Picard groups on moduli of K3 surfaces with Mukai models

We discuss the Picard group of moduli space $\mathcal{K}_g$ of quasi-polarized K3 surfaces of genus $g\leq 12$ and $g\neq 11$. In this range, $\mathcal{K}_g$ is unirational and a general element in $\mathcal{K}_g$ is a complete intersection with respect to a vector bundle on a homogenous space, by the work of Mukai. In this paper, we find generators of the Picard group $Pic_\mathbb{Q}(\mathcal{K}_g)$ using Noether-Lefschetz theory. This verifies the Noether-Lefschetz conjecture on moduli of K3 surfaces in these cases.Comment: fix some typo

Innovation Through Interpretation: How Judges Make Policy in China

My dissertation explores the role of courts in making the law respond to the social and economic transformations that have defined contemporary China. In particular, I find that Chinese judges working in the civil law tradition are nevertheless able to effect incremental changes in existing law without having to resort to the formal legislative process.Part I reviews the theory and practice of Chinese statutory interpretation, paying special attention to the use of sources and methodology. I demonstrate that despite the sometimes overdrawn differences between civil law and common law jurisdictions, techniques of statutory interpretation can and are employed by Chinese judges to give the law a fluid and dynamic character, thereby facilitating its adaptation to emergent societal circumstances.A legal innovation can spread as a court’s novel reading of a statute is adopted by other courts and becomes mainstream. Part II describes and accounts for the diffusion of judicial innovations in Chinese courts since the 1980s. The confluence of two factors, the norm of judicial openness and the medium of the internet, have made prior judicial decisions readily accessible and a convenient resource for Chinese judges confronting hard cases. These prior judicial decisions serve as a form of political communication between courts that indicates the acceptability and feasibility of policy innovations in the law. Three case studies – the “Guiding Cases” issued by Chinese Supreme People’s Court, and a series of provincial-level cases on driving under the influence (DUI) and ATM Theft – demonstrate how innovative statutory interpretations diffuse through the court system and eventually precipitate legislative amendment of outdated statutes. I supplement these case studies with surveys, survey experiment, and interviews. Finally, Part III of my dissertation describes the law-making function of the judiciary in other civil law countries, such as Japan and Germany. Drawn from the convergence of judicial roles between common law and civil law systems, it further assesses the social, political, and legal conditions necessary for judicially initiated policy innovations to succeed in China. This chapter demonstrates that judicial innovations in China survive because of their silent and gradual character of their assimilation by the legal system. Some of these innovations fade, however, due to political reasons or the transience of the societal conditions that gave rise to them.Overall, I conclude that despite their protestations to the contrary, Chinese courts balance the tension between the unchanging code and the changing social and economic conditions in Chinese society by engaging in experimentation through statutory interpretation. In this function, Chinese courts are not that different from their sisters in common law jurisdictions or, for that matter, from courts everywhere

Bone in vivo: Surface mapping technique

Bone surface mapping technique is proposed on the bases of two kinds of uniqueness of bone in vivo, (i) magnitude of the principal moments of inertia, (ii) the direction cosines of principal axes of inertia relative to inertia reference frame. We choose the principal axes of inertia as the bone coordinate system axes. The geographical marks such as the prime meridian of the bone in vivo are defined and methods such as tomographic reconstruction and boundary development are employed so that the surface of bone in vivo can be mapped. Experimental results show that the surface mapping technique can both reflect the shape and help study the surface changes of bone in vivo. The prospect of such research into the surface shape and changing laws of organ, tissue or cell will be promising.Comment: 9 pages, 6 figure

Unraveling the Relationship between Content Quality, Design, and User Engagement in Douyin's Adolescent Mode

In recent years, short video social platforms have garnered widespread attention, with Douyin (the Chinese version of TikTok) being a typical representative. The daily active users of the teen segment in Douyin are estimated to exceed 42 million. However, there still exists a certain blind spot in the research of Douyin's teen-specific content. This study conducts a content analysis of 360 short videos in Douyin's adolescent mode, and employs a Structural Equation Model (SEM) to analyze the relationships between the content quality, design features, learning objectives, age appropriateness, and user engagement. The results reveal that age appropriateness and learning objectives have a significant positive impact on content quality, and content quality and design features significantly positively impact user engagement. Further discussions point out that Douyin's adolescent mode faces challenges in dealing with issues like gender bias and algorithm bias, which may have adverse effects on the holistic development of teen users. The research findings provide empirical evidence for short video creators and platform optimization, and put forward targeted suggestions for the design of short video content in adolescent mode