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Data augmentation is a widely adopted technique for avoiding overfitting when training deep neural networks. However, this approach requires domain-specific knowledge and is often limited to a fixed set of hard-coded transformations. Recently, several work ...
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 ...
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
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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 ...
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 ...
We consider a class of branching processes with countably many types which we refer to as Lower Hessenberg branching processes. These are multitype Galton-Watson processes with typeset X = {0, 1, 2,...}, in which individuals of type i may give birth to off ...
In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge n operator in the U (1) model at the Wilson-Fisher fixed point in D = 4 - epsilon can be computed semiclassically for arbitrary values of lambda n, where lambda is the pertu ...
In every dimension d >= 2, we give an explicit formula that expresses the values of any Schwartz function on R-d only in terms of its restrictions, and the restrictions of its Fourier transform, to all origin-centered spheres whose radius is the square roo ...
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
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In structural health monitoring (SHM), risk assessment and decision strategies rely primarily on sensor responses. Simulated data can be generated to emulate the monitoring phenomena under different natural operational and environmental conditions in order ...
