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In this research, we have used machine learning methods to approach the problem of human activity recognition. As the process of labeling the data in this problem is so costly and time consuming, and regarding the copious available unlabeled data, semi supervised methods have a high performance in this problem. In recent years, graph based methods have became very populaer among semi supervised learning methods. However, constructing a graph on the data which presents their structure in a proper manner has remained a main challenge in these methods. One of the causes of this problem is the existance of the shortcut edges. In this report, we will first introduce a method to solve the problem... 

The manifolds that will play the central role in this thesis are b-Poisson manifolds. These manifolds are a special sub-class of Poisson manifolds which are in many ways close to being symplectic: For π the Poisson structure dual to a symplectic form, the top wedge π^nnever meets the zero section of Λ^2n TM (non-degeneracy of the symplectic form). We define a b-Poisson manifold to be a Poisson manifold (M,π)such that π^n vanishes transversally to the zero section in Λ^2n TM. A pivotal result about the dynamics of integrable systems is the Liouville-Arnold-Mineur theorem (or action-angle coordinate theorem), which states that the compact common level sets of the integrals f_iare tori that...