The feasibility of capturing learner interactions based on logs informed by eye-tracking and remote observation studies

Two small studies, one an eye-tracking study and the other a remote observation study, have been conducted to investigate ways to identify two kinds of online learner interactions: users flicking through the web pages in "browsing" action, and users engaging with the content of a page in "learning" action. The video data from four participants of the two small studies using the OpenLearn open educational resource materials offers some evidence for differentiating between 'browsing' and 'learning'. Further analysis of the data has considered possible ways of identifying similar browsing and learning actions based on automatic user logs. This research provides a specification for researching the pedagogical value of capturing and transforming logs of user interactions into external forms of representations. The paper examines the feasibility and challenge of capturing learner interactions giving examples of external representations such as sequence flow charts, timelines, and table of logs. The objective users information these represent offer potential for understanding user interactions both to aid design and improve feedback means that they should be given greater consideration alongside other more subjective ways to research user experience

Supersymmetric Casimir Energy and SL(3,Z)\mathrm{SL(3,\mathbb{Z})} Transformations

We provide a recipe to extract the supersymmetric Casimir energy of theories defined on primary Hopf surfaces directly from the superconformal index. It involves an $\mathrm{SL(3,\mathbb{Z})}$ transformation acting on the complex structure moduli of the background geometry. In particular, the known relation between Casimir energy, index and partition function emerges naturally from this framework, allowing rewriting of the latter as a modified elliptic hypergeometric integral. We show this explicitly for $\mathcal{N}=1$ SQCD and $\mathcal{N}=4$ supersymmetric Yang-Mills theory for all classical gauge groups, and conjecture that it holds more generally. We also use our method to derive an expression for the Casimir energy of the nonlagrangian $\mathcal{N}=2$ SCFT with $\mathrm{E_6}$ flavour symmetry. Furthermore, we predict an expression for Casimir energy of the $\mathcal{N}=1$ $\mathrm{SP(2N)}$ theory with $\mathrm{SU(8)\times U(1)}$ flavour symmetry that is part of a multiple duality network, and for the doubled $\mathcal{N}=1$ theory with enhanced $\mathrm{E}_7$ flavour symmetry.Comment: 20 pages, more explicit examples added, published in JHE

Scarring in open quantum systems

We study scarring phenomena in open quantum systems. We show numerical evidence that individual resonance eigenstates of an open quantum system present localization around unstable short periodic orbits in a similar way as their closed counterparts. The structure of eigenfunctions around these classical objects is not destroyed by the opening. This is exposed in a paradigmatic system of quantum chaos, the cat map.Comment: 4 pages, 4 figure