the group algebra is a symmetric algebra and this is not always the case fo ...

Elsevier2015

Algorithm 941: htucker-A MATLAB Toolbox for Tensors in Hierarchical Tucker Format

Daniel Kressner, Christine Tobler

The hierarchical Tucker format is a storage-efficient scheme to approximate and represent tensors of possibly high order. This article presents a MATLAB toolbox, along with the underlying methodology and algorithms, which provides a convenient way to work ...

Assoc Computing Machinery2014

Dynamical Approximation By Hierarchical Tucker And Tensor-Train Tensors

We extend results on the dynamical low-rank approximation for the treatment of time-dependent matrices and tensors (Koch and Lubich; see [SIAM J. Matrix Anal. Appl., 29 (2007), pp. 434-454], [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2360-2375]) to the re ...

Society for Industrial and Applied Mathematics2013

Tensors, Monads And Actions

Gavin Jay Seal

We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg-Moore category C^T that represents bimorphisms. The category of actions in C^T is then shown to be monadic over the base catego ...

Mount Allison University2013

Quotient Submanifolds for Static Feedback Linearization

Philippe Müllhaupt

A procedure for finding locally the linearizing output of a single input nonlinear affine system is proposed. It relies on successive integrations of one-dimensional distributions and projections along these submanifolds. The algorithm proceeds recursively ...

2006