There is a growing interest in how data generated in learning platforms, especially the interaction data, can be used to improve teaching and learning. Social network analysis and machine learning methods take advantage of network topology to detect relational patterns and model interaction behaviors. Specifically, small induced subgraphs called graphlets, provide an efficient topological description of the way each node is embedded in the meso-scale structure of a network. Here we propose to detect the roles occupied by the different participants, students and teachers, in the successive phases of courses modeled by a sequence of static snapshots. The detected positions, obtained thanks to graphlet enumeration combined with a clustering method, reveal the different roles observed in each snapshot. We also track the role changes through the overall sequence of snapshots. We apply our method to the Sqily platform and describe the mutual skill validation process. The detected roles, the transitions between roles and a overall visualization through Sankey diagrams help interpreting the course dynamics. We found that some roles act like necessary steps to engage students within an active exchange process with their classmates.
The optimization of multi-energy systems (MESs) in which multiple energy carriers interact with each other is a complex problem. Their optimal operation and design can be determined through mathematical programming. A classical technology used in MESs is the combined heat and power units (CHP) whose efficiency is modeled through non-linear equations. These non-linear functions are approximated through piecewise linear ones by introducing binary decision variables, which generates a mixed-integer linear program (MILP). Consequently, optimizing such systems over a long time period with a high temporal resolution becomes infeasible in a reasonable amount of time. In this work, we propose a fast heuristic algorithm to optimize the design and operation of such an MES. Our case study is an MES at the scale of a district with five types of generation units, including a CHP, over a time period of one year with a temporal resolution of one hour. Comparison of the proposed heuristic and a state-of-the-art MILP solver over smaller time periods shows that the heuristic is up to 99.9 % faster, with a mean error of 2.3 × 10 −4 % compared to the optimal solution. The heuristic can also solve the optimal design and operation problem over a year in about 10 minutes.
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