We relate the expected hyperbolic length of the perimeter of the convex hull of the trajectory of Brownian motion in the hyperbolic plane to an expectation of a certain exponential functional of a one-dimensional real-valued Brownian motion, and hence derive small- and large-time asymptotics for the expected hyperbolic perimeter. In contrast to the case of Euclidean Brownian motion with non-zero drift, the large-time asymptotics are a factor of two greater than the lower bound implied by the fact that the convex hull includes the hyperbolic line segment from the origin to the endpoint of the hyperbolic Brownian motion. We also obtain an exact expression for the expected perimeter length after an independent exponential random time.

Michael Otsuka, Alex Voorhoeve and Marc Fleurbaey have proposed competing claims egalitarianism and hybrid egalitarianism in their attempts to justify giving priority to the worse off, especially in cases involving risk. However, neither view adequately explains why it matters that some are worse off than others. And combining these accounts within a broader egalitarian theory or modular principle is problematic. I sketch an alternative version of egalitarianism and compare it with competing claims egalitarianism, hybrid egalitarianism and restricted prioritarianism.

We develop a continuous-time stochastic model for optimal cybersecurity investment under the threat of cyberattacks. The arrival of attacks is modeled using a Hawkes process, capturing the empirically relevant feature of clustering in cyberattacks. Extending the Gordon–Loeb model, each attack may result in a breach, with breach probability depending on the system’s vulnerability. We aim at determining the optimal cybersecurity investment to reduce vulnerability. The problem is cast as a two-dimensional Markovian stochastic optimal control problem and solved using dynamic programming methods. Numerical results illustrate how accounting for attack clustering leads to more responsive and effective investment policies, offering significant improvements over static and Poisson-based benchmark strategies. Our findings underscore the value of incorporating realistic threat dynamics into cybersecurity risk management.

Let p be a prime number. We consider diagonal p-permutation functors over a (commutative, unital) ring $\mathsf {R}$ in which all prime numbers different from p are invertible. We first determine the finite groups G for which the associated essential algebra $\mathcal {E}_{\mathsf {R}}(G)$ is non-zero: These are groups of the form $G=L\langle u\rangle $, where $(L,u)$ is a $D^\Delta $-pair. When $\mathsf {R}$ is an algebraically closed field $\mathbb {F}$ of characteristic 0 or p, this yields a parameterization of the simple diagonal p-permutation functors over $\mathbb {F}$ by triples $(L,u,W)$, where $(L,u)$ is a $D^\Delta $-pair, and W is a simple $\mathbb {F}\mathrm {Out}(L,u)$-module. Finally, we describe the evaluations of the simple functor $\mathsf {S}_{L,u,W}$ parameterized by the triple $(L,u,W)$. We show in particular that if G is a finite group and $\mathbb {F}$ has characteristic p, the dimension of $\mathsf {S}_{L,1,\mathbb {F}}(G)$ is equal to the number of conjugacy classes of p-regular elements of G with a defect group isomorphic to L.

This study evaluates the effectiveness of high-fidelity maritime simulators in improving seafarer training, focusing on navigation and emergency response skills. Using Kongsberg Polaris full-mission simulators, 98 participants (students, professionals and instructors) completed structured simulator exercises and were assessed using customised post-exercise questionnaires. Results indicate improved practical skills, with professionals reporting higher confidence and perceived control than students. Emotional engagement was also important: professionals showed more balanced responses, whereas students exhibited higher arousal and more variable perceptions of control. Instructors emphasised real-time feedback and scenario customisation as key to effective training. Limitations included challenges with certain manoeuvres, lack of integrated assessment tools and high simulator costs limiting wider adoption. The study concludes that high-fidelity simulators are valuable in maritime education, although further technological development and adaptation for less experienced trainees are needed.

Prior work has suggested that musical abilities are associated with second language (L2) learning at both segmental and prosodic levels: For example, musicians are better at encoding lexical tone or stress in an L2 than non-musicians are. However, it remains unclear how the weighting of distinct acoustic cues when producing L2 prosody may be supported by musical abilities. Our current study investigated two different sub-domains of music perception, melody and rhythm, and their link to the accurate production of English lexical stress by native Mandarin speakers, as measured by differences from native English speakers in duration, F0, and amplitude. Melody, but not rhythm perception (and controlling for other speech perception skills, including the perception of lexical stress), significantly contributed to the production of duration and was also marginally predictive of amplitude, but not F0 production. We argue that the weak or null effects of music perception on F0 production may be due to Mandarin speakers’ F0 sensitivity from their native language, which may complicate the mapping of auditory perception onto L2 speech production skills. Results suggest complex associations between music and language in learners’ use of specific acoustic cues in their production of L2 prosody.

