372 citations
- Centre National de la Recherche ScientifiqueFR95 papers
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- École Nationale Supérieure de l'Électronique et de ses ApplicationsFR73 papers
- Université de Cergy-PontoiseFR22 papers
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- Commissariat à l'Énergie Atomique et aux Énergies AlternativesFR10 papers
- Université Paris-SeineFR9 papers
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- University of ArizonaUS6 papers
8 papers · 1 filter
Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms
Philippe Gravejat, Mathieu Lewin, Eric Sere
We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The…
Dynamic of threshold solutions for energy-critical NLS
Thomas Duyckaerts, Frank Merle
We consider the radial energy-critical non-linear focusing Schrödinger equation in dimension N=3,4,5. An explicit stationnary solution, W, of this equation is known. In a previous…
Anisotropic Lavine's formula and symmetrised time delay in scattering theory
Rafael Tiedra de Aldecoa
We consider, in quantum scattering theory, symmetrised time delay defined in terms of sojourn times in arbitrary spatial regions symmetric with respect to the origin. For potential…
Effects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons
Benoit Siri, Mathias Quoy, Bruno Delord +2
The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate popu…
Asymptotic stability of solitons of the gKdV equations with general nonlinearity
Yvan Martel, Frank Merle
We consider the generalized Korteweg-de Vries equation \partial_t u + \partial_x (\partial_x^2 u + f(u))=0, \quad (t,x)\in [0,T)\times \mathbb{R}, (1) with general nonlineari…
A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks
Benoit Siri, Hugues Berry, Bruno Cessac +2
We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and dif…