The Curry–Howard correspondence is often described as relating proofs (in intuitionistic natural deduction) to programs (terms in simply-typed lambda calculus). However, this narrative is hardly a perfect fit, due to the computational content of cut-elimination and the logical origins of the lambda calculus. We revisit Howard’s work and interpret it as an isomorphism between a category of formulas and proofs in intuitionistic sequent calculus and a category of types and terms in simply-typed lambda calculus. In our telling of the story, the fundamental duality is not between proofs and programs but between emphlocal (sequent calculus) and global (lambda calculus or natural deduction) points of view on a common logico-computational mathematical structure.

We introduce a geometric model of shallow multiplicative exponential linear logic (MELL) using the Hilbert scheme. Building on previous work interpreting multiplicative linear logic (MLL) proofs as systems of linear equations, we show that shallow MELL proofs can be modelled by locally projective schemes. The key insight is that while MLL proofs correspond to equations between formulas, the exponential fragment of shallow proofs corresponds to equations between these equations. We prove that the model is invariant under cut-elimination by constructing explicit isomorphisms between the schemes associated with proofs related by cut-reduction steps. A key technical tool is the interpretation of the exponential modality using the Hilbert scheme, which parameterises closed subschemes of projective space. We demonstrate the model through detailed examples, including an analysis of Church numerals that reveals how the Hilbert scheme captures the geometric content of promoted formulas. This work establishes new connections between proof theory and algebraic geometry, suggesting broader relationships between computation and scheme theory.

Neurological and musculoskeletal diseases have seriously impacted the quality of people’s lives. Various types of exoskeleton robots have been introduced to address this challenge in recent years. In this study, a lightweight and wearable underactuated cable-driven soft robotic intention-controlled glove exoskeleton (SRIG-Exo) is developed for assistance and rehabilitation training of individuals with injuries and disorders. The device comprises a soft robotic glove, a detachable cable connector, an underactuated linear actuator, and an active intention-controlled algorithm technique. The SRIG glove is equipped with tactile and flex sensors, along with tendons routed to facilitate finger movements. The detachable cable connector connects the glove with the actuator unit. The design of the linear actuator incorporates the threaded rod and nut mechanism to exert tension on the tendons. The intent signal from the glove sensors is utilized to activate the motor for opening and closing the hand, enabling active-controlled assistance and rehabilitation. This integration enhances the functionality and rehabilitation capabilities of the device. The constraints include the fingers having one degree of freedom (DoF), the control system requiring partial finger movement, and the wearer’s strength capability for normal device usage. The SRIG-Exo can support a maximum cable displacement range of 10 cm with a maximum grasping force of 30 N. Socially, this SRIG-Exo may improve independence in activities of daily living (ADLs), such as eating and drinking, for individuals with weakened strength and hand disorders, offering significant social and economic benefits.

Artificial intelligence is increasingly interwoven with design thinking (DT), yet comparative, stage-by-stage syntheses across canonical DT models remain scarce. This literature review maps how AI augments and challenges the major stages of widely used models and relates these effects to five illustrative domains. Following the SPAR-4-SLR protocol, we searched the Web of Science (2005–August 2025), screened records in two stages and assembled a corpus of 205 eligible studies for comparative synthesis. Across models, AI scales early-stage evidence work through large-N text and behavioral analytics, widens ideation via generative systems and accelerates prototyping and testing through simulation and predictive evaluation; at the same time, risks include bias, privacy and sovereignty concerns, evaluation opacity and homogenization of creative output. The weight of evidence supports hybrid intelligence: allocate divergent exploration primarily to AI while retaining human judgment for convergent selection and ethical decision-making. A complementary AI-native “Stingray” model highlights concurrent train–develop–iterate workflows that treat AI as a co-designer, while underscoring governance needs around interpretability and auditability. Overall, the review offers a model-by-model, stage-specific map of AI’s roles in DT, along with practical guidance for responsible deployment and research priorities for assessing boundary conditions and external validity.

Given the shift to technology-mediated communication, this study investigated the factors that influence Chinese EFL learners’ willingness to communicate (WTC) in the second language (L2) in MOOCs. While most previous studies conceptualized L2WTC as a unified construct, this study made a first attempt to distinguish its oral and written dimensions, thereby addressing an underexplored gap and capturing the complexities of both modes in online learning environments. Data were collected through questionnaires from 323 Chinese undergraduate EFL learners and complemented by semi-structured interviews with 24 learners representing high, medium, and low levels of oral and written L2WTC. Unexpectedly, the results indicated that trait-like factors (perceived communicative competence and foreign language anxiety) negatively impacted both forms of L2WTC, whereas the influence of context-specific factors (teacher support and classroom environment) was more complex. Teacher support positively affected oral L2WTC but had a limited impact on written L2WTC. The positive aspects of the classroom environment, such as its flexibility and technological use, enhanced both oral and written L2WTC, though technical difficulties and a lack of peer connection also emerged as barriers to communication. These findings provided new insights for research in online learning environments and further suggested strategies to promote positive factors while mitigating negative ones to enhance oral and written L2WTC.

