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Publications associées (32)

The inductive bias of deep learning: Connecting weights and functions

Years of a fierce competition have naturally selected the fittest deep learning algorithms. Yet, although these models work well in practice, we still lack a proper characterization of why they do so. This poses serious questions about the robustness, trus ...

EPFL2023

Phase of Topological Lattice with Leaky Guided Mode Resonance

Kirsten Emilie Moselund, Chang Won Lee

Topological nature in different areas of physics and electronics has often been characterized and controlled through topological invariants depending on the global properties of the material. The validity of bulk-edge correspondence and symmetry-related to ...

Basel2023

Detecting whether a stochastic process is finitely expressed in a basis

Victor Panaretos, Neda Mohammadi Jouzdani

Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Einstein's quantum elevator: Hermitization of non-Hermitian Hamiltonians via a generalized vielbein formalism

Fabrizio Minganti

The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbeinlike formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional ones, rendering th ...

AMER PHYSICAL SOC2022

Frequency-Domain Non-intrusive Greedy Model Order Reduction Based on Minimal Rational Approximation

Fabio Nobile, Davide Pradovera

We present a technique for Model Order Reduction (MOR) of frequency-domain problems relying on rational interpolation of vector-valued functions. The selection of the sample points is carried out adaptively according to a greedy procedure. We describe seve ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

MATHICSE Technical Report: Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale

Assyr Abdulle, Andrea Zanoni, Grigorios A. Pavliotis

We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the eigenfunctions of the hom ...

MATHICSE2021

Restriction of 3D arithmetic Laplace eigenfunctions to a plane

We consider a random Gaussian ensemble of Laplace eigenfunctions on the 3D torus, and investigate the 1-dimensional Hausdorff measure ('length') of nodal intersections against a smooth 2-dimensional toral sub-manifold ('surface'). A prior result of ours pr ...

2020

Frequency domain theory for functional time series: Variance decomposition and an invariance principle

Neda Mohammadi Jouzdani

This paper is concerned with frequency domain theory for functional time series, which are temporally dependent sequences of functions in a Hilbert space. We consider a variance decomposition, which is more suitable for such a data structure than the varia ...

INT STATISTICAL INST2020

Singular global components and frequency shift of the geodesic acoustic continuum modes in shaped tokamaks

Jonathan Graves

Within the ideal magnetohydrodynamic (MHD) model, the geodesic acoustic modes (GAMs) in tokamaks derived by Winsor et al (1968 Phys. Fluids 11 2448) belong to the continuous spectrum, characterised by unbounded non-square integrable eigenfunctions (delta f ...

2019

On The Behavior Of Clamped Plates Under Large Compression

We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical ...

2019

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