We introduce a model of information dissemination in signed networks. It is a discrete-time process in which uninformed actors incrementally receive information from their informed neighbors or from the outside. Our goal is to minimize the number of confused actors — that is, the number of actors who receive contradictory information. We prove upper bounds for the number of confused actors in signed networks and in equivalence classes of signed networks. In particular, we show that there are signed networks where, for any information placement strategy, almost 60% of the actors are confused. Furthermore, this is also the case when considering the minimum number of confused actors within an equivalence class of signed graphs.

Traditional assembly tasks often require robots to transfer the acquired skills to new tasks. However, previous transfer reinforcement learning methods typically ignore the inherent relationship between the source and the target domain tasks. This requires a substantial amount of interaction data to compensate for this deficiency, and generally results in poor transfer effects. To address this issue, a strategy transfer method that establishes a shared feature space between the source domain and the target domain is proposed to enhance the efficiency of strategy learning on peg-in-hole assembly. Initially, by calculating the distance between each feature in the source and target domains, the features with small distance are selected as shared features. Subsequently, in order to determine the successful search state, this paper uses the jump state of contact force and the relative position between the peg and the hole as the judgment criterion. Lastly, search and insertion peg-in-hole assembly experiments are conducted to validate the generalization of the proposed strategy, demonstrating its capability to transfer from simulation to the real world.

Steinberg's conjecture states that planar graphs without 4- and 5-cycles are 3-colorable. This conjecture, though disproved recently, has motivated a lot of work in the literature. A plane graph is a planar graph $G$ together with an embedding of $G$ into the Euclidean plane. A 7-cycle $C$ of a plane graph is ext-triangular if it is adjacent to a triangle $T$ such that the areas inside $C$ and inside $T$ have no intersection. In this paper, we prove that plane graphs without 4- and 5-cycles are 3-colorable if they contain no ext-triangular 7-cycles, which improves a number of known results. In particular, our result implies that (1) planar graphs without 4-, 5-, and 7-cycles are 3-colorable, and (2) planar graphs without 4-, 5-, and 8-cycles are 3-colorable.