Related papers: Stromatolites: why do we care?

We consider the numerical solution of coupled volume-surface reaction-diffusion systems having a detailed balance equilibrium. Based on the conservation of mass, an appropriate quadratic entropy functional is identified and an…

SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…

We analyse the behaviour of thin composite plates whose material properties vary periodically in-plane and possess a high degree of contrast between the individual components. Starting from the equations of three-dimensional linear…

We investigate the elastic properties of small droplets under compression. The compression of a bubble by two parallel plates is solved exactly and it is shown that a lowest-order expansion of the solution reduces to a form similar to that…

This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…

Quantum--Mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those…

Data deduplication saves storage space by identifying and removing repeats in the data stream. Compared with traditional compression methods, data deduplication schemes are more time efficient and are thus widely used in large scale storage…

High-energy scattering spectroscopy is a widely-established technique for probing the characteristic properties of complex physical systems. Motivated by the recent observation of long-sought supersolid states in dipolar quantum Bose gases,…

When analyzing cell trajectories, we often have to deal with noisy data due to the random motion of the cells and possible imperfections in cell center detection. To smooth these trajectories, we present a mathematical model and numerical…

We study the elasto-plastic behavior of dense attractive emulsions under mechanical perturbation. The attraction is introduced through non-specific depletion interactions between the droplets and is controlled by changing the concentration…

Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed…

Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…

We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…

How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on…

We consider two volume-surface reaction-diffusion systems arising from cell biology. The first system describes the localisation of the protein Lgl in the asymmetric division of Drosophila SOP stem cells, while the second system models the…

Epitaxial growth methods are a key technology used in producing large-area thin films on substrates but as a result of various factors controlling growth processes the rational optimization of growth conditions is rather difficult.…

Aligning diffusion models with user preferences has been a key challenge. Existing methods for aligning diffusion models either require retraining or are limited to differentiable reward functions. To address these limitations, we propose a…

Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers.We use a series of related theoretical investigations to probe the origin of these…

Multivariate entropy quantification algorithms are becoming a prominent tool for the extraction of information from multi-channel physiological time-series. However, in the analysis of physiological signals from heterogeneous organ systems,…