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Concept

Eigenvalues and eigenvectors

Related publications (32)

Exceptional points at bound states in the continuum in photonic integrated circuits

Haoye Qin

We propose the realization of exceptional points (EP) at bound states in the continuum (BIC), with two coupled strips, made of an electron-beam resist and patterned on the thin film photonic integrated platform, which makes possible etchless photonics inte ...

WALTER DE GRUYTER GMBH2022

Koopmans Spectral Functionals in Periodic Boundary Conditions

Nicola Marzari, Nicola Colonna, Edward Baxter Linscott, Riccardo De Gennaro

Koopmans spectral functionals aim to describe simultaneously ground-state properties and charged excitations of atoms, molecules, nanostructures, and periodic crystals. This is achieved by augmenting standard density functionals with simple but physically ...

AMER CHEMICAL SOC2022

Failure and success of the spectral bias prediction for Laplace Kernel Ridge Regression: the case of low-dimensional data

Matthieu Wyart, Antonio Sclocchi, Umberto Maria Tomasini

Recently, several theories including the replica method made predictions for the generalization error of Kernel Ridge Regression. In some regimes, they predict that the method has a 'spectral bias': decomposing the true function f* on the eigenbasis of the ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

A smooth basis for atomistic machine learning

Michele Ceriotti, Filippo Bigi, Kevin Kazuki Huguenin-Dumittan

Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to ...

AIP Publishing2022

Weakly nonlinear evolution of stochastically driven non-normal systems

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

We consider nonlinear dynamical systems driven by stochastic forcing. It has been largely evidenced in the literature that the linear response of non-normal systems (e.g. fluid flows) may exhibit a large variance amplification, even in a linearly stable re ...

Cambridge University Press2022

Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance

Fabrizio Minganti

The exceptional points (EPs) of non-Hermitian Hamiltonians (NHHs) are spectral degeneracies associated with coalescing eigenvalues and eigenvectors, which are associated with remarkable dynamical properties. These EPs can be generated experimentally in ope ...

AMER PHYSICAL SOC2022

Model order reduction for compressible flows solved using the discontinuous Galerkin methods

Jan Sickmann Hesthaven

Projection-based reduced order models (ROM) based on the weak form and the strong form of the discontinuous Galerkin (DG) method are proposed and compared for shock-dominated problems. The incorporation of dissipation components of DG in a consistent manne ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

CovNet: Covariance networks for functional data on multidimensional domains

Victor Panaretos, Soham Sarkar

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address ...

WILEY2022

Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Espen Sande

We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...

2022

Spectral Coarse Spaces for the Substructured Parallel Schwarz Method

Tommaso Vanzan

The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...

2022

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Jean Louis-Alexandre Fornerod

The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...

EPFL2022

turboMagnon - A code for the simulation of spin-wave spectra using the Liouville-Lanczos approach to time-dependent density-functional perturbation theory

Iurii Timrov

We introduce turboMagnon, an implementation of the Liouville-Lanczos approach to linearized time-dependent density-functional theory, designed to simulate spin-wave spectra in solid-state materials. The code is based on the noncollinear spin-polarized fram ...

ELSEVIER2022