Publications related to Functional equation

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...

Amer Mathematical Soc2024

High-resolution tomographic volumetric additive manufacturing

Christophe Moser, Paul Delrot, Damien Claude-Marie Loterie

Tomographic additive manufacturing produces complex parts with a wide range of printable materials but remains limited in terms of resolution. Here, the authors tune the etendue of the light source and accurately control the photopolymerization kinetics us ...

Nature Publishing Group2020

On the Discreteness of Transmission Eigenvalues for the Maxwell Equations

Hoài-Minh Nguyên

In this paper, we establish the discreteness of transmission eigenvalues for Maxwell's equations. More precisely, we show that the spectrum of the transmission eigenvalue problem is discrete, if the electromagnetic parameters $\eps, , \mu, , \heps, , \h ...

2021

Adaptive Gradient Descent without Descent

Konstantin Mishchenko

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Apparent diffusion coefficient measured by diffusion MRI of moving and deforming domains

Jan Sickmann Hesthaven

The modeling of the diffusion MRI signal from moving and deforming organs such as the heart is challenging due to significant motion and deformation of the imaged medium during the signal acquisition. Recently, a mathematical formulation of the Bloch-Torre ...

Academic Press Inc - Elsevier Science2020

Functional relations in nineteen-vertex models with domain-wall boundaries

Aleksi Antoine Bossart

This work is concerned with functional properties shared by partition functions of nineteen-vertex models with domain-wall boundary conditions. In particular, we describe both Izergin-Korepin and Fateev-Zamolodchikov models with the aforementioned boundary ...

2019

Gradients of structure-function tethering across neocortex

Patric Hagmann

The white matter architecture of the brain imparts a distinct signature on neuronal coactivation patterns. Interregional projections promote synchrony among distant neuronal populations, giving rise to richly patterned functional networks. A variety of sta ...

National Academy of Sciences2019

Conformal Mapping of Impedance Stability Models for System-Level Dynamics Assessments

Drazen Dujic, Francisco Daniel Freijedo Fernández, Uzair Javaid

Impedance stability methods are suitable for assessing the dynamics of power converters controllers, but also for ac/dc microgrids system level studies. This work proposes the combination of impedance modeling and conformal mapping for the identification o ...

2017

Grasping for the Task : Human Principles for Robot Hands

Ravin Luis De Souza

The significant advances made in the design and construction of anthropomorphic robot hands, endow them with prehensile abilities reaching that of humans. However, using these powerful hands with the same level of expertise that humans display is a big cha ...

EPFL2016

Mechanistically Consistent Reduced Models of Synthetic Gene Networks

Vassily Hatzimanikatis

Designing genetic networks with desired functionalities requires an accurate mathematical framework that accounts for the essential mechanistic details of the system. Here, we formulate a time-delay model of protein translation and mRNA degradation by syst ...

Cell Press2013

The Bounded Confidence Model Of Opinion Dynamics

Jean-Yves Le Boudec, Javier Gomez Serrano

The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions evolve globally into ...

World Scientific Publishing2012

Revised self-consistent continuum solvation in electronic-structure calculations

Nicola Marzari, Oliviero Andreussi

The solvation model proposed by Fattebert and Gygi [J. Comput. Chem. 23, 662 (2002)] and Scherlis et al. [J. Chem. Phys. 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. ...

2012

On Regularized Reconstruction of Vector Fields

Michaël Unser, Pouya Dehghani Tafti

In this paper, we give a general characterization of regularization functionals for vector field reconstruction, based on the requirement that the said functionals satisfy certain geometric invariance properties with respect to transformations of the coord ...

IEEE2011

A visualization framework for the analysis of neuromuscular simulations

Daniel Thalmann, Anders Sandholm

We present a visualization framework for exploring and analyzing data sets from biomechanical and neuromuscular simulations. These data sets describe versatile information related to the different stages of a motion analysis. In studying these data using a ...

Springer-Verlag2011

Sur la méthode de Buser-Silhol pour l'uniformisation des surfaces de Riemann hyperelliptiques

Grégoire Aubry

The Uniformization Theorem due to Koebe and Poincaré implies that every compact Riemann surface of genus greater or equal to 2 can be endowed with a metric of constant curvature – 1. On the other hand, a compact Riemann surface is a complex algebraic curve ...

EPFL2010

Atom-wall dispersive forces: a microscopic approach

We present a study of atom-wall interactions in non-relativistic quantum electrodynamics by functional integral methods. The Feynman-Kac path integral representation is generalized when the particle interacts with a radiation field, providing an additional ...

2009

Cellular toxicity of carbon-based nanomaterials

László Forró, Arnaud Magrez, Sandor Kasas, Jin Won Seo

The cellular toxicity of carbon-based nanomaterials was studied as a function of their aspect ratio and surface chemistry. These structures were multiwalled carbon nanotubes, carbon nanofibers, and carbon nanoparticles. Their toxicity was tested in vitro o ...

2006

Variational reconstruction of scalar and vector images from non-uniform samples

Muthuvel Arigovindan

We address the problem of reconstructing scalar and vector functions from non-uniform data. The reconstruction problem is formulated as a minimization problem where the cost is a weighted sum of two terms. The first data term is the quadratic measure of go ...

EPFL2005

Semantics-based representation of virtual environments

Daniel Thalmann, Frédéric Vexo

In this paper we present an object representation based on the semantics and functionality of interactive digital items - virtual objects - within a virtual environment (VE). We consider every object participating in a VE application not only as a 3D shape ...

2005

Variational Image Reconstruction from Arbitrarily Spaced Samples: A Fast Multiresolution Spline Solution

Michaël Unser, Michael Sühling, Muthuvel Arigovindan

We propose a novel method for image reconstruction from nonuniform samples with no constraints on their locations. We adopt a variational approach where the reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms: 1) the ...

IEEE2005