Publications related to Polynomial

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

A set

R\subset \mathbb{N}

is called rational if it is well approximable by finite unions of arithmetic progressions, meaning that for every

\unicode[STIX]{x1D716}>0

there exists a set

B=\bigcup _{i=1}^{r}a_{i}\mathbb{N}+b_{i}

, where $a_{1},\ldots ,a_ ...

2019

The committee machine: computational to statistical gaps in learning a two-layers neural network

Nicolas Macris, Florent Gérard Krzakala, Lenka Zdeborová, Jean François Emmanuel Barbier

Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this paper, we provide a rigor ...

IOP PUBLISHING LTD2019

Cryptanalysis of Plantlet

Subhadeep Banik, Khashayar Barooti

Plantlet is a lightweight stream cipher designed by Mikhalev, Armknecht and Muller in IACR ToSC 2017. It has a Grain-like structure with two state registers of size 40 and 61 bits. In spite of this, the cipher does not seem to lose in security against gene ...

2019

Distributed sampling for rational approximation of the acoustic scattering of an airfoil

Francesca Bonizzoni, Davide Pradovera

In this paper we compute a reduced order model for a time‐harmonic external acoustic scattering problem with parametric frequency. The employed technique is minimal rational interpolation, an explicit moment‐matching method for Hilbert space‐valued meromor ...

2019

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

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham

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

Arithmetic and metric aspects of open de Rham spaces

Dimitri Stelio Wyss, Tamás Hausel, Michael Lennox Wong

In this paper we determine the motivic class---in particular, the weight polynomial and conjecturally the Poincar'e polynomial---of the open de Rham space, defined and studied by Boalch, of certain moduli of irregular meromorphic connections on the trivia ...

2018

A Preconditioned Graph Diffusion LMS for Adaptive Graph Signal Processing

Ali H. Sayed, Roula Nassif

Graph filters, defined as polynomial functions of a graph-shift operator (GSO), play a key role in signal processing over graphs. In this work, we are interested in the adaptive and distributed estimation of graph filter coefficients from streaming graph s ...

IEEE COMPUTER SOC2018

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

Jan Sickmann Hesthaven, Boris Bonev

We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and non-conforming, curved meshes in a well-balanced manner. This requires a well-balanced discretization, that can ...

2018

Small Extended Formulation for Knapsack Cover Inequalities from Monotone Circuits

Ola Nils Anders Svensson, Abbas Bazzi, Sangxia Huang

Initially developed for the min-knapsack problem, the knapsack cover inequalities are used in the current best relaxations for numerous combinatorial optimization problems of covering type. In spite of their widespread use, these inequalities yield linear ...

UNIV CHICAGO, DEPT COMPUTER SCIENCE2018

Polynomial

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Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

The committee machine: computational to statistical gaps in learning a two-layers neural network

Cryptanalysis of Plantlet

Distributed sampling for rational approximation of the acoustic scattering of an airfoil

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Four-Variable Expanders Over The Prime Fields

Arithmetic and metric aspects of open de Rham spaces

A Preconditioned Graph Diffusion LMS for Adaptive Graph Signal Processing

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

Small Extended Formulation for Knapsack Cover Inequalities from Monotone Circuits

Cryptanalysis of Plantlet

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

Arithmetic and metric aspects of open de Rham spaces

A Preconditioned Graph Diffusion LMS for Adaptive Graph Signal Processing

The committee machine: computational to statistical gaps in learning a two-layers neural network

Distributed sampling for rational approximation of the acoustic scattering of an airfoil

Four-Variable Expanders Over The Prime Fields

Small Extended Formulation for Knapsack Cover Inequalities from Monotone Circuits