Related papers: Transience/Recurrence and Growth Rates for Diffusi…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
The temporal modal and nonmodal growth of three-dimensional perturbations in the boundary-layer flow over an infinite compliant flat wall is considered. Using a wall-normal velocity/wall-normal vorticity formalism, the dynamic boundary…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
The effect of diffusively correlated spatial fluctuations on the proliferation-extinction transition of autocatalytic agents is investigated numerically. Reactants adaptation to spatio-temporal active regions is shown to lead to…
We prove the consistency of an adaptive importance sampling strategy based on biasing the potential energy function $V$ of a diffusion process $dX_t^0=-\nabla V(X_t^0)dt+dW_t$; for the sake of simplicity, periodic boundary conditions are…
This work focuses on recurrence and ergodicity of switching diffusions consisting of continuous and discrete components, in which the discrete component takes values in a countably infinite set and the rates of switching at current time…
In this work, we study the transient growth of the principal resolvent modes in the minimal flow unit using a reformulation of resolvent analysis in a time-localized wavelet basis. We target the most energetic spatial wavenumbers for the…
Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is…
We study the asymptotic behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the…
Foundation models, particularly Large Language Models (LLMs), have revolutionized text and video processing, yet time series data presents distinct challenges for such approaches due to domain-specific features such as missing values,…
Denoising diffusion models are a novel class of generative algorithms that achieve state-of-the-art performance across a range of domains, including image generation and text-to-image tasks. Building on this success, diffusion models have…
This paper investigates a reaction-advection-diffusion system modeling interspecific competition between two species over bounded domains. The kinetic terms are assumed to satisfy the Beddington-DeAngelis functional responses. We consider…
We propose a unified four-dimensional (4D) spatiotemporal formulation for time-dependent convection-diffusion problems that preserves underlying physical structures. By treating time as an additional space-like coordinate, the evolution…
This paper is devoted to the anomalous diffusion limit of kinetic equations with a fractional Fokker-Planck collision operator in a spatially bounded domain. We consider two boundary conditions at the kinetic scale: absorption and specular…
Diffusion Transformer (DiT), an emerging diffusion model for visual generation, has demonstrated superior performance but suffers from substantial computational costs. Our investigations reveal that these costs primarily stem from the…
Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward…
Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either…
Diffusion models have shown promising generative capabilities across diverse domains, yet aligning their outputs with desired reward functions remains a challenge, particularly in cases where reward functions are non-differentiable. Some…
We study a frequency-dependent damping model of hyper-diffusion within the generalized Langevin equation. The model allows for the colored noise defined by its spectral density, assumed to be proportional to $\omega^{\delta-1}$ at low…
We study the small-time fluctuations for diffusion processes which are conditioned by their initial and final positions, under the assumptions that the diffusivity has a sub-Riemannian structure and that the drift vector field lies in the…