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We present an asymptotic analysis of a stochastic two-compartmental cell division system with regulatory mechanisms inspired by Getto et al. (2013). The hematopoietic system is modeled as a two-compartment system, where the first…

Medical image segmentation is crucial for clinical diagnosis and treatment planning. Traditional methods typically produce a single segmentation mask, failing to capture inherent uncertainty. Recent generative models enable the creation of…

Separating shared and independent features is crucial for multi-phase contrast-enhanced (CE) MRI synthesis. However, existing methods use deep autoencoder generators with low parameter efficiency and lack interpretable training strategies.…

Dynamic contrast-enhanced (DCE) MRI is essential for breast cancer diagnosis and treatment. However, its reliance on contrast agents introduces safety concerns, contraindications, increased cost, and workflow complexity. To this end, we…

Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…

We present a new modeling approach for G protein coupled receptors signaling systems, that take into account the compartmentalization of receptors and their effectors, both at plasma membrane and in dynamic intra-cellular vesicles called…

We extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state hybrid DFT (ngH-DFT) to calculate absorption spectra within linear-response time-dependent Generalized Kohn-Sham DFT (LR-GKS-TDDFT), for…

The electronic structure of the molecular compound (TTM-TTP)I_3, which exhibits a peculiar intra-molecular charge ordering, has been studied using multi-configuration ab initio calculations. First we derive an effective Hubbard-type model…

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…

Diffusion Probabilistic Models (DPMs) suffer from inefficient inference due to their slow sampling and high memory consumption, which limits their applicability to various medical imaging applications. In this work, we propose a novel…

Despite the widespread use of deep learning methods for semantic segmentation of images that are acquired from a single source, clinicians often use multi-domain data for a detailed analysis. For instance, CT and MRI have advantages over…

The reaction-diffusion master equation (RDME) is a lattice stochastic reaction-diffusion model that has been used to study spatially distributed cellular processes. The RDME is often interpreted as an approximation to spatially-continuous…

Automatic liver segmentation plays an important role in computer-aided diagnosis and treatment. Manual segmentation of organs is a difficult and tedious task and so prone to human errors. In this paper, we propose an adaptive 3D region…

We introduce a novel approach for estimating Latent Dirichlet Allocation (LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full conditional distributions over the latent variable assignments to efficiently average over…

Diffusion probabilistic model (DPM) recently becomes one of the hottest topic in computer vision. Its image generation application such as Imagen, Latent Diffusion Models and Stable Diffusion have shown impressive generation capabilities,…

Quantum many-body systems may defy thermalization even without disorder. Intriguingly, non-ergodicity may be caused by a fragmentation of the many-body Hilbert-space into dynamically disconnected subspaces. The tilted one-dimensional…

Physics-guided sampling with diffusion priors has recently shown strong performance in solving complex systems of partial differential equations (PDEs) from sparse observations. However, these methods are typically evaluated on benchmark…

This paper proposes a novel low-rank approximation to the multivariate State-Space Model. The Stochastic Partial Differential Equation (SPDE) approach is applied component-wise to the independent-in-time Mat\'ern Gaussian innovation term in…

In this paper, we present a novel numerical framework for solving a specific biological reaction-diffusion-advection system of cancer growth in three dimensions (3D) using particles of variable mass. We adopt empirical particle measures to…

Despite its benefits for tumour detection and treatment, the administration of contrast agents in dynamic contrast-enhanced MRI (DCE-MRI) is associated with a range of issues, including their invasiveness, bioaccumulation, and a risk of…