We prove that for every homogeneous and strongly locally homogeneous Polish space X there is a Polish group admitting a transitive action on X. We also construct an example of a homogeneous Polish space which is not a coset space and on which no separable metrizable topological group acts transitively.

In this paper we study homogeneous geodesics in a three-dimensional connected Lie group G equipped with a left invariant Randers metric and investigates the set of all homogeneous geodesics. We show that there is a three-dimensional unimodular Lie group with a left invariant non-Berwaldian Randers metric which admits exactly one homogeneous geodesic through the identity element. Mathematics Sub...

The notion of quantum group equivariant homogeneous vector bundles on quantum homogeneous spaces is introduced. The category of such quantum vector bundles is shown to be exact, and its Grothendieck group is determined. It is also shown that the algebras of functions on quantum homogeneous spaces are noetherian.

The emergence of cooperation in wolf-pack hunting is studied using a simple, homogeneous, particle-based computational model. Wolves and prey are modelled as particles that interact through attractive and repulsive forces. Realistic patterns of wolf aggregation readily emerge in numerical simulations, even though the model includes no explicit wolf-wolf attractive forces, showing that the form ...