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Concept

Square-free polynomial

Related publications (23)

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, Dragana Milovancevic, Mario Bucev

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

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

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

Four-Variable Expanders Over The Prime Fields

Van Thang Pham, Adrian Claudiu Valculescu, 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 ...

American Mathematical Society (AMS)2018

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Damian Mateusz Straszak

Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most s ...

EPFL2018

Optimal Software Patching Plan for PMUs

Jean-Yves Le Boudec, Ola Nils Anders Svensson, Teklemariam Tsegay Tesfay

Phasor measurement units (PMUs) deployed to monitor the state of an electrical grid need to be patched from time to time to prevent attacks that exploit vulnerabilities in the software. Applying some of these patches requires a PMU reboot, which takes the ...

2017

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Frank de Zeeuw

Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...

Duke Univ Press2016

Considerations for Rank-based Cryptosystems

Cryptosystems based on rank metric codes have been considered as an alternative to McEliece cryptosystems due to the relative difficulty of solving the rank syndrome decoding problem. Generic attacks have recently seen several improvements, notably in the ...

Ieee2016

Efficient Algorithms for the Data Exchange Problem

Michael Christoph Gastpar

In this paper, we study the data exchange problem, where a set of users is interested in gaining access to a common file, but where each has only partial knowledge about it as side-information. Assuming that the file is broken into packets, the side-inform ...

Institute of Electrical and Electronics Engineers2016

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

Giovanni Migliorati

We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is ...

Elsevier2015

Virtually Moving Base Stations for Energy Efficiency in Wireless Sensor Networks

Martin Vetterli, Patrick Thiran, Runwei Zhang

Energy efficiency of wireless sensor networks (WSNs) can be improved by moving base stations (BSs), as this scheme evenly distributes the communication load in the network. However, physically moving BSs is complicated and costly. In this paper, we propose ...

ACM New York2015

Polynomial-Time Computation Of Homotopy Groups And Postnikov Systems In Fixed Dimension

For several computational problems in homotopy theory, we obtain algorithms with running time polynomial in the input size. In particular, for every fixed k >= 2, there is a polynomial-time algorithm that, for a 1-connected topological space X given as a f ...

Siam Publications2014

Convex computation of the region of attraction of polynomial control systems

Milan Korda

We address the long-standing problem of computing the region of attraction (ROA) of a target set (typically a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We ...

Institute of Electrical and Electronics Engineers2014

On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods

Fabio Nobile, Lorenzo Tamellini

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by mu ...

World Scientific Publ Co Pte Ltd2012

On Sums of Locally Testable Affine Invariant Properties

Ghid Maatouk

Affine-invariant properties are an abstract class of properties that generalize some central algebraic ones, such as linearity and low-degree-ness, that have been studied extensively in the context of property testing. Affine invariant properties consider ...

Springer2011

New Algorithms for Approximate Nash Equilibria in Bimatrix Games

We consider the problem of computing additively approximate Nash equilibria in noncooperative two-player games. We provide a new polynomial time algorithm that achieves an approximation guarantee of 0.36392. We first provide a simpler algorithm, that achie ...

2010

2D-TUCKER Is PPAD-Complete

Doemoetoer Palvoelgyi

Tucker's lemma states that if we triangulate the unit disc centered at the origin and color the vertices with {1, 1,2, 2} in an antipodal way (if vertical bar z vertical bar = 1, then the sum of the colors of z and -z is zero), then there must be an edge F ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2009

Singularities of generic characteristic polynomials and smooth finite splittings of Azumaya algebras over surfaces

Manuel Ojanguren

Let k be an algebraically closed field. Let P(X-11,...,X-nn, T) be the characteristic polynomial of the generic matrix (X-ij) over k. We determine its singular locus as well as the singular locus of its Galois splitting. If X is a smooth quasi-projective s ...

Springer-Verlag2009

Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties

Mohammad Amin Shokrollahi, Mahdi Cheraghchi Bashi Astaneh

We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common zero of the polynom ...

2009

Related publications (23)

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

Giovanni Migliorati

Elsevier2015