Publications related to Green's identities

A Determinantal Identity for the Permanent of a Rank 2 Matrix

We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that t ...

TAYLOR & FRANCIS INC2022

Three-Dimensional Optical Diffraction Tomography With Lippmann-Schwinger Model

Michaël Unser, Demetri Psaltis, Thanh-An Michel Pham, Emmanuel Emilien Louis Soubies, Joowon Lim, Ahmed Ayoub, Ahmed Bassam Sayed Ayoub Mohamed Emam

A broad class of imaging modalities involve the resolution of an inverse-scattering problem. Among them, three-dimensional optical diffraction tomography (ODT) comes with its own challenges. These include a limited range of views, a large size of the sampl ...

2020

Sparse Spline Approximation on the Hypersphere by Generalised Total Variation Basis Pursuit

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field –namely a scalar quantity defined over a continuum of directions– from generalised samples of the latter. Typically, a convex optimisation problem is formulated in terms ...

2019

Treatment of long-range interactions arising in the Enskog-Vlasov description of dense fluids

Mohammadhossein Gorji

The kinetic theory of rarefied gases and numerical schemes based on the Boltzmann equation, have evolved to the cornerstone of non-equilibrium gas dynamics. However, their counterparts in the dense regime remain rather exotic for practical non-continuum sc ...

2019

On flexible Green function methods for atomistic/continuum coupling

Max Ludwig Hodapp

Atomistic/continuum (A/C) coupling schemes have been developed during the past twenty years to overcome the vast computational cost of fully atomistic models, but have not yet reached full maturity to address many problems of practical interest. This work ...

EPFL2018

On the development and evaluation of spatial domain Green Functions for multilayered structures with conductive sheets

Juan Ramon Mosig, Michael Mattes, Ioannis Koufogiannis

This work focuses on Green Functions (GFs) of planar multilayered structures that may include arbitrary number of conductive sheets. The spectral domain GFs are derived through an automatized strategy based on the propagator matrix technique, while the spa ...

2014

Darwinians, Communitarians and Missionaries: The Role of Founder Identity in Entrepreneurship

Marc Gruber, Emmanuelle Fauchart Foray

Drawing on social identity theory, we explore the identities, behaviors and actions of 49 firm founders in the sports-related equipment industry. Our analysis suggests the existence of three pure types of founder identities and shows how these identities s ...

Academy of Management2011

Self-Similar Vector Fields

Pouya Dehghani Tafti

We propose statistically self-similar and rotation-invariant models for vector fields, study some of the more significant properties of these models, and suggest algorithms and methods for reconstructing vector fields from numerical observations, using the ...

EPFL2011

Contribution to Integral Equation Techniques for Solving Electromagnetic Problems

Sergio Lopez Pena

Surface Mixed Potential Integral Equation (MPIE) formulations together with the Method of Moments (MoM) are widely used to solve electromagnetic problems. An accurate evaluation of the Green functions (GF) associated to the integral equation and of the cou ...

EPFL2010

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

We introduce a family of elementary singularities that are point-Holder alpha-regular. These singularities are self-similar and are the Green functions of fractional derivative operators; i.e., by suitable fractional differentiation, one retrieves a Dirac ...

Institute of Electrical and Electronics Engineers2010

The surface Laplacian operator of the potentials on a bounded volume conductor has a unique inverse

In the discussion on the use of the surface Laplacian (SL) of the distribution of bioelectric potentials on the body surface, the question remained open whether a complete specification of the SL of the potential over the surface bounding a volume conducto ...

2006

Cardinal Exponential Splines: Part I—Theory and Filtering Algorithms

Michaël Unser, Thierry Blu

Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and self-contained signal processing formulation of exponential splines defined on a uniform grid. We specify the ...

IEEE2005

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