Sphere-of-Influence Graphs in Normed Spaces

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Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

Annalisa Buffa, Rafael Vazquez Hernandez

We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these result ...

Springer2020

A Unifying Representer Theorem for Inverse Problems and Machine Learning

Michaël Unser

Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements. The method is applicable whenever the problem is formulated as an optimization task. The standar ...

2021

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Georges Samarine

The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union ...

2019

Isogeometric analysis with C1 hierarchical functions on planar two-patch geometries

Rafael Vazquez Hernandez

Adaptive isogeometric methods for the solution of partial diifferential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of hierarchical spline ...

2020

Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

Maria Colombo, Luigi Forcella, Luigi De Rosa

Given any solutionuof the Euler equations which is assumed to have some regularity in space-in terms of Besov norms, natural in this context-we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure ...

IOP2019

Coordinate Difference Matrices

Martin Vetterli, Gilles Baechler, Golnooshsadat Elhami, Miranda Krekovic

In many problems such as phase retrieval, molecular biology, source localization, and sensor array calibration, one can measure vector differences between pairs of points and attempt to recover the position of these points; this class of problems is called ...

SIAM PUBLICATIONS2020

Beyond Wiener's Lemma: Nuclear Convolution Algebras and the Inversion of Digital Filters

Michaël Unser, Julien René Fageot, John Paul Ward

A convolution algebra is a topological vector space X that is closed under the convolution operation. It is said to be inverse-closed if each element of X whose spectrum is bounded away from zero has a convolution inverse that is also part of the algebra. ...

SPRINGER BIRKHAUSER2019

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b, x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m), and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2020

Collective Memory and Resistance: Visual explorations in the Historic Centre and Films of Mexico City

Lesslie Astrid Herrera Quiroz

Today, institutionalised discourses surrounding heritage have social and physical impacts, with the potential to lead to a break between inhabitants' collective memory of popular neighbourhoods, and their transforming territories. In this context, the acti ...

EPFL2019

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Michaël Unser, Pakshal Narendra Bohra

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

2020

Path properties of the solution to the stochastic heat equation with Levy noise

Robert Dalang, Carsten Hao Ye Chong, Thomas Marie Jean-Baptiste Humeau

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

SPRINGER2019