Related papers: Programmable reaction-diffusion fronts
Reaction-Diffusion (RD) systems provide a computational framework that governs many pattern formation processes in nature. Current RD system design practices boil down to trial-and-error parameter search. We propose a differentiable…
Alan Turing's work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided…
Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly…
Couplings between biochemical and mechanical processes have a profound impact on embryonic development. However, in-vitro studies capable of quantifying these interactions have remained elusive. Here, we investigate a synthetic system where…
Morphogenesis, the establishment and repair of emergent complex anatomy by groups of cells, is a fascinating and biomedically-relevant problem. One of its most fascinating aspects is that a developing embryo can reliably recover from…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
Diffusion models have emerged as a powerful class of generative models for molecular design, capable of capturing complex structural distributions and achieving high fidelity in 3D molecule generation. However, their widespread use remains…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
Diffusion models have become a central tool in deep generative modeling, but standard formulations rely on a single network and a single diffusion schedule to transform a simple prior, typically a standard normal distribution, into the…
In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD…
DNA strand displacement (SD) reactions are central to the operation of many synthetic nucleic acid systems, including molecular circuits, sensors, and machines. Over the years, a broad set of design frameworks has emerged to accommodate…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
Spontaneous pattern formation in homogeneous systems is ubiquitous in nature. Although Turing demonstrated that spatial patterns can emerge in reaction-diffusion (RD) systems when the homogeneous state becomes linearly unstable, it remains…
A numerical study of the role of anomalous diffusion in front propagation in reaction-diffusion systems is presented. Three models of anomalous diffusion are considered: fractional diffusion, tempered fractional diffusion, and a model that…
Diffusion models exhibit impressive scalability in robotic task learning, yet they struggle to adapt to novel, highly dynamic environments. This limitation primarily stems from their constrained replanning ability: they either operate at a…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large "finite" intervals…
Diffusion-based models demonstrate impressive generation capabilities. However, they also have a massive number of parameters, resulting in enormous model sizes, thus making them unsuitable for deployment on resource-constraint devices.…
Spatio-temporal biochemical signaling in a large class of protein-protein interaction networks is well modeled by a reaction-diffusion system. The global existence of the solution to the reaction-diffusion system is determined by the…