Progressor: Personalized visual access to programming problems

This paper presents Progressor, a visualization of open student models intended to increase the student's motivation to progress on educational content. The system visualizes not only the user's own model, but also the peers' models. It allows sorting the peers' models using a number of criteria, including the overall progress and the progress on a specific topic. Also, in this paper we present results of a classroom study confirming our hypothesis that by showing a student the peers' models and ranking them by progress it is possible to increase the student's motivation to compete and progress in e-learning systems. © 2011 IEEE

"Spread" restricted Young diagrams from a 2D WZNW dynamical quantum group

The Fock representation of the Q-operator algebra for the diagonal WZNW model on SU(n) at level k, where Q is the matrix of the 2D WZNW "zero modes" generating certain dynamical quantum group, is finite dimensional and has a natural basis labeled by su(n) Young diagrams Y of "spread" not exceeding h := k+n (spr (Y) = #(columns) + #(rows))Comment: 10 pages, 8 figures, submitted to the Proceedings of the 11th International Workshop "Lie Theory and Its Applications in Physics" (Varna, Bulgaria, 15-21 June 2015); v.2 - amended Introduction, figures and list of reference

Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde

Proton Zemach radius from measurements of the hyperfine splitting of hydrogen and muonic hydrogen

While measurements of the hyperfine structure of hydrogen-like atoms are traditionally regarded as test of bound-state QED, we assume that theoretical QED predictions are accurate and discuss the information about the electromagnetic structure of protons that could be extracted from the experimental values of the ground state hyperfine splitting in hydrogen and muonic hydrogen. Using recent theoretical results on the proton polarizability effects and the experimental hydrogen hyperfine splitting we obtain for the Zemach radius of the proton the value 1.040(16) fm. We compare it to the various theoretical estimates the uncertainty of which is shown to be larger that 0.016 fm. This point of view gives quite convincing arguments in support of projects to measure the hyperfine splitting of muonic hydrogen.Comment: Submitted to Phys. Rev.

Open social student modeling: Visualizing student models with parallel introspectiveviews

This paper explores a social extension of open student modeling that we call open social student modeling. We present a specific implementation of this approach that uses parallel IntrospectiveViews to visualize models representing student progress with QuizJET parameterized self-assessment questions for Java programming. The interface allows visualizing not only the student's own model, but also displaying parallel views on the models of their peers and the cumulative model of the entire class or group. The system was evaluated in a semester-long classroom study. While the use of the system was non-mandatory, the parallel IntrospectiveViews interface caused an increase in all of the usage parameters in comparison to a regular portal-based access, which allowed the student to achieve a higher success rate in answering the questions. The collected data offer some evidence that a combination of traditional personalized guidance with social guidance was more effective than personalized guidance alone. © 2011 Springer-Verlag

Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus

After giving a short description, in terms of action of categories, of some of the structures associated with sl(2) and sl(3) boundary conformal field theories on a torus, we provide tables of dimensions describing the semisimple and co-semisimple blocks of the corresponding weak bialgebras (quantum groupoids), tables of quantum dimensions and orders, and tables describing induction - restriction. For reasons of size, the sl(3) tables of induction are only given for theories with self-fusion (existence of a monoidal structure).Comment: 25 pages, 5 tables, 9 figures. Version 2: updated references. Typos corrected. Several proofs added. Examples of ADE and generalized ADE trigonometric identities have been removed to shorten the pape

The solution to the q-KdV equation

Let KdV stand for the Nth Gelfand-Dickey reduction of the KP hierarchy. The purpose of this paper is to show that any KdV solution leads effectively to a solution of the q-approximation of KdV. Two different q-KdV approximations were proposed, one by Frenkel and a variation by Khesin et al. We show there is a dictionary between the solutions of q-KP and the 1-Toda lattice equations, obeying some special requirement; this is based on an algebra isomorphism between difference operators and D-operators, where $Df(x)=f(qx)$. Therefore, every notion about the 1-Toda lattice can be transcribed into q-language.Comment: 18 pages, LaTe

Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields

The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective gauge groups U(N) and O(N) confirms the expectations based on general results obtained in the framework of local nets in algebraic quantum field theory, but the approach using standard Lie algebra methods rather than abstract duality theory is complementary. The result indicates that one does not lose interesting models if one postulates the absence of scalar fields of dimension D-2 in models with global conformal invariance. Another remarkable outcome is the observation that, with an appropriate choice of the Hamiltonian, a Lie algebra embedded into the associative algebra of observables completely fixes the representation theory.Comment: 27 pages, v3: result improved by eliminating redundant assumptio

Quantum Fluctuations of the Gravitational Field and Propagation of Light: a Heuristic Approach

Quantum gravity is quite elusive at the experimental level; thus a lot of interest has been raised by recent searches for quantum gravity effects in the propagation of light from distant sources, like gamma ray bursters and active galactic nuclei, and also in earth-based interferometers, like those used for gravitational wave detection. Here we describe a simple heuristic picture of the quantum fluctuations of the gravitational field that we have proposed recently, and show how to use it to estimate quantum gravity effects in interferometers.Comment: LaTeX2e, 8 pages, 2 eps figures: Talk presented at QED2000, 2nd Workshop on Frontier Tests of Quantum Electrodynamics and Physics of the Vacuum; included in conference proceeding