Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

The Future of International Investment Regulation: Towards a World Investment Organisation?

With growth in foreign investment and in the number of companies investing in foreign countries, the application of general principles of public international law has not been deemed adequate to regulate foreign investment and there is, as yet, no comprehensive international treaty on the regulation of foreign investment. Consequently, states have resorted to bilateral investment treaties (BITs), regional trade and international investment agreements (IIAs) and free trade agreements (FTAs) to supplement and complement the regime of protection for foreign investors. In the absence of an international investment court, states hosting foreign investment or investor states have opted for investor-state dispute settlement mechanism (ISDS). This mechanism has brought about its own challenges to the international law of foreign investment due to inconsistency in the application and interpretation of the key principles of international investment law by such arbitration tribunals, and further, there is no appellate mechanism to bring about some cohesion and consistency in jurisprudence. Therefore, there are various proposals mooted by scholars to address these challenges and they range from tweaks to BITs and IIAs, the creation of an appellate mechanism and the negotiation of a multilateral treaty to proposals for reform of ISDS only. After assessing the merits and demerits of such proposals, this study goes further, arguing for the creation of a World Investment Organisation (WIO) with a standing mechanism for settlement of investment disputes in order to ensure legal certainty, predictability and the promotion of the flow of foreign investment in a sustainable and responsible manner

An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition

An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach

Ability Tracking and Social Capital in China's Rural Secondary School System

The goal of this paper is describe and analyze the relationship between ability tracking and student social capital, in the context of poor students in developing countries. Drawing on the results from a longitudinal study among 1,436 poor students across 132 schools in rural China, we find a significant lack of interpersonal trust and confidence in public institutions among poor rural young adults. We also find that there is a strong correlation between ability tracking during junior high school and levels of social capital. The disparities might serve to further widen the gap between the relatively privileged students who are staying in school and the less privileged students who are dropping out of school. This result suggests that making high school accessible to more students would improve social capital in the general population

An Analysis of Adherence to Vaccination Recommendations in a Thoracic Organ Transplant Cohort

(1) Background: Vaccination of solid organ transplant (SOT) candidates and recipients is vital to decrease infection-related morbidity and mortality. Here we describe our heart and lung transplant programs’ rates of completion of hepatitis B and pneumococcal vaccinations and identify potential opportunities for improvement. (2) Methods: This is a single-center retrospective study that included all heart and lung transplant recipients between 1 July 2013 and 31 July 2018. We assessed demographics, causes of organ failure, pretransplant hepatitis B immune status, and completion rates for hepatitis B vaccine series, pneumococcal conjugate vaccine (PCV13), and pneumococcal polysaccharide vaccine (PPSV23). (3) Results: A total of 41 patients were included in the heart transplant cohort. Twelve (29.3%) had baseline hepatitis B immunity. Only 8/29 (27.6%) completed the entire 3-dose hepatitis B vaccination series pretransplant. Pretransplant PCV13 and PPSV23 vaccination rates were 58.5% (24/41) and 48.8% (20/41), respectively; no additional patients received PCV13 or PPSV23 post-transplant. In the heart transplant cohort, a majority (82.9%) of patients were evaluated by the Transplant Infectious Diseases consultative service (TxID) pretransplant, and this had a statistically significant association with increased pneumococcal vaccination rates (p = 0.0017, PCV13 and p = 0.0103, PPSV23). In total, 55 patients were included in the lung transplant cohort. Five (9.1%) had baseline hepatitis B immunity; 33/50 (66.0%) completed the hepatitis B vaccine series in the pretransplant setting. Pretransplant PCV13 and PPSV23 vaccination rate was 40.0% (22/55) and 69.1% (38/55), respectively. There was only a 47.3% and 72.3% completion rate overall in the post-transplant setting. (4) Conclusions: There continues to be a need for a comprehensive and coordinated effort to increase vaccine adherence for all SOT candidates in the pretransplant setting