Related papers: Nonlinear diffusion processes: geometric ideas and…
The Comments are devoted to the paper ``Solutions of Multitime Reaction-Diffusion PDE'' (Mathematics, vol. 10 (2022), 3623), in which main results are misleading and can be derived in a simple way from those obtained earlier. Moreover, it…
This is an expository paper about applications of ruled surface theory in incidence geometry. It surveys the results that have been proven, gives an overview of the methods, and discusses some open problems and further directions. It will…
Positional reasoning is the process of ordering unsorted parts contained in a set into a consistent structure. We present Positional Diffusion, a plug-and-play graph formulation with Diffusion Probabilistic Models to address positional…
Generative artificial intelligence (AI) refers to algorithms that create synthetic but realistic output. Diffusion models currently offer state of the art performance in generative AI for images. They also form a key component in more…
We construct non-symmetric diffusion processes associated with Dirichlet forms consisting of uniformly elliptic forms and derivation operators with killing terms on RCD spaces by aid of non-smooth differential structures introduced by Gigli…
In this Letter, we employ the complex screen method to investigate the dynamic evolution of partially coherent pulses with specified properties as they propagate through a nonlinear Kerr medium. Our results reveal that partially coherent…
We revise the format proposed by Bowen in [R.~M. Bowen. Int. J. Eng. Sci., 18(9):1129--1148, 1980.] to describe incompressible porous media by use of the theory of mixtures. We then show that this format is equivalent the those proposed…
We propose a discussion on the synthesis and scattering analysis of nonlinear metasurfaces. For simplicity, we investigate the case of a second-order nonlinear isotropic metasurface possessing both electric and magnetic linear and nonlinear…
Deep generative models have garnered significant attention in low-level vision tasks due to their generative capabilities. Among them, diffusion model-based solutions, characterized by a forward diffusion process and a reverse denoising…
This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in the paper…
We introduce a new method for the estimation of the angular parameters [i.e., central directions of arrival (DOAs) and angular spreads] of multiple non-circular and incoherently-distributed (ID) sources and thoroughly analyze its…
Non-Gaussian shapes, despite a linear form of the mean-squared displacement, have been observed for the displacement distribution in a large range of diffusive systems. Stochastic models for such "Brownian yet non-Gaussian" diffusion will…
This article is a survey article that gives detailed constructions and illustrations of some of the standard examples of non-orientable surfaces that are embedded and immersed in 4-dimensional space. The illustrations depend upon their…
Spatial branching processes became increasingly popular in the past decades, not only because of their obvious connection to biology, but also because superprocesses are intimately related to nonlinear partial differential equations.…
The analysis of diffusion processes in real-world propagation scenarios often involves estimating variables that are not directly observed. These hidden variables include parental relationships, the strengths of connections between nodes,…
We survey the field of nonparametric inference under shape constraints, providing a historical overview and a perspective on its current state. An outlook and some open problems offer thoughts on future directions.
Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…
Diffusion models have emerged as the leading paradigm in generative modeling, excelling in various applications. Despite their success, these models often misalign with human intentions and generate results with undesired properties or even…
This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the…
Our purpose is to obtain gradient estimates for certain nonlinear partial differential equations by coupling methods. First we derive uniform gradient estimates for a certain semi-linear PDEs based on the coupling method introduced in Wang…