This review is dedicated to two-dimensional sigma models with flag manifold target spaces, which are generalizations of the familiar $CP^{n-1}$ and Grassmannian models. They naturally arise in description continuum limits spin chains, their phase structure sensitive values topological angles, determined by representations spins chain. Gapless phases can certain cases be explained presence discr...

One approach to invariant object recognition employs a recurrent neural network as an associative memory. In the standard depiction of the network's state space, memories of objects are stored as attractive fixed points of the dynamics. I argue for a modification of this picture: if an object has a continuous family of instantiations, it should be represented by a continuous attractor. This ide...