Asocial balance-how your friends determine your enemies: understanding the co-evolution of friendship and enmity interactions in a virtual world.

Social interactions take place simultaneously through different interaction types, such as communication, friendship, trade, exchange, enmity, revenge, etc. These interactions can be conveniently described with time-dependent multi-layer networks. Little is known about the dynamics of social network formation on single layers.

Physiologically motivated multiplex Kuramoto model describes phase diagram of cortical activity.

We derive a two-layer multiplex Kuramoto model from Wilson-Cowan type physiological equations that describe neural activity on a network of interconnected cortical regions. This is mathematically possible due to the existence of a unique, stable limit cycle, weak coupling, and inhibitory synaptic time delays. We study the phase diagram of this model numerically as a function of the inter-regional connection strength that is related to cerebral blood flow, and a phase shift parameter that is associated with synaptic GABA concentrations.