In 1972, Heilbronn introduced the notion of virtual characters and used it to study simple real zeros of Dedekind zeta functions. One of the consequences of his elegant work is the following. Let $\mathrm{K}/ \mathrm{F}$ be a Galois extension of number fields of odd degree. Then any real simple zero of $\zeta_{\mathrm{K}}$ is necessarily a simple zero of $\zeta_{\mathrm{F}}$. The ethos of this paper is to carry out investigation for arbitrary odd order real zeros. While the Riemann zeta function is conjectured to have only simple zeros, the same does not hold for arbitrary Dedekind zeta functions. One of the consequences of our work is that any Galois number field K of odd degree cannot have a non-trivial odd order real zero. Such parity is at least in conformity with extended Riemann hypothesis as the order of vanishing of the Dedekind zeta function $\zeta_{\mathrm{K}}$ at $1/2$ is necessarily even. We also indicate, via a number of illustrative examples (see Remarks 1·1 and 1·2), that in some sense our results are optimal.

People with intellectual and other cognitive disabilities often face barriers to participating in clinical research, particularly related to the informed consent process. Recent federal policy and legal efforts have advanced strategies to address these challenges, including using supported decision-making. This article discusses this recent progress and the risks and potential opportunities to continuing it in a shifting federal landscape.

Pension policies are an increasingly important topic in British elections. This paper discusses what the first year under a Labour government has meant for pension policy, drawing on the Labour Party’s pre-election pledges, before critically considering future directions of pension policy and areas not currently addressed by the Labour government, or where policies could go further. The paper argues that structural inequalities in the labour market and the pension system persist, with consistent evidence of gender and ethnic inequalities in labour market participation, the nature of such participation, pension outcomes, and a range of financial and non-financial wellbeing indicators. Placing adequacy and fairness at the heart of Labour policy can send a strong message on the government’s part of understanding the complex interactions of opportunities and costs across the lifecourse for individuals from diverse backgrounds, and anticipating further demographic and socio-economic changes in the British society and economy.

This case study explores the interaction of brain pathology, criminal behaviour and art in forensic psychiatry through the case of a 68-year-old man exhibiting neuropsychiatric symptoms and delusions. His progressive cognitive and emotional deterioration led to aggressive behaviour, threats towards colleagues and family and allegations of violent and sexual assault. After months of his refusing treatment, magnetic resonance imaging revealed a grade IV glioblastoma. Despite the terminal diagnosis, he was placed in a forensic acute psychiatric unit while under prosecutorial investigation, because his actions remained criminally relevant. In this restrictive setting, he turned to drawing as his primary coping strategy. His artwork offered both an outlet for suffering and a means of transcending a situation characterised by severe illness, legal deprivation of liberty and existential despair. The case illustrates the benefit of creative expression when medical and legal circumstances appear intractable. It also raises ethical and forensic concerns, including impaired culpability due to amygdala and prefrontal damage, refusal of care, thoughts of physician-assisted suicide and the attribution of legal responsibility.

We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients are not too large and do not differ from each other by too much. Additionally, we prove a number of multiplicity one type results for the number-theoretic objects attached to L-functions. These results follow from our main result, which has slightly weaker hypotheses than previous multiplicity one theorems for L-functions. Significantly stronger results are available when the L-function is known to be automorphic.

The aim of this study was to characterize the physiological variation of somatic cell count (SCC) and milk somatic cell subsets in relation to total bacterial count and milk production parameters, in mastitis-free local Greek ewes. To this end, we studied the SCC, daily milk yield and composition, milk somatic cell subset distribution and total bacterial count in the milk of first and second parity Frizarta ewes, at different lactation stages. As there is a total lack of evidence for differential milk somatic cell distribution in local Greek ewes, we chose to study the Frizarta breed, one of the most promising local sheep breeds, extensively reared in Western Greece, highly productive and well adapted to geoclimatic conditions. Partial correlation analysis was performed between SCC and somatic cell subtype populations with milk yield, composition and total bacterial count. Total SCC in Frizarta ewes ranged between 35 and 74 × 103 cells/ml and was significantly influenced by lactation stage and parity number. Neutrophils and lymphocytes were the most abundant immune cell types followed by mammary epithelial cells and macrophages. A positive association of bacterial count with neutrophils and macrophages and a negative association with lymphocytes were observed. Finally, a negative association between total bacterial count with daily milk yield was detected. Our data forms the basis for understanding how parity and stage of lactation affects different immune and epithelial cell populations in the milk of healthy Frizarta ewes and can be used in future studies investigating the effect of the health status on differential cell count in ewe milk.

This paper examines letters from the casebooks of the Valkenberg Lunatic Asylum in the Cape Colony during the South African War. Valkenberg was opened in 1891 in Cape Town, and was the only asylum established exclusively for white patients in the Cape. The South African War took place between 1899 and 1902, and several soldiers serving in the War were treated at Valkenberg during this period. The letters were written by a male patient who used bureaucratic and legal channels to claim his sanity and secure release from the asylum, showcasing a rare example from the archive of a patient’s voice as well as a view into the inner workings of a colonial asylum in South Africa. These letters allow a view into the personal lives of patients and attendants, the medical rules doctors followed, and instances of racism, unexpected solidarity, and loneliness. Analysing these letters reveals the changes taking place in a turbulent South Africa, including the tensions and conflicts of a country at war, the racism and nationalism of early twentieth-century South Africa, and the violence present within the asylum network. By examining letters written directly by a patient, which give voice to a perspective that official institutional records would not ordinarily allow, this paper seeks to contribute to the literature on patient voices in the history of psychiatry.

This study assessed changes in complete pneumococcal vaccination coverage (CPVC) among Peruvian children <5 years before and after the COVID 19 pandemic and evaluated regional differences, associated sociodemographic factors and wealth-related inequality. 2018–2023 Demographic and Health Surveys (DHS) was analyzed. CPVC was defined as receiving the full 2 + 1 schedule of the 13 valent pneumococcal vaccine. Children aged 13–60 months were included. Multivariable analysis used modified Poisson regression and wealth related inequality was assessed using the Concentration index and Erreygers’s corrected Concentration index at national and regional levels. Among 95,586 children, CPVC decreased from 71.9% in 2019 to 69.4% in 2020 (p = 0.003), then returned to pre Covid levels from 2021 onward (72.2% in 2023; p = 0.001), particularly in Lima Metropolitana. Puno (53.3–58.6%) and Madre de Dios (50.9–62.1%) consistently showed the lowest coverage. Nationally, wealth- or sociodemographic related inequalities were minimal; however, regional interactions indicated that the effect of wealth on CPVC varied by area. Depending on the region, factors such as age group, household members and mather’s education were associated with lower CPVC, whereas age at first pregnancy, institutional birth, antenatal care and access to information increased CPVC. Ucayali showed persistently higher CPVC among wealthier populations. Despite a temporary decline during the pandemic, CPVC in Peru rapidly recovered, although regional gaps persist.

The probabilistic no-miracle argument (NMA) for scientific realism has faced significant criticism from Colin Howson’s base-rate fallacy objection, which claims the argument violates Bayesian reasoning principles. This paper argues that such criticisms are premature. Through systematic mathematical analysis, I show that, for theories with high predictive precision, NMA would be inferentially fallacious only if opponents assume prior probabilities of approximate truth that are either “miraculously low” or “super miraculously low.” These assumptions are implausible, question-begging against realism, and unsupported by standard anti-realist arguments. The burden of proof thus shifts to critics to justify these extraordinary claims about prior probabilities.

The global wave of anti-racist social movements in the summer of 2020 was marked by calls for the removal or recontextualization of statues in public space. Conservative politicians and pundits, in turn, framed cultural activism as a “culture war” and a crisis that entailed “erasing history” by calling national heroes into question. I argue that framing the toppling of statues as a historical crisis derives from a colonial understanding of knowledge as singular, universal, and fundamentally European. This understanding of knowledge analytically bifurcates the past and refuses anti-colonial histories of insurgency and contestation. To counter this approach, I engage with the concept of postcolonial critical realism, which theorizes the power of colonial discourses to shape material institutions and esthetic forms, as well as the anti-colonial potential of counter-discourses. To illustrate this argument, I consider the history of two contested statues: Robert E. Lee in Richmond, Virginia, and Joséphine de Beauharnais in Fort-de-France, Martinique. By revisiting this crisis and the responses it engendered, we can make sense of the present “culture war” not as a contemporary crisis but as a response to a longer historical crisis.

Streptococcus agalactiae, a major bovine mastitis pathogen, poses significant economic and antimicrobial resistance (AMR) challenges. This study evaluated AMR in 128 isolates from Shandong, Hebei and Inner Mongolia using the broth microdilution method. Results showed high sensitivity to most antibiotics (e.g. 100% resistance to penicillin, ceftiofur, amoxicillin, cefquinome and vancomycin) but significant resistance to tetracycline (80.7%) and daptomycin (99.3%). Inner Mongolia isolates exhibited higher resistance and mimimum inhibitory concentrations (MIC) values, reflecting regional antibiotic usage differences, guiding mastitis treatment and antibiotic stewardship in China's dairy industry.

As climate crises intensify, youth inclusion in climate governance becomes increasingly important, for their presence could help mitigate the structural restraints of conventional democracies, which inherently incentivise short-term policies. This dispatch reflects what is happening on the ground and examines youth participation in climate governance, comparing three key youth inclusion models: quota-based (Rwanda), consultative (Finland), and donor-supported (Pakistan). The analysis employs a triangulated analytical framework combining Structural Injustice, Participation Ladders, and Intergenerational Justice Theories. Cross-case analysis demonstrates that all models provide partial but insufficient pathways toward intergenerational accountability and ecological sustainability. The research outlines a Youth Quotas Climate Democracy Framework combining youth quotas with safeguards for autonomy, intergenerational youth councils, and democratic innovations to systemically reconfigure democracy toward more inclusive climate governance for future generations.

In this paper, we investigate the extension of uniformisation results for Gromov hyperbolic spaces beyond the standard geodesic setting. By establishing a Gehring-Hayman type theorem for conformal deformations of any intrinsic Gromov hyperbolic space, we provide a framework for analysing spaces that do not necessarily admit geodesics. As a primary application, we prove that any complete intrinsic hyperbolic space with at least two points in the Gromov boundary can be uniformised by densities induced by Busemann functions. Furthermore, we establish that there exists a natural identification between the Gromov boundary of the original space and the metric boundary of the deformed space.

Patient involvement in health technology assessment (HTA) at the organizational level remains relatively underreported in Asia. In 2022, Singapore’s Agency for Care Effectiveness (ACE) established a Consumer Panel to provide strategic advice on strengthening patient participation in HTA processes and policy development. The Panel comprises representatives from local patient organizations, collectively covering a range of health conditions and bringing extensive lived experience within Singapore’s healthcare system. This Perspective outlines ACE’s approach to forming the Panel and highlights its contributions during the inaugural term, including co-developing patient involvement processes, supporting health literacy efforts, and fostering collaboration between ACE and patient communities. Panel members’ reflections on their role and future directions for advancing patient partnership in HTA are also discussed. Beyond improving the quality and relevance of ACE’s work, the Consumer Panel’s achievements provide a valuable example for health authorities in other countries seeking to meaningfully involve patients at the organizational level.