Related papers: Solving reaction-diffusion equations on evolving s…
A theoretical model was developed to investigate the rod phototransduction process in the mouse. In particular, we explored the biochemical reactions of several chemical components that contribute to the signaling process into/around the…
Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
We present a method for computing fluid-structure interaction problems for multi-body systems. The fluid flow equations are solved using a fractional-step method with the immersed boundary method proposed by Uhlmann [J. Comput Phys. 209…
Recently 3D hydrodynamical simulations of stellar surface convection have become feasible thanks to advances in computer technology and efficient numerical algorithms. Available observational diagnostics indicate that these models are…
In non-destructive imaging the information about the spatial pattern of a samples interior has to be transferred to the sample surface by certain waves, e.g. ultrasound or electromagnetic waves. At the sample surface these waves can be…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…
We address the problem of data augmentation in a rotating turbulence set-up, a paradigmatic challenge in geophysical applications. The goal is to reconstruct information in two-dimensional (2D) cuts of the three-dimensional flow fields,…
The Fitzhugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing to better understand the essential dynamics of the interaction of the membrane potential and the restoring force and to capture,…
In this paper we consider the mathematical relationship between nonlocal interactions of convolution type and multiple diffusive substances in high dimensions. Motivated by that the nonlocal evolution equations reproduce similar patterns to…
Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
The interaction of a protein with its environment can be understood and controlled via its 3D structure. Experimental methods for protein structure determination, such as X-ray crystallography or cryogenic electron microscopy, shed light on…
Generating physically realistic 3D molecular structures remains a core challenge in molecular generative modeling. While diffusion models equipped with equivariant neural networks have made progress in capturing molecular geometries, they…
We study convex relaxation algorithms for phase retrieval on imaging problems. We show that structural assumptions on the signal and the observations, such as sparsity, smoothness or positivity, can be exploited to both speed-up convergence…
Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently,…
In this paper we present a mathematical study of particle diffusion inside and outside a spherical biological cell that has been exposed on one side to a propagating planar diffusive front. The media inside and outside the spherical cell…
Stellar evolution is driven by the changing composition of a star from nuclear reactions. At the late stages of evolution and during explosive events, the timescale can be short and drive strong hydrodynamic flows, making simulations of…
Diffusion-based generative models in SE(3)-invariant space have demonstrated promising performance in molecular conformation generation, but typically require solving stochastic differential equations (SDEs) with thousands of update steps.…