题名：Liuoville Theorem and Singularity for some Hessian Equation
摘要：Via the methods of integration by parts, some hessian equations are studied, including classical hessian equation, conformal hessian equation, hessian equation of curvature operators of Fuchsian convex surfaces in Minkowski space.
题名：Variable Selection Methods in Change-point Detection
摘要：In this talk, we discuss some change-point detection problem by using variable selection technique. Especially we propose a new model named mixture-regression model which combines auto-regression and regression. We investigate the estimation of the location of change-points in mixture- regression model. Using a penalized least-square criterion with a l1-type penalty and some suitable modification, the problem is cast as a sparse regression, and can be solved by resorting to the least-absolute shrinkage and selection operator(Lasso). With the way to select the tuning parameter by minimizing information criterion, an efficient block-coordinate descent algorithm is developed to implement the novel method. With probability tending to one, this method can efficiently determine the unknown number of change-points, and the estimated break locations are sufficently close to the true break locations. Finally, numerical tests using synthetic and real data are presented, which corroborate the merits of the method in mixture-regression model.