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We propose a novel approach for probabilistic generative modeling of 3D shapes. Unlike most existing models that learn to deterministically translate a latent vector to a shape, our model, Point-Voxel Diffusion (PVD), is a unified,…
We study solute-laden flow through permeable geological formations with a focus on advection-dominated transport and volume reactions. As the fluid flows through the permeable medium, it reacts with the medium, thereby changing the…
In this study, we model avascular tumour growth in epithelial tissue. This can help us to get a macroscopic view of the interaction between the tumour with its surrounding microenvironment and the physical changes within the tumour…
The present work revisits the problem of modeling diffusion above a stagnant liquid interface in a capillary tube geometry. In this revisitation we elucidate a misconception found in the classical model proposed by Bird et. al. Furthermore,…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface…
This paper presents a model of van der Waals forces in the framework of diffusion-convection equations. The model consists of a nonlinear and degenerated diffusion-convection equation, which furthermore can be considered as a model for slow…
A new mathematical model and numerical approach are proposed for the simulation of fluid and chemical exchanges between a growing capillary network and the surrounding tissue, in the context of tumor-induced angiogenesis. Thanks to proper…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…
The manifestation of symptoms associated with lung diseases can vary in different depths for individual patients, highlighting the significance of 3D information in CT scans for medical image classification. While Vision Transformer has…
Recent advances in diffusion models have set an impressive milestone in many generation tasks, and trending works such as DALL-E2, Imagen, and Stable Diffusion have attracted great interest. Despite the rapid landscape changes, recent new…
In this paper, we argue that iterative computation with diffusion models offers a powerful paradigm for not only generation but also visual perception tasks. We unify tasks such as depth estimation, optical flow, and amodal segmentation…
Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…
Mathematical modeling is an important theoretical tool which provides researchers with quantification of the permeability of dialyzing systems in renal replacement therapy. In the paper we provide a short review of the most successful…
The study of interactions between biomimetic membranes and micron-sized particles is crucial for understanding various biological processes. Here, we control microparticle spontaneous engulfment by giant lipid vesicles by tuning particle…
In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…
Diffusion models have been central to the development of recent image, video, and even text generation systems. They posses striking geometric properties that can be faithfully portrayed in low-dimensional settings. However, existing…
The dynamics of compressible liquid-vapor flow depends sensitively on the microscale behavior at the phase boundary. We consider a sharp-interface approach, and propose a multiscale model to describe liquid-vapor flow accurately, without…
The goal of this paper is to extract the visual-language correspondence from a pre-trained text-to-image diffusion model, in the form of segmentation map, i.e., simultaneously generating images and segmentation masks for the corresponding…