Related papers: Concentration-Dependent Domain Evolution in Reacti…
Diffusion Models (DMs), as a leading class of generative models, offer key advantages for reinforcement learning (RL), including multi-modal expressiveness, stable training, and trajectory-level planning. This survey delivers a…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
Attention mechanisms have become a foundational component in diffusion models, significantly influencing their capacity across a wide range of generative and discriminative tasks. This paper presents a comprehensive survey of attention…
Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…
We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two…
End-to-end deep learning improves breast cancer classification on diffusion-weighted MR images (DWI) using a convolutional neural network (CNN) architecture. A limitation of CNN as opposed to previous model-based approaches is the…
The growth of domains of stripes evolving from random initial conditions is studied in numerical simulations of models of systems far from equilibrium such as Rayleigh-Benard convection. The scaling of the size of the domains deduced from…
Learning a model of dynamics from high-dimensional images can be a core ingredient for success in many applications across different domains, especially in sequential decision making. However, currently prevailing methods based on…
Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter…
It is a well known fact that subdiffusion equations in terms of fractional derivatives can be obtained from Continuous Time Random Walk (CTRW) models with long-tailed waiting time distributions. Over the last years various authors have…
Based on a recently proposed non-equilibrium mechanism for spatial pattern formation [cond-mat/0312366] we study how morphogenesis can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of…
We investigate the non-equilibrium properties of an N-component scalar field theory. The time evolution of the correlation functions for an arbitrary ensemble of initial conditions is described by an exact functional differential equation.…
The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of corre- lation functions are closed, are considered. A transfer matrix method is used to find the…
Conformal field theories with central charge $c\le1$ on random surfaces have been extensively studied in the past. Here, this discussion is extended from their equilibrium distribution to their critical dynamics. This is motivated by the…
The microscopic structure and movement of reaction fronts in reaction diffusion systems far from equilibrium are investigated. We show that some three-site interaction models exhibit exact diffusive shock measures, i.e. domains of different…
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…
Humans continuously adapt their style and language to a variety of domains. However, a reliable definition of `domain' has eluded researchers thus far. Additionally, the notion of discrete domains stands in contrast to the multiplicity of…