Let n be a positive integer and f belong to the smallest ring of functions $\mathbb R^n\to \mathbb R$ that contains all real polynomial functions of n variables and is closed under exponentiation. Then there exists $d\in \mathbb N$ such that for all $m\in \{0,\dots , n\}$ and $c\in \mathbb R^{m}$, if $x\mapsto f(c,x)\colon \mathbb R^{n-m}\to \mathbb R$ is harmonic, then it is polynomial of degree at most d. In particular, f is polynomial if it is harmonic.

This paper offers a formal analysis of continuity, welfarism, value satiability, lifeboat cases, along with their interconnectedness with sufficientarianism, with particular attention to the recent defences of sufficientarianism by Ben Davies and Lasse Nielsen in response to Hun Chung’s Prospect Utilitarianism (PU). It demonstrates how precise formal definitions help resolve conceptual ambiguities and sharpen philosophical argumentation in distributive ethics. Without such precision, one risks misidentifying or mischaracterizing important normative concepts and theories, leading to confusion or strawman critiques. By highlighting these risks, the paper underscores the methodological importance of precise definitions and formal analysis in ensuring clarity, consistency, and rigor in ethical theorizing.

Parkinson’s disease, the second most prevalent neurological disorder, is a multisystem neurodegenerative disease characterized by both motor and non-motor symptoms. Transcranial direct current stimulation (tDCS) is a non-invasive brain neuromodulation technique that has been shown to be effective in some neurological conditions and for some clinical outcomes. To evaluate the efficacy of tDCS combined with gait training in Parkinson’s disease, compared to placebo, absence of treatment, conventional therapy, or other therapies. A systematic review and meta-analysis were performed in accordance with the PRISMA guidelines and registered in PROSPERO CRD42024542552. The literature search was conducted in PubMed, CINAHL, SPORT Discus, Web of Science, Scopus, MEDLINE, and Academic Search Ultimate (EBSCO) databases up to May 2024, limited to trials from the last 10 years. A total of 600 articles were identified; 9 were included in the systematic review and 8 in the meta-analysis. Significant intra-group changes were observed, but in the meta-analysis, no significant differences were seen between tDCS + gait training and tDCS placebo + gait training, although variables such as motor function slightly favored the combination (MD = −0.49; 95% CI [−1.55; 0.57], I2 = 0%). The combination of tDCS and gait training could provide significant motor benefits in terms of gait speed, functional mobility, cadence, motor function, quality of life, 6MWT, coordination and dynamic balance, flexibility, and stretch resistance in patients with Parkinson’s disease, but not in a more effective way than the same training without stimulation.

Blood 25-hydroxyvitamin D (25(OH)D) concentrations vary considerably by season and sex. The present study aimed to determine associations between vitamin D deficiency and mortality in Japanese adults and identify risk thresholds according to 25(OH)D concentrations. This was a cohort study with an 11-year follow-up. Participants were 8285 community-dwelling Japanese adults aged 40–74 years. Plasma 25(OH)D concentrations were measured by chemiluminescent immunoassay at baseline and divided into quintiles for each of the subgroups stratified by season and sex (denoted as season- and sex-stratified quintiles). The main outcome was all-cause mortality. Hazard ratios (HR) were calculated using a Cox proportional hazards model. Mean age and 25(OH)D concentration were 59·9 years (sd = 9·1) and 50·1 nmol/l (sd = 18·1), respectively. Lower season- and sex-stratified quintiles were associated with higher hazards of all-cause mortality (Pfor trend = 0·0015), with the first quintile (median = 28·2 nmol/l) having a higher HR (HR = 1·46, 95 % CI, 1·13, 1·88) than the highest quintile (reference). When crude quintiles were used, the overall association was similar (Pfor trend = 0·0027), with the first (median = 28·0 nmol/l) and second (median = 39·7 nmol/l) quintiles having higher HR (HR = 1·40, 95 % CI, 1·06, 1·85 and 1·38, 95 % CI, 1·07, 1·77, respectively) than the reference. The risk threshold difference was estimated to be approximately 10 nmol/l. In conclusion, low blood 25(OH)D concentrations are associated with high mortality risk. Crude blood 25(OH)D concentration may modulate the estimated risk threshold for vitamin D deficiency associated with mortality.

Sex and gender are often overlooked factors in the delivery of mental healthcare, resulting in a gender blindness that ignores the specific needs of women and, in some circumstances, men. A lack of gender-disaggregated data and balanced sex and gender representation in clinical research has led to knowledge gaps in women’s health overall. This article explores the influence of gender bias across a spectrum of conditions where disparities in diagnosis, treatment and research exist, including psychosis, mood disorders, neurodevelopmental disorders, eating disorders and substance use disorders. The influence of female reproductive hormones (oestrogen and progesterone) on symptom onset, presentation and treatment response is also discussed where clinically relevant. Gender-aware approaches to delivering mental healthcare are needed, including trauma-informed care, in order to deliver equitable and effective mental healthcare for all.

This study examines how changes in political leadership and rising U.S. polarization flow through societal culture to corporate culture. Using quasi-experimental methods, we find that executives adjust culture messaging in earnings calls on extensive and intensive margins across varying political contexts. These changes follow two pathways: under political alignment, executives emphasize their firm’s culture, motivated by pride; and under political misalignment, executives reduce cultural messaging—particularly innovation, quality, and respect—due to lower perceived growth opportunities. Additional tests reveal these changes reflect strategic communication rather than fundamental cultural changes. Our findings highlight how cultural messaging varies with political context.

In the course of seeking indigenous documentation in a European-centered colonial archival repository, we uncovered a collection of African sources that highlight the literary work of African and Asian literate agents. The research enabled us to identify numerous indigenous African and Asian writings within an archive originally intended to support the Portuguese colonial administration. This article presents an archival survey on African documentation from Mozambique held in the Overseas Historical Archive (Arquivo Histórico Ultramarino), in Lisbon, Portugal.

What determines the outcomes of negotiations is a central question in political science, and such negotiations are crucial in coalition systems where political parties distribute policy payoffs during coalition negotiations. In this paper, we argue that due to the combination of the non-separability of most public policies and the shared responsibility for policy outcomes under coalition governments, which policies a party manages to get included in a coalition agreement will reflect these policies’ popularity among the other governing coalition parties, rather than policy payoffs being driven by proportionality or relative salience. Using a unique dataset containing novel data on the budgetary impact of every measure proposed in election manifestos and coalition agreements over five government formations, we can directly observe the policy payoffs extracted by each party for participating in government, using a measure that is directly comparable across parties, policy areas, and time. The results have substantial implications for our understanding of the formation process and functioning of coalition governments.