We give a complete and explicit characterization of the connected graphs which admit a continuous 3-to-1 map onto the circle, and of the connected graphs which admit a continuous 2-to-l map onto the circle. This generalizes earlier work of Heath and Hilton who considered the mappings of trees onto the circle.

The importance of infrastructure for growth is well established in the macroeconomic literature. Previous research has treated public investment in infrastructure as exogenous. We remedy this shortcoming by providing a political economy analysis of infrastructure choice based upon consumer preferences derived from spatial competition models. In this setting, infrastructure investment has two po...

Yeates, Jones, Wills, Aitken, McLaren and McLaren (2012) devised a serial reaction time (SRT) task that provided evidence for human learning without awareness. Adapting the SRT paradigm usually employed to investigate implicit learning, participants responded to two simple white circle fills on either side of a screen. Instead of these following a sequence that participants were unaware of (e.g...