H. H. Chan, K. S. Chua and P. Solé [‘Quadratic iterations to $\pi $ associated to elliptic functions to the cubic and septic base’, Trans. Amer. Math. Soc. 355(4) (2002), 1505–1520] found that, for each positive integer d, there are theta series $A_d, B_d$ and $C_d$ of weight one that satisfy the Pythagoras-like relationship $A_d^2=B_d^2+C_d^2$. In this article, we show that there are two collections of theta series $A_{b,d}, B_{b,d}$ and $C_{b,d}$ of weight one that satisfy $A_{b,d}^2=B_{b,d}^2+C_{b,d}^2,$ where b and d are certain integers.

In the early stages of the COVID-19 pandemic, the treatment of cruise ships by coastal states was inconsistent, with some ships being allowed to dock while others were not. To that end, this Note focuses on the obligations that a coastal state owes to the individuals onboard the cruise ships in the context of the COVID-19 pandemic, including the rights to life and health. It further considers whether and how such rights are to be balanced with other countervailing considerations of such states, such as the risk of transmission to the local communities. This author concludes with the view that individuals onboard the cruise ships can, and should, consider turning to international human rights law for guidance and recourse. After all, the human rights regime is most suited for and accustomed to governing the relationship between individuals and a state, as compared to between states.

A proof of a proposition in the published paper was erroneous. We clarify the effects in this erratum.

As relations between the United States and China have grown tenser, how has the Chinese Communist Party's (CCP) portrayal of the United States changed? And what might portrayals of the United States tell us about domestic messaging in China? This study systematically investigates CCP messaging about the United States in the contemporary era. To do this, we hand code, categorize and analyse 1,761 editorials about the United States published between 2003 and 2022 in People's Daily, the Party's flagship newspaper. In addition to showing a sustained rise in critical portrayals since 2018, we identify and elaborate three distinct critical narratives about the United States: it is a dangerous hegemon abroad, it has poor values at home, and it is increasingly weak and in decline. These narratives appear both independently and in combination and are often framed to contrast with portrayals of China. We argue that these narratives are not just negative propaganda to discredit the United States but can also be a strategy to promote a positive vision of the CCP's virtues and governance at home. This study contributes empirically and theoretically to research on propaganda and legitimation in China.

In 2017, the authors supervised the recovery of a pre-Hispanic stone sculpture near the community of La Victoria, in the Sierra de los Tuxtlas, southern Veracruz, Mexico. The fortuitous discovery of this monument afforded a rare research opportunity to conduct a controlled, systematic archaeological investigation of a known, but poorly documented, Early Classic–period (a.d. 300–450) sculptural tradition. Moreover, this archaeological salvage project facilitated a crucial dialogue with local stakeholders regarding the recovery and final disposition of the monument. This collaborative effort enabled researchers to wed governmental oversight and academic interests with the concerns of local stakeholders, thereby furthering the investigation, conservation, and public appreciation of Classic-period archaeology along Mexico's southern Gulf Lowlands.

The current review will examine the field of food intake biomarkers and the potential use of such biomarkers. Biomarkers of food intake have the potential to be objective measures of intake thus addressing some of the limitations associated with self-reported dietary assessment methods. They are typically food derived biomarkers present in biological samples and distinct from endogenous metabolites. To date, metabolomic profiling has been successful in identifying several putative food intake biomarkers. With respect to food intake biomarkers there has been a proliferation of publications in this field. However, caution is needed when interpreting these as food intake biomarkers. Many have not been validated thus hampering their use. While much of the focus to date is on discovery of food intake biomarkers there are excellent examples of how to utilise these biomarkers in nutrition research. Applications include but are not limited to: (1) measurement of adherence to diets in intervention studies (2) objectively predicting intake with no reliance on self reported data and (3) calibrating self reported data in large epidemiological studies. Examples of these applications will be covered in this review. While significant progress is achieved to date in the food intake biomarkers field there are a number of key challenges that remain. Examples include lack of databases focused on food derived metabolites thus hindering the discovery of new biomarkers and the need for new statistical approaches to deal with multiple biomarkers for single foods. Addressing these and other key challenges will be key to development of future opportunities.

Sexual and gender–based violence (SGBV) is a multifaceted, endemic, and nefarious phenomenon that remains poorly measured and understood, despite greater global awareness of the issue. While efforts to improve data collection methods have increased–including the implementation of the Demographic and Health Survey (DHS) in some countries–the lack of reliable SGBV data remains a significant challenge to developing targeted policy interventions and advocacy initiatives. Using a recent mixed–methods research project conducted by the authors in Sierra Leone as a case study, this paper discusses the current status of SGBV data, challenges faced, and potential research a pproaches.

Climate change exacerbates existing risks and vulnerabilities for people globally, and migration is a longstanding adaptation response to climate risk. The mechanisms through which climate change shapes human mobility are complex, however, and gaps in data and knowledge persist. In response to these gaps, the United Nations Development Programme’s (UNDP) Predictive Analytics, Human Mobility, and Urbanization Project employed a hybrid approach that combined predictive analytics with participatory foresight to explore climate change-related mobility in Pakistan and Viet Nam from 2020 to 2050. Focusing on Karachi and Ho Chi Minh City, the project estimated temporal and spatial mobility patterns under different climate change scenarios and evaluated the impact of such in-migration across key social, political, economic, and environmental domains. Findings indicate that net migration into these cities could significantly increase under extreme climate scenarios, highlighting both the complex spatial patterns of population change and the potential for anticipatory policies to mitigate these impacts. While extensive research exists on foresight methods and theory, process reflections are underrepresented. The innovative approach employed within this project offers valuable insights on foresight exercise design choices and their implications for effective stakeholder engagement, as well as the applicability and transferability of insights in support of policymaking. Beyond substantive findings, this paper offers a critical reflection on the methodological alignment of data-driven and participatory foresight with the aim of anticipatory policy ideation, seeking to contribute to the enhanced effectiveness of foresight practices.