Related papers: Compartmental-reaction diffusion framework for mic…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…
We present spatio-temporal characteristics of spreading depolarizations (SD) in two experimental systems: retracting SD wave segments observed with intrinsic optical signals in chicken retina, and spontaneously occurring re-entrant SD waves…
Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity…
We train a neural network to predict distributional responses in gene expression following genetic perturbations. This is an essential task in early-stage drug discovery, where such responses can offer insights into gene function and inform…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…
We study a model of interacting neurons. The structure of this neural system is composed of two layers of neurons such that the neurons of the first layer send their spikes to the neurons of the second one: if $N$ is the number of neurons…
Sub-diffusion in biological systems is conventionally treated as anomalous, requiring fractional derivatives, heavy-tailed waiting times, or fitted memory kernels. We argue that this anomaly is an artifact of an incomplete phase space.…
In view of some recent results in case of the dopaminergic neurons exhibiting long range correlations in VTA of the limbic brain we are interested to find out whether any stochastic nonlinear response may be reproducible in the nano scales…
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which…
The reaction of volatile matter plays an important role in the process of bringing matter from the surface of the planet to the atmosphere. Therefore, by simulating the mixing and chemical reaction process of volatile matter in the…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
A frequency-based omni-temporal dispersion theory is developed to capture the transient interplay between diffusion, advection, and reaction during solute transport through porous media. Unlike classical asymptotic dispersion theories,…
Motivated by compartmental analysis in engineering and biophysical systems, we present a variational framework for the nonequilibrium thermodynamics of systems involving both distributed and discrete (finite dimensional) subsystems by…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…
The theoretical basis of neuronal coding, associated with short term degradation in synaptic transmission, is a matter of debate in the literature. In fact, electrophysiological signals are commonly characterized as inversely proportional…