This is the second post (here’s the first one) about an approach to introducing the derivative to calculus students that is counter to what I’ve seen in textbooks and other traditional treatments of ...

The mathematical foundation of deep learning is the theorem that any continuous function can be approximated within any specified accuracy by using a neural network with certain non-linear activation ...

Abstract: Artificial neural networks (ANNs) rely significantly on activation functions for optimal performance. Traditional activation functions such as ReLU and Sigmoid are commonly used. However, ...

We use the formalism of Fourier transformation to derive a functional calculus for the generator of an abstract group. As an application we obtain a new direct solution of Cauchy's problem for ...