We study the relation between the coregularity, the index of log Calabi–Yau pairs and the complements of Fano varieties. We show that the index of a log Calabi–Yau pair $(X,B)$ of coregularity $1$ is at most $120\lambda ^2$, where $\lambda $ is the Weil index of $K_X+B$. This extends a recent result due to Filipazzi, Mauri and Moraga. We prove that a Fano variety of absolute coregularity $0$ admits either a $1$-complement or a $2$-complement. In the case of Fano varieties of absolute coregularity $1$, we show that they admit an N-complement with N at most 6. Applying the previous results, we prove that a klt singularity of absolute coregularity $0$ admits either a $1$-complement or $2$-complement. Furthermore, a klt singularity of absolute coregularity $1$ admits an N-complement with N at most 6. This extends the classic classification of $A,D,E$-type klt surface singularities to arbitrary dimensions. Similar results are proved in the case of coregularity $2$. In the course of the proof, we prove a novel canonical bundle formula for pairs with bounded relative coregularity. In the case of coregularity at least $3$, we establish analogous statements under the assumption of the index conjecture and the boundedness of B-representations.

In One Savings Bank plc v Catherine Waller-Edwards,1 the Court of Appeal considered – for the first time – whether banks are put on constructive notice to potential undue influence in joint benefit remortgage/suretyship hybrid transactions. At a time where there is an increasing awareness of economic abuse as a form of domestic abuse,2 this appeal offered an important opportunity to reassess banks’ responsibilities in assisting potential victim-survivors. Unfortunately, that opportunity was not seized. In this case comment, I set out the negative impacts the Court of Appeal judgment could have on victim-survivors of economic abuse going forward, and how these concerns could – since this case has now been given leave to appeal – be addressed by the Supreme Court.

In the rural villages of the Sierra Madre region of Chiapas, women experiencing hardship show signs of emotional distress that are diagnosed as depression and anxiety by health professionals. In this study, we critically analyze the impact of a pilot mental health group intervention (Women’s Circles) facilitated by community mental health workers. The intervention consisted of eight structured sessions that included psychoeducation from a gender perspective, mindfulness exercises, interactive activities, arts and crafts, and sharing personal experiences. We carried out participant observation and 27 semi-structured interviews with the participants. The main outcomes were, first, that participants’ moods improved, and second, that the improvement was mainly due to gathering with others and having someone to talk to. In addition, we observed that lessons during the Circles were often prescriptive, which, rather than creating a space for reflection on personal experiences, imposed globalized views of mental health and gender. In sum, we describe both the positive impact this program had on mental well-being and the problematic spreading of psychoeducation.

The relationships between the Japanese beetle (JB) Popillia japonica Newman, 1841 and the grapevine agroecosystem were investigated in Piedmont in 2020 and 2021, to assess the impact of the species and its distribution within vineyards in relation to the proximity of environmental risk factors. Grubs were sampled by soil coring in the inter-rows of vineyards, whereas both adult beetles and defoliation were counted directly on grapevine plants. The presence of spatial autocorrelation was assessed and the influence of environmental variables (distance from woodlands, meadows and the margin of the vineyard, soil parameters, year of sampling, and year of first detection of the JB) was evaluated through generalized linear mixed models. Beetles and defoliation were more clustered at the edges of vineyards, whereas grubs were localized in few hot spots, generally close to meadows. Spatial autocorrelation was weaker for grubs with respect to adults and defoliation. Grub density depended on distance from meadows, and partially on soil features. Adults abundance was influenced by the proximity to meadows, woodlands, and their presence was clustered at the margin of vineyards. The JBs seem to rely on grapevine mainly as a food source rather than a reproductive site, preferring meadows for egg-laying: therefore, pest management in vineyards should be more focused on adult beetles rather than larvae in the vineyard inter-rows.

Employees’ organizational citizenship behavior (OCB) is an important determinant of organizational effectiveness; hence, scholars and practitioners are particularly interested in the factors, mechanisms, and conditions that promote such behaviors. Guided by the ability–motivation–opportunity framework, we draw on the social cognitive theory of moral thought and action to conceptualize a model that delineates the role of ethics-oriented human resource management (HRM) systems in promoting OCBs through the mediating role of employees’ moral attentiveness. We also refer to the job demands–resources theory to describe the moderating role of work-family balance in the indirect relationship between HRM systems and OCBs. The findings of an experiment involving 157 working adults (Study 1) and a three-wave field survey of 328 employees (Study 2) converge to support the hypothesized direct and indirect (via moral attentiveness) relationships between ethics-oriented HRM systems and OCBs as well as the first-stage moderating role of work-family balance.

