Publications related to Irreducible polynomial

The 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

Academic Press Inc Elsevier Science2023

Linear 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 ...

Ieee Computer Soc2023

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Michaël Unser

The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator L\documentclass[12pt]{ ...

Springer2023

Formula Normalizations in Verification

Viktor Kuncak, Simon Guilloud, Mario Bucev, Dragana Milovancevic

We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

2023

Quadrature-free immersed isogeometric analysis

Pablo Antolin Sanchez, Thibaut Hirschler

This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the eva ...

SPRINGER2022

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

Soham Basu

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 PRESS2021

Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

Ali H. Sayed, Stefan Vlaski

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [3] of this work we established that agents cluster around a network centroid and pr ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Development of a new method to determine the axial void velocity profile in BWRs from measurements of the in-core neutron noise

Mathieu Hursin

Determination of the local void fraction in BWRs from in-core neutron noise measurements requires the knowledge of the axial velocity of the void. The purpose of this paper is to revisit the problem of determining the axial void velocity profile from the t ...

PERGAMON-ELSEVIER SCIENCE LTD2021

Efficient Sequential and Parallel Algorithms for Multistage Stochastic Integer Programming Using Proximity

Friedrich Eisenbrand, Moritz Andreas Venzin, Jana Tabea Cslovjecsek

We consider the problem of solving integer programs of the form min {c^⊺ x : Ax = b, x ∈ ℤ_{⩾ 0}}, where A is a multistage stochastic matrix in the following sense: the primal treedepth of A is bounded by a parameter d, which means that the columns of A ca ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021

Distributed Learning in Non-Convex Environments-Part I: Agreement at a Linear Rate

Ali H. Sayed, Stefan Vlaski

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available wor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Automorphisms of even unimodular lattices and equivariant Witt groups

Eva Bayer Fluckiger

We characterize the irreducible polynomials that occur as the characteristic polynomial of an automorphism of an even unimodular lattice of a given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion i ...

EUROPEAN MATHEMATICAL SOC2020

Markov cubature rules for polynomial processes

Damir Filipovic, Martin Larsson, Sergio Andres Pulido Nino

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rul ...

ELSEVIER2020

Polynomial Jump-Diffusion Models

Damir Filipovic, Martin Larsson

We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial trans ...

2020

Minimal Polynomials Of Unipotent Elements Of Non-Prime Order In Irreducible Representations Of The Exceptional Algebraic Groups In Some Good Characteristics

Donna Testerman

In a number of cases the minimal polynomials of the images of unipotent elements of non-prime order in irreducible representations of the exceptional algebraic groups in good characteristics are found. It is proved that if p > 5 for a group of type E-8 and ...

2019

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Ali H. Sayed, Stefan Vlaski

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In this work we establish that agents cluster around a network centroid in the mean-fourth sen ...

IEEE2019

Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space

Simone Deparis, Luca Pegolotti, Antonio Iubatti

This work focuses on the development of a non-conforming method for the coupling of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a finite number of Lagrange multipliers defined over the interfac ...

2019

A Hybrid High-Order Method for Highly Oscillatory Elliptic Problems

Simon Clément Damien Lemaire

We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh; those attached to ...

WALTER DE GRUYTER GMBH2019

Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic

Mikko Tapani Korhonen

Let

G

be a classical group with natural module

V

over an algebraically closed field of good characteristic. For every unipotent element

u

of

G

, we describe the Jordan block sizes of

u

on the irreducible

G

-modules which occur as compositio ...

2019

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham, Seyed Hossein Nassajianmojarrad

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

AMER MATHEMATICAL SOC2018

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

2022