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We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…
Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction…
We investigate the massive Sine-Gordon model in the finite ultraviolet regime on the two-dimensional Minkowski spacetime $(\mathbb{R}^2,\eta)$ with an additive Gaussian white noise. In particular we construct the expectation value and the…
A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a…
Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay…
We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstable regime, and was previously analysed in the context of…
Many visual scenes can be described as compositions of latent factors. Effective recognition, reasoning, and editing often require not only forming such compositional representations, but also solving the decomposition problem. One popular…
A transport PDE with a spatial integral and recirculation with constant delay has been a benchmark for neural operator approximations of PDE backstepping controllers. Introducing a spatially-varying delay into the model gives rise to a gain…
We discuss numerically the non-perturbative effects in exponential random graphs which are analogue of eigenvalue instantons in matrix models. The phase structure of exponential random graphs with chemical potential for 4-cycles and degree…
Graph neural ordinary differential equations (Graph ODEs) extend graph learning from discrete message-passing layers to continuous-time representation flows. While it supports adaptive long-range propagation, we show that Graph ODEs with…
This paper is concerned with the output feedback boundary stabilization of general 1-D reaction diffusion PDEs in the presence of an arbitrarily large input delay. We consider the cases of Dirichlet/Neumann/Robin boundary conditions for the…
Spatiotemporal pattern formations in two-layer coupled reaction-diffusion Lengyel-Epstein system with distributed delayed couplings are investigated. Firstly, for the original decoupled system, it is proved that when the intra-reactor…
In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs) are presented. The results are based on the observation that the composite system…
Random delays weaken the temporal correspondence between actions and subsequent state feedback, making it difficult for agents to identify the true propagation process of action effects. In cross-task scenarios, changes in task objectives…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…
This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the…
This paper discusses the boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a…
Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only…
Reinforcement learning (RL) with continuous time and state/action spaces is often data-intensive and brittle under nuisance variability and shift, motivating methods that exploit value-preserving structures to stabilize and improve…
Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…