Stochastic embeddings of finite metric spaces into graph-theoretic trees have proven to be a vital tool for constructing approximation algorithms in theoretical computer science. In the present work, we build out some of the basic theory of stochastic embeddings in the infinite setting with an aim toward applications to Lipschitz free space theory. We prove that proper metric spaces stochastically embedding into $\mathbb {R}$-trees have Lipschitz free spaces isomorphic to $L^1$-spaces. We then undergo a systematic study of stochastic embeddability of Gromov hyperbolic metric spaces into $\mathbb {R}$-trees by way of stochastic embeddability of their boundaries into ultrametric spaces. The following are obtained as our main results: (1) every snowflake of a compact, finite Nagata-dimensional metric space stochastically embeds into an ultrametric space and has Lipschitz free space isomorphic to $\ell ^1$, (2) the Lipschitz free space over hyperbolic n-space is isomorphic to the Lipschitz free space over Euclidean n-space and (3) every infinite, finitely generated hyperbolic group stochastically embeds into an $\mathbb {R}$-tree, has Lipschitz free space isomorphic to $\ell ^1$, and admits a proper, uniformly Lipschitz affine action on $\ell ^1$.

Natasha Abrahart was a physics student at the University of Bristol. She was suffering from depression and social anxiety disorder, which seriously impacted her ability to partake in oral assessments. Eventually, Natasha sadly took her own life. Her father, Dr Robert Abrahart, as personal representative and estate administrator, sued the University of Bristol for negligence and breach of sections 15, 19 and 20 of the Equality Act 2010, read with section 91(2)(a) and/or (f) of the same Act.1 Under such provisions, universities have a duty to provide reasonable adjustments and support, in educational provision and assessments, to disabled students, defined by section 6(1) of the Equality Act 2010 as ‘a physical or mental impairment’ which has ‘a substantial and long-term adverse effect’ on the ability to ‘carry out normal day-to-day activities’. However, Schedule 13, para 4(2), to the Equality Act 2010 exempts those assessments which constitute a competency standard, defined as ‘an academic, medical or other standard applied for the purpose of determining whether or not a person has a particular level of competence or ability’.2

To assess the therapeutic effects of probiotic oral therapy in pediatric patients with anorexia nervosa and to investigate its impact on intestinal flora composition, brain-gut peptide levels, and overall clinical outcomes. A retrospective study was conducted involving 100 children diagnosed with anorexia nervosa at Xingtang County People’s Hospital between January 2023 and June 2024. Patients were divided into two groups: a control group (n=50) receiving zinc gluconate oral solution alone and an observation group (n=50) receiving zinc gluconate plus probiotics. Outcome measures included intestinal flora analysis, brain-gut peptide levels (SS, NO), clinical efficacy, serum trace element levels (calcium, zinc, iron), and prognosis, including recurrence rates six months post-treatment. Baseline characteristics were similar between the two groups (P>0.05). After treatment, the observation group showed significantly higher levels of Bifidobacterium and Lactobacillus and lower levels of Enterobacter compared to the control group (P<0.05). Additionally, the observation group had lower levels of SS and NO (P<0.05), indicating improved brain-gut communication. Clinical efficacy was significantly higher in the observation group (P<0.05), with improved serum trace element levels (P<0.05 for calcium, zinc, and iron). Furthermore, the recurrence rate six months post-treatment was significantly lower in the observation group compared to the control group (P<0.05). Probiotic supplementation in children with anorexia nervosa effectively modulates intestinal flora, improves brain-gut peptide levels, and enhances clinical outcomes.

Liberals experience more distress than conservatives. Why? We offer a novel explanation, the social support hypothesis. Maintaining social support and avoiding exclusion are basic human motivations, but people differ in their sensitivity to the threat of social exclusion. Among people high in the personality trait neuroticism, exclusion easily triggers feelings of vulnerability and neediness. The social support hypothesis translates this to politics. Concerned with their own vulnerability, we find that neurotic people prefer policies of care – social welfare and redistribution – but not other left-wing policies. Specifically, it is anxiety – the facet of neuroticism tapping sensitivity to social threats – that drives this link. And it is only for people experiencing exclusion that anxiety predicts support for social welfare. Our results come from two experiments and four representative surveys across two continents. They help to resolve the puzzle of liberal distress while providing a new template for research on personality and politics.

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.