Related papers: Nonlocal Models in Biology and Life Sciences: Sour…
Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and…
The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migration of cell populations driven by this non-local form of…
Preliminary research in the area of biophysics appears to indicate the existence of quantum entanglement and nonlocality at the biological level, both for human subjects and for neurons derived from human neural stem cells. The lack of…
Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate…
Quantitative modeling has become an essential tool in modern biophysics, driven by advances in both experimental techniques and theoretical frameworks. Powerful high-resolution techniques now provide detailed datasets spanning molecular to…
Integral-type nonlocal damage models describe the fracture process zones by regular strain profiles insensitive to the size of finite elements, which is achieved by incorporating weighted spatial averages of certain state variables into the…
A nonlocal vector calculus was introduced in [2] that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A generalization is developed that provides a more general setting for…
Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than…
In this manuscript, we consider the modelling of cellular adhesions, which is a key interaction between biological cells. Continuum models of the diffusion-advection-reaction type have long been used in tissue modelling. In 2006, Armstrong,…
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted $H^1$-semi norm to model the local part, while two different weighted $H^s$-semi norms,…
The current science of cities can provide a useful foundation for future urban policies, provided that these proposals have been validated by correct observations of the diversity of situations in the world. However, international…
Quantum mechanical nonlocality considered as posssible mechanism of long-distance correlations in living organisms and plants, which regulate their coherent development and functioning. It's shown that Doebner-Goldin nonlinear quantum…
This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…
This work studies a nonlocal extension of the Klausmeier vegetation model in $\mathbb{R}^N$ $(N \ge 1)$ that incorporates both local and nonlocal diffusion. The biomass dynamics are driven by a nonlocal convolution operator, representing…
Clinical management of cancer has continuously evolved for several decades. Biochemical, molecular and genomics approaches have brought and still bring numerous insights into cancerous diseases. It is now accepted that some phenomena,…
Many cognitive neuroscience studies use large feature sets to predict and interpret brain activity patterns. Feature sets take many forms, from human stimulus annotations to representations in deep neural networks. Of crucial importance in…
We present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into a control problem where the states are the solutions of the nonlocal and local equations, the…
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…