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Due to the high complexity and technical requirements of industrial production processes, surface defects will inevitably appear, which seriously affects the quality of products. Although existing lightweight detection networks are highly…

Anomalous diffusion phenomena have been observed in many complex physical and biological systems. One significant advance recently is the physical extension of particle's motion in static medium to uniformly (and even nonuniformly)…

Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not…

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…

We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…

It is well known that, in the study of the dynamical properties of nonlinear reaction-diffusion systems, the sign of the principal eigenvalue of the linearized system plays an important role. However, for the nonlocal dispersal systems, due…

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

I study partial identification of distributional parameters in triangular systems. This model consists of a nonparametric outcome equation and a selection equation. This allows for general unobserved heterogeneity and selection on…

Diffusion models have emerged as powerful tools for high-quality image generation and editing, but guiding these models to produce specific outputs remains a challenge. Conventional approaches rely on conditioning mechanisms, such as text…

Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed…

We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds…

Earth System Models (ESMs) are essential for understanding the interaction between human activities and the Earth's climate. However, the computational demands of ESMs often limit the number of simulations that can be run, hindering the…

The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…

Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…

Most research designing novel predictive models, or employing existing ones, assumes that training and testing data are independent and identically distributed. In practice, the data encountered at serving time often deviate from the…

The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional…

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…

Understanding visual scenes is fundamental to human intelligence. While discriminative models have significantly advanced computer vision, they often struggle with compositional understanding. In contrast, recent generative text-to-image…

Earth System Models (ESMs) are essential tools for understanding the impact of human actions on Earth's climate. One key application of these models is studying extreme weather events, such as heat waves or dry spells, which have…

In this paper we propose a new state observer design technique for nonlinear systems. It consists of an extension of the recently introduced parameter estimation-based observer, which is applicable for systems verifying a particular…