Third party funding for dispute resolution:a comparative study of England, Hong Kong, Singapore, the Netherlands and Mainland China

This thesis seeks to review Third Party Funding (hereafter TPF) from a comparative perspective. TPF is often defined as the provision of funding to parties in litigation and arbitration by a third party on a non-recourse basis in exchange for a proportion of the final proceeds. It serves not only access to justice but also various other public and private interests. Nonetheless, TPF is not risk-free. Abuses associated with TPF are not unobservable in practice. The question that needs to be asked is how to integrate TPF into the legal system without compromising the integrity of the law and the legal profession. With the focus on commercial cases, this book is allowed to employ the comparative method to examine the practice and the regulation of TPF in more than one jurisdiction. It includes not only jurisdictions with well-developed TPF markets but also new emerging markets where the regulation of TPF is absent or has not been put to the test on a large scale. With these efforts, this thesis aims to report new developments of TPF and the related legal instruments. It also manages to analyze and compare the distinctive features of TPF and its regulation in the chosen jurisdictions. Comparative results are taken into account when making policy prescriptions for China. Apart from these results, Chinese legislators are suggested to contemplate the legal tradition and the existing laws in China

A Bayesian adaptive marker‐stratified design for molecularly targeted agents with customized hierarchical modeling

It is well known that the treatment effect of a molecularly targeted agent (MTA) may vary dramatically, depending on each patient's biomarker profile. Therefore, for a clinical trial evaluating MTA, it is more reasonable to evaluate its treatment effect within different marker subgroups rather than evaluating the average treatment effect for the overall population. The marker‐stratified design (MSD) provides a useful tool to evaluate the subgroup treatment effects of MTAs. Under the Bayesian framework, the beta‐binomial model is conventionally used under the MSD to estimate the response rate and test the hypothesis. However, this conventional model ignores the fact that the biomarker used in the MSD is, in general, predictive only for the MTA. The response rates for the standard treatment can be approximately consistent across different subgroups stratified by the biomarker. In this paper, we proposed a Bayesian hierarchical model incorporating this biomarker information into consideration. The proposed model uses a hierarchical prior to borrow strength across different subgroups of patients receiving the standard treatment and, therefore, improve the efficiency of the design. Prior informativeness is determined by solving a “customized” equation reflecting the physician's professional opinion. We developed a Bayesian adaptive design based on the proposed hierarchical model to guide the treatment allocation and test the subgroup treatment effect as well as the predictive marker effect. Simulation studies and a real trial application demonstrate that the proposed design yields desirable operating characteristics and outperforms the existing designs

Migration and Growth of Protoplanetary Embryos I: Convergence of Embryos in Protoplanetary Disks

According to the core-accretion scenario, planets form in protostellar disks through the condensation of dust, coagulation of planetesimals, and emergence of protoplanetary embryos. At a few AU in a minimum mass nebula, embryos' growth is quenched by dynamical isolation due to the depletion of planetesimals in their feeding zone. However, embryos with masses ($M_p$) in the range of a few Earth masses ($M_\oplus$) migrate toward a transition radius between the inner viscously heated and outer irradiated regions of their natal disk. Their limiting isolation mass increases with the planetesimals surface density. When $M_p > 10 M_\oplus$, embryos efficiently accrete gas and evolve into cores of gas giants. We use numerical simulation to show that, despite streamline interference, convergent embryos essentially retain the strength of non-interacting embryos' Lindblad and corotation torque by their natal disks. In disks with modest surface density (or equivalently accretion rates), embryos capture each other in their mutual mean motion resonances and form a convoy of super Earths. In more massive disks, they could overcome these resonant barriers to undergo repeated close encounters including cohesive collisions which enable the formation of massive cores.Comment: 9 pages, 6 figures, accepted for publication in Ap

Large deviation principle for reflected SPDE on infinite spatial domain

We study a large deviation principle for a reflected stochastic partial differential equation on infinite spatial domain. A new sufficient condition for the weak convergence criterion proposed by Matoussi, Sabbagh and Zhang ({\it Appl. Math. Optim.} 83: 849-879, 2021) plays an important role in the proof.Comment: 16 page