We present a new explicit formula for the determinant that contains superexponentially fewer terms than the usual Leibniz formula. As an immediate corollary of our formula, we show that the tensor rank of the $n \times n$ determinant tensor is no larger than the $n$-th Bell number, which is much smaller than the previously best-known upper bounds when $n \geq 4$. Over fields of non-zero characteristic we obtain even tighter upper bounds, and we also slightly improve the known lower bounds. In particular, we show that the $4 \times 4$ determinant over ${\mathbb{F}}_2$ has tensor rank exactly equal to $12$. Our results also improve upon the best-known upper bound for the Waring rank of the determinant when $n \geq 17$, and lead to a new family of axis-aligned polytopes that tile ${\mathbb{R}}^n$.

We consider two continuous-time generalizations of conservative random walks introduced in Englander and Volkov (2022), an orthogonal and a spherically symmetrical one; the latter model is also known as random flights. For both models, we show the transience of the walks when $d\ge 2$ and that the rate of direction changing follows a power law $t^{-\alpha}$, $0<\alpha\le 1$, or the law $(\!\ln t)^{-\beta}$ where $\beta>2$.

Sextic double solids, double covers of $\mathbb P^3$ branched along a sextic surface, are the lowest degree Gorenstein terminal Fano 3-folds, hence are expected to behave very rigidly in terms of birational geometry. Smooth sextic double solids, and those which are $\mathbb Q$-factorial with ordinary double points, are known to be birationally rigid. In this paper, we study sextic double solids with an isolated compound $A_n$ singularity. We prove a sharp bound $n \leq 8$, describe models for each n explicitly, and prove that sextic double solids with $n> 3$ are birationally nonrigid.

The article evaluates clerical professionalisation in the eighteenth-century Polish-Lithuanian Commonwealth by examining the division of labour within parishes. It argues that proponents of the Catholic Enlightenment endeavoured to achieve post-Tridentine reforms while also assigning to the clerical profession responsibilities for the material well-being of parishioners and service to the Commonwealth. It concludes that the process of clerical professionalisation remained incomplete. Firstly, approval for hiring assistant priests resulted in the delegation of many, if not all, ecclesiastical duties to them. Secondly, the improved professional education of priests occasionally led to unexpected withdrawal from pastoral duties seen as falling below their acquired competencies.

This article examines manuscript sermons to reveal how a Calvinist minister, Hugh Ramsden, preached predestination from his parish pulpit in the late 1620s. It shows how he adapted a scholarly work for this purpose, sought to balance inclusive and exclusive visions of the Christian community, and attempted to frame the doctrine as a comfort. By comparing two manuscripts for the same sermon, the extempore aspects of his live preaching are explored. Lastly, it considers the negotiation that allowed Hugh's like-minded brother, Henry, to continue with Calvinist preaching under the Laudian regime of Richard Neile in the 1630s.

The international migration literature has highlighted four key stylized facts from the perspective of the source country: (i) Migration rates are notably high, with some nations seeing over ten percent of their population living abroad. (ii) Certain developing countries have witnessed a significant exodus of skilled workers, commonly referred to as brain drain, spanning several decades. (iii) Migrants often maintain strong ties to their country of origin, evidenced by the substantial remittances they send back to their relatives. (iv) Migration is not necessarily permanent, as a considerable number of individuals return to their home country after a period spent abroad. In this paper, we present a theoretical model that endogenously explains these facts. Our model allows us to explore key issues in migration literature from a theoretical standpoint. We analyze the general equilibrium effects of migration, its long-term implications, and its welfare consequences. Additionally, we investigate whether the combined impact of return migration and remittances can counterbalance the effects of skilled migration. Finally, we evaluate the efficacy of policy interventions designed to mitigate the adverse effects of brain drain.

Assessing the conservation status of a species is important for designing effective conservation measures. Consequently, it is often vital to review it to update biodiversity management initiatives. The Parana Antwren Formicivora acutirostris is a bird found in pioneering formations (coastal marshes) of Brazil’s southern flood plains. It is considered threatened in Brazil but near threatened globally. In 2007, its distribution, habitat, and population size were estimated based on aerial photographs from 1978 and 1980. Since the species is threatened and occupies a small area across a region under pressure, we aimed to reassess its conservation status and assess its Green Status. We compiled new records, conducted new density estimates, and compared them with the previous mapping with satellite imagery to estimate the current distribution in terms of extent of occurrence (EOO), area of occupancy (AOO), area of habitat (AOH), habitat loss, and population size, and review its conservation status. The species is distributed across 10 populations, including two new populations further south. We estimated the EOO at 26,655 km², AOO at 320 km², AOH at 41 km², and the population as 6,285 mature territorial individuals. The previously mapped AOH decreased by 15.35 km² due to ecological succession. The loss of habitat due to invasion by exotic grasses is the main anthropogenic impact. We recommend that the species be considered “Vulnerable”. The Green Status indicates that the Conservation Legacy of actions taken thus far and the Conservation Dependence of ongoing actions are inefficient due to their small scales, but it highlights the importance of future actions for species conservation. We propose the establishment of exotic-free zones as small areas with a significant amount of minimally invaded environments, which we suggest as priority areas for the conservation of the species due to their cost-effective management potential. We also propose assisted colonisation to enhance its long-term conservation.

Although forensic psychiatrists are often asked to comment on a defendant's capacity to form the necessary mens rea for their alleged offence, little has been written on how mental disorders map onto legal concepts of mens rea, particularly those of intention. In this article we explore legal concepts of mens rea and the relevance of mental disorders and alcohol intoxication. We briefly consider philosophical approaches to intentional action and a variety of common mental disorders. We conclude that despite the presence of significant psychopathology it is rare for mental disorders to cause a defendant to lack the ability to form mens rea. Experts should therefore be cautious about coming to the conclusion that they do lead to a lack of capacity to form mens rea and should make clear the limits of their expertise, given the difficulty of translating clinical mental states into legal concepts of liability.

In 1920, the Syrian Congress at Damascus ratified a democratic constitution that would have been beyond the dreams of activists in the 2011 Arab Spring. Under the leadership of the leading Islamic reformer of the day, Sheikh Rashid Rida, the constitution disestablished Islam as a state religion, guaranteed one-third of parliamentary seats to non-Muslim minorities, and promised autonomy to the majority Christian territory of Mount Lebanon. Unlike the Ottoman constitution that had once reigned in Greater Syria, the Syrian document granted the preponderance of power to parliament, not the monarch. Nonetheless, the British and French colluded in the willful destruction of this nascent democracy. And with League of Nations’ support, they divided the Syrian Arab Kingdom into sectarian mandatory states. By stripping Syrian Arabs of a self-determined political community, Europeans denied them the “right to have rights,” as Hannah Arendt argued. The political backlash against European rule transformed the minority question in Syria into a polarized and violent contest, leading to the sectarian conflicts that overwhelmed Syria, Lebanon, and Palestine in the remainder of the 20th century.

Climate change is no longer a problem for future generations and the impact is already taking a toll in many parts of the world. Climate change has already caused substantial, and increasingly irreversible, damage to ecosystems. All these issues combined will inevitably lead to an increase in human suffering and forced displacement. This has significant ramifications for health care systems. In this editorial we outline how climate change is already impacting both physical and mental health. Health professionals have a role to play in addressing this great challenge of our time. Health professionals should reflect on how to promote means of climate change mitigation and adaptation within their spheres of influence – clinical, education, advocacy, administration, and research.

To reconstruct behavioural changes that underpin evolutionary transitions between solitary and eusocial behaviour, we need detailed behavioural information about both solitary and eusocial species. Most behavioural studies of sweat bees have focused on sociality. We addressed the lack of detailed information about solitary species using pinned specimens of Lasioglossum leucozonium (Schrank) and L. zonulum (Smith) from Ontario (2003–2019) and Alberta (2016). We used weekly abundance of trapped bees to evaluate flight phenology (univoltine versus bivoltine), delineating two phases of flight activity, P1 and P2, before and after the first appearance of males, and evaluated female traits related to reproduction (body size, wear, and ovary development). All populations were confirmed to be solitary. The Ontario L. leucozonium and Alberta L. zonulum were univoltine, with P1 and P2 females being similar in size but P2 females more worn and with less-developed ovaries. Ontario L. zonulum were bivoltine, with P2 females being larger, more worn, and having more ovary development than P1 females, a unique pattern among bivoltine sweat bees. Contrasting observations between univoltine and bivoltine populations support the contention that solitary reproduction is not necessarily “simple” and that detailed information is needed to illuminate behavioural changes during bee social evolution.