The Dutch city of Leiden experienced economic and demographic growth from the last quarter of the sixteenth century onwards. This article analyses its effects on the urban private housing market by charting both the ratio of owners to tenants and the spatial patterns of housing wealth. Housing inequality increased in Leiden, reinforcing existing economic disparities and patterns of residential segregation. These dynamics were mainly caused by migration, which created great demand for housing. Gaining an insight into the pre-modern housing market also helps us to understand how inequalities were (re)produced and how they affected the daily lives of urbanites differently.

The Belt and Road Initiative (BRI) has advanced in various regions. While analyses have predominantly focused on its political and economic impacts, its legal aspects received less attention. This article explores whether the Chinese legal model implemented via the initiative represents a novel approach to international law-making. The focus is on its application in the Middle East and North Africa, where a set of primary mechanisms are utilised: soft law instruments that establish a theoretical and practical framework for collaboration. The author provides a comparative analysis of the European Union (EU) and United States (US) legal models, considering the overall pros and cons of Beijing’s strategy. The article concludes that while these mechanisms represent a pragmatic governance model relying on flexible rules, they are not a novel approach. The US and the EU have employed such soft law instruments, under which binding agreements were established to ensure formal commitments.

We study the computational problem of rigorously describing the asymptotic behavior of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit, both as a spatial object (attractor set) and as a statistical distribution (physical measure), and we prove upper bounds on the computational resources of computing descriptions of these objects with arbitrary accuracy. We also study how these bounds are affected by different dynamical constraints and provide several examples showing that our bounds are sharp in general. In particular, we exhibit a computable interval map having a unique transitive attractor with Cantor set structure supporting a unique physical measure such that both the attractor and the measure are non-computable.

This paper introduces an equivalent series mechanism model to improve ankle rehabilitation robots’ ability to recurrence the complex movements of the anthropo-ankle and enhance human-machine locomotion compatibility. The model emulates the true anatomical architecture of the ankle joint and is integrated with a parallel rehabilitative mechanism. The rehabilitative robot includes dual virtual motion centers to mimic the ankle joint’s intricate motion, accommodate individual patient variations, and address the rehabilitation requirements of both right and left feet. Firstly, a serial equivalence model of anthropo-ankle is developed based on the kinematic and anatomical characteristics of the human ankle. The type design for the 4-degree of freedom (4-DOF) parallel ankle rehabilitative robot is then conducted on the basis of the kinematical and restrictive properties of the anthropo-ankle equivalence kinematic model. Secondly, the mechanism’s motion properties allow it to be equivalent to a series branch chain, enabling the establishment of an inverse kinematics model. The kinematical performance of the mechanisms is analyzed using the transmissibility and constrainability indices, followed by workspace analysis and dimensional optimization of the rehabilitative mechanism. Finally, a human-machine coupled rehabilitative simulation model is developed using OpenSim biomechanics software to evaluate the recovery effect.

This editorial suggests ways in which mental health science reform could yield more robust research and faster clinical progress. These include better animal and other models, a shift to transdiagnostic and clinically pragmatic classification systems, improved measurement, mission mapping and an entrepreneurial mindset aimed at taking advances rapidly to scale.

We compute the large size limit of the moment formula derived in [14] for the Hermitian Jacobi process at fixed time. Our computations rely on the polynomial division algorithm which allows to obtain cancellations similar to those obtained in [3, Lemma 3]. In particular, we identify the terms contributing to the limit and show they satisfy a double recurrence relation. We also determine explicitly some of them and revisit a special case relying on Carlitz summation identity for terminating $1$-balanced ${}_4F_3$ functions taken at unity.

Democratic backsliding, the slow erosion of institutions, processes, and norms, has become more pronounced in many nations. Most scholars point to the role of parties, leaders, and institutional changes, along with the pursuit of voters through what Daniel Ziblatt has characterized as alliances with more extremist party surrogate organizations. Although insightful, the institutionalist literature offers little reflection about the growing role of social technologies in organizing and mobilizing extremist networks in ways that present many challenges to traditional party gatekeeping, institutional integrity, and other democratic principles. We present a more integrated framework that explains how digitally networked publics interact with more traditional party surrogates and electoral processes to bring once-scattered extremist factions into conservative parties. When increasingly reactionary parties gain power, they may push both institutions and communication processes in illiberal directions. We develop a model of communication as networked organization to explain how Donald Trump and the Make America Great Again (MAGA) movement rapidly transformed the Republican Party in the United States, and we point to parallel developments in other nations.

Starting from a uniquely ergodic action of a locally compact group G on a compact space $X_0$, we consider non-commutative skew-product extensions of the dynamics, on the crossed product $C(X_0)\rtimes _\alpha {\mathbb Z}$, through a $1$-cocycle of G in ${\mathbb T}$, with $\alpha $ commuting with the given dynamics. We first prove that any two such skew-product extensions are conjugate if and only if the corresponding cocycles are cohomologous. We then study unique ergodicity and unique ergodicity with respect to the fixed-point subalgebra by characterizing both in terms of the cocycle assigning the dynamics. The set of all invariant states is also determined: it is affinely homeomorphic with ${\mathcal P}({\mathbb T})$, the Borel probability measures on the one-dimensional torus ${\mathbb T}$, as long as the system is not uniquely ergodic. Finally, we show that unique ergodicity with respect to the fixed-point subalgebra of a skew-product extension amounts to the uniqueness of an invariant conditional expectation onto the fixed-point subalgebra.

There has been limited research on African policy instruments’ historical and institutional nature in health policy literature. However, in the field of health systems research, there are many examples that show the permanent use of financing instruments inspired by liberal (pro-market) ideas such as user fees, performance bonuses, or private practice of medicine in Africa. Through an analysis of archives (1840–1960), this article shows the presence of these instruments in the health system during the French colonial period in Senegal. Thus, this study shows that these financing policy instruments’ institutional presence and longevity are part of a liberal approach that predates international organizations’ contemporary (and liberal) promotion. This study uses a historical and institutionalist approach to understand the context, actors, and underlying factors that allowed for this historical continuity, resulting in the permanence of these instruments.

Gaseous hydrogen chemically reacting with air in lean premixed mode yields essentially water vapour enabling to decarbonise aeronautical propulsion systems. When hydrogen fuel is produced by electrolysis, the impact on Earth is neutral on a life-cycle basis. Hydrogen fuel, combined to swirled premixed combustion mode, is a sustainable method for thermal-powered aviation. Knowledge gaps have hindered progress in the field and no laboratory-scale demonstrations have been made to date in the specific 100% H2/Air swirled premixed regime. This study describes an experiment established to: (1) demonstrate this highly swirled lean fully premixed H2/Air combustion mode and (2) -describe the underlying flame stabilisation principle. Theoretical results enable pioneering the first-to-date experimental stabilisation for these flames. Measurements with optical diagnostics including chemiluminescence and shadowgraphy direct imaging provide insights into the flame position and the flame regime. This experimental demonstration confirms that the kinematic balance between the flame displacement speed and the flow velocity is critical along with the flame-wall interaction at the bluff-body. It is shown that flashback can be mitigated. The present experiment can be replicated and utilised for application in several scientific disciplines and for advancing technologies. The experimental demonstration, regime characterisation method and mechanism description documented here open the perspective to deploy clean hydrogen combustion to decarbonise aviation with low nitrogen oxides emissions. The combination of high-swirl fully premixed H2/Air experimental data and the theoretical results are unique.

This paper focuses on the developmental tendencies and mechanisms underlying the unfolding of mood systems in Romance complement clauses. In view of the fact that the subsequent dynamics of change can be better understood and motivated against the backdrop of the Latin system, we take the basic structure of the Latin mood system as the reference and necessary starting point of our analysis. After briefly discussing the basic approaches to the mechanisms of mood change in the relevant research literature that puts forward notions like ‘modal harmony’, ‘regrammation’, ‘lexicalization’, and ‘conventionalization’, the article develops a modal–semantic perspective that casts a different light on the convergent and divergent developments of mood in the complement clause domain of Romance languages. The modal–semantic approach allows, apart from a coherent description and analysis of the developments, recasting the question of whether mood, especially the subjunctive, also comes with its own semantic value(s) in complement clauses. This modal–semantic approach not only provides a coherent description and analysis of the developments but also allows for a re-examination of the abstract semantics of the subjunctive mood (in complement clauses), spelling out its basic semantic features.

Thomas Cranmer appropriated the eucharistic theology of Cyril of Alexandria for the purposes of constructing a Reformed eucharistic theology and in a way that did not do justice to Cyril’s eucharistic theology. Cyril argued for a mingling of both the corporal and spiritual presence of Christ in both the incarnation and the Eucharist, whereas Cranmer affirms such a mingling in the incarnation alone but not in the Eucharist. Ashley Null has recently defended Cranmer’s appropriation of Cyril for the construction of Reformed eucharistic theology. This article concludes that both Thomas Cranmer’s appropriation and Null’s defence of Cranmer are not viable interpretations of Cyril’s eucharistic theology.

Global path planning using roadmap (RM) path-planning methods including Voronoi diagram (VD), rapidly exploring random trees (RRT), and probabilistic roadmap (PRM) has gained popularity over the years in robotics. These global path-planning methods are usually combined with other path-planning techniques to achieve collision-free robot control to a specified destination. However, it is unclear which of these methods is the best choice to compute the efficient path in terms of path length, computation time, path safety, and consistency of path computation. This article reviewed and adopted a comparative research methodology to perform a comparative analysis to determine the efficiency of these methods in terms of path optimality, safety, consistency, and computation time. A hundred maps of different complexities with obstacle occupancy rates ranging from 50.95% to 78.42% were used to evaluate the performance of the RM path-planning methods. Each method demonstrated unique strengths and limitations. The study provides critical insights into their relative performance, highlighting application-specific recommendations for selecting the most suitable RM method. These findings contribute to advancing robot path-planning techniques by offering a detailed evaluation of widely adopted methods.