Related papers: Coupling vs decoupling approaches for PDE/ODE syst…
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or…
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling…
We analyze oscillatory instabilities for a coupled PDE-ODE system modeling the communication between localized spatially segregated dynamically active signaling compartments that are coupled through a passive extracellular bulk diffusion…
Cellular signaling is essential in information processing and decision making. Therefore, a variety of experimental approaches have been developed to study signaling on bulk and single-cell level. Single-cell measurements of signaling…
Cell movement and intercellular signaling occur simultaneously during the development of tissues, but little is known about how movement affects signaling. Previous theoretical studies have shown that faster moving cells favor…
Many physical systems are governed by ordinary or partial differential equations (see, for example, Chapter ''Differential equations'', ''System of Differential Equations''). Typically the solution of such systems are functions of time or…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
Cell association in cellular networks has traditionally been based on the downlink received signal power only, despite the fact that up and downlink transmission powers and interference levels differed significantly. This approach was…
The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a…
Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…
In order to cope with the ever increasing traffic load that networks will need to support, a new approach for planning cellular networks deployments should be followed. Traditionally, cell association and resource allocation has been based…
We study decoupled numerical methods for multi-domain, multi-physics applications. By investigating various stages of numerical approximation and decoupling and tracking how the information is transmitted across the interface for a typical…
Multistationarity in molecular systems underlies switch-like responses in cellular decision making. Determining whether and when a system displays multistationarity is in general a difficult problem. In this work we completely determine the…
In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the…
Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal…
Our traditional notion of a cell is changing dramatically given the increasing degree of heterogeneity in 4G and emerging 5G systems. Rather than belonging to a specific cell, a device would choose the most suitable connection from the…
The model of coupled oscillators plays an important role in modern physics. It is used for description of various processes: from vibrations atoms in solid states to electromagnetic oscillations in slow-wave structures. The model with…
Motivation: Modeling biological signaling networks using ordinary differential equations (ODEs) has proven to be a powerful technique for generating insight into cellular dynamics, but it typically requires estimating rate parameters based…
Both stochastic and PDE modeling approaches have been used and compared in various context in biology. Typically, stochastic models are easier to parameterize, can be used to integrate underlying biological phenomena, but hard to analyze…
Downlink/Uplink decoupling (DUDe) in LTE net- works has caught the attention of researchers as it provides better uplink SINR and reduced power consumption per device due to decoupled connection of a device with the Macro (in downlink) and…