Mining Classroom Observation Data for Understanding Teachers’ Technological Pedagogical Content Knowledge Structure

On the basis of teachers’ pedagogical content knowledge proposed by Shulman, Koehler and Mishra explicitly put forward technological pedagogical content knowledge (TPACK) framework. The study shows that TPACK is a necessary knowledge for teachers to use technology for carrying effective teaching (Koehler & Mishra, 2005). It has been found that technological pedagogical knowledge (TPK) has a significant influence on TPACK structure of pre-service teachers (Zhang, 2015). This paper mainly explores the teaching structure of classroom and the TPK structure presented by teachers. Based on the existing video analysis and coding system, this study adapted and revised a curriculum teaching code table. Methods of quantitative and qualitative combination and comparative analysis are used to explore four aspects: teaching links, students’ expected cognitive level, teaching media and TPK. This study uses the classroom video analysis method to make a comparative analysis of short teaching video of award-winninged teachers and non award-winninged teachers in a competition and explores the influence of teaching activities and TPK structure of teachers on teaching effect. The statistical analysis of the results showed that the teaching link, the teaching media, and the student’s expected cognitive level have no significant effect on the teaching effect, and TPK has a significant impact on the teaching effect

A simple model for the anomalous intrinsic viscosity of dendrimers

The intrinsic viscosity of dendrimers in solution shows several anomalous behaviors that have hitherto not been explained within the existing theoretical frameworks of either Zimm or Rouse. Here we propose a simple two-zone model based on the radial segmental density profile of the dendrimers and combine a non-draining core with a free-draining outer region description, to arrive at a simple formula that captures most of the main features in the intrinsic viscosity data obtained in experiments

Session-based Recommendation with Graph Neural Networks

The problem of session-based recommendation aims to predict user actions based on anonymous sessions. Previous methods model a session as a sequence and estimate user representations besides item representations to make recommendations. Though achieved promising results, they are insufficient to obtain accurate user vectors in sessions and neglect complex transitions of items. To obtain accurate item embedding and take complex transitions of items into account, we propose a novel method, i.e. Session-based Recommendation with Graph Neural Networks, SR-GNN for brevity. In the proposed method, session sequences are modeled as graph-structured data. Based on the session graph, GNN can capture complex transitions of items, which are difficult to be revealed by previous conventional sequential methods. Each session is then represented as the composition of the global preference and the current interest of that session using an attention network. Extensive experiments conducted on two real datasets show that SR-GNN evidently outperforms the state-of-the-art session-based recommendation methods consistently.Comment: 9 pages, 4 figures, accepted by AAAI Conference on Artificial Intelligence (AAAI-19

Nonlinear Rheological Behaviors in Polymer Melts after Step Shear

Using molecular dynamics simulation, we investigate the evolution of chain conformation, stress relaxation, and fracture for a polymer melt between two walls after step shear. We find that the characteristic overlap time for the reduced relaxation moduli and the time that the stretched primitive chain retracts to its equilibrium length are both much longer than the Rouse time. Importantly, we observe significant fracture-like flow after shear cessation. While there is considerable randomness in the location of the fracture plane and the magnitude of displacement from sample to sample, our analysis suggests that the randomness is not due to thermal noise, but may reflect inherent structural and dynamic heterogeneity in the entangled polymer network

Two-step relaxation and the breakdown of the Stokes-Einstein relation in glass-forming liquids

It is well known that glass-forming liquids exhibit a number of anomalous dynamical phenomena, most notably a two-step relaxation in the self-intermediate scattering function and the breakdown of the Stokes-Einstein (SE) relation, as they are cooled toward the glass transition temperature. While these phenomena are generally ascribed to dynamic heterogeneity, specifically to the presence of slow- and fast-moving particles, a quantitative elucidation of the two-step relaxation and the violation of the SE relation in terms of these concepts has not been successful. In this work, we propose a classification of particles according to the rank order of their displacements (from an arbitrarily defined origin of time), and we divide the particles into long-distance (LD), medium-distance, and short-distance (SD) traveling particle groups. Using molecular-dynamics simulation data of the Kob-Andersen model, we show quantitatively that the LD group is responsible for the fast relaxation in the two-step relaxation process in the intermediate scattering function, while the SD group gives rise to the slow (α) relaxation. Furthermore, our analysis reveals that τ_α is controlled by the SD group, while the ensemble-averaged diffusion coefficient D is controlled by both the LD and SD groups. The combination of these two features provides a natural explanation for the breakdown in the SE relation at low temperature. In addition, we find that the α-relaxation time, τ_α, of the overall system is related to the relaxation time of the LD particles, τ_(LD), as τ_α = τ₀exp(Ωτ_(LD)/k_BT)

Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Data

Two higher order time stepping methods for solving subdiffusion problems are studied in this paper. The Caputo time fractional derivatives are approximated by using the weighted and shifted Gr\"unwald-Letnikov formulae introduced in Tian et al. [Math. Comp. 84 (2015), pp. 2703-2727]. After correcting a few starting steps, the proposed time stepping methods have the optimal convergence orders $O(k^2)$ and $O(k^3)$, respectively for any fixed time $t$ for both smooth and nonsmooth data. The error estimates are proved by directly bounding the approximation errors of the kernel functions. Moreover, we also present briefly the applicabilities of our time stepping schemes to various other fractional evolution equations. Finally, some numerical examples are given to show that the numerical results are consistent with the proven theoretical results