Double stochastic wave models of multidimensional random fields

Abstract

The paper deals with the development of mathematical models of random fields to describe and simulate images. In the wave model, a random field is the result of the influence of perturbations (waves) that occur at random times in random places and have random shapes. This model allows representing and simulate isotropic and anisotropic images (and their temporal sequences) defined on arbitrary areas of multidimensional space, as well as on any surfaces. The problems of correlation analysis and synthesis can be relatively easily solved. However, this model allows representing only homogeneous fields. In this paper, we consider «double stochastic» wave models, when the first wave random field (control field) sets the parameters of the second (controlled field). As a result, the controlled field becomes nonuniform, since its parameters vary randomly. We also consider options when two fields mutually influence each other. These models allow us to represent and simulate multidimensional inhomogeneous images (and their temporal sequences), as well as systems of such images with mutual correlations.

We’re Afraid Language Models Aren’t Modeling Ambiguity

“…there are often issues of ambiguous or underspecified event and entity references (Min et al, 2020;Cole et al, 2023), leading to work on generating clarification questions (Kuhn et al, 2023;Krasheninnikov et al, 2022). In particular, our approach to ambiguity is inspired by AMBIGQA (Min et al, 2020), where the task input is disambiguated in natural language to account for variation in possible outputs.…”