Social Synchrony is an important catalyst for learning environments. For a learner, learning outcomes can be greatly enhanced by associating with other compatible peers as part of their learning journey. In many learning environments, learners often autonomously use certain heuristics to connect with other peers. Understanding how these heuristic connections lead to emergent properties at the network level, is important to design learning interventions. In this work, we build simulation models to study the network-level impact of different kinds of heuristics used by learners to form connections. We consider four different heuristics and show their impact both on learning outcomes, and the bookkeeping cost posed by the connections on the learners.

The web is seen as a promising platform for designing scalable educational practices across large populations. Many of the efforts in this space use the web primarily as an amplifier over existing models of learning that are based on the classroom. In this paper, we propose a pedagogic model called mediated learning where the web acts as a platform for nurturing a learning community by continuously mediating between knowledge need and expertise. Mediated learning has the potential to invert the learning pyramid by interfacing the learner with several experts as part of a single learning experience. For supporting mediated learning, an approach is needed that is data-intensive and driven by social semantics. This paper outlines the proposed pedagogic model, which comprises two primary components: a user-end navigator component that provides a rich interface enabling users to independently navigate through a learning space; and a back-end community component, that performs meaningful mediations between participants in the logical learning space.

We show that the space of all binary Huffman codes for a finite alphabet defines a lattice, ordered by the imbalance of the code trees. Representing code trees as path-length sequences, we show that the imbalance ordering is closely related to a majorization ordering on real-valued sequences that correspond to discrete probability density functions. Furthermore, this tree imbalance is a partial ordering that is consistent with the total orderings given by either the external path length (sum of tree path lengths) or the entropy determined by the tree structure. On the imbalance lattice, we show the weighted path-length of a tree (the usual objective function for Huffman coding) is a submodular function, as is the corresponding function on the majorization lattice. Submodular functions are discrete analogues of convex functions. These results give perspective on Huffman coding and suggest new approaches to coding as optimization over a lattice.