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

Talcum powder and photoprotection

Context: Talcum powder is a popular daily use cosmetic product in India with a high urban and rural penetration. Aim: To examine the photoprotective ability of a popular brand of talcum powder. Design: Nonrandomized controlled efficacy study. Subjects and Methods: Minimal erythema dose (MED) following narrowband ultraviolet B irradiation among ten volunteers was recorded. Sun protection factor (SPF) of talcum powder was determined by standard in vivo method. Percentages of zinc oxide in the test sample and ten other commercially available brands of talcum powder were estimated by atomic absorption spectrophotometry. Statistical Analysis Used: Calculation of mean. Results: The mean MED of volunteers was 310 milli Joule (mJ) without talcum powder and 400 mJ with talcum powder. The mean SPF of talcum powder was 1.29. The percentage of zinc oxide in the test sample was estimated to be 1.5%. Conclusions: Talcum powder offers low photoprotection due to low zinc oxide content

Efficacy of rapid-onset oral fentanyl formulations vs. oral morphine for cancer-related breakthrough pain: a meta-analysis of comparative trials

Context: Breakthrough cancer pain (BTcP) is widely recognized as a clinically significant complication of chronic cancer pain. With most BTcP episodes peaking in intensity within a few minutes and lasting for approximately 30 minutes, speed of onset is crucial for effective pain management. Although the last decade has seen the development of a number of rapid-onset fentanyl preparations, BTcP is still typically managed by supplemental or rescue doses of the patient's around-the-clock medication, such as oral morphine. Importantly, although the fentanyl preparations, such as fentanyl buccal tablet (FBT), sublingual fentanyl citrate orally disintegrating tablet (ODT), and oral transmucosal fentanyl citrate lozenge (OTFC), have all been proven to be efficacious in clinical studies, oral morphine has never been specifically tested in BTcP, other than as a comparator in studies of OTFC and fentanyl pectin nasal spray. Objectives: To determine the relative contributions to pain relief from oral morphine and the fentanyl preparations using placebo as a common comparator. Methods: Relevant studies were identified by review of the literature and used in a mixed-treatment meta-analysis to indirectly compare fentanyl preparations, morphine, and placebo for the treatment of BTcP. Results: Analysis incorporating the five relevant studies identified revealed that although the fentanyl preparations provide superior pain relief vs. placebo in the first 30 minutes after dosing (FBT provided an 83% probability of superior pain relief, ODT 66%, and OTFC 73% vs. placebo), oral morphine performed little better than placebo (56% probability). Conclusion: This mixed-treatment analysis suggests that FBT, ODT, and OTFC might provide more efficacious treatment options than oral morphine for BTcP