We study asymptotically Lifshitz solutions to three dimensional higher spin gravity in the SL(3, R) × SL(3, R) Chern-Simons formulation. We begin by specifying the most general connections satisfying Lifshitz boundary conditions, and we verify that their algebra of symmetries contains a Lifshitz sub-algebra. We then exhibit connections that can be viewed as higher spin Lifshitz black holes. We show that when suitable holonomy conditions are imposed, these black holes obey sensible thermodynamics and possess a gauge in which the corresponding metric exhibits a regular horizon.

We study the applicability of the covariant holographic entanglement entropy proposal to asymptotically warped AdS 3 spacetimes with an SL(2, R) × U (1) isometry.We begin by applying the proposal to locally AdS 3 backgrounds which are written as an R 1 fibration over AdS 2 . We then perturb away from this geometry by considering a warping parameter a = 1 + δ to get an asymptotically warped AdS 3 spacetime and compute the dual entanglement entropy perturbatively in δ. We find that for large separation in the fiber coordinate, the entanglement entropy can be computed to all orders in δ and takes the universal form appropriate for two-dimensional CFTs. The warpingdependent central charge thus identified exactly agrees with previous calculations in the literature. Performing the same perturbative calculations for the warped BTZ black hole again gives universal two-dimensional CFT answers, with the left-moving and right-moving temperatures appearing appropriately in the result.

In some educational contexts, such as during assessments, it is essential to avoid errors. In other contexts, however, generating an error can foster valuable learning opportunities. For instance, generating errors can improve memory for correct answers. In two surveys conducted at three large public universities in North America, we investigated undergraduate students' and instructors' awareness of the pedagogical benefits of generating errors, as well as related practices, attitudes, and beliefs. Surveyed topics included the incorporation of errors into learning activities, opinions about the consequences of studying errors, and approaches to feedback. Many students had an aversion towards making errors during learning and did not use opportunities to engage in errorful generation, yet studied or analysed errors when they occurred. Many instructors had a welcoming attitude towards errors that occur during learning, yet varied in providing students with resources that facilitate errorful generation. Overall, these findings reveal the prevalence of an ambivalent approach to errors: Students and instructors avoid generating errors but prioritise learning from them when they occur. These results have important implications for the implementation of pretesting, productive failure, and other error-focused learning techniques in educational contexts.

Solutions of (d + 1)-dimensional gravity coupled to a scalar field are obtained, which holographically realize interface and boundary CFTs. The solution utilizes a Janus-like AdS d slicing ansatz and corresponds to a deformation of the CFT by a spatially-dependent coupling of a relevant operator. The BCFT solutions are singular in the bulk, but physical quantities such as the holographic entanglement entropy can be calculated.

We investigated whether continuously alternating between topics during practice, or interleaved practice, improves memory and the ability to solve problems in undergraduate physics. Over 8 weeks, students in two lecture sections of a university-level introductory physics course completed thrice-weekly homework assignments, each containing problems that were interleaved (i.e., alternating topics) or conventionally arranged (i.e., one topic practiced at a time). On two surprise criterial tests containing novel and more challenging problems, students recalled more relevant information and more frequently produced correct solutions after having engaged in interleaved practice (with observed median improvements of 50% on test 1 and 125% on test 2). Despite benefiting more from interleaved practice, students tended to rate the technique as more difficult and incorrectly believed that they learned less from it. Thus, in a domain that entails considerable amounts of problem-solving, replacing conventionally arranged with interleaved homework can (despite perceptions to the contrary) foster longer lasting and more generalizable learning.