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Concept

Dualité de Hodge

Publications associées (21)

Null energy constraints on two-dimensional RG flows

Grégoire Olivier Mathys

We study applications of spectral positivity and the averaged null energy condition (ANEC) to renormalization group (RG) flows in two-dimensional quantum field theory. We find a succinct new proof of the Zamolodchikov c-theorem, and derive further independ ...

Springer Nature2024

Cochains are all you need

Kelly Spry Maggs

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

EPFL2024

RMAML: Riemannian meta-learning with orthogonality constraints

Soumava Kumar Roy

Meta-learning is the core capability that enables intelligent systems to rapidly generalize their prior ex-perience to learn new tasks. In general, the optimization-based methods formalize the meta-learning as a bi-level optimization problem, that is a nes ...

ELSEVIER SCI LTD2023

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

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Alexis Arnaudon

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...

NATURE PORTFOLIO2022

Reduced representations of complexes, signals, and multifiltrations

Celia Camille Hacker

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Victor Panaretos, Julien René Fageot, Matthieu Martin Jean-André Simeoni, Alessia Caponera

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

2022

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

EPFL2022

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

Homogenization of Multiscale Eddy Current Problem by Localized Orthogonal Decomposition Method

Xiaotao Ren

A homogenization approach for the solution of multiscale eddy current problem is proposed. The method is based on the subspace decomposition and it involves a coarse space and a nested fine space. The homogenized problem is posed in the coarse space with t ...

Institute of Electrical and Electronics Engineers2019

Generalized Norm-compatible Systems on Unitary Shimura Varieties

Mohamed Réda Boumasmoud

We define and study in terms of integral Iwahoriâ Hecke algebras a new class of geometric operators acting on the Bruhat-Tits building of connected reductive groups over p-adic fields. These operators, which we call U-operators, generalize the geometric n ...

EPFL2019

Limiting absorption principle and well-posedness for the Helmholtz equation with sign changing coefficients

Hoài-Minh Nguyên

In this paper, we investigate the limiting absorption principle associated to and the well-posedness of the Helmholtz equations with sign changing coefficients which are used to model negative index materials. Using the reflecting technique introduced in [ ...

Elsevier2016

Renormalization and blow up for wave maps from $S^2 \times \mathbb{R}$ to $S^2$

Sohrab Mirshams Shahshahani

We construct a one parameter family of nite time blow ups to the co-rotational wave maps problem from

S^2\times R

S^2

parameterized by

\nu \epsilon (\frac{1}{2},1]

. The longitudinal function

u(t,\alpha)

which is the main object of study will be ...

2016

Calculus of Variations for Differential Forms

Swarnendu Sil

In this thesis we study calculus of variations for differential forms. In the first part we develop the framework of direct methods of calculus of variations in the context of minimization problems for functionals of one or several differential forms of th ...

EPFL2016

Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term

Fabio Nobile, Annalisa Buffa, Francesca Bonizzoni

We study the mixed formulation of the stochastic Hodge-Laplace problem dened on a

n

-dimensional domain

D (n ≥ 1)

, with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three dimensional case. We ...

2014

Thermodynamics of a continuous medium with electric and magnetic dipoles

Jean-Philippe Ansermet, Sylvain Bréchet

The thermodynamics of an electrically charged, multicomponent fluid with spontaneous electric and magnetic dipoles is analysed in the presence of electromagnetic fields. Taking into account the chemical composition of the current densities and stress tenso ...

EDP Sciences, Springer2013

On the Hodge decomposition in $\mathbb{R}^n$

Marc Troyanov

We prove a version of the

L^p

hodge decomposition for differential forms in Euclidean space and a generalization to the class of Lizorkin currents. We also compute the

L_{qp}-

cohomology of

\mathbb{R}^n

. ...

2009

Some linear and nonlinear problems involving differential forms

Saugata Bandyopadhyay

In this thesis, we study some linear and nonlinear problems involving differential forms. We begin by studying the problem of pullbacks which asks the following question: for two given differential forms, if one is the pullback of the other via a diffeomor ...

EPFL2007

From Differential Equations to the Construction of New Wavelet-Like Bases

Michaël Unser, Ildar Khalidov

In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the ...

IEEE2006

Generalized L-Spline Wavelet Bases

Michaël Unser, Thierry Blu, Ildar Khalidov

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

SPIE2005

Publications associées (21)

Null energy constraints on two-dimensional RG flows

Grégoire Olivier Mathys

Springer Nature2024

Cochains are all you need

Kelly Spry Maggs

EPFL2024

RMAML: Riemannian meta-learning with orthogonality constraints

Soumava Kumar Roy

ELSEVIER SCI LTD2023

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

Olga Fink, Ismail Nejjar

IEEE2023

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Alexis Arnaudon

NATURE PORTFOLIO2022

Reduced representations of complexes, signals, and multifiltrations

Celia Camille Hacker

EPFL2022

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Victor Panaretos, Julien René Fageot, Matthieu Martin Jean-André Simeoni, Alessia Caponera

2022

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

EPFL2022

Bootstrapping Heisenberg magnets and their cubic instability

Alessandro Vichi, Ning Su

American Physical Society2021

Homogenization of Multiscale Eddy Current Problem by Localized Orthogonal Decomposition Method

Xiaotao Ren

Institute of Electrical and Electronics Engineers2019

Generalized Norm-compatible Systems on Unitary Shimura Varieties

Mohamed Réda Boumasmoud

EPFL2019

Limiting absorption principle and well-posedness for the Helmholtz equation with sign changing coefficients

Hoài-Minh Nguyên

Elsevier2016

Renormalization and blow up for wave maps from $S^2 \times \mathbb{R}$ to $S^2$

Sohrab Mirshams Shahshahani

We construct a one parameter family of nite time blow ups to the co-rotational wave maps problem from

S^2\times R

S^2

parameterized by

\nu \epsilon (\frac{1}{2},1]

. The longitudinal function

u(t,\alpha)

which is the main object of study will be ...

2016

Calculus of Variations for Differential Forms

Swarnendu Sil

EPFL2016

Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term

Fabio Nobile, Annalisa Buffa, Francesca Bonizzoni

We study the mixed formulation of the stochastic Hodge-Laplace problem dened on a

n

-dimensional domain

D (n ≥ 1)

, with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three dimensional case. We ...

2014

Thermodynamics of a continuous medium with electric and magnetic dipoles

Jean-Philippe Ansermet, Sylvain Bréchet

EDP Sciences, Springer2013

On the Hodge decomposition in $\mathbb{R}^n$

Marc Troyanov

We prove a version of the

L^p

hodge decomposition for differential forms in Euclidean space and a generalization to the class of Lizorkin currents. We also compute the

L_{qp}-

cohomology of

\mathbb{R}^n

. ...

2009

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

SPIE2005