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Concept

Brouwer fixed-point theorem

Related publications (28)

Numerical methods for structural anomaly detection using model order reduction and data-driven techniques

Caterina Bigoni

The objective of this thesis is to provide a mathematical and computational framework for the proactive maintenance of complex systems with a particular application to structural health monitoring (SHM). SHM techniques rely primarily on sensor responses to ...

EPFL2020

Efficient Treatment of Correlation Energies at the Basis-Set Limit by Monte Carlo Summation of Continuum States

Ursula Röthlisberger, Martin Peter Bircher, Justin Villard

The calculation of electron correlation is vital for the description of atomistic phenomena in physics, chemistry, and biology. However, accurate wavefunction-based methods exhibit steep scaling and often sluggish convergence with respect to the basis set ...

AMER CHEMICAL SOC2020

Fast Transformers with Clustered Attention

François Fleuret, Apoorv Vyas, Angelos Katharopoulos

Transformers have been proven a successful model for a variety of tasks in sequence modeling. However, computing the attention matrix, which is their key component, has quadratic complexity with respect to the sequence length, thus making them prohibitivel ...

2020

Spectral Properties of the Signal in Phase-Sensitive Optical Time-Domain Reflectometry with Direct Detection

Luc Thévenaz, Marcelo Alfonso Soto Hernandez, Li Zhang, Xin Lu

The spectral properties of the Rayleigh backscattered traces measured by a phase-sensitive optical time-domain reflectometer (øOTDR) with direct detection are theoretically and experimentally analyzed. The spectrum of the measured øOTDR signal is found to ...

IEEE Institute of Electrical and Electronics Engineers2020

Stability of standing waves for a nonlinear Klein-Gordon equation with delta potentials

François Samer Genoud

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike ...

2019

Travelling heteroclinic waves in a Frenkel-Kontorova chain with anharmonic on-site potential

Boris Buffoni

The Frenkel-Kontorova model for dislocation dynamics from 1938 is given by a chain of atoms, where neighbouring atoms interact through a linear spring and are exposed to a smooth periodic on-site potential. A dislocation moving with constant speed correspo ...

ELSEVIER SCIENCE BV2019

Structural Properties Of Dendrite Groups

Nicolas Monod

Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many nonisomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric G-action on any metr ...

AMER MATHEMATICAL SOC2019

Sampling sufficiency for determining hydraulic habitat diversity

Anton Schleiss, Mário Jorge Rodrigues Pereira Da Franca, Severin Stähly, Walter Gostner

The geometry and hydrodynamics of river reaches are key ecohydraulic descriptors. Statistics of water depth and velocity measurements are usually taken as proxies for habitat suitability in rivers. However, little is known about the sufficiency of data to ...

2018