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Concept

Monomial basis

Related publications (12)

Optimal radial basis for density-based atomic representations

Michele Ceriotti, Félix Benedito Clément Musil, Jigyasa Nigam, Sergey Pozdnyakov, Alexander Jan Goscinski

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

2021

Local invertibility and sensitivity of atomic structure-feature mappings

Michele Ceriotti, Sergey Pozdnyakov

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...

2021

Probing the Unfolded Configurations of a β-Hairpin Using Sketch-Map

Michele Ceriotti

This work examines the conformational ensemble involved in beta-hairpin folding by means of advanced molecular dynamics simulations and dimensionality reduction. A fully atomistic description of the protein and the surrounding solvent molecules is used, an ...

2015

Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis

Daniel Kressner

Novel memory-efficient Arnoldi algorithms for solving matrix polynomial eigenvalue problems are presented. More specifically, we consider the case of matrix polynomials expressed in the Chebyshev basis, which is often numerically more appropriate than the ...

Wiley-Blackwell2014

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

Silvia Sabatini

In [GT], Goldin and Tolman extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99,Kn08].) The main goal of this paper is to build on this ...

Int Press Boston, Inc2013

ElimLin Algorithm Revisited

Serge Vaudenay, Pouyan Sepehrdad, Petr Susil

ElimLin is a simple algorithm for solving polynomial systems of multivariate equations over small finite fields. It was initially proposed as a single tool by Courtois to attack DES. It can reveal some hidden linear equations existing in the ideal generate ...

Springer2012

Chebyshev interpolation for nonlinear eigenvalue problems

Daniel Kressner, Peter Cedric Effenberger

This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix-valued function is computationally expensive. ...

Springer Netherlands2012

High order methods for the approximation of the incompressible Navier-Stokes equations in a moving domain

Alfio Quarteroni

In this paper we address the numerical approximation of the incompressible Navier-Stokes equations in a moving domain by the spectral element method and high order time integrators. We present the Arbitrary Lagrangian Eulerian (ALE) formulation of the inco ...

Elsevier2012

Groebner Basis Methods for Multichannel Sampling with Unknown Offsets

Martin Vetterli, Luciano Sbaiz, Patrick Vandewalle

In multichannel sampling, several sets of sub-Nyquist sampled signal values are acquired. The offsets between the sets are unknown, and have to be resolved, just like the parameters of the signal itself. This problem is nonlinear in the offsets, but linear ...

Elsevier2008

Northern and southern innovativity: a comparison across European and Latin American countries

Julio Diego Salvador Raffo

This paper compares the role of innovation and economic performance across European and Latin American countries, using firm-level data from France, Spain, Switzerland, Argentina, Brazil and Mexico. We implement a standard structural model linking R&D inte ...

2008

Nonorthogonal theory of polarons and application to pyramidal quantum dots

Elyahou Kapon, Marc-André Dupertuis, Danail Obreschkow, Sascha Dalessi

We present a general theory for semiconductor polarons in the framework of the Frohlich interaction between electrons and phonons. The latter is investigated using noncommuting phonon creation/annihilation operators associated with a natural set of nonorth ...

2007

Super-resolution from unregistered aliased images

Patrick Vandewalle

Aliasing in images is often considered as a nuisance. Artificial low frequency patterns and jagged edges appear when an image is sampled at a too low frequency. However, aliasing also conveys useful information about the high frequency content of the image ...

EPFL2006