Direct collocation (DC) methods are utilized for addressing trajectory optimization challenges in robotics due to their ability to generate dynamically consistent solutions. However, in the cable-driven robotic systems, where tension constraints impose kinodynamic restrictions, maintaining accuracy becomes significantly complex. This article addresses robot tensionability and proposes a method to overcome the limitations. A DC method is proposed to minimize the actuator force rate in a trajectory planning problem for a designed cable-driven parallel robot. The system comprises a 3-cable parallel mechanism with a central spine to counteract the end-effector’s weight and enhance tensionability. Integrating a pneumatic cylinder into the system that supports trajectory planning implementation is essential to minimize jerky motions. The DC method is applied through the proposed quadratic programming approach and benchmarked against existing packages to achieve and compare the resulting smoother trajectory. The numerical results demonstrate that the proposed method significantly reduces computation cost and enhances accuracy. Experimental data corroborate the simulation results, validating the method’s efficacy.

In this paper, we show that the Day monoidal product generalises in a straightforward way to other algebraic constructions and partial algebraic constructions on categories. This generalisation was motivated by its applications in logic, for example, in hybrid and separation logic. We use the description of the Day monoidal product using profunctors to show that the definition generalises to an extension of an arbitrary algebraic structure on a category to a pseudo-algebraic structure on a functor category. We provide two further extensions. First, we consider the case where some of the operations on the category are partial, and second, we show that the resulting operations on the functor category have adjoints (they are residuated).

We identify the size of the largest connected component in a subcritical inhomogeneous random graph with a kernel of preferential attachment type. The component is polynomial in the graph size with an explicitly given exponent, which is strictly larger than the exponent for the largest degree in the graph. This is in stark contrast to the behaviour of inhomogeneous random graphs with a kernel of rank one. Our proof uses local approximation by branching random walks going well beyond the weak local limit and novel results on subcritical killed branching random walks.

Manes (1998). Implementing Collection Classes with Monads. Mathematical Structures in Computer Science 8 (231–276) introduced the notion of a collection monad on the category of sets as a suitable semantics for collection types. The canonical example of collection monad is the finite powerset monad. In order to account for the algorithmic aspects, the category of sets should be replaced with categories whose arrows are maps computable by low-complexity algorithms. Inspired by realizability, we give a systematic way for constructing categories of small sets and low-complexity functions and define an analogue of collection monads on such categories.

Drawing on Umberto Eco’s epistemological metaphor of the open work, this paper explores the intersection of two open forms of notation, inherent scores and text scores, with generative AI. Building on the notion of inherent scores, in which the interface merges with the notation, we introduce embodied sketching, a notational approach that streamlines composition and performance with real-time neural audio synthesis (NAS). We then examine text scores in text-to-audio NAS, presenting Mouja+, a work combining real-time NAS with embodied sketches and AI-generated audio from Fluxus scores. Based on the experience of composing and performing Mouja+, we show how AI’s statistical processing of language introduces interpretative gaps between the human understanding of the scores and the model’s output and propose prompting strategies to streamline the use of text scores with text-to-audio generative AI. We continue by discussing how NAS adds to the open work through algorithmic processes that coalesce into an elusive and deferring sense of presence. Through Derrida’s notion of hauntology, we thus extend the open work into what we term the ‘haunted work’, an epistemological metaphor encompassing a growing corpus of works engaging with the tension between presence and absence as a source of openness.

Bayu Nokturnal II is an electroacoustic soundscape composition commissioned by the Borneo Ensemble in 2024, developed as a reimagining of Seed of Life 4: Rest and Shelters, a binaural fixed-media work composed in 2021. Rooted in the ecological and cultural identity of Gua Tempurung, a limestone cave in Perak, Malaysia, the piece explores how the interplay of acoustic instruments and environmental field recordings evokes a sense of place, space and belonging. Inspired by Chris Watson’s El Tren Fantasma, the work expands from fixed media into a live, spatialised dialogue with geophonic and biophonic elements. This paper positions Bayu Nokturnal II within the evolving discourse of ecocomposition, a practice shaped by environmental awareness and sonic interactivity. It draws on Matthew Burtner’s Syntax of Snow and Hildegard Westerkamp’s Fantasie for Horns II. These works foreground the role of soundscape as an active compositional agent. Bayu Nokturnal II employs an aural-feedback score using grid-cell timing, Scientific Pitch Notation and gesture-based instructions to foster real-time responsiveness to the soundscape. This strategy replaces conventional metre with listening-driven interaction. The result is a Malaysian site-specific composition contributing to global dialogues in acoustic ecology, environmental music and performative listening.

This paper examines Summermood (1981), an electroacoustic work composed by Antonio Russek for bass flute and live electronics, situating it within the Mexican electroacoustic scene of the 1980s and in dialogue with international developments in live electronic performance. A pivotal work in both Russek’s career and flutist Marielena Arizpe’s repertoire, Summermood, stands among the earliest Mexican compositions for electronically modified acoustic instruments. It has not been able to be studied or performed due to the absence of published documentation, its dependence on the obsolete DeltaLab DL-4 digital delay unit, and its original association with Arizpe, who retired early following an accident-related injury. Drawing on archival documents, interviews, recordings and the graphic score and Russek’s notes, this paper analyses the work’s aesthetic conception, its integration of extended flute timbres with electronic processing, its graphic notation and the collaborative practices that informed its creation, arguing for its significance in the historiography of Mexican electroacoustic music. While briefly acknowledging the preservation challenges posed by obsolete technologies, the central aim of this paper is to reassemble Summermood as a case study that illuminates Mexico’s underexplored contribution to the global avant-garde of the late twentieth century.

Extropy-based divergence measures offer distinct advantages over entropy-based counterparts, owing to their mathematical simplicity and enhanced interpretability. Relative extropy by Lad et al. [5] is a symmetric divergence measure between two probability distributions, and Mohammadi et al. [8] introduced the asymmetric divergence between two distributions based on extropy. We further study these measures, their properties, and interrelationships in this article. To address the divergence between truncated lifetime distributions, we define dynamic relative extropy for residual and past lifetime scenarios. Exploring the interrelationships of dynamic cases of relative extropy, extropy divergence, and extropy inaccuracy, we derive some unique properties and characterizations for the exponential distribution. A nonparametric estimator for relative extropy is developed, and its performance is assessed through numerical simulation studies. The practical applicability of relative extropy is used to analyze the divergence in lifetime patterns of mice under a lifetime feeding experiment and the shopping patterns of customers based on age and income groups. Further, the application of relative extropy is also applied to find the dissimilarity between two images.

This paper investigates the emergence, development and creative potential of three-dimensional musical scores, examining their transformation from physical layered media to contemporary mixed reality implementations. Through analysis of key historical works and recent technological innovations, it explores how depth and spatial materiality in musical notation create new possibilities for compositional organisation, performance practice and aesthetic expression. The study examines pioneering works utilising transparent overlays and physical depth by composers such as Cage and Takemitsu, before analysing contemporary applications in augmented and virtual reality environments that enable dynamic, interactive score generation and networked performance possibilities. Drawing on phenomenological perspectives and spatial theory, the research demonstrates how three-dimensional scores challenge traditional temporal-spatial relationships in musical notation while suggesting new frameworks for understanding musical structure and interpretation. Technical affordances and limitations of current mixed reality platforms are evaluated, alongside consideration of their implications for future developments in notation and composition. The paper argues that while three-dimensional scores offer compelling new creative possibilities, their successful implementation requires both technological expertise and collaborative approaches that may reshape traditional models of compositional practice.

Consecutive $k$-type systems have become important in both reliability theory and applications; in spite of a large literature existing on them, three-dimensional consecutive $k$-type systems have not yet been studied for multi-state case. In this paper, we introduce several different types of multi-state linear three-dimensional consecutive $k$-type systems for the first time, with due consideration to possible overlapping of failure blocks. The finite Markov chain imbedding approach is then used for the derivation of their reliability functions with state spaces and transition matrices provided in a novel way, and the involved computational process is illustrated through several numerical examples. Finally, some possible applications of the work and potential extensions are pointed out.

Feedback is integral to second language (L2) writing instruction. However, large class sizes and limited teacher time often challenge the delivery of personalized feedback, prompting interest in AI-powered solutions such as ChatGPT (Escalante et al., 2023; Huete-García & Tarp, 2024; Steiss et al., 2024; Yoon et al., 2023; Zhang, 2024). This study evaluates a task-customized GPT model, “Belinda,” trained to assess A1-level Spanish learners’ writing and provide feedback. Two research questions guided the investigation: (1) Can Belinda accurately score beginner Spanish writing using a provided rubric? (2) Can Belinda deliver constructive qualitative feedback? Human and GPT-generated scores were compared for inter- and intrarater reliability, and qualitative analyses categorized the feedback for usability in the classroom. Results revealed moderate alignment between Belinda’s scores and human raters, though reliability of the GPT fell short of calibration benchmarks. Feedback quality varied, with Belinda often providing vague, incomplete, or inaccurate suggestions. Despite iterative training, the GPT struggled to balance error correction with encouragement, a critical need for novice learners. Additionally, inconsistencies in identical GPT versions raised concerns about reliability. While Belinda showed potential in automating feedback, its limitations in accuracy, contextual understanding, and positivity suggest it is not yet a viable substitute for human evaluation by itself. These findings emphasize the challenges of integrating AI into L2 instruction and call for the need for extensive datasets, robust training, and human–AI collaboration to achieve pedagogically sound outcomes. Future research should explore hybrid feedback models and scalable solutions to enhance AI’s role in language education without compromising learner progress or confidence.