Comprehension of wh-questions often poses challenges for children with autism spectrum disorder (ASD) in wh-movement languages like English. However, it remains unclear whether wh-in situ languages like Mandarin present similar difficulties. Moreover, the present study explores potential differences in comprehension between Mandarin subject and object wh-questions. We hypothesize a subject wh-question advantage, given that Mandarin object wh-questions exhibit a longer dependency than subject wh-questions. If confirmed, it would support that Mandarin wh-questions involve covert movement. Using eye-movement measures of the intermodal preferential looking (IPL) paradigm, this study investigates the comprehension of matrix subject and object wh-questions in Mandarin-speaking children with ASD (N = 35, mean age = 60.94 months) compared to their typically developing (TD) peers (N = 38, mean age = 29.66 months), matched on expressive vocabulary levels. The results showed that children in the TD group comprehended both subject and object wh-questions. However, in the ASD group, children comprehended only subject wh-questions. Overall, Mandarin-speaking children with ASD exhibited weaker comprehension of wh-questions than their TD counterparts, with particular difficulty processing object wh-questions. The subject-over-object advantage in wh-questions among Mandarin-speaking children with ASD suggests that they were sensitive to the longer dependency involved in object wh-questions. These findings support the involvement of covert movement in Mandarin wh-questions.

This paper compares the acoustic properties of lateral consonants in two syllable positions in four languages – Russian, English, Romanian, and Georgian – each one representative of a distinct allophonic pattern. This study is also the first production study of Georgian lateral allophony including data from multiple speakers. By relying on both static formant measurements and dynamic analyses of formant trajectories, the study provides deeper insights into the role of syllable position and of vowel context in shaping lateral variation cross-linguistically. The results highlight differences in the production of laterals in two ways: they capture the gradience of the ‘dark’/‘light’ lateral variation across the four languages, and they contribute to our understanding of how intrinsic and extrinsic factors interact in lateral consonant production. The findings contribute to the growing body of research on lateral allophony. They underscore the importance of integrating dynamic methods, and of including less well studied languages.

The transnational cleavage captures a divide between those with cosmopolitan orientations who are more positive about international migration, trade, and governance and those with more nationalist outlooks. Recent research has demonstrated that polarisation along this cleavage in Europe is increasingly linked to urban-rural differences: people living in urban areas tend to be more cosmopolitan than people in rural areas, but existing studies have not yet elaborately analysed differences in voting behaviour. Moreover, education is the most consistent predictor of attitudes related to the transnational cleavage, and higher-educated individuals more often live in cities. Urban-rural political differences may therefore reflect differences in educational attainment between urban and rural inhabitants. We take a longitudinal perspective to assess the degree of overlap between urban-rural and educational differences in voting for parties at the opposite ends of the transnational cleavage (‘GAL’ and ‘TAN’ parties), using data from all 11 rounds of the European Social Survey (2002–2024). We find that urban voters are overrepresented in the electorates of GAL parties and underrepresented in the electorates of TAN parties. These urban-rural differences are growing over time and, only for a small portion, overlap with educational divides in GAL/TAN voting. Although, overall, educational attainment remains more strongly related to GAL/TAN voting, both educational attainment and urban-rural residence have their own explanatory value. These findings underscore that ‘place’ increasingly matters in structuring political conflict across Europe and highlight the importance of further incorporating geography into future research on the transnational cleavage.

A sparse high-gain multifaceted circularly polarized antenna array based on partially reflecting surfaces (PRSs) is designed. Circular polarization is obtained by implementing the sequential phase rotation method at the source antenna level. Beamforming is implemented using phase compensation combined with amplitude weighting proportional to the radiated intensity of the given facet in the targeted direction, following the maximum ratio transmission concept. The radiation pattern is scanned across the angular region specified by the angular gap between adjacent facets. The obtained beamformed result shows a maximum gain fluctuation smaller than 0.5 dB across the scanned sector, together with a sidelobe suppression of 10.27 dB, and the obtained embedded element pattern exhibits a flat top.

In technology-enhanced language learning (TELL), self-regulated language learning (SRLL) strategies are essential for supporting English as a foreign language (EFL) learners’ writing development. As collaborative learning becomes increasingly prominent in TELL, SRLL has expanded from individual regulation to collaborative contexts. However, limited research has compared how individual and collaborative SRLL contexts influence learners’ strategy use, writing performance, and learning behaviors. To address this gap, this study used WeChat as a mobile learning platform to compare university-level EFL learners’ SRLL strategy use, writing performance, and behavioral patterns in individual and collaborative self-regulated writing programs. Two intact classes were assigned to either a WeChat-based individual group (WIG) or a WeChat-based collaborative group (WCG). The collected data included SRLL strategy use questionnaire, writing scores, and WeChat learning logs. Results showed that the collaborative context promoted learners’ overall, cognitive, metacognitive, and behavioral SRLL strategy use, although no significant difference was found in motivational strategy use. The WCG also achieved higher writing performance and showed distinctive regulatory behaviors related to time monitoring and feedback awareness. These findings suggest that SRLL is a dynamic and cyclical process shaped by task demands, technological affordances, and social interaction. They also highlight the value of integrating individual and collaborative learning modes to support learners’ movement between self-regulation, co-regulation, and socially shared regulation.