A Proof of Fusion Rules Formula

A new proof of the fusion rules formula in the context of vertex operator algebra is given. Some more general relations between the space of intertwining operators and $A(V)$ bimodules are obtained

Cosmological constraints on neutrino masses in light of JWST red and massive candidate galaxies

The overabundance of the red and massive candidate galaxies observed by the James Webb Space Telescope (JWST) implies efficient structure formation or large star formation efficiency at high redshift $z\sim 10$. In the scenario of a low or moderate star formation efficiency, because massive neutrinos tend to suppress the growth of structure of the universe, the JWST observation tightens the upper bound of the neutrino masses. Assuming $\Lambda$ cold dark matter cosmology and a star formation efficiency $\in [0.05, 0.3]$ (flat prior), we perform joint analyses of Planck+JWST and Planck+BAO+JWST, and obtain improved constraints $\sum m_\nu < 0.196\,\mathrm{eV}$ and $\sum m_\nu < 0.111\,\mathrm{eV}$ at 95% confidence level, respectively. Based on the above assumptions, the inverted mass ordering, which implies $\sum m_\nu\geq 0.1\mathrm{eV}$, is excluded by Planck+BAO+JWST at 92.7% confidence level.Comment: 9 pages, 8 figure

Twisted restricted conformal blocks of vertex operator algebras II: twisted restricted conformal blocks on totally ramified orbicurves

In this paper, we introduce a notion of twisted restricted conformal blocks on totally ramified orbicurves and establish an isomorphism between the space of twisted restricted conformal blocks and the space of twisted conformal blocks. The relationships among twisted (restricted) conformal blocks, $g$-twisted (restricted) correlation functions, and twisted intertwining operators are explored. Furthermore, by introducing a geometric generalization of Zhu's algebra and its modules, we obtain a description of the space of coinvariants by modules over associative algebras and show it is finite-dimensional under some conditions. In particular, a more conceptual proof of the $g$-twisted fusion rules theorem in vertex operator algebra theory is provided.Comment: 54 pages. New applications are adde

An exploration of Chinese Doctoral Student’s motivations and expectations of studying in the UK.

This qualitative research study delves into the perceived impact of UK doctoral programmes on Chinese doctoral students (CDS), aiming to elucidate their motivations, experiences, and expectations throughout their academic journey. Focused on understanding the academic experience and professional development of CDS, the research investigates the reasons behind their decision-making and the influencing factors on their behaviour. At the same time, the push and pull theoretical framework offers this research a valuable lens through which to examine the complex dynamics of migration. Through a qualitative research methodology, including semi-structured interviews and focus groups, firsthand experiences and perceptions of CDS studying abroad in the UK are collected and analysed. The study explores various dimensions, including motivations for studying in the UK, perceptions of learning and teaching experiences, expectations regarding the impact on future academic careers, and motivations for returning to China post-graduation.The key findings of this study are threefold: Firstly, there are a number of reasons why the respondents selected the UK as their preferred destination for further study. These included: the quality of education, career prospects, economic prosperity, their own interests, family pressure, peer influence and policy-related factors. Secondly, regarding to teaching and learning experience in the UK, CDS generally exhibit a positive outlook on the learning environment in the UK, acknowledging the emphasis on critical thinking, independent study, and research skills. Thirdly, despite the allure of opportunities and experiences abroad, a significant proportion of CDS harbour a deep-rooted commitment to contributing to the development and advancement of their home country. They perceive their education overseas not only as a means to enhance their individual skills and knowledge but also as a means to contribute to China's socio-economic progress and global standing.Findings from this study offer insights and practical recommendations for universities, policymakers, and academic staff members seeking to enhance the experiences of doctoral students studying abroad. Ultimately, this research contributes to the improvement of international doctoral education and provides valuable guidance for facilitating the academic and professional development of Chinese doctoral students in the UK

TFormer: A throughout fusion transformer for multi-modal skin lesion diagnosis

Multi-modal skin lesion diagnosis (MSLD) has achieved remarkable success by modern computer-aided diagnosis technology based on deep convolutions. However, the information aggregation across modalities in MSLD remains challenging due to severity unaligned spatial resolution (dermoscopic image and clinical image) and heterogeneous data (dermoscopic image and patients' meta-data). Limited by the intrinsic local attention, most recent MSLD pipelines using pure convolutions struggle to capture representative features in shallow layers, thus the fusion across different modalities is usually done at the end of the pipelines, even at the last layer, leading to an insufficient information aggregation. To tackle the issue, we introduce a pure transformer-based method, which we refer to as ``Throughout Fusion Transformer (TFormer)", for sufficient information intergration in MSLD. Different from the existing approaches with convolutions, the proposed network leverages transformer as feature extraction backbone, bringing more representative shallow features. We then carefully design a stack of dual-branch hierarchical multi-modal transformer (HMT) blocks to fuse information across different image modalities in a stage-by-stage way. With the aggregated information of image modalities, a multi-modal transformer post-fusion (MTP) block is designed to integrate features across image and non-image data. Such a strategy that information of the image modalities is firstly fused then the heterogeneous ones enables us to better divide and conquer the two major challenges while ensuring inter-modality dynamics are effectively modeled. Experiments conducted on the public Derm7pt dataset validate the superiority of the proposed method. Our TFormer outperforms other state-of-the-art methods. Ablation experiments also suggest the effectiveness of our designs

RTrack: Accelerating Convergence for Visual Object Tracking via Pseudo-Boxes Exploration

Single object tracking (SOT) heavily relies on the representation of the target object as a bounding box. However, due to the potential deformation and rotation experienced by the tracked targets, the genuine bounding box fails to capture the appearance information explicitly and introduces cluttered background. This paper proposes RTrack, a novel object representation baseline tracker that utilizes a set of sample points to get a pseudo bounding box. RTrack automatically arranges these points to define the spatial extents and highlight local areas. Building upon the baseline, we conducted an in-depth exploration of the training potential and introduced a one-to-many leading assignment strategy. It is worth noting that our approach achieves competitive performance to the state-of-the-art trackers on the GOT-10k dataset while reducing training time to just 10% of the previous state-of-the-art (SOTA) trackers' training costs. The substantial reduction in training costs brings single-object tracking (SOT) closer to the object detection (OD) task. Extensive experiments demonstrate that our proposed RTrack achieves SOTA results with faster convergence

LiteTrack: Layer Pruning with Asynchronous Feature Extraction for Lightweight and Efficient Visual Tracking

The recent advancements in transformer-based visual trackers have led to significant progress, attributed to their strong modeling capabilities. However, as performance improves, running latency correspondingly increases, presenting a challenge for real-time robotics applications, especially on edge devices with computational constraints. In response to this, we introduce LiteTrack, an efficient transformer-based tracking model optimized for high-speed operations across various devices. It achieves a more favorable trade-off between accuracy and efficiency than the other lightweight trackers. The main innovations of LiteTrack encompass: 1) asynchronous feature extraction and interaction between the template and search region for better feature fushion and cutting redundant computation, and 2) pruning encoder layers from a heavy tracker to refine the balnace between performance and speed. As an example, our fastest variant, LiteTrack-B4, achieves 65.2% AO on the GOT-10k benchmark, surpassing all preceding efficient trackers, while running over 100 fps with ONNX on the Jetson Orin NX edge device. Moreover, our LiteTrack-B9 reaches competitive 72.2% AO on GOT-10k and 82.4% AUC on TrackingNet, and operates at 171 fps on an NVIDIA 2080Ti GPU. The code and demo materials will be available at https://github.com/TsingWei/LiteTrack