This paper is devoted to the investigation of weighted mean topological dimension in dynamical systems. We show that not larger than metric dimension, which generalizes classical result Lindenstrauss and Weiss [16] . also establish relationship between entropy systems, indicates each system with finite or small boundary property has zero dimension.

Variational inference is an important class of approximate inference techniques that has been applied to many graphical models, including topic models. We propose to improve the efficiency of mean field inference for Dirichlet-based models by introducing an approximative framework that converts weighted geometric means in the updates into weighted arithmetic means. This paper also discusses a c...

In this paper, we study the convergence property of several discrete schemes of the surface normal. We show that the arithmetic mean, area-weighted averaging, and angle-weighted averaging schemes have quadratic convergence rate for a special triangulation scenario of the surfaces. By constructing a counterexample, we also show that it is impossible to find a discrete scheme of normals that has ...