Trialing project-based learning in a new EAP ESP course: A collaborative reflective practice of three college English teachers

Currently in many Chinese universities, the traditional College English course is facing the risk of being ‘marginalized’, replaced or even removed, and many hours previously allocated to the course are now being taken by EAP or ESP. At X University in northern China, a curriculum reform as such is taking place, as a result of which a new course has been created called ‘xue ke’ English. Despite the fact that ‘xue ke’ means subject literally, the course designer has made it clear that subject content is not the target, nor is the course the same as EAP or ESP. This curriculum initiative, while possibly having been justified with a rationale of some kind (e.g. to meet with changing social and/or academic needs of students and/or institutions), this is posing a great challenge for, as well as considerable pressure on, a number of College English teachers who have taught this single course for almost their entire teaching career. In such a context, three teachers formed a peer support group in Semester One this year, to work collaboratively co-tackling the challenge, and they chose Project-Based Learning (PBL) for the new course. This presentation will report on the implementation of this project, including the overall designing, operational procedure, and the teachers’ reflections. Based on discussion, pre-agreement was reached on the purpose and manner of collaboration as offering peer support for more effective teaching and learning and fulfilling and pleasant professional development. A WeChat group was set up as the chief platform for messaging, idea-sharing, and resource-exchanging. Physical meetings were supplementary, with sound agenda but flexible time, and venues. Mosoteach cloud class (lan mo yun ban ke) was established as a tool for virtual learning, employed both in and after class. Discussions were held at the beginning of the semester which determined only brief outlines for PBL implementation and allowed space for everyone to autonomously explore in their own way. Constant further discussions followed, which generated a great deal of opportunities for peer learning and lesson plan modifications. A reflective journal, in a greater or lesser detailed manner, was also kept by each teacher to record the journey of the collaboration. At the end of the semester, it was commonly recognized that, although challenges existed, the collaboration was overall a success and they were all willing to continue with it and endeavor to refine it to be a more professional and productive approach

Entanglement in a second order topological insulator on a square lattice

In a $d$-dimensional topological insulator of order $d$, there are zero energy states on its corners which have close relationship with its entanglement behaviors. We studied the bipartite entanglement spectra for different subsystem shapes and found that only when the entanglement boundary has corners matching the lattice, exact zero modes exist in the entanglement spectrum corresponding to the zero energy states caused by the same physical corners. We then considered finite size systems in which case these corner states are coupled together by long range hybridizations to form a multipartite entangled state. We proposed a scheme to calculate the quadripartite entanglement entropy on the square lattice, which is well described by a four-sites toy model and thus provides another way to identify the higher order topological insulators from the multipartite entanglement point of view.Comment: 5 pages, 3 figure

Dark Energy Search with Supernovae

To determine the nature of dark energy from observational data, it is important that we use model-independent and optimal methods. We should probe dark energy using its density (allowed to be a free function of cosmic time) instead of its equation of state. We should minimize gravitational lensing effect on supernovae by flux-averaging. We need to include complementary data (for example, from the Cosmic Microwave Background [CMB] and large scale structure [LSS]) in a consistent manner to help break the degeneracy between the dark energy density and the matter density fraction. We should push for ambitious future supernova surveys that can observe a large number of supernovae at the highest possible redshifts. I discuss these and other issues that will be important in our quest to unravel the mystery of the nature of dark energy. Current supernova, CMB, and LSS data already rule out dark energy models with dark energy densities that vary greatly with time; with the cosmological constant model providing an excellent fit to the data. A precise measurement of dark energy density as a free function of cosmic time will have a fundamental impact on particle physics and cosmology.Comment: 9 pages, 3 color figures, to appear in proceedings of the 6th UCLA Symposium on "Sources and Detection of Dark Matter and Dark Energy in the Universe

Twisted Dirac Operators and the Noncommutative Residue for Manifolds with Boundary

In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and twisted signature operators on 4-dimensional manifolds with (resp. without) boundary.Comment: arXiv admin note: text overlap with arXiv:1303.371

Relative entropy of entanglement of rotationally invariant states

We calculate the relative entropy of entanglement for rotationally invariant states of spin-1/2 and arbitrary spin-$j$ particles or of spin-1 particle and spin-$j$ particle with integer $j$. A lower bound of relative entropy of entanglement and an upper bound of distillable entanglement are presented for rotationally invariant states of spin-1 particle and spin-$j$ particle with half-integer $j$.Comment: 13 pages, 3 figure