Effective design of massive open online courses for mathematics teachers to support their professional learning

Three MOOCs for Educators (MOOC-Eds) were designed for mathematics and statistics teachers based on principles of effective online professional development     

A method for constructing a resolving control in an approach problem based on attraction to the feasibility set

The problem of the approach of a nonlinear control system to a compact target set in the phase space at a fixed time is studied. An algorithm for constructing a solution of this problem based on maximum attraction of the system’s motion to the feasibility set is proposed.     

A machine learning approach to algorithm selection for $\mathcal{NP}$ -hard optimization problems: a case study on the MPE problem

Given one instance of an \(\mathcal{NP}\)-hard optimization problem, can we tell in advance whether it is exactly solvable or not? If it is not, can we predict which approximate algorithm is the best to solve it? Since the behavior of most approximate, randomized, and heuristic search algorithms for \(\mathcal{NP}\)-hard problems is usually very difficult to characterize analytically, researchers have turned to experimental methods in order to answer these questions. In this paper we present a machine learning-based approach to address the above questions. Models induced from algorithmic performance data can represent the knowledge of how algorithmic performance depends on some easy-to-compute problem instance characteristics. Using these models, we can estimate approximately whether an input instance is exactly solvable or not. Furthermore, when it is classified as exactly unsolvable, we can select the best approximate algorithm for it among a list of candidates. In this paper we use the MPE (most probable explanation) problem in probabilistic inference as a case study to validate the proposed methodology. Our experimental results show that the machine learning-based algorithm selection system can integrate both exact and inexact algorithms and provide the best overall performance comparing to any single candidate algorithm.