Related papers: Pattern alternations induced by nonlocal interacti…
It is crucial to detect when an instance lies downright too far from the training samples for the machine learning model to be trusted, a challenge known as out-of-distribution (OOD) detection. For neural networks, one approach to this task…
Dryland vegetation ecosystems are known to be susceptible to critical transitions between alternative stable states when subjected to external forcing. Such transitions are often discussed through the framework of bifurcation theory, but…
Deep neural networks are vulnerable to adversarial examples (AEs), which have adversarial transferability: AEs generated for the source model can mislead another (target) model's predictions. However, the transferability has not been…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical…
Coevolutionary arms races form between interacting populations that constitute each other's environment and respond to mutual changes. This inherently far-from-equilibrium process finds striking manifestations in the adaptive immune system,…
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…
The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to…
We consider a two dimensional Turing like system with two diffusing species which interact with each other. Considering the species to be charged, we include the effect of an electric field along a given direction which can lead to a drift…
The main objective of this article is to study the three-dimensional Rayleigh-Benard convection in a rectangular domain from a pattern formation perspective. It is well known that as the Rayleigh number crosses a critical threshold, the…
Reaction-Diffusion (RD) systems provide a computational framework that governs many pattern formation processes in nature. Current RD system design practices boil down to trial-and-error parameter search. We propose a differentiable…
Stochastic modelling provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. In practice, the common challenge is to calibrate a large number of model parameters against the…
We study Turing bifurcations on one-dimensional random ring networks where the probability of a connection between two nodes depends on the distance between the two nodes. Our approach uses the theory of graphons to approximate the graph…
The study of reaction-diffusion systems on networks is of paramount relevance for the understanding of nonlinear processes in systems where the topology is intrinsically discrete, such as the brain. Until now reaction-diffusion systems have…
Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is…
Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor…
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,…
Recently, evolving networks are becoming a suitable form to model many real-world complex systems, due to their peculiarities to represent the systems and their constituting entities, the interactions between the entities and the…
In population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this Letter, we study a reaction-diffusion (RD) model of population growth and dispersion in one dimension, which incorporates…