Discussions of the difference between Indigenous and Western legal systems, and the subsequent potential weaving of the two, have become a focus of Aotearoa New Zealand (NZ) law academics and practitioners in recent years. Furthermore, industrial relations may have the potential to further some of this weaving within the world of work. This paper explores the weaving of tikanga Māori (Māori legal systems) and English-derived state law within Aotearoa NZ workplace personal grievance processes, by explaining the meaning of tikanga Māori concepts and their potential application to workplace personal grievance processes. It asks: what is the tikanga Māori take–utu–ea (∼cause–reciprocation–satisfaction) framework in relation to workplace personal grievances? What role could such a framework potentially have in ensuring reciprocal, mana (status)-enhancing approaches for personal grievance processes? This paper shows how current workplace personal grievance processes in Aotearoa NZ often produce ‘winners’ and ‘losers’, and such outcomes are not conducive to maintaining or improving employment relationships. Such processes not only uphold obligations and duties to Indigenous peoples in a workplace context but also improve outcomes for all working peoples. Overall, this paper contributes to an emerging, broader discussion about the world of work and current grievance systems, and how these are unsuitable for the modern era, concluding that Indigenous solutions offer much prospect.

We analyze a formal model of social contact and discrimination in the context of policing. Officers decide how to interact with members of two social groups while working and while socializing. The officers do not fully distinguish between their experiences of crime across these two contexts (“coarse thinking”), so they end up with excessively positive views of groups they socialize with and excessively negative views of those they police. This creates dual feedback loops as officers choose to socialize more with groups they view favorably and over-police those they view as “more criminal.” Interventions that induce positive contact with an overpoliced group can mitigate the officer’s discriminatory policing. However, this beneficial effect only persists if the policy intervention creates sustained positive contact. Our results provide a novel theoretical microfoundation for the contact hypothesis and highlight why effects of many policy interventions aimed at increasing positive contact may be short-lived.

This article argues that practices of gratitude were central to Franco-American relations in the early Cold War. Through the story of the French Gratitude Train to the American People in 1948–1949, it brings the diplomacy of gratitude to the heart of the post-war years, reflecting on the complicated relations between the two countries and on the ability of emotional performances of gratitude to shape as well as nuance post-1945 dynamics. Rather than focusing on political elites, this is a grassroots story which revolves around lace doilies and metal toys; women, children and veterans; lingering traumas mixed with genuine amazement. Through the lens of gratitude practice and performance, the article highlights the importance of ordinary citizens, material culture and feelings in the ideological battles and geopolitical reconfigurations of the mid-twentieth century.

In the UK, when people with dementia are regarded as a risk to themselves or others, they are usually admitted compulsorily onto a National Health Service dementia inpatient ward, under the 1983 Mental Health Act. Remarkably little is known about the experiences of informal (family) carers supporting these individuals with dementia during their stay; this study is the first to explore those experiences.

Qualitative, semi-structured interviews with 12 informal carers with a family member admitted to an NHS dementia inpatient ward in the Northwest of England were analysed. The reflexive thematic analysis identified 4 main themes – (1) Initial adjustment and transition; (2) Becoming a visitor; (3) Receiving support and sharing expertise; (4) Planning for the future – and 15 sub-themes. Some carers experienced traumatic events in the build-up to admission and felt overwhelmed, worried, guilty and stressed during the stay, whilst others felt relieved that the person with dementia was no longer at home. The ward environment was regarded as safe and practical, albeit ‘stark’. Staff care was seen as high-quality; carers appreciated support, when available, from a range of care staff and carer groups. Communication with ward staff was reported as ‘mixed’; positives were receiving information leaflets, attending ward rounds and having informal conversations with staff. Carers often felt excluded from future care planning.

Preliminary suggestions for practice and policy recommendations include enhanced informal carer support during the admission, improved communication with ward staff, making the ward environment accessible and ‘homely’, and explaining staffing levels prior to admission.

The setting is a tutorial on program verification in Agda. Please consult the programme for further details. [See also Appendix A.]

Why do some areas experience lower voter turnout even under compulsory voting systems? This paper examines the impact of migration turnover – encompassing both in- and out-migration – on voter turnout across communities. While past research has focused on migrant/non-migrant differences or in-/out-migration separately, we propose that both migratory movements tend to decrease political participation due to increased transaction and social costs. Using surveys and a new panel dataset combining census and voting records from over 5,000 Brazilian municipalities, we identify a robust negative association between local migratory turnover and voter turnout. This relationship holds across various time frames, levels of aggregation, analytical approaches, and variable definitions. Individual-level data analyses further corroborate these results. Additional tests suggest social costs constitute a key mechanism deterring turnout. These findings highlight the need to consider the broader consequences of population mobility for democratic processes and representation, particularly in areas experiencing higher levels of turnover.

The Imalia polyphase polymetallic deposit, located in the Mahakoshal belt of Central India, is hosted by carbonate rocks. The major part of mineralisation at Imalia results from hydrothermal activity induced by the intrusion of quartz porphyry dykes, which also formed an alteration halo of silicate and oxide minerals during their interaction with the host lithology. The initial silicates to form were hydrothermal Ca-amphibole and a minor amount of garnet, followed by potassic phases including biotite and K-feldspar, as well as rutile, apatite, titanite, pyrite, magnetite and rare calcite and ilmenite. A subsequent, cooler pulse of hydrothermal fluid overprinted the earlier-formed silicates and was responsible for the bulk of the sulphide mineralisation at Imalia. During this transformation phase, propylitic silicates primarily consisting of chlorite and epidote, along with a modest proportion of actinolite, albite, titanite, sericite and calcite, formed, accompanied by iron-rich oxide phases including magnetite, hematite and ilmenite. These silicates mostly formed under high water-to-rock ratios with significant meteoric water influence. Geothermometric and fluid inclusion data indicate that alteration zone minerals formed at temperatures between approximately 150°C and 550°C, at pressures of around 1 kbar and depths of less than 10 km, with a mean oxygen fugacity of log fO2 -32, closely aligned with the FMQ buffer. The alteration zone minerals record the evolution of hydrothermal fluids in a predominantly brittle structural regime, characterised by episodic decompression due to fluid overpressuring and hydrofracturing, as evidenced by various types of breccias, diverse quartz veins, open space-filling textures and fluid inclusion data.

Modern India is a political creation. The citizens of the world’s most populous country speak 100 languages, practice eight major religions, and belong to over 700 tribal groups and thousands of castes. The challenge of democratically representing such a range of interests is compounded by deep material scarcity and striking economic and social inequality.

Various factors are considered when designing a floorplan layout, including the plan’s outer boundary, room shape and size, adjacency, privacy, and circulation space, among others. While graph-theoretic approaches have proven effective for floorplan generation, existing algorithms generally focus on defining the boundary of the plan or different room shapes, lacking the investigation of designing circulation space within a floorplan. However, the circulation design in architectural planning is a crucial factor that affects the functionality and efficiency of areas within a building. This paper presents a graph-theoretic approach for integrating circulation within a floorplan. In this study, we use plane graphs to represent floorplans and develop graph algorithms to incorporate various types of circulation within a floorplan as follows:

1. i. The first phase generates a spanning circulation, that is, a corridor leading to each room using a circulation graph.

2. ii. Subsequently, using an approximation algorithm, the circulation space is minimized, that is, generation of minimum circulation space covering all the rooms, thereby enhancing space utilization in the floorplan.

3. iii. Furthermore, customized circulations are generated to cater to user preferences, distinguishing between public and private spaces within the floorplan.

In addition to the theoretical framework, we have implemented our algorithms in Python and developed a user-friendly graphical interface (GUI), enabling seamless integration of our algorithms into architectural design processes.

We consider a pair of identical theta neurons in the active regime, each coupled to the other via a delayed Dirac delta function. The network can support periodic solutions and we concentrate on solutions for which the neurons are half a period out of phase with one another, and also solutions for which the neurons are perfectly synchronous. The dynamics are analytically solvable, so we can derive explicit expressions for the existence and stability of both types of solutions. We find two branches of solutions, connected by symmetry-broken solutions which arise when the period of a solution as a function of delay is at a maximum or a minimum.

Scalar relative invariants play an important role in the theory of group actions on a manifold as their zero sets are invariant hypersurfaces. Relative invariants are central in many applications, where they often are treated locally since an invariant hypersurface may not be a locus of a single function. Our aim is to establish a global theory of relative invariants.

For a Lie algebra ${\mathfrak g}$ of holomorphic vector fields on a complex manifold M, any holomorphic ${\mathfrak g}$-invariant hypersurface is given in terms of a ${\mathfrak g}$-invariant divisor. This generalizes the classical notion of scalar relative ${\mathfrak g}$-invariant. Any ${\mathfrak g}$-invariant divisor gives rise to a ${\mathfrak g}$-equivariant line bundle, and a large part of this paper is therefore devoted to the investigation of the group $\mathrm {Pic}_{\mathfrak g}(M)$ of ${\mathfrak g}$-equivariant line bundles. We give a cohomological description of $\mathrm {Pic}_{\mathfrak g}(M)$ in terms of a double complex interpolating the Chevalley-Eilenberg complex for ${\mathfrak g}$ with the Čech complex of the sheaf of holomorphic functions on M.

We also obtain results about polynomial divisors on affine bundles and jet bundles. This has applications to the theory of differential invariants. Those were actively studied in relation to invariant differential equations, but the description of multipliers (or weights) of relative differential invariants was an open problem. We derive a characterization of them with our general theory. Examples, including projective geometry of curves and second-order ODEs, not only illustrate the developed machinery but also give another approach and rigorously justify some classical computations. At the end, we briefly discuss generalizations of this theory.