We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological ideas to study decentralised computing systems. Semitopologies generalise topology by removing the condition that intersections of open sets are necessarily open. The motivation comes from identifying the notion of an actionable coalition in a distributed system – a set of participants with sufficient resources for its members to collaborate to take some action – with an open set, since just because two sets are actionable (have the resources to act) does not necessarily mean that their intersection is. We define notions of category and morphism and prove a categorical duality between (sober) semiframes and (spatial) semitopologies, and we investigate how key well-behavedness properties that are relevant to understanding decentralised systems transfer (or do not transfer) across the duality.

Partial difference operators for a large class of functors between presheaf categories are introduced, extending our previous work on the difference operator to the multivariable case. These combine into the Jacobian profunctor that provides the setting for a lax chain rule. We introduce a functorial version of multivariable Newton series whose aim is to recover a functor from its iterated differences. Not all functors are recovered; however, we get a best approximation in the form of a left adjoint, and the induced comonad is idempotent. Its fixed points are what we call soft analytic functors, a generalization of the well-studied multivariable analytic functors.

Addressing and predicting degenerative phenomena in domains such as health care and engineering, two fundamental fields of vital importance for society, offers valuable insights into early warning steps and critical event forecasting, leading to far-reaching implications for safety and resource allocation. By harnessing the power of data-driven insights, prognostics becomes the principal component of predicting such phenomena. Developing clustering techniques as feature extractors acts as an intermediate step between the raw incoming data and prognostics and provides the opportunity to unveil hidden relationships within complex datasets. However, when limited, noisy, and multimodal data are available in a label-free format, extensive preprocessing, and unreliable, complicated models are required for extracting meaningful features. This prohibits the development of adaptable methods in diverse domains that are in favor of robustness and interpretability. In this regard, this study introduces a novel unsupervised deep clustering model for feature extraction in degenerative phenomena. The model innovatively extracts prognostic-related features from raw data via clustering analysis, characterized by an increasing monotonic behavior representing system deterioration. This monotonicity is partial rather than complete, to incorporate the potential occurrence of oscillations in the degradation trajectory of the system or noise-related data, reflecting real-world scenarios. Its performance, robustness, generalizability, and interpretability are evaluated across diverse domains utilizing three datasets from health care and engineering featuring limited, noisy, high-dimensional, and multimodal raw signals. Results show that the model extracts meaningful prognostic-related features in both domains and all datasets, without a significant alteration in its architecture and independently of the chosen prognostic algorithm.

In recent decades, design creativity and design theory have made great progress in terms of understanding and supporting the logic of engineering design for breakthrough and disruptive innovation. Design for transition relies on these new methods, but it also requires the capacity to be creative to facilitate more effective preservation – whether in terms of natural resources, biodiversity, energy, ways of life or other factors. Design for transition calls for a type of engineering design that is not Schumpeterian, not a ‘creative destruction’, but rather a design that manages creative preservation, creativity for better preservation and preservation for improved creativity. In the first section, we clarify the notion of creative preservation for transition; in the second section, we show how creative preservation can be addressed by recent advances in design theory, namely, C-K/Topos. Finally, in the conclusion, we demonstrate the implications of C-K/Topos for the management of the unknowns of transitions and the underlying logic of creative preservation.

We study time-inhomogeneous random walks on finite groups in the case where each random walk step need not be supported on a generating set of the group. When the supports of the random walk steps satisfy a natural condition involving normal subgroups of quotients of the group, we show that the random walk converges to the uniform distribution on the group and give bounds for the convergence rate using spectral properties of the random walk steps. As an application, we use the moment method of Wood to prove a universality theorem for cokernels of random integer matrices allowing some dependence between entries.

This article examines the rise of conspiratorial thinking in wartime Russia as a response to a deeper collective anxiety – not merely the replacement of people, but the erasure of narrative agency. While the Russian version of the ‘Great Replacement’ echoes familiar Western themes such as elite betrayal, cultural erosion, and demographic decline, its central concern shifts towards symbolic displacement. Drawing on Mark Sedgwick’s interpretation of the Great Replacement as a stable narrative structure and J.V. Wertsch’s concept of narrative as a cultural tool, this article argues that conspiracy operates here as a means of reclaiming authorship in a national story whose core meanings have grown unstable. The analysis draws on social media discourse, pro-war commentary, volunteer statements, and nationalist media, showing how anxieties are shaped through emotionally resonant storylines of betrayal and erasure. Yet the reassertion of control paradoxically intensifies fragmentation, turning the Great Replacement into a narrative of narrative disappearance – where the gravest loss is not demographic, but symbolic.

Currently, quadruped robots are widely used in diverse scenarios due to their high mobility, creating a demand for more advanced interaction capabilities. This study proposes a whole-body planning and control framework that integrates adaptive control into a hierarchical model predictive control (MPC) and whole-body control (WBC) structure, enhancing the environmental adaptability and interaction performance of quadruped mobile manipulators. Key innovations include: a recursive least squares and feedforward compensation strategy for accurate end-effector force estimation; relaxed barrier functions embedded in the MPC to combine dynamic obstacle avoidance with adaptive control; and a WBC-based priority hierarchy to enforce critical constraints. Validated in Gazebo simulation and on the B1-Z1 platform, the method allows the robot to handle unknown loads up to 3 kg and maintain tracking errors under 2 cm despite 35 N external disturbances. It also demonstrates strong adaptability in non-uniform object transportation, providing a reliable solution for unstructured environments.

Algebraic effects and handlers is an increasingