Sharif Digital Repository

For a compact Riemannian manifold with negative curvature, the Liouville measure, the Bowen-Margulis measure and the Harmonic measure are three natural invariant measures under the geodesic flow. We show that if any two of the above three measure classes coincide then the space is locally symmetric, provided the function with respect to which the equilibrium state is the Harmonic measure, depends only on the foot points. © 2007 University of Houston  

The existing learning methods usually assume that training data and test data follow the same distribution, while this is not always true. Thus, in many cases the performance of these methods on the test data will be severely degraded. In this paper, we study the problem of unsupervised domain adaptation, where no labeled data in the target domain is available. The proposed method first finds a new representation for both the source and the target domain and then learns a prediction function for the classifier by optimizing an objective function which simultaneously tries to minimize the loss function on the source domain while also maximizes the consistency of manifold (which is based on...