Related papers: Estimation of Parameter Distributions for Reaction…

The density ratio model (DRM) is a semiparametric model that relates the distributions from multiple samples to a nonparametrically defined reference distribution via exponential tilting, with finite-dimensional parameters governing their…

Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…

In recent years, discrete fractional epidemic models with reaction-diffusion have become increasingly popular in the literature, not only for its necessity of numerical simulation, but also for its defined physical processes. In this paper,…

Diffusion Probabilistic Models (DPMs) have achieved significant success in generative tasks. However, their training and sampling processes suffer from the issue of distribution mismatch. During the denoising process, the input data…

The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…

We develop a new method for multivariate scalar on multidimensional distribution regression. Traditional approaches typically analyze isolated univariate scalar outcomes or consider unidimensional distributional representations as…

Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…

We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW) we formulate a system of the balance equations for the cancer cells…

This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…

The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction-radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the…

Generative adversarial networks constitute a powerful approach to generative modeling. While generated samples often are indistinguishable from real data, there is no guarantee that they will follow the true data distribution. For…

Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states,…

Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…

In a mathematical model of interacting biological organisms, where external interventions may alter behavior over time, traditional models that assume fixed parameters usually do not capture the evolving dynamics. In oncology, this is…

The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…

Longitudinal imaging analysis tracks disease progression and treatment response over time, providing dynamic insights into treatment efficacy and disease evolution. Radiomic features extracted from medical imaging can support the study of…

A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material,…

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…