8 problems

Let the H-K particle model be a bounded-confidence opinion dynamics model with confidence radius $R$, and consider its final clusters. 2R-conjecture. The final clusters typically f…

Approximation conjecture. There exist $\mathbf{x}'\in C_\delta(\mathbf{x})$, a sequence $\{\gamma^{(\ell)}\}_\ell$, and a sequence $\{\mathbf{x}^{(\ell)}\}_\ell$ such that

Let $K$ denote the equilibrium number of opinion groups, and consider cycles and prism graphs with an increasing proportion of random edges. Complete-graph approximation conjecture…

Let $K$ denote the number of opinion groups at equilibrium, and consider cycles with random edges, where the proportion of random edges measures the amount of added randomness. Ran…

Let $N$ be the number of nodes in a cycle, $c$ the confidence bound, $m$ the parameter governing the Deffuant dynamics, and $T$ the convergence time. Eventual convergence conjectur…

Let an Eulerian HK system have a uniform initial mass distribution $mu_0$ supported on a closed interval, and let the input satisfy…

Let $n$ be a positive integer, let $\triangle^{n-1}\subset\mathbb R^n$ be the simplex of opinion distributions, and let $(p(t))_{t\in\mathbb N_0}$ be the interactive Hegselmann–Kra…

Let $n$ be a positive integer, let $\triangle^{n-1}\subset\mathbb R^n$ be the simplex of opinion distributions, and let $(p(t))_{t\in\mathbb N_0}$ be the interactive Deffuant–Weisb…