in this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the gray-scott model, in which spot patterns have been observed. we focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. a complete bifurcation study of these solutions is presented. the main mathematic...

Modeling non-linear data as symmetric positive definite (SPD) matrices on Riemannian manifolds has attracted much attention for various classification tasks. In the context of deep learning, SPD matrix-based networks have been shown to be a promising solution classifying electroencephalogram (EEG) signals, capturing geometry within their structured 2D feature representation. However, existing a...

the significance of spatial heterogeneity in understanding ecological processes has been recognized long ago. one of the earliest expressions of this recognition is the habitat heterogeneity hypothesis that links spatial  heterogeneity to niche vegetation patterns formation and species coexistence. yet, an  important if not crucial  aspect of landscape heterogeneity has escaped deep considerati...

Poverty can have spatial dimensions. While general figures might show the spatial pattern of poverty, there is a need for more detailed examination of this pattern. Relying on simple figures of spatial patterns and ranking regions based on them might be misleading. This paper tries to apply spatial analysis methodsm, namely spatial autoregressive models to find out the impacts of space on the h...