The point cloud is the basis for 3D object surface reconstruction. An incomplete significantly reduces accuracy of downstream work such as reconstruction and recognition. Therefore, point-cloud repair indispensable work. However, original shape difficult to restore due uncertainty position new filling point. Considering advantages convex set in dealing with problems, we propose a method via tha...

Type-2 fuzzy set theory is one of the most powerful tools for dealing with the uncertainty and imperfection in dynamic and complex environments. The applications of type-2 fuzzy sets and soft computing methods are rapidly emerging in the ecological fields such as air pollution and weather prediction. The air pollution problem is a major public health problem in many cities of the world. Predict...

Partially Observable Markov Decision Processes (POMDPs) model sequential decision-making problems under uncertainty and partial observability. Unfortunately, some problems cannot be modeled with state-dependent reward functions, e.g., problems whose objective explicitly implies reducing the uncertainty on the state. To that end, we introduce ρPOMDPs, an extension of POMDPs where the reward func...

These are very schematic notes for lectures given at Tsinghua in July 2016. Setting : convex co-compact hyperbolic surfaces. I have chosen this setting because it appears in so many different areas of mathematics and gives rise to interesting problems for resonances, many of which still have not been answered. I will not talk about Pollicott–Ruelle resonances since covering both kinds of resona...

The corner polyhedron is described by minimal valid inequalities from maximal lattice-free convex sets. For the Relaxed Corner Polyhedron (RCP) with two free integer variables and any number of non-negative continuous variables, it is known that such facet defining inequalities arise from maximal lattice-free splits, triangles and quadrilaterals. We improve on the tightest known upper bound for...

in this paper, we investigate the concept of topological stationary for locally compact semigroups. in [4], t. mitchell proved that a semigroup s is right stationary if and only if m(s) has a left invariant mean. in this case, the set of values ?(f) where ? runs over all left invariant means on m(s) coincides with the set of constants in the weak* closed convex hull of right translates of f. th...

We propose piecewise linear kernel-based support vector clustering (SVC) as a new approach tailored to data-driven robust optimization. By solving a quadratic program, the distributional geometry of massive uncertain data can be effectively captured as a compact convex uncertainty set, which considerably reduces conservatism of robust optimization problems. The induced robust counterpart proble...