Related papers: Diffusion with rearranging traps
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and…
We consider the classical map proposed previously to be the exact classical analogue of Rydberg Molecules calculated with the approximations relevant to the multi-channel quantum defect theory. The resulting classical map is analyzed at…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…
The potential of applying diffusion models (DMs) for multiple antenna communications is discussed. A unified framework of applying DM for multiple antenna tasks is first proposed. Then, the tasks are innovatively divided into two…
Language models with recurrent depth, also referred to as universal or looped when considering transformers, are defined by the capacity to increase their computation through the repetition of layers. Recent efforts in pretraining have…
A number of results for reactions involving subdiffusive species all with the same anomalous exponent gamma have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time t in…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
We consider one dimensional lattice diffusion model on a microscale grid with many discrete diffusivity values which repeat periodicially. Computer algebra explores how the dynamics of small coupled `patches' predict the slow emergent…
Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple,…
Propagation of chaos is a well-studied phenomenon and shows that weakly interacting diffusions may become independent as the system size converges to infinity. Most of the literature focuses on the case of exchangeable systems where all…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
The diffusion and flow of amorphous materials, such as glasses and granular materials, has resisted a simple microscopic description, analogous to defect theories for crystals. Early models were based on either gas-like inelastic collisions…
Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…
The distribution function for the intensity of radiation propagating in a random medium is analyzed for arbitrary multiplicity of scattering (for arbitrary relation between the distance of propagation and mean free path), including as…