Concept
Chebyshev polynomials
Related publications (188)
K3 surfaces, cyclotomic polynomials and orthogonal groups
Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...
Springer Int Publ Ag2024Unlabeled Principal Component Analysis and Matrix Completion
We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...
Microtome Publ2024Interpolation and Quantifiers in Ortholattices
Viktor Kuncak, Simon Guilloud, Sankalp Gambhir
We study quantifiers and interpolation properties in orthologic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based pro ...
Cham2024Interpolation and Quantifiers in Ortholattices
Viktor Kuncak, Simon Guilloud, Sankalp Gambhir
We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...
2024Filter-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 INC2023The multivariate Serre conjecture ring
It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension
San Diego2023Linear Complexity Self-Attention With 3rd Order Polynomials
Grigorios Chrysos, Filippos Kokkinos
Self-attention mechanisms and non-local blocks have become crucial building blocks for state-of-the-art neural architectures thanks to their unparalleled ability in capturing long-range dependencies in the input. However their cost is quadratic with the nu ...
Los Alamitos2023Gyrokinetic moment-based simulations of the Dimits shift
Paolo Ricci, Baptiste Jimmy Frei, Antoine Cyril David Hoffmann
We present a convergence study of the gyromoment (GM) approach, which is based on projecting the gyrokinetic distribution function onto a Hermite–Laguerre polynomial basis, focused on the cyclone base case (CBC) (Lin et al., Phys. Rev. Lett., vol. 83, no. ...
2023Regularization of polynomial networks for image recognition
Volkan Cevher, Grigorios Chrysos, Bohan Wang
Deep Neural Networks (DNNs) have obtained impressive performance across tasks, however they still remain as black boxes, e.g., hard to theoretically analyze. At the same time, Polynomial Networks (PNs) have emerged as an alternative method with a promising ...
2023Finite free convolutions of polynomials
We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric addi ...
SPRINGER HEIDELBERG2022