Publications related to Polynomial-time algorithms for the factorization of polynomials

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain combinatorial applic ...

2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

,

b \in \Z^m

,

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Single and multiple recurrence along non-polynomial sequences

Florian Karl Richter

We establish new recurrence and multiple recurrence results for a rather large family of non-polynomial functions which contains tempered functions and (non-polynomial) functions from a Hardy field with polynomial growth. In particular, we show that, somew ...

2020

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

Felix Schürmann, Francesco Cremonesi, Timothée Ewart

The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. ...

2020

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

Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability

Davide Pradovera

We present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR str ...

2020

New Graph Algorithms via Polyhedral Techniques

Jakub Tarnawski

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. S ...

EPFL2019

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

Florian Karl Richter

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

MATHICSE Technical Report: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability

Davide Pradovera

We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR stategy co ...

MATHICSE2019

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

Polynomial-time algorithms for the factorization of polynomials

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Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

New Results in Integer and Lattice Programming

Single and multiple recurrence along non-polynomial sequences

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

Automorphisms of even unimodular lattices and equivariant Witt groups

Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability

New Graph Algorithms via Polyhedral Techniques

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

MATHICSE Technical Report: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

New Results in Integer and Lattice Programming

New Graph Algorithms via Polyhedral Techniques

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability

MATHICSE Technical Report: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability

Automorphisms of even unimodular lattices and equivariant Witt groups

Single and multiple recurrence along non-polynomial sequences