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Concept

Borel functional calculus

Related publications (11)

koopmans: An Open-Source Package for Accurately and Efficiently Predicting Spectral Properties with Koopmans Functionals

Nicola Marzari, Nicola Colonna, Edward Baxter Linscott, Ngoc Linh Nguyen, Giovanni Borghi, Riccardo De Gennaro

Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise linearity conditio ...

Amer Chemical Soc2023

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a cont ...

2021

SPHARMA approximations for stationary functional time series on the sphere

Alessia Caponera

In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressi ...

2021

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

Stochastic approximation methods for PDE constrained optimal control problems with uncertain parameters

Matthieu Claude Martin

This thesis work focuses on optimal control of partial differential equations (PDEs) with uncertain parameters, treated as a random variables. In particular, we assume that the random parameters are not observable and look for a deterministic control which ...

EPFL2019

The Hamiltonian of the harmonic oscillator with an attractive delta '-interaction centred at the origin as approximated by the one with a triple of attractive delta-interactions

In this note we provide an alternative way of defining the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive delta'-interaction, of strength beta, centred at 0 (the bottom of the confining parabolic potential), that was rigorou ...

Iop Publishing Ltd2016

A mathematical approach in the design of arterial bypass using unsteady Stokes equations

Alfio Quarteroni, Gianluigi Rozza

In this paper we present an approach for the study of aorto-coronaric bypass anastomoses configurations using unsteady Stokes equations. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the ...

2006

Shape design in aorto-coronaric bypass anastomoses using perturbation theory

Alfio Quarteroni, Gianluigi Rozza

We present a new approach in the study of aorto-coronaric bypass anastomoses configurations based on small perturbation theory. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming ...

2006

Complex B-Splines

Michaël Unser, Thierry Blu

We propose a complex generalization of Schoenberg's cardinal splines. To this end, we go back to the Fourier domain definition of the B-splines and extend it to complex-valued degrees. We show that the resulting complex B-splines are piecewise modulated po ...

Elsevier2006

On optimization, control and shape design of an arterial bypass

Gianluigi Rozza

Multi-level geometrical approaches in the study of aorto-coronaric bypass anastomoses configurations are discussed. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the incoming branch of the bypass (t ...

2005