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

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

A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems

Florian Karl Richter

We investigate how spectral properties of a measure-preserving system (X, B, mu, T) are reflected in the multiple ergodic averages arising from that system. For certain sequences a :N -> N, we provide natural conditions on the spectrum sigma (T) such that, ...

2019

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

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 this work we establish that agents cluster around a network centroid in the mean-fourth sen ...

IEEE2019

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

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

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

Sampling at unknown locations, with an application in surface retrieval

Martin Vetterli, Benjamin Bejar Haro, Adam James Scholefield, Michalina Wanda Pacholska

We consider the problem of sampling at unknown locations. We prove that, in this setting, if we take arbitrarily many samples of a polynomial or real bandlimited signal, it is possible to find another function in the same class, arbitrarily far away from t ...

2017

Distinct distances on regular varieties over finite fields

Van Thang Pham

In this paper we study some generalized versions of a recent result due to Covert, Koh, and Pi (2015). More precisely, we prove that if a subset in a regular variety satisfies vertical bar epsilon vertical bar >> q(d-1/2 + 1/k-1), then Delta(k,F)(epsilon) ...

Elsevier2017

Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth

Michaël Unser, John Paul Ward, Quy Ha Nguyen

The Poisson summation formula (PSF) describes the equivalence between the sampling of an analog signal and the periodization of its frequency spectrum. In engineering textbooks, the PSF is usually stated formally without explicit conditions on the signal f ...

2017

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

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Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

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

Arithmetic and metric aspects of open de Rham spaces

Four-Variable Expanders Over The Prime Fields

Sampling at unknown locations, with an application in surface retrieval

Distinct distances on regular varieties over finite fields

Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth

A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

Distinct distances on regular varieties over finite fields

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Sampling at unknown locations, with an application in surface retrieval

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

Arithmetic and metric aspects of open de Rham spaces

Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth

Four-Variable Expanders Over The Prime Fields