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How many times a diffusing molecule can permeate across a membrane or be adsorbed on a substrate? We employ the encounter-based approach to find the statistics of adsorption or permeation events for molecular diffusion in a general…
Solving 3D medical inverse problems such as image restoration and reconstruction is crucial in modern medical field. However, the curse of dimensionality in 3D medical data leads mainstream volume-wise methods to suffer from high resource…
The problem of resolving point-like light sources not only serves as a benchmark for optical resolution but also holds various practical applications ranging from microscopy to astronomy. In this research, we aim to resolve two thermal…
This paper considers the optimal sensor allocation for estimating the emission rates of multiple sources in a two-dimensional spatial domain. Locations of potential emission sources are known (e.g., factory stacks), and the number of…
This paper introduces and solves the simultaneous source separation and phase retrieval (S$^3$PR) problem. S$^3$PR is an important but largely unsolved problem in a number application domains, including microscopy, wireless communication,…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
Cell nuclei segmentation is one of the most important tasks in the analysis of biomedical images. With ever-growing sizes and amounts of three-dimensional images to be processed, there is a need for better and faster segmentation methods.…
Particle diffusion in a two dimensional curved surface embedded in $R_3$ is considered. In addition to the usual diffusion flow, we find a new flow with an explicit curvature dependence. New diffusion equation is obtained in $\epsilon$…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
Source localization is widely used in many areas including GPS, but the influence of possible noises is not so negligible. Many optimization methods are attempted to alleviate different kinds of noises. Needless to say the stability of the…
In this paper, we apply dimensional analysis to study a diffusive molecular communication system that uses diffusing enzymes in the propagation environment to mitigate intersymbol interference. The enzymes bind to information molecules and…
We consider an inverse source problem in the two-time-scale mobile-immobile fractional diffusion model from partial interior observation. Theoretically, we combine the fractional Duhamel's principle with the weak vanishing property to…
This paper presents a two-step approach for narrowband source localization within reverberant rooms. The first step involves dereverberation by modeling the homogeneous component of the sound field by an equivalent decomposition of…
Diffusion models have recently emerged as a powerful technique in image generation, especially for image super-resolution tasks. While 2D diffusion models significantly enhance the resolution of individual images, existing diffusion-based…
Image stitching is typically decomposed into three phases: registration, which aligns the source images with a common target image; seam finding, which determines for each target pixel the source image it should come from; and blending,…
During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases,…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…
We study the angle-resolved spontaneous emission of near-infrared light sources in 3D photonic crystals over a wavelength range from 1200 to 1550 nm. To this end PbSe quantum dots are used as light sources inside titania inverse opal…
Designing a single molecule that modulates two targets is a promising strategy for polypharmacology, but it remains substantially harder than standard single-target generation because one candidate must satisfy two binding requirements…
We seek to give users precise control over diffusion-based image generation by modeling complex scenes as sequences of layers, which define the desired spatial arrangement and visual attributes of objects in the scene. Collage Diffusion…