Arid ecosystems are liable to undergo sudden discontinuous transitions from a vegetated to a desert state as a result of human pressure and climate change. A predictive framework about the conditions under which such transitions occur is lacking. Here, we derive and analyze a general model describing the spatial dynamics of vegetation in arid ecosystems considering local facilitation as an esse...

Horn's model is generalized to state that the "optimal" pattern o f distribution for foragerswill correlate with the degree o f resource patchiness; in particular (1) where resource attributes are less patchy, the "optimal" distribution for foragers is to be dispersed, and (2) where resource attributes are more patchy, the "optimal" distribution for foragers is to be aggregated. "Optimality" is...

Patches (lateral heterogeneities) of cell surface membrane proteins and lipids have been imaged by a number of different microscopy techniques. This patchiness has been taken as evidence for the organization of membranes into domains whose composition differs from the average for the entire membrane. However, the mechanism and specificity of patch formation are not understood. Here we show how ...

We prove that the K-k-Schur functions are part of a family inhomogenous symmetric whose top homogeneous components Catalan functions, Euler characteristics certain vector bundles on flag variety. Lam-Schilling-Shimozono identified as Schubert representatives for K-homology affine Grassmannian SLk+1. Our perspective reveals satisfy shift invariance property, and we deduce positivity their branch...