In the averaging-plus-learning dynamics Xₜ₊₁=AXₜ+E(barσ-Xₜ) of Popescu and Vaidya, n agents average their neighbours' opinions with the weights of a row-stochastic matrix A while each is pulled towards an external ground truth barσ at its own learning rate…
Fixed-step gradient descent with step size a on the double-well loss 1/4(x²-1)² is the odd cubic map gₐ(x)=(1+a)x-ax³. Hofmann (arXiv:2607.04993) uses it as the scalar core of a hierarchy of solvable learning models: the edge of stability a=1 is its first f…
Joshi and Roffelsen have shown that the q-discrete first Painlevé equation, resolved on Sakai's initial value space, defines a bijection of a set of (q+1)² points over a finite field 𝔽_q, and they conjecture on the strength of a Magma computation over ever…
For d ≥ 2 let f_(c)(z) = zᵈ+c, let Mₙ ∈ ℤ[c,λ] be the n-th multiplier polynomial of this family and let Δₙ = disc_(λ) Mₙ ∈ ℤ[c]. Huguin factors Δₙ = aₙ Qₙ Rₙ² with aₙ a squarefree integer, the roots of Qₙ being the parameters at which f_(c) has a cycle of p…
Mukwembi's graph-based model of HIV infection is a deterministic three-state cellular automaton on a graph G, driven by one integer parameter R, the rate at which depleted cells are replenished. Its extinction set E(G) is the set of those R for which the in…
