9 problems

Let $\Gamma$ and $H$ be smooth functions with all derivatives bounded, and let the initial data be correspondingly regular and compatible. Let $\mathrm{Red}_\varepsilon$ denote the…

Asymptotic critical-line conjecture. There is a critical line asymptotically as $\kappa \to \infty$.

Let a social network evolve through a minor adjustment of its network structure, and let the consensus time denote the time required for the system to reach consensus. Consensus-sp…

Heterogeneous-network VFPE conjecture. For heterogeneous networks, the Vlasov–Fokker–Planck equation associated with the stochastic network should be

The paper studies multiscale dynamics in adaptive networks, including continuous-time and continuous-state-space systems with a slowly varying network weight. Multiscale network-sc…

The paper considers adaptive networks with a linear average consensus protocol, including a slowly varying edge whose weight may range over the real numbers. The resulting dynamics…

Giant-component formation-time conjecture. As $d\to+\infty$ in the giant-component regime, the formation of an initial cycle and the formation of an autocatalytic set are respectiv…

Fast ACS-formation conjecture. If $dp>1$ and the process starts from a typical cycle, then formation of a single ACS according to the JK update requires at most ${\mathcal O}(1)$ t…

Fast cycle-formation conjecture. If $dp>1$, then formation of a cycle according to the Jain–Krishna update requires ${\mathcal O}(1)$ time steps as $d\to\infty$ with $dp$ kept cons…