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

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

Plasmonic Light Trapping in an Ultrathin Photovoltaic Layer with Film-Coupled Metamaterial Structures

A film-coupled metamaterial structure is numerically investigated for enhancing the light absorption in an ultrathin photovoltaic layer of crystalline gallium arsenide (GaAs). The top subwavelength concave grating and the bottom metallic film could not only effectively trap light with the help of wave interference and magnetic resonance effects excited above the bandgap, but also practically serve as electrical contacts for photon-generated charge collection. The energy absorbed by the active layer is greatly enhanced in the film-coupled metamaterial structure, resulting in significant enhancement on the short-circuit current density by three times over a free-standing GaAs layer at the same thickness. The results would facilitate the development of next-generation ultrathin solar cells with lower cost and higher efficiency

Promoting learner autonomy through a “5-i” show project in large EFL classes: Strategies and challenges

Project-based learning (PBL) has been believed beneficial for learner autonomy in that it requires learners to actively participate and take responsibility in the learning process. While interest and research in PBL is growing, few empirical studies have been found investigating the application of PBL in China, and fewer have explored large EFL classes in tertiary institutions. This presentation reports on a longitudinal study of promoting learner autonomy through a 5i (intriguing, informing, involving, interactive, and inspiring) Show project. The study is conducted over an academic year in a Chinese university with six large non-English major classes (approximately 80 students in each). It is currently in progress and to be completed in August, 2018. With preliminary findings from a questionnaire conducted among a larger number of students, data for this study is collected through a follow-up questionnaire and semi-structured interviews. The presentation will report in greater detail on the project in relation to its design and classroom operation, including the strategies adopted by the teachers, students’ receptiveness, achievements and perceptions, as well as challenges encountered by both the participating teachers and students. It is hoped that the project can have practical implications for both classroom teachers utilising PBL in similar contexts and researchers for further exploration in this area

KV-match: A Subsequence Matching Approach Supporting Normalization and Time Warping [Extended Version]

The volume of time series data has exploded due to the popularity of new applications, such as data center management and IoT. Subsequence matching is a fundamental task in mining time series data. All index-based approaches only consider raw subsequence matching (RSM) and do not support subsequence normalization. UCR Suite can deal with normalized subsequence match problem (NSM), but it needs to scan full time series. In this paper, we propose a novel problem, named constrained normalized subsequence matching problem (cNSM), which adds some constraints to NSM problem. The cNSM problem provides a knob to flexibly control the degree of offset shifting and amplitude scaling, which enables users to build the index to process the query. We propose a new index structure, KV-index, and the matching algorithm, KV-match. With a single index, our approach can support both RSM and cNSM problems under either ED or DTW distance. KV-index is a key-value structure, which can be easily implemented on local files or HBase tables. To support the query of arbitrary lengths, we extend KV-match to KV-match$_{DP}$, which utilizes multiple varied-length indexes to process the query. We conduct extensive experiments on synthetic and real-world datasets. The results verify the effectiveness and efficiency of our approach.Comment: 13 page