<p style='text-indent:20px;'>Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization dimension reduction. We follow framework circular coordinate representation, which allows perform reduction high-dimensional datasets on torus usi...

This paper investigates penalty calls in the National Hockey League (NHL). Our study shows that there are various situational effects that are associated with the next penalty call. These situational effects are related to the accumulated penalty calls, the goal differential, the stage of the match and the relative strengths of the two teams. We also investigate individual referee effects acros...

A penalty framework for globally solving mixed-integer nonlinear programming problems is presented. Both integrality constraints and nonlinear constraints are handled separately by hyperbolic tangent penalty functions. The preliminary numerical experiments show that the proposed penalty approach is effective and the hyperbolic tangent penalties compete with other popular penalties.