Cooperative Learning in Videoconferencing: The Influence of Content Schemes and Cooperation Scripts on Shared External Representations and Individual Learning Outcomes

Video-conferencing is expected to become increasingly important for tele-learning environments. This study investigates how to foster cooperative learning in videoconferencing. The learning environment was a peer-teaching scenario, which demanded the learners to teach each other theories. In this study the effects of different types of support for cooperation were investigated. The main research question is how (1) content schemes and (2) cooperation scripts enhance the construction of collaborative external representations and foster learning outcomes. Re-sults indicate that content schemes as well as cooperation scripts foster the construction of shared external representations. Furthermore, the cooperation script enhances learning outcomVideokonferenzen werden in Telelernumgebungen zunehmend wichtiger. Im Rahmen dieser Studie wird untersucht, wie man kooperatives Lernen in Videokonferenzen unterstützen kann. Als Lernumgebung wurde ein Peer-Teaching Szenario gewählt, bei dem es die Aufgabe der Lernenden war, sich gegenseitig eine Theorie zu vermitteln. Dabei werden die Auswirkungen einer Unterstützung durch die Faktoren (1) Wissensschemata und (2) Kooperationsskripts auf die Erstellung einer gemeinsamen externalen Repräsentation und auf den Lernerfolg untersucht. Die Ergebnisse zeigen, dass sowohl Wissensschemata als auch Kooperationsskripts positive Effekte auf die Erstellung der gemeinsamen externalen Repräsentation haben. Lernende mit Kooperationsskript wiesen zusätzlich einen höheren Lernerfolg auf als Lernende ohne Kooperationsskr

On algebraic fusions of association schemes

We give a complete description of the irreducible representations of algebraic fusions of association schemes, in terms of the irreducible representations of a Schur cover of the corresponding group of algebraic automorphisms.Comment: This paper has been withdrawn by one of the authors, since it requires more wor

RNNs Implicitly Implement Tensor Product Representations

Recurrent neural networks (RNNs) can learn continuous vector representations of symbolic structures such as sequences and sentences; these representations often exhibit linear regularities (analogies). Such regularities motivate our hypothesis that RNNs that show such regularities implicitly compile symbolic structures into tensor product representations (TPRs; Smolensky, 1990), which additively combine tensor products of vectors representing roles (e.g., sequence positions) and vectors representing fillers (e.g., particular words). To test this hypothesis, we introduce Tensor Product Decomposition Networks (TPDNs), which use TPRs to approximate existing vector representations. We demonstrate using synthetic data that TPDNs can successfully approximate linear and tree-based RNN autoencoder representations, suggesting that these representations exhibit interpretable compositional structure; we explore the settings that lead RNNs to induce such structure-sensitive representations. By contrast, further TPDN experiments show that the representations of four models trained to encode naturally-occurring sentences can be largely approximated with a bag of words, with only marginal improvements from more sophisticated structures. We conclude that TPDNs provide a powerful method for interpreting vector representations, and that standard RNNs can induce compositional sequence representations that are remarkably well approximated by TPRs; at the same time, existing training tasks for sentence representation learning may not be sufficient for inducing robust structural representations.Comment: Accepted to ICLR 201

An Algebraic Approach to Linear-Optical Schemes for Deterministic Quantum Computing

Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U(N)). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a CNOT gate and a Bell-State Generator/Analyzer.Comment: new version with minor modification

The Ring of Support-Classes of SL_2(F_q)\mathrm{SL}\_2(\mathbb F\_q)

We introduce and study a subring $\mathcal{SC}$ of $\mathbb Z[\mathrm{SL}\_2(\mathbb F\_q)]$ obtained by summing elements of $\mathrm{SL}\_2(\mathbb F\_q)$ according to their support. The ring $\mathcal SC$ can be used for the construction of several association schemes