Social investment can act as an empowering funding mechanism that could activate the economic agency of marginalised people while addressing their social needs. Nonetheless, political agendas might cause divergence in the achievement of social investment’s potential benefits. To develop our understanding in this area, this paper aims to extract discursive policy framings of social investment by comparing the UK and Scottish Government policies to identify the use of social investment and its implications on social innovation. Using corpus linguistic methods that allows for a framing analysis, the paper’s findings are twofold. Firstly, both the UK and Scottish Governments share similarities in the framing of social investment policy, especially in the proclivity towards the privatisation of social welfare delivery using market mechanisms. Secondly, the governments differ in their intensity of conviction for social investment which creates divergent implications for social innovation practice in the countries.

We define duality triples and duality pairs in compactly generated triangulated categories and investigate their properties. This enables us to give an elementary way to determine whether a class is closed under pure subobjects, pure quotients and pure extensions, as well as providing a way to show the existence of approximations. One key ingredient is a new characterization of phantom maps. We then introduce an axiomatic form of Auslander–Gruson–Jensen duality, from which we define dual definable categories, and show that these coincide with symmetric coproduct closed duality pairs. This framework is ubiquitous, encompassing both algebraic triangulated categories and stable homotopy theories. Accordingly, we provide many applications in both settings, with a particular emphasis on silting theory and stratified tensor-triangulated categories.

This introduction develops a theoretical framework for understanding authoritarian backsliding against the backdrop of existing historical and European socio-legal scholarship. It introduces a number of key distinctions to better understand socio-legal variance among autocratisation. Specifically, it highlights the distinction between authoritarian backsliding and complete breakdown of judicial independence and human rights

Authoritarian backsliding is an aggravated form of rule of law decay, where functioning of key rule of law institutions comes under direct threat and it is mostly observable in the contemporary Central and Eastern European context. This differs from historical instances of authoritarian turn referring to the complete breakdown of judicial independence and human rights, characterised by the politicisation of courts as a mainly historical phenomenon. The differentiation and their socio-legal implications is crucial for developing a roadmap to identify different forms of autocratisation and their different contexts (actors, institutional and political context) that need to be considered when addressing rule of law decay in Europe, both at the national and supranational levels. Ultimately, this general overview also offers the possibility to identify and address latent discontinuities in rule of law development at both the supranational and national levels. Identification of such latent discontinuities is of importance when assessing the risks involved in the introduction of emergency measures to combat perceived threats to the state and the society.

In this essay I read debates about amenities of water and waste in the British Caribbean in the late and immediate post-Victorian period through histories of intimacy and kinship centered in fiction by Caribbean writers of the last twenty years. In these novels and short stories, collecting water at a stream or a standpipe or emptying a chamber pot are actions that produce or recall moments of desire and aspiration, shame and punishment, in storylines that move between a past of enslavement and indentureship in the eighteenth and nineteenth centuries and a present of political and psychological stasis or upheaval in the 1950s, 1970s, or the early twenty-first century. Nineteenth-century discussions about fire hydrants or standpipes index a British Caribbean colony's evolving landscape of modernization and the disagreements about what shape and speed this process should take, and recent fiction allows us to discern how these amenities inherit and bequeath associations of trauma.

Autonomous exploration in unknown environments has become a critical capability of mobile robots. Many methods often suffer from problems such as exploration goal selection based solely on information gain and inefficient tour optimization. Recent reinforcement learning-based methods do not consider full area coverage and the performance of transferring learned policy to new environments cannot be guaranteed. To address these issues, a dual-stage exploration method has been proposed, which combines spatial clustering of possible exploration goals and Traveling Salesman Problem (TSP) based tour planning on both local and global scales, aiming for efficient full-area exploration in highly convoluted environments. Our method involves two stages: exploration and relocation. During the exploration stage, we introduce to generate local navigation goal candidates straight from clusters of all possible local exploration goals. The local navigation goal is determined through tour planning, utilizing the TSP framework. Moreover, during the relocation stage, we suggest clustering all possible global exploration goals and applying TSP-based tour planning to efficiently direct the robot toward previously detected but yet-to-be-explored areas. The proposed method is validated in various challenging simulated and real-world environments. Experimental results demonstrate its effectiveness and efficiency. Videos and code are available at https://github.com/JiatongBao/exploration.

A monic polynomial $f(x)\in {\mathbb Z}[x]$ of degree N is called monogenic if $f(x)$ is irreducible over ${\mathbb Q}$ and $\{1,\theta ,\theta ^2,\ldots ,\theta ^{N-1}\}$ is a basis for the ring of integers of ${\mathbb Q}(\theta )$, where $f(\theta )=0$. We prove that there exist exactly three distinct monogenic trinomials of the form $x^4+bx^2+d$ whose Galois group is the cyclic group of order 4. We also show that the situation is quite different when the Galois group is not cyclic.

According to Charles Travis, Frege’s principle to “always to sharply separate the psychological from the logical, the subjective from the objective” involves a move called “the fundamental abstraction.” I try to explain what this abstraction is and why it is interesting. I then raise a problem for it, and describe what I think is a better way to understand Frege’s principle.

In this textual comparison of seventeenth-century herbals, I show in detail that most of the descriptions and medicinal uses of English herbs included in Culpeper’s small folio The English Physitian (1652) and its enlargement of the following year were lifted straight out of the works of John Parkinson, apothecary. This was a deliberate act by Culpeper, to make available to the people of England the best information on native plant medicines for use in treating their illnesses. He attacked the College of Physicians of London, whom the great majority of the population could not afford to engage, for trying to keep this knowledge secret. Among later historians of the herbal tradition, Culpeper’s work was not accorded the same status as the great English herbals of William Turner, John Gerard, and John Parkinson, not because this borrowing was recognised but because its astrological content worked to divert attention from the quality and source of much of its guidance on treatment. Even contemporaries of Culpeper did not recognise the extent of the borrowing. Comparisons also reveal the limitations of Culpeper’s powers of plant description and his lack of interest in the developing science of botany. The editorial decisions Culpeper made to reduce a great folio herbal to a much smaller book to be sold for 3d touch on domestic and other non-medical uses, while points of discussion common to both authors such as the doctrine of signatures and superstitious beliefs about plants are explored.

Generalised arterial calcification of infancy, an autosomal recessive disorder characterised by abnormal calcification of medium and large-sized arteries, represents a rare cause of dilated cardiomyopathy. We present the case of a two-month-old girl diagnosed posthumously with dilated cardiomyopathy. Studies suggest that early initiation of treatment can improve prognosis in generalised arterial calcification of infancy, so clinicians should be alert to the condition, especially in patients displaying generalised narrowing of medium and large-sized arteries.