Actions ~ Transformations

What defines an action like "kicking ball"? We argue that the true meaning of an action lies in the change or transformation an action brings to the environment. In this paper, we propose a novel representation for actions by modeling an action as a transformation which changes the state of the environment before the action happens (precondition) to the state after the action (effect). Motivated by recent advancements of video representation using deep learning, we design a Siamese network which models the action as a transformation on a high-level feature space. We show that our model gives improvements on standard action recognition datasets including UCF101 and HMDB51. More importantly, our approach is able to generalize beyond learned action categories and shows significant performance improvement on cross-category generalization on our new ACT dataset

Open group transformations

Open groups whose generators are in arbitrary involutions may be quantized within a ghost extended framework in terms of a nilpotent BFV-BRST charge operator. Previously we have shown that generalized quantum Maurer-Cartan equations for arbitrary open groups may be extracted from the quantum connection operators and that they also follow from a simple quantum master equation involving an extended nilpotent BFV-BRST charge and a master charge. Here we give further details of these results. In addition we establish the general structure of the solutions of the quantum master equation. We also construct an extended formulation whose properties are determined by the extended BRST charge in the master equation.Comment: 17 pages,Latexfile,signs corrected in appendix

Invertible Darboux Transformations

For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones were Laplace transformations (and their compositions), which are special cases of Darboux transformations for hyperbolic bivariate operators of order 2. In the present paper we find a criteria for a bivariate linear partial differential operator of an arbitrary order d to have an invertible Darboux transformation. We show that Wronkian formulae may fail in some cases, and find sufficient conditions for such formulae to work