19 problems

Influence submodularity conjecture. The function $\sigma$ is submodular.

Let $\mathcal{N}$ denote the target state set of the two-queue system, and consider anti-cooperative social network structures. Persistence conjecture. Anti-cooperative social netw…

Consider a system in which information fidelity is locally averaged within clusters and globally transported by bridge nodes. Universality conjecture. Any such system will exhibit…

Let $F_i(t)\in[0,1]$ denote the information fidelity at node $i$ of a multiplex network with three communication layers, and let $D_i^{(\ell)}[\{F_j\}]$ be the layer-specific socia…

Let a thresholded chimpanzee social-interaction network be represented by a graph whose vertices are individuals and whose cliques are sets of individuals with pairwise social conn…

For a graph $G$, let each node initially hold one token. In each round, with probability $1-q$ for a constant $0<q<1$, all tokens at a node remain there, and with probability $q$,…

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…

The coevolutionary dynamics involve opinions, actions, an opinion-weight parameter $\lambda$, and the innovation and status quo actions. When $\lambda$ is sufficiently large, opini…

The work studies adaptive diffusion protocols on the infinite $d$-regular tree $\mathbb{T}_{d}$, with $d\geq 3$, where an adversary observes multiple independent snapshots to detec…

Scenario B long-jump conjecture. In scenario B, the infection will take long jumps between communities.

In the revealed belief model, agents broadcast their full beliefs rather than estimates of the state. Polynomial-precision revealed-belief conjecture. If the agents broadcast their…

Multilayer random-network conjecture. Under these conditions,

Random-network ideality conjecture. As $L_1$ and $L_2$ increase, for $L_1/L_2>1$ and arbitrary $p$, the probability that the final estimate is ideal satisfies

Bias propagation conjecture. The biases of agents that communicate their estimates to many agents downstream should be disproportionately represented in the final estimate.

High-variance network conjecture. For the final estimate to have large variance, some upstream agents should have a disproportionately large out-degree, while the remaining agents…

Strong triadic closure hypothesis. If two pairs of actors in a triad are strongly tied, then the third pair will tend to be at least weakly tied.

Triangle-ordering conjecture. Ordering the vertices from largest to smallest by their triangle number $tr(v)$ should give vertices that are more constrained in their choices of col…

Complete-network conjecture. A complete network achieves a lower steady state MSD in the learning process than other networks.

The network model has receiver groups $G_1,\ldots,G_k$, where $k$ is the number of groups, and the analysis establishes bounds with an exponential dependence on $k$. Improved-depen…