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Applications of diffusion models for visual tasks have been quite noteworthy. This paper targets making classification models more robust to occlusions for the task of object recognition by proposing a pipeline that utilizes a frozen…
We first review classical results on cloaking and mirage effects for electromagnetic waves. We then show that transformation optics allows the masking of objects or produces mirages in diffusive regimes. In order to achieve this, we…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…
This paper presents a new method for determining the diffusive properties of diffuse body waves, specifically diffusivity and dissipation, in concrete with multiple planar boundaries. Instead of relying on the analytical solution to the…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
Transparent glass ceramic materials, with microstructures comprised of dispersed nanocrystallites in a residual glass matrix, offer the prospect of nonlinear optical properties. However, good transparency requires low optical scattering and…
On the basis of general theoretical results developed previously in [JETP 112, 246 (2011)], we analyze the reflection of quasiresonant light from a plane surface of dense and disordered ensemble of motionless point scatters. Angle…
We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…
Human body restoration plays a vital role in various applications related to the human body. Despite recent advances in general image restoration using generative models, their performance in human body restoration remains mediocre, often…
The paradigmatic model for heterogeneous media used in diffusion studies is built from reflecting obstacles and surfaces. It is well known that the crowding effect produced by these reflecting surfaces slows the dispersion of Brownian…
Diffusion models have achieved remarkable progress in generative modelling, particularly in enhancing image quality to conform to human preferences. Recently, these models have also been applied to low-level computer vision for…
We define and study on Lorentz manifolds a family of covariant diffusions in which the quadratic variation is locally determined by the curvature. This allows the interpretation of the diffusion effect on a particle by its interaction with…
Realistic modeling of scattering from curved metallic bodies - such as vehicles and roadside structures - is essential for cellular and vehicular channel modeling as well as radar applications. A practical approach is to approximate curved…
The diffusion of particles in confining walls forming a tube is discussed. Such a transport phenomenon is observed in biological cells and porous media. We consider the case in which the tube is winding with curvature and torsion, and the…
Using event-driven molecular dynamics simulations, we quantify how the self diffusivity of confined hard-sphere fluids depends on the nature of the confining boundaries. We explore systems with featureless confining boundaries that treat…
Considering the diffraction of a plane wave by a periodically corrugated half-space, we show that the transformation of the refracting medium from positive/negative phase-velocity to negative/positive phase-velocity type has an influence on…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
Image-based virtual try-on is an increasingly important task for online shopping. It aims to synthesize images of a specific person wearing a specified garment. Diffusion model-based approaches have recently become popular, as they are…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
In finite-volume-based flow simulations, absorbing layers are widely used to reduce pressure wave reflections at boundaries of the computational domain. A disadvantage of absorbing layers is that they contain case-dependent parameters; thus…