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Large Sieve Inequalities for Algebraic Trace Functions

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Petersson inner products of weight-one modular forms

Maryna Viazovska

In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that ...

2019

Combining Fourier Analysis And Machine Learning To Estimate The Shallow-Ground Thermal Diffusivity In Switzerland

Jean-Louis Scartezzini, Dan Assouline, Nahid Mohajeri Pour Rayeni

We propose a methodology combining physical modelling and machine learning (ML) to estimate the apparent ground thermal diffusivity at the scale of a country. Based on ground temperature time series at different depths, we estimate the diffusivity at 49 Sw ...

IEEE2018

Discreteness of interior transmission eigenvalues revisited

Hoài-Minh Nguyên, Quoc Hung Nguyen

This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the ...

Springer Verlag2017

Predicting the Success of Online Petitions Leveraging Multidimensional Time-Series

Karl Aberer, Philippe Cudré-Mauroux, Julia Proskurnia, Carlos Castillo

Applying classical time-series analysis techniques to online content is challenging, as web data tends to have data quality issues and is often incomplete, noisy, or poorly aligned. In this paper, we tackle the problem of predicting the evolution of a time ...

Some remarks on rearrangement for nonlocal functionals

Hoài-Minh Nguyên

We prove that a nonlocal functional approximating the standard Dirichlet p-norm fails to decrease under two-point rearrangement. Furthermore, we get other properties related to this functional such as decay and compactness. ...

2017

Undecidability through Fourier series

In computability theory a variety of combinatorial systems are encountered (word problems, production systems) that exhibit undecidability properties. Here we seek such structures in the realm of Analysis, more specifically in the area of Fourier Analysis. ...

Elsevier Science Bv2016

Models of crowding: a comparative study

Michael Herzog, Gregory Francis, Adrien Christophe Doerig, Aaron Michael Clarke

In crowding, the perception of an object deteriorates in the presence of nearby elements. Obviously, crowding is a ubiquitous phenomenon, since elements are rarely seen in isolation. Despite this ubiquity, there exists no consensus on how to model crowding ...

2016

Audio inpainting with similarity graphs

Nathanaël Perraudin

In this contribution, we present a method to compensate for long duration data gaps in audio signals, in particular music. To achieve this task, a similarity graph is constructed, based on a short-time Fourier analysis of reliable signal segments, e.g. the ...

2016

Towards More Accurate and Efficient Beamformed Radio Interferometry Imaging

Matthieu Martin Jean-André Simeoni

The Square Kilometre Array (SKA) will form the largest radio telescope ever built, generating on the order of one terabyte of data per second. To reduce the data flow sent to the central processor, hierarchical designs have been proposed: the data is prima ...

2015

Fourier Analysis of MAC Polarization

Emre Telatar, Rajai Nasser

A problem of the polar code construction for multiple access channels (MACs) is that they do not always achieve the whole capacity region. Although polar codes achieve the sum-capacity of symmetric MACs, polarization may induce a loss in the capacity regio ...

2015