Homotopy type theory (HoTT) enables reasoning about groups directly as the types of symmetries (automorphisms) of mathematical structures. The HoTT approach to groups—first put forward by Buchholtz, van Doorn, and Rijke—identifies a group with the type of objects of which it is the symmetries. This type is called the “delooping” of the group, taking a term from algebraic topology. This approach naturally extends the group theory to higher groups which have symmetries between symmetries, and so on. In this paper, we formulate and prove a higher version of Schreier’s classification of all group extensions of a given group. Specifically, we prove that extensions of a group G by a group K are classified by actions of G on a delooping of K. Our proof is formalized in Cubical Agda, a dependently typed programming language and proof assistant which implements HoTT.

Presentamos la caracterización tecnológica y composicional de cerámica de estilo Molinos hallada en la localidad de Punta de la Peña en Antofagasta de la Sierra (puna meridional argentina) y en sitios de la cuenca del río Molinos, valle Calchaquí Medio (Salta). Desde una perspectiva arqueométrica y un acercamiento comparativo aportamos a la interacción entre sus habitantes para una cronología entre 800 y 1200 dC. Concluimos que los ejemplares recuperados en este sector puneño fueron elaborados con las mismas materias primas y elecciones técnicas que los del valle Calchaquí medio. Además, los antiplásticos presentes en la alfarería coinciden con los afloramientos del entorno de la cuenca de Molinos. A partir de ello, proponemos que los recipientes circularon desde el valle, posiblemente como parte de vínculos establecidos con familias que habitaron en Punta de la Peña.

I develop and defend a novel account of the private law of remedies according to which it is best understood as facilitating deliberations between the parties about the just outcome of their dispute rather than correcting injustice or righting wrongs. According to my democratic conception, the parties are the ones who ideally ought to resolve moral uncertainty about justice between them by deliberating together in good faith about what justice requires. The law of remedies should therefore often refrain from offering a final judgment about what justice between the parties requires, instead setting and implementing fair default rules and principles in the shadow of which the parties will ideally articulate for themselves a joint vision of justice for their relationship.

Traditional radiometric tracking navigation increasingly fails to meet the demands of deep space exploration. In contrast, optical navigation enables interplanetary spacecraft to navigate autonomously with higher precision. The effectiveness of image processing algorithms plays a crucial role in determining the accuracy of optical navigation systems. This paper presents a robust centroid extraction method based on a hybrid genetic algorithm. First, noise interference is effectively reduced by leveraging proximity information. Second, a fitness evaluation mechanism is introduced to assess model performance throughout the iterative process. Third, an annealing mutation operator is incorporated to prevent premature convergence to local optima. Finally, extensive comparative testing demonstrates that the proposed method offers substantial improvements in both accuracy and robustness, thereby substantially improving the reliability of the navigation system under complex conditions.

The recently discovered social place cells and grid cells in hippocampal formation are believed to be the neural basis underlying relative navigation of conspecifics. In this paper, we propose a new brain-inspired relative navigation model in a large-scale 3D environment for collective UAVs that translates the neurodynamics of the social place cell–grid cell circuit to robotic relative navigation algorithm for the first time. Our approach comprises three key parts: (1) a 3D isotropic Gaussian function-based cube social place cell network (cube-SPCNet), (2) a 3D continuous attractor neural network-based cube grid cell network (cube-GCNet), and (3) a population vector-based neural decoding module. The resulting brain-inspired relative navigation model incorporates the good relative information abstraction capabilities of the cube-SPCNet with the powerful temporal filtering capabilities of the cube-GCNet, yielding robustness and accuracy performance improvement for relative navigation. Experimental results show the new method can provide more robust and precise relative navigation results than its conventional counterpart, displaying a possible brain-inspired solution for relative navigation enhancement for collective UAVs.

Many claim that if a state is responsible for structural injustice, then that state lacks the standing to hold marginalized offenders to account. Call this the compromised standing claim. I argue that this claim sits in tension with a further assumption: that states hold offenders to account in their people’s name. Specifically, I argue that when A holds B accountable in the name of C, A’s own hypocrisy and complicity are not sufficient to undermine her standing to hold B accountable. This means that there exists a gap between a state’s responsibility for structural injustice and its compromised standing. After motivating this challenge, I consider one response according to which the people have lost their standing with respect to marginalized offenders and that the state, qua representative, inherits the standing of its people. I propose two strategies for making this response precise and argue that neither can vindicate the compromised standing claim in its standard form.

The Agreement on Fisheries Subsidies is designed to promote fisheries sustainability by curbing harmful subsidies that contribute to overfishing and overcapacity. However, the current approach to applying unconditional and non-negotiable special and differential treatment provisions in the Agreement is based on a North–South binary division and essentially fails to achieve the United Nations' Sustainable Development Goal 14.6. This article explores the linkage between sustainable development and a conditional right to special and differential treatment, and further presents a conditionality approach to applying appropriate and effective special and differential treatment that necessarily takes into account the diverse needs of different developing countries and better reconciles with economic, environmental, and societal sustainability. A conditionality approach shifts the basis of special and differential treatment from self-claimed ‘developing country’ status to multi-dimensions conditions embedded in the Agreement that can be objectively identified and assessed to achieve fisheries sustainability.

Understanding population change in late medieval English towns is crucial for interpreting urban development and economic shifts. Traditional estimates, based on taxation records from 1377 to the Tudor period, provide arbitrary population figures at two fixed points and fail to capture short—term fluctuations. This study proposes an alternative methodology that integrates multiple strands of evidence, including court records, tax lists, and archaeological data, offering a more nuanced understanding of demographic change. Using Nottingham as a case study, it challenges prevailing models of urban population decline. The evidence suggests that after sustained population growth into at least the 1330s, approximately 60 per cent of the townspeople died during the Black Death of 1349. However, significant migration by the early 1350s, and again in the late fourteenth and early fifteenth centuries, led to periods of population recovery. Archaeological evidence, together with documentary sources, indicates urban expansion from the second half of the fourteenth century, with substantial growth by the early sixteenth century—contradicting traditional narratives of abandonment and decline. The findings demonstrate that demographic change was far more complex than traditional methodologies suggest and that this alternative approach provides deeper insight into population trends. This approach is applicable to towns with comparable source material.

This article explores the ways that ecclesiastical record books produced by national and local Church courts in Scotland were bound up in the contests for legitimacy around the Scottish Revolution. The article argues that adherents to the National Covenant used paper record books and the practices that surrounded them, as well as their printed output, to legitimise their protest movement and to attack their opponents. Reconstructing the Church in paper represented an essential part of the Covenanters’ protest, reconstructing the Church after the fall of episcopacy.