Concept
Classical orthogonal polynomials
Related publications (56)
Filter-Informed Spectral Graph Wavelet Networks for Multiscale Feature Extraction and Intelligent Fault Diagnosis
Intelligent fault diagnosis has been increasingly improved with the evolution of deep learning (DL) approaches. Recently, the emerging graph neural networks (GNNs) have also been introduced in the field of fault diagnosis with the goal to make better use o ...
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023Automated mixing of maximally localized Wannier functions into target manifolds
Nicola Marzari, Giovanni Pizzi, Junfeng Qiao
Maximally localized Wannier functions (MLWFs) are widely used in electronic-structure calculations. We have recently developed automated approaches to generate MLWFs that represent natural tight-binding sets of atomic-like orbitals; these describe accurate ...
Berlin2023Numerical Studies of Brillouin-induced Polarization Pulling of Probe and Pump in Weakly-Birefringent Optical fibers with Applications to BOTDA
Luc Thévenaz, Marcelo Alfonso Soto Hernandez
Numerical solution of the involved governing equations confirm that the commonly used two orthogonal sets of gain- and loss-probes in BOTDA, differently affect the evolution of the pump state-of- polarization, thereby potentially compromising the minimizat ...
Optica Publishing Group2022Finding a vocation for validation: taking proteomics beyond association and location
First established in the seventies, proteomics, chemoproteomics, and most recently, spatial/proximity-proteomics technologies have empowered researchers with new capabilities to illuminate cellular communication networks that govern sophisticated decision- ...
ROYAL SOC CHEMISTRY2022Interlacing families III: Sharper restricted invertibility estimates
We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafriri's Restricted Invertibility Principle, and then to sharpen the result in two ways. We show that the stable rank can be replaced by the Schatten 4-norm ...
HEBREW UNIV MAGNES PRESS2021Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing
Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...
CAMBRIDGE UNIV PRESS2021The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the quasar sample in configuration space between redshift 0.8 and 2.2
We measure the anisotropic clustering of the quasar sample from Data Release 16 (DR16) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS). A sample of 343 708 spectroscopically confirmed quasars between redshift 0.8 ...
OXFORD UNIV PRESS2021Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths
In this paper we study the moments of polynomials from the Askey scheme, and we focus on Askey-Wilson polynomials. More precisely, we give a combinatorial proof for the case where d = 0. Their values have already been computed by Kim and Stanton in 2015, h ...
ELECTRONIC JOURNAL OF COMBINATORICS2021A p-weighted limiter for the discontinuous Galerkin method on one-dimensional and two-dimensional triangular grids
This paper presents an accuracy-preserving p-weighted limiter for discontinuous Galerkin methods on one-dimensional and two-dimensional triangular grids. The p-weighted limiter is the extension of the second-order WENO limiter by Li et al. [W. Li, J. Pan a ...
2020On the Experimental Transferability of Spectral Graph Convolutional Networks
Spectral Graph Convolutional Networks (GCNs) are generalisations of standard convolutional for graph-structured data using the Laplacian operator. Recent work has shown that spectral GCNs have an intrinsic transferability. This work verifies this by studyi ...
2020