Publications related to Undecidability through Fourier series

Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics

Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of localizing any inferred differences ...

American Statistical Association2016

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Joachim Krieger, Roland Donninger

We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

2016

3D-Printed Shepp-Logan Phantom as a Real-World Benchmark for MRI

Dimitri Nestor Alice Van De Ville, Jeffrey Adam Kasten, François Lazeyras

Purpose: As prescribed and reliable geometrical entities, phantoms have served as indispensable validation tools in a variety of MR-related topics. Though a number of phantoms have been conceived, certain applications may warrant highly customized geometri ...

Wiley-Blackwell2016

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

Determination of a shear rate threshold for thrombus formation in intracranial aneurysms

Orestis Pileas Malaspinas, Ricardo Alberto Corredor Jerez, Bastien Chopard

Particular intra-aneurysmal blood flow conditions, created naturally by the growth of an aneurysm or induced artificially by implantation of a flow diverter stent (FDS), can potentiate intra-aneurysmal thrombosis. The aim of this study was to identify hemo ...

2015

Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks

Pierre Vandergheynst, Michael Bronstein

In this paper, we propose a generalization of convolutional neural networks (CNN) to non-Euclidean domains for the analysis of deformable shapes. Our construction is based on localized frequency analysis (a generalization of the windowed Fourier transform ...

Wiley-Blackwell2015

Algebraic twists of modular forms and Hecke orbits

Philippe Michel

We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistri ...

Springer Verlag2015

Fourier Analysis of Functional Time Series, with Applications to DNA Dynamics

Shahin Tavakoli

This work is about time series of functional data (functional time series), and consists of three main parts. In the first part (Chapter 2), we develop a doubly spectral decomposition for functional time series that generalizes the Karhunen–Loève expansion ...

EPFL2014

Method and system for computing Fourier series coefficients for mask layouts using FFT

Paul Hurley, Robin Scheibler, Krzysztof Kryszczuk

A method and system for computing Fourier coefficients for a Fourier representation of a mask transmission function for a lithography mask. The method includes: sampling a polygon of a mask pattern of the lithography mask to obtain an indicator function wh ...

United States Patent and Trademark Office2013

Undecidability through Fourier series

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Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics

A vector field method on the distorted Fourier side and decay for wave equations with potentials

3D-Printed Shepp-Logan Phantom as a Real-World Benchmark for MRI

Towards More Accurate and Efficient Beamformed Radio Interferometry Imaging

Fourier Analysis of MAC Polarization

Determination of a shear rate threshold for thrombus formation in intracranial aneurysms

Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks

Algebraic twists of modular forms and Hecke orbits

Fourier Analysis of Functional Time Series, with Applications to DNA Dynamics

Method and system for computing Fourier series coefficients for mask layouts using FFT

Towards More Accurate and Efficient Beamformed Radio Interferometry Imaging

3D-Printed Shepp-Logan Phantom as a Real-World Benchmark for MRI

Algebraic twists of modular forms and Hecke orbits

Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics

Method and system for computing Fourier series coefficients for mask layouts using FFT

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Fourier Analysis of MAC Polarization

Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks

Fourier Analysis of Functional Time Series, with Applications to DNA Dynamics

Determination of a shear rate threshold for thrombus formation in intracranial aneurysms