Publications associées à Équation diophantienne

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

Witness encryption is a cryptographic primitive which encrypts a message under an instance of an NP language and decrypts the ciphertext using a witness associated with that instance. In the current state of the art, most of the witness encryption construc ...

Springer2023

Weakly nonlinear versus semi-linear models of the nonlinear evolution of the centrifugal instability

François Gallaire, Eunok Yim

We carry out a weakly nonlinear analysis of the centrifugal instability for a columnar vortex in a rotating fluid, and compare the results to those of the semi-linear model derived empirically by Yim et al. (J. Fluid Mech., vol. 897, 2020, A34). The asympt ...

CAMBRIDGE UNIV PRESS2023

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

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

A Local Law for Singular Values from Diophantine Equations

Marius Christopher Lemm

We introduce the

N\times N

random matrices

X_{j,k}=\exp\left(2\pi i \sum_{q=1}^d\ \omega_{j,q} k^q\right) \quad \text{with } \{\omega_{j,q}\}_{\substack{1\leq j\leq N\\ 1\leq q\leq d}} \text{ i.i.d. random variables},

and

d

a fixed integer. We pr ...

2020

On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem

Mika Tapani Göös

We study the search problem class PPA_q defined as a modulo-q analog of the well-known polynomial parity argument class PPA introduced by Papadimitriou (JCSS 1994). Our first result shows that this class can be characterized in terms of PPA_p for prime p. ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2020

MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields

Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni

A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients requires solving loc ...

EPFL2020

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

David Valentin Strütt

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

EPFL2018

Proactive Synthesis of Recursive Tree-to-String Functions from Examples

Viktor Kuncak, Mikaël Mayer, Jad Hamza

Synthesis from examples enables non-expert users to generate programs by specifying examples of their behavior. A domain-specific form of such synthesis has been recently deployed in a widely used spreadsheet software product. In this paper we contribute t ...

2017

On infinite dimensional linear programming approach to stochastic control * *This research is partially supported by M. Kamgarpour’s European Union ERC Starting Grant, CONENE and by T. Summers’ the US National Science Foundation under grant CNS-1566127.

Maryam Kamgarpour, Tyler Summers

We consider the infinite dimensional linear programming (inf-LP) approach for solving stochastic control problems. The inf-LP corresponding to problems with uncountable state and input spaces is in general computationally intractable. By focusing on linear ...

2017

Équation diophantienne

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

Weakly nonlinear versus semi-linear models of the nonlinear evolution of the centrifugal instability

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

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

A Local Law for Singular Values from Diophantine Equations

On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem

MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

Proactive Synthesis of Recursive Tree-to-String Functions from Examples

On infinite dimensional linear programming approach to stochastic control * *This research is partially supported by M. Kamgarpour’s European Union ERC Starting Grant, CONENE and by T. Summers’ the US National Science Foundation under grant CNS-1566127.

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MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré