This thesis aims to introduce the notions of linkage and its confguration space, that can be motivated as a model that describes the motion of mechanical linkages. We focus on cyclic linkages that give place to the polygon ...

Morse homology studies the topology of smooth manifolds by examining the critical points of a real-valued function defined on the manifold, and connecting them with the negative gradient of the function. Rather surprisingly, ...

Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids ...