Applied Analysis Seminar Radialization in Iterative Convolution-Thresholding Dynamics
- Donnerstag, 12. November 2026, 15:00 Uhr
- Mathematikon, Im Neuenheimer Feld 205, Seminar Room 2
- Mirabel Reid (TU Darmstadt)
Adresse
Mathematikon
Im Neuenheimer Feld 205
Seminar Room 2Veranstaltungstyp
Vortrag
We study a discrete-time spatially extended dynamical system motivated by the continuum limit of binary neuron networks on geometric random graphs. The model evolves a function ψ: Rᵈ → [0,1] by iterative smoothing and sharpening; that is, ψt+1 = γt ∘ (g ∗ ψt), where g is a radial convolution kernel and γt is a monotone map. Under mild regularity conditions on g and γt, we prove that ψt tends toward radial symmetry in the limit as time goes to infinity. Notably, a special case of this process recovers the Merriman–Bence–Osher (MBO) scheme for the motion of interfaces by mean curvature, and we provide a novel analysis of its behavior. Our results connect the dynamics of spatial binary neuron networks with classical models of interface motion, and we establish general conditions under which spatial dependence drives activity toward radial symmetry.