Deep limits of residual neural networks

Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The contribution of this paper is to show that, for the residual neural network model, the deep layer limit...

Quadratic systems with a symmetrical solution

In this paper we study the existence and uniqueness of limit cycles for so-called quadratic systems with a symmetrical solution: dx(t)/dt = P₂(x, y) ≡ a₀₀+ a₁₀x + a₀₁y + a₂₀x²+ a₁₁xy + a₀₂y²dy(t)/dt = Q₂(x, y) ≡ b₀₀+ b<sub...

Fast calculation of electrical transients in power systems after a change of topology

A power system is composed of various components such as generators, transformers, transmission lines, switching devices and loads. They have their mathematical model and graphical representation. Sometimes, a power system’s change of topology occurs due to events like short circuits, lightning striking a transformer, or a reconfiguration of the...