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The ongoing usage of artificial intelligence technologies in virtual reality has led to a large number of researchers exploring immersive virtual reality interaction. Gesture controllers and head-mounted displays are the primary pieces of hardware used in virtual reality applications. This article analyzes the advantages and disadvantages of various hardware tools as well as possible use cases for hand gesture recognition. Several popular data sets used in data pre-processing and hand gesture detection systems are also summarized. This paper's primary objectives are to evaluate the current state of the art in gesture recognition research and to offer potential routes for future study to guide researchers working on immersive virtual reality interaction. Comparing recent study results and taking into account the state of the development of human-computer interaction technology, a number of potential research directions are highlighted, including the following: input data noise should be filtered, a lightweight network should be designed, tactile feedback should be created, and eye and gesture data should be combined.

Sign language has been extensively studied as a means of facilitating effective communication between hearing individuals and the deaf community. With the continuous advancements in virtual reality (VR) and gamification technologies, an increasing number of studies have begun to explore the application of these emerging technologies in sign language learning. This paper describes a user study that compares the impact of 2D and 3D games on the user experience in ASL learning. Empirical evidence gathered through questionnaires supports the positive impact of 3D game environments on user engagement and overall experience, particularly in relation to attractiveness, usability, and efficiency. Moreover, initial findings demonstrate a similar behaviour of 2D and 3D games in terms of enhancing user experience. Finally, the study identifies areas where improvements can be made to enhance the dependability and clarity of 3D game environments. These findings contribute to the understanding of how game-based approaches, and specifically the utilisation of 3D environments, can positively influence the learning experience of ASL.

The field of Knowledge Tracing aims to understand how students learn and master knowledge over time by analyzing their historical behaviour data. To achieve this goal, many researchers have proposed Knowledge Tracing models that use data from Intelligent Tutoring Systems to predict students' subsequent actions. However, with the development of Intelligent Tutoring Systems, large-scale datasets containing long-sequence data began to emerge. Recent deep learning based Knowledge Tracing models face obstacles such as low efficiency, low accuracy, and low interpretability when dealing with large-scale datasets containing long-sequence data. To address these issues and promote the sustainable development of Intelligent Tutoring Systems, we propose a LSTM BERT-based Knowledge Tracing model for long sequence data processing, namely LBKT, which uses a BERT-based architecture with a Rasch model-based embeddings block to deal with different difficulty levels information and an LSTM block to process the sequential characteristic in students' actions. LBKT achieves the best performance on most benchmark datasets on the metrics of ACC and AUC. Additionally, an ablation study is conducted to analyse the impact of each component of LBKT's overall performance. Moreover, we used t-SNE as the visualisation tool to demonstrate the model's embedding strategy. The results indicate that LBKT is faster, more interpretable, and has a lower memory cost than the traditional deep learning based Knowledge Tracing methods.

The convergence of variable-step L1 scheme is studied for the time-fractional molecular beam epitaxy (MBE) model with slope selection.A novel asymptotically compatible $L^2$ norm error estimate of the variable-step L1 scheme is established under a convergence-solvability-stability (CSS)-consistent time-step constraint. The CSS-consistent condition means that the maximum step-size limit required for convergence is of the same order to that for solvability and stability (in certain norms) as the small interface parameter $\epsilon\rightarrow 0^+$. To the best of our knowledge, it is the first time to establish such error estimate for nonlinear subdiffusion problems. The asymptotically compatible convergence means that the error estimate is compatible with that of backward Euler scheme for the classical MBE model as the fractional order $\alpha\rightarrow 1^-$. Just as the backward Euler scheme can maintain the physical properties of the MBE equation, the variable-step L1 scheme can also preserve the corresponding properties of the time-fractional MBE model, including the volume conservation, variational energy dissipation law and $L^2$ norm boundedness. Numerical experiments are presented to support our theoretical results., Comment: 23 pages,21 figures,4 tables

In this work, we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo's form. The L1 implicit scheme is shown to preserve a variational energy dissipation law on arbitrary nonuniform time meshes by using the recent discrete analysis tools, i.e., the discrete orthogonal convolution kernels and discrete complementary convolution kernels. Then the discrete embedding techniques and the fractional Gr\"onwall inequality were applied to establish an $L^2$ norm error estimate on nonuniform time meshes. An adaptive time-stepping strategy according to the dynamical feature of the system is presented to capture the multi-scale behaviors and to improve the computational performance., Comment: 17 pages, 20 figures, 2 tables