Related papers: Nonlocal Models in Biology and Life Sciences: Sour…
The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes…
We consider an epidemic model with nonlocal diffusion and free boundaries, which describes the evolution of an infectious agents with nonlocal diffusion and the infected humans without diffusion, where humans get infected by the agents, and…
We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly…
Sensitivity analysis is an effective tool for systematically identifying specific perturbations in parameters that have significant effects on the behavior of a given biosystem, at the scale investigated. In this work, using a…
The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological…
Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…
In this paper, we inspect well-known population genetics and social dynamics models. In these models, interacting individuals, while participating in a self-organizing process, give rise to the emergence of complex behaviors and patterns.…
Biological systems perform an astonishing array of dynamical processes -- including development and repair, regulation, behavior and motor control, sensing and signaling, and adaptation, among others. Powered by the transduction of stored…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
Formation of organs and specialized tissues in embryonic development requires migration of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here explore a recent local approximation of nonlocal…
Much of our mechanistic understanding of the functions of biological macromolecules is based on static structural experiments, which can be modelled either as single structures or conformational ensembles. While these provide us with…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks and theoretical methods, we can begin to probe the complex lives of microscopic motile…
Biologists and physicists have a rich tradition of modeling living systems with simple models composed of a few interacting components. Despite the remarkable success of this approach, it remains unclear how to use such finely tuned models…
We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires…
We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
An important task for many if not all the scientific domains is efficient knowledge integration, testing and codification. It is often solved with model construction in a controllable computational environment. In spite of that, the…
While fields like Artificial Life have made huge strides in quantifying the mechanisms that distinguish living systems from non-living ones, particular mechanisms remain difficult to reproduce in silico. Known as open-endedness, we've been…
Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood…