This paper builds on the connection between graph neural networks and traditional
dynamical systems. We propose continuous graph neural networks (CGNN), which …

We construct a Wasserstein gradient flow of the maximum mean discrepancy (MMD) and
study its convergence properties. The MMD is an integral probability metric defined for a …

Many real-world systems such as social networks and moving planets are dynamic in
nature, where a set of coupled objects are connected via the interaction graph and exhibit …

In the vicinity of ground-state phase transitions quantum correlations can display nonanalytic
behavior and critical scaling. This signature of emergent collective effects has been widely …

In this paper, we apply the Bernstein collocation method to construct the solution set of the
Sylvester matrix differential equation (Sy-MDE) which involves the Lyapunov matrix …

We investigate parity-time (PT) phase transitions in open quantum systems and discuss a
criterion of Liouvillian PT symmetry proposed recently by Huber et al.[SciPost Phys. 9, 52 …

Ultra-wideband (UWB) systems are becoming increasingly popular as a means of inter-robot
ranging and communication. A major constraint associated with UWB is that only one pair of …

Along with the numerous highly interconnected nodes in real networks, a complex
dynamical network shows the dynamic behaviors not only in the nodes but also in the links …

The continuous-time differential Lyapunov equation is widely used in linear optimal control
theory, a branch of mathematics and engineering. In quantum physics, it is known to appear …

Abstract Systems of reaction–diffusion partial differential equations (RD-PDEs) are widely
applied for modeling life science and physico-chemical phenomena. In particular, the …