Ni Chuangao

Mathematical Properties, Stability Theory, and Experimental Validation of the Double Exponential Activation Function in Complex-Valued Neural Networks

Complex-valued neural networks (CVNNs) can naturally process complex signals, phase information, and two-dimensional data, and have been widely applied in various fields. However, Liouville's theorem states that a bounded entire function must be constant, which implies that there...

Quaternionic Geometry of Chiral Helices on a Cone: Riemannian Structure, Topological Classification, Variational Characterization,and Holomorphic Representation

Using quaternions as the algebraic tool, this paper systematically constructs the Riemannian geometric theory of chiral helices on a cone. The cone $C_\alpha(\mathbf u)$ is determined by a unit purely imaginary quaternion $\mathbf u$ and the semi-vertical angle $\alpha$; its indu...