A restricted-orientation convex set is a set of points whose intersection with lines from some fixed set is empty or connected. This notion generalizes both standard convexity and orthogonal convexity. We explore basic properties of restricted-orientation convex sets in three dimensions. In particular, we establish analogs of the following properties of standard convex sets: The intersection of...

Expectation of reward motivates our behaviors and influences our decisions. Indeed, neuronal activity in many brain areas is modulated by expected reward. However, it is still unclear where and how the reward-dependent modulation of neuronal activity occurs and how the reward-modulated signal is transformed into motor outputs. Recent studies suggest an important role of the basal ganglia. Senso...

Parts orienting, the process of bringing parts in initially unknown orientations to a goal orientation, is an important aspect of automated assembly. The most common industrial orienting systems are vibratory bowl feeders, which use the shape and mass properties of parts to orient them. Bowl feeders rely on a sequence of mechanical operations and typically do not use sensors. In this paper, we ...

Insects maintain a constant bearing across a wide range of spatial scales. Monarch butterflies and locusts traverse continents [1, 2], and foraging bees and ants travel hundreds of meters to return to their nests [1, 3, 4], whereas many other insects fly straight for only a few centimeters before changing direction. Despite this variation in spatial scale, the brain region thought to underlie l...