Concept

Closed and exact differential forms

Publications associées (23)

Cochains are all you need

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

Quasiconvexity and Relaxation in Optimal Transportation of Closed Differential Forms

Bernard Dacorogna

This manuscript extends the relaxation theory from nonlinear elasticity to electromagnetism and to actions defined on paths of differential forms. The introduction of a gauge allows for a reformulation of the notion of quasiconvexity in Bandyopadhyay et al ...

SPRINGER2019

Calculus of variations: A differential form approach

Swarnendu Sil

We study integrals of the form integral(Omega) f(d omega(1), ..., d omega(m)), where m >= 1 is a given integer, 1

WALTER DE GRUYTER GMBH2019

On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

Max-Olivier Hongler, Roger Filliger

We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial dif ...

Springer2019

Exact Smooth Term Structure Estimation

Damir Filipovic, Sander Félix M Willems

We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is eas ...

2018

Exact Smooth Term-Structure Estimation

Damir Filipovic, Sander Félix M Willems

We present a nonparametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is easy ...

SIAM PUBLICATIONS2018

Notions of affinity in calculus of variations with differential forms

Saugata Bandyopadhyay, Swarnendu Sil

Ext-int. one affine functions are functions affine in the direction of one-divisible exterior forms with respect to the exterior product in one variable and with respect to the interior product in the other. The purpose of this article is to prove a charac ...

Walter De Gruyter Gmbh2016

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

Optimal transport of closed differential forms for convex costs

Bernard Dacorogna, Olivier Kneuss

Let c : A(k-1) -> R+ be convex and Omega subset of R-n be a bounded domain. Let f(0) and f(1) be two closed k-forms on Omega satisfying appropriate boundary conditions. We discuss the minimization of integral(Omega) c (A) dx over a subset of (k - 1)-forms ...

Elsevier France-Editions Scientifiques Medicales Elsevier2015

Some New Results On Differential Inclusions For Differential Forms

Bernard Dacorogna, Olivier Kneuss, Saugata Bandyopadhyay

In this article we study some necessary and sufficient conditions for the existence of solutions in W-0(1,infinity) (Omega; Lambda(k)) of the differential inclusion d omega is an element of E a.e. in Omega where E subset of Lambda(k+1) is a prescribed set. ...

Amer Mathematical Soc2015

Calculus of variations with differential forms

Bernard Dacorogna, Saugata Bandyopadhyay, Swarnendu Sil

We study integrals of the form integral(Omega) f (d omega), where 1

European Mathematical Soc2015

The second order pullback equation

Bernard Dacorogna, Olivier Kneuss, Gyula Csató

Let f, g be two closed k-forms over R-n. The pullback equation studies the existence of a diffeomorphism phi : R-n -> R-n such that phi*(g) = f. We prove two types of results. The first one sharpens some of the existing regularity results. The second one d ...

Springer2014

Principal Polynomial Analysis

Devis Tuia

This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of ma ...

World Scientific Publ Co Pte Ltd2014

L'équation de rappel

Olivier Kneuss

In this thesis we are interested in the following problem : given two differential k–forms g and f, most of the time they will be assumed closed, on what conditions can we pullback g to f by a map φ ? In other words we ask when it is possible to solve the ...

EPFL2011

Linear Local Models for Monocular Reconstruction of Deformable Surfaces

Pascal Fua, Mathieu Salzmann

Recovering the 3D shape of a nonrigid surface from a single viewpoint is known to be both ambiguous and challenging. Resolving the ambiguities typically requires prior knowledge about the most likely deformations that the surface may undergo. It often take ...

2011

Optimal image alignment with random projections of manifolds: algorithm and geometric analysis

Pascal Frossard, Daniel Kressner, Effrosyni Kokiopoulou

This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is prov ...

2011

Looping probabilities of elastic chains: A path integral approach

John Maddocks, Ludovica Cotta-Ramusino

We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit ...

2010

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

Lq,p-cohomology of Riemannian manifolds and simplicial complexes of bounded geometry

Stephen Ducret

The Lq,p-cohomology of a Riemannian manifold (M, g) is defined to be the quotient of closed Lp-forms, modulo the exact forms which are derivatives of Lq-forms, where the measure considered comes from the Riemannian structure. The Lq,p-cohomology of a simpl ...

EPFL2009

Stabilized finite element schemes for incompressible flow using Scott-Vogelius elements

Erik Burman

We propose a stabilized mixed finite element method based on the Scott-Vogelius element tor the Oseen equation. Here. only convection has to he stabilized since by construction both the discrete pressure and the divergence of the discrete velocities, are c ...

2008