Publications associées à Système d'équations algébriques

Unlabeled 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 Publishing2024

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Stefano Alberti, Jean-Philippe Hogge, Joaquim Loizu Cisquella, Jérémy Genoud, Francesco Romano, Guillaume Michel Le Bars

This paper presents the new 2D electrostatic particle -in -cell code FENNECS developed to study the formation of magnetized non -neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun desi ...

2024

Certification of Bottleneck Task Assignment With Shortest Path Criteria

Maryam Kamgarpour, Tony Alan Wood

Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in an environment wi ...

2023

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

On Preconditioning of Decentralized Gradient-Descent When Solving a System of Linear Equations

Nirupam Gupta

This article considers solving an overdetermined system of linear equations in peer-to-peer multiagent networks. The network is assumed to be synchronous and strongly connected. Each agent has a set of local data points, and their goal is to compute a line ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Structure-preserving approaches and data-driven closure modeling for model order reduction

Nicolò Ripamonti

In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...

EPFL2022

Tight Vector Bin Packing with Few Small Items via Fast Exact Matching in Multigraphs

Adam Teodor Polak, Alexandra Anna Lassota

We solve the Bin Packing problem in O^*(2^k) time, where k is the number of items less or equal to one third of the bin capacity. This parameter measures the distance from the polynomially solvable case of only large (i.e., greater than one third) items. O ...

Schloss Dagstuhl – Leibniz-Zentrum fur Informatik2022

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

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Riccardo Puppi

Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...

EPFL2022

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

EPFL2022

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

A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bezout's identities

Cyril Cayron

Deformation twinning on a plane is a simple shear that transforms a unit cell attached to the plane into another unit cell equivalent by mirror symmetry or 180 degrees rotation. Thus, crystallographic models of twinning require the determination of the sho ...

INT UNION CRYSTALLOGRAPHY2021

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

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

Vessel scheduling with pilotage and tugging considerations

Michel Bierlaire

This paper considers vessel scheduling with pilotage and tugging constraints in berthing operations with channel restrictions at seaports. To our knowledge, pilotage and tugging requirements have not been simultaneously considered in the literature. This w ...

PERGAMON-ELSEVIER SCIENCE LTD2021

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

Multilevel weighted least squares polynomial approximation

Fabio Nobile

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...

2020

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

Analogue computing with metamaterials

Romain Christophe Rémy Fleury, Farzad Zangeneh Nejad

Despite their widespread use for performing advanced computational tasks, digital signal processors suffer from several restrictions, including low speed, high power consumption and complexity, caused by costly analogue-to-digital converters. For this reas ...

2021

A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

Alfio Quarteroni, Ondine Gabrielle Chanon

In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods and NURBS-based Isogeometric Analysis in its basic form, that is in the framework of the Galerkin method, for the approximation of the Poisso ...

SPRINGER/PLENUM PUBLISHERS2020