7 problems

Equality conjecture. The expected adoption levels are identical:

Let $\vec{z}_t$ denote the disagreement component of the opinion vector at time $t$, and let $\lambda$ be the parameter appearing in the model. Here $\mathbb{E}$ denotes expectatio…

For each positive external influence rate $p$ and internal influence rate $q$, let $f_d(t;p,q)$ be the diffusion curve on an infinite homogeneous Cartesian network of dimension $d$…

Let an infinite homogeneous Cartesian network have dimension $d$, with external influence rate $p>0$ and total internal influence rate $q>0$. Let $f_d(t;p,q)$ denote its diffusion…

Uniform boundedness and compact-support conjecture. In a globally optimal solution, all departure rates $\bar u_{k,p}$ are uniformly bounded and have compact support.

Let $V$ be the finite set of agents, let $X_v(t)$ be the estimator of agent $v$ at time $t$ in the model where agents retain their previous values, and let $X(\infty)$ denote the l…

Let $V$ be the finite set of agents, let $X_v(t)$ denote the estimator held by agent $v\in V$ at iteration $t$, and let $X(\infty)$ be a common limiting estimator. Convergence conj…