Concept

Foncteur adjoint

Publications associées (30)

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

Walter De Gruyter Gmbh2024

Correspondence functors and duality

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. By means of a suitably defined duality, new correspondence functors are constructed, having remarkable p ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Conditional Flatness, Fiberwise Localizations, And Admissible Reflections

Jérôme Scherer

We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localizatio ...

CAMBRIDGE UNIV PRESS2023

Constructing periodic orbits of high-dimensional chaotic systems by an adjoint-based variational method

Tobias Schneider, Omid Ashtari, Sajjad Azimi

Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatiotemporal systems including fluid turbulence is supported by nonchaotic, exactly recurring time-periodic solutions of the governing equations ...

2022

Multi-Level Monte Carlo Methods for Uncertainty Quantification and Risk-Averse Optimisation

Sundar Subramaniam Ganesh

This work aims to study the effects of wind uncertainties in civil engineering structural design. Optimising the design of a structure for safety or operability without factoring in these uncertainties can result in a design that is not robust to these per ...

EPFL2022

Homotopical relations between 2-dimensional categories and their infinity-analogues

Lyne Moser

In this thesis, we study the homotopical relations of 2-categories, double categories, and their infinity-analogues. For this, we construct homotopy theories for the objects of interest, and show that there are homotopically full embeddings of 2-categories ...

EPFL2021

Differentiable inverse rendering based on radiative backpropagation

Wenzel Alban Jakob, Merlin Eléazar Nimier-David

A computer-implemented inverse rendering method is provided. The method comprises: computing an adjoint image by differentiating an objective function that evaluates the quality of a rendered image, image elements of the adjoint image encoding the sensitiv ...

2021

ON THE DESIGN AND OPTIMIZATION OF WIDE ANGLE DIFFRACTIVE OPTICAL ELEMENTS

Dong Cheon Kim

Diffractive optical elements (DOEs) which consist of microstructure surface relief permit the generation of the spatial distribution of light beams by using a single element. Due to their compact size, design flexibility, and mass productivity, they are us ...

EPFL2021

The algebra of Boolean matrices, correspondence functors, and simplicity

Jacques Thévenaz, Serge Bouc

We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ...

2020

A multiphase CMAQ version 5.0 adjoint

Athanasios Nenes

We present the development of a multiphase adjoint for the Community Multiscale Air Quality (CMAQ) model, a widely used chemical transport model. The adjoint model provides location- and time-specific gradients that can be used in various applications such ...

2020

On design strategies for binary dielectric metasurfaces based on the Fourier modal method

Kévin Müller

Binary dielectric metasurfaces are arrays of sub-wavelength structures that act as a thin layer of artificial material. They are generally lossless and relatively simple to fabricate since only a single structuring step is required. By carefully designing ...

EPFL2020

Correspondence functors and lattices

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. A main tool for this study is the construction of a correspondence functor associated to any finite latt ...

2019

Twisting structures and morphisms up to strong homotopy

Kathryn Hess Bellwald

We define twisted composition products of symmetric sequences via classifying morphisms rather than twisting cochains. Our approach allows us to establish an adjunction that simultaneously generalizes a classic one for algebras and coalgebras, and the bar- ...

2020

Simple and projective correspondence functors

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. We determine exactly which simple correspondence functors are projective. We also determine which simple ...

2021

The Homotopy Theory Of Coalgebras Over Simplicial Comonads

Kathryn Hess Bellwald, Magdalena Kedziorek

We apply the Acyclicity Theorem of Hess, Kedziorek, Riehl, and Shipley (recently corrected by Garner, Kedziorek, and Riehl) to establishing the existence of model category structure on categories of coalgebras over comonads arising from simplicial adjuncti ...

INT PRESS BOSTON, INC2019

Injective And Projective Model Structures On Enriched Diagram Categories

Lyne Moser

In the enriched setting, the notions of injective and projective model structures on a category of enriched diagrams also make sense. In this paper, we prove the existence of these model structures on enriched diagram categories under local presentability, ...

2019

$A_1$-type subgroups containing regular unipotent elements

Donna Testerman

Let be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic and let be a subgroup of containing a regular unipotent element of . By a theorem of Testerman, is contained in a connected subgroup of of type ...

2019

Hyperbolicity as an obstruction to smoothability for one-dimensional actions

Yash Lodha

Ghys and Sergiescu proved in the 1980s that Thompson's group T, and hence F, admits actions by C-infinity diffeomorphisms of the circle. They proved that the standard actions of these groups are topologically conjugate to a group of C-infinity diffeomorphi ...

GEOMETRY & TOPOLOGY PUBLICATIONS2019

Model-based image reconstruction method

Jean-Philippe Thiran, Marcel Arditi, Adrien Georges Jean Besson, Dimitris Perdios

The present invention concerns a pulse wave image reconstruction method to be used for example in ultrasound imaging. The proposed method is based on an image measurement model and its adjoint operator. The proposed method introduces matrix-free formulatio ...

2019

Correspondence functors and finiteness conditions

Jacques Thévenaz, Serge Bouc

We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties wh ...

2018