Nonlinear reduced basis using mixture Wasserstein barycenters: application to an eigenvalue problem inspired from quantum chemistry

The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of parametric eigenvalue problems inspired from quantum chemistry applications. More precisely, we consider here a one-dimensional model which is a toy model for the computation of the electronic ground state wavefunction of a system of electrons within a molecule, solution to the many-body electronic Schr\"odinger equation, where the varying parameters are the positions of the nuclei in the molecule. We estimate the decay rate of the Kolmogorov n-width of the set of solutions for this parametric problem in several settings, including the standard L2-norm as well as with distances based on optimal transport. The fact that the latter decays much faster than in the traditional L2-norm setting motivates us to propose a practical nonlinear reduced basis method, which is based on an offline greedy algorithm, and an efficient stochastic energy minimization in the online phase. We finally provide numerical results illustrating the capabilities of the method and good approximation properties, both in the offline and the online phase

Tolerability and safety of fluvoxamine and other antidepressants

Selective serotonin [5-hydroxytryptamine (5-HT)] reuptake inhibitors (SSRIs) and the 5-HT noradrenaline reuptake inhibitor, venlafaxine, are mainstays in treatment for depression. The highly specific actions of SSRIs of enhancing serotonergic neurotransmission appears to explain their benefit, while lack of direct actions on other neurotransmitter systems is responsible for their superior safety profile compared with tricyclic antidepressants. Although SSRIs (and venlafaxine) have similar adverse effects, certain differences are emerging. Fluvoxamine may have fewer effects on sexual dysfunction and sleep pattern. SSRIs have a cardiovascular safety profile superior to that of tricyclic antidepressants for patients with cardiovascular disease; fluvoxamine is safe in patients with cardiovascular disease and in the elderly. A discontinuation syndrome may develop upon abrupt SSRI cessation. SSRIs are more tolerable than tricyclic antidepressants in overdose, and there is no conclusive evidence to suggest that they are associated with an increased risk of suicide. Although the literature suggests that there are no clinically significant differences in efficacy amongst SSRIs, treatment decisions need to be based on considerations such as patient acceptability, response history and toxicity

MARQUEURS DE VULNERABILITE DANS LA SCHIZOPHRENIE (INTERET DES ANOMALIES DES MOUVEMENTS OCULAIRES ; A PROPOS DE DEUX ETUDES)

LYON1-BU Santé (693882101) / SudocPARIS-BIUM (751062103) / SudocSudocFranceF

RECHERCHE DE FACTEURS DE RISQUE DE SURVENUE DES EFFETS INDESIRABLES EXTRAPYRAMIDAUX MEDICAMENTEUX (PHARMACOGENETIQUE : CYP2D6 PHENOTYPE ET GENOTYPE)

LYON1-BU Santé (693882101) / SudocPARIS-BIUP (751062107) / SudocSudocFranceF

Nonlinear reduced basis using mixture Wasserstein barycenters: application to an eigenvalue problem inspired from quantum chemistry

The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of parametric eigenvalue problems inspired from quantum chemistry applications. More precisely, we consider here a onedimensional model which is a toy model for the computation of the electronic ground state wavefunction of a system of electrons within a molecule, solution to the many-body electronic Schrödinger equation, where the varying parameters are the positions of the nuclei in the molecule. We estimate the decay rate of the Kolmogorov n-width of the set of solutions for this parametric problem in several settings, including the standard L2-norm as well as with distances based on optimal transport. The fact that the latter decays much faster than in the traditional L2-norm setting motivates us to propose a practical nonlinear reduced basis method, which is based on an offline greedy algorithm, and an efficient stochastic energy minimization in the online phase. We finally provide numerical results illustrating the capabilities of the method and good approximation properties, both in the offline and the online phase

Nonlinear reduced basis using mixture Wasserstein barycenters: application to an eigenvalue problem inspired from quantum chemistry

The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of parametric eigenvalue problems inspired from quantum chemistry applications. More precisely, we consider here a onedimensional model which is a toy model for the computation of the electronic ground state wavefunction of a system of electrons within a molecule, solution to the many-body electronic Schrödinger equation, where the varying parameters are the positions of the nuclei in the molecule. We estimate the decay rate of the Kolmogorov n-width of the set of solutions for this parametric problem in several settings, including the standard L2-norm as well as with distances based on optimal transport. The fact that the latter decays much faster than in the traditional L2-norm setting motivates us to propose a practical nonlinear reduced basis method, which is based on an offline greedy algorithm, and an efficient stochastic energy minimization in the online phase. We finally provide numerical results illustrating the capabilities of the method and good approximation properties, both in the offline and the online phase

Nonlinear reduced basis using mixture Wasserstein barycenters: application to an eigenvalue problem inspired from quantum chemistry

The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of parametric eigenvalue problems inspired from quantum chemistry applications. More precisely, we consider here a onedimensional model which is a toy model for the computation of the electronic ground state wavefunction of a system of electrons within a molecule, solution to the many-body electronic Schrödinger equation, where the varying parameters are the positions of the nuclei in the molecule. We estimate the decay rate of the Kolmogorov n-width of the set of solutions for this parametric problem in several settings, including the standard L2-norm as well as with distances based on optimal transport. The fact that the latter decays much faster than in the traditional L2-norm setting motivates us to propose a practical nonlinear reduced basis method, which is based on an offline greedy algorithm, and an efficient stochastic energy minimization in the online phase. We finally provide numerical results illustrating the capabilities of the method and good approximation properties, both in the offline and the online phase