Irreducible weight modules over Witt algebras with infinite dimensional weight spaces

Let $d>1$ be an integer. In 1986, Shen defined a class of weight modules $F^\alpha_b(V)$ over the Witt algebra $\mathcal{W}_d$ for \a\in\C^d, b\in\C, and an irreducible module $V$ over the special linear Lie algebra \sl_d. In 1996, Eswara Rao determined the necessary and sufficient conditions for these modules to be irreducible when $V$ is finite dimensional. In this note, we will determine the necessary and sufficient conditions for all these modules $F^\alpha_b(V)$ to be irreducible where $V$ is not necessarily finite dimensional. Therefore we obtain a lot of irreducible $\mathcal{W}_d$-modules with infinite dimensional weight spaces

Harish-Chandra modules over the \Q Heisenberg-Virasoro Algebra

In this paper, it is proved that all irreducible Harish-Chandra modules over the \Q Heisenberg-Virasoro algebra are of intermediate series (all weight spaces are 1-dimensional)

A Decade's Battle on Dataset Bias: Are We There Yet?

We revisit the "dataset classification" experiment suggested by Torralba and Efros a decade ago, in the new era with large-scale, diverse, and hopefully less biased datasets as well as more capable neural network architectures. Surprisingly, we observe that modern neural networks can achieve excellent accuracy in classifying which dataset an image is from: e.g., we report 84.7% accuracy on held-out validation data for the three-way classification problem consisting of the YFCC, CC, and DataComp datasets. Our further experiments show that such a dataset classifier could learn semantic features that are generalizable and transferable, which cannot be simply explained by memorization. We hope our discovery will inspire the community to rethink the issue involving dataset bias and model capabilities

Collaborative socially responsible practices for improving the position of Chinese workers in global supply chains

In this paper we evaluate three projects with the participation of 40 supplier firms in several Chinese coastal provinces representing multi-stakeholder efforts to provide alternative channels through which workers can voice their concerns. The supplier firms took on these projects to reduce worker dissatisfaction and employee turnover. The projects fill an institutional void in employer–employee relations within Chinese supplier firms as they provide alternative channels for workers to voice their concerns. The role of civil society organisations focusing on labour interests was a crucial feature of the projects, through capacity-building for workers and by providing independence. The supplier firms and their workers have benefitted as firms take measures to enhance worker satisfaction, while the reduced employee turnover positively impacted firm performance. We propose that these collaborative socially responsible practices are a potential way to strengthen the positions of workers and supplier firms in global supply chain