J. C. Tzou

TL;DR: The hybrid approach has the advantage of eliminating the difficulty with resolving small spatial scales in a full numerical treatment of the partial differential equation (PDE).

TL;DR: A quantitative treatment of receptor triggering reliant only on TCR dwell time in phosphatase-depleted cell contacts constrained in area by cell topography is developed and tested and it is found that ligand discrimination likely depends crucially on individual contacts being ∼200 nm in radius, matching the dimensions of the surface protrusions used by T cells to interrogate their targets.

TL;DR: High-order asymptotic formulas for the MFPT and the fundamental eigenvalue of the Laplacian are derived and it is found that subdividing the absorbing portions of the trap reduces the mean first passage time of the diffusing particle.

TL;DR: In this article, the authors argue that the deciding factors are the speed of resource depletion and the amount of the background noise (seasonal climate changes) in the system, and illustrate this phenomenon on a model of patterned vegetation.

TL;DR: In this paper, the authors analyzed the delay effect in partial differential equations (PDE) and showed that the system must pass well into the unstable regime before the onset of instability is fully observed, indicating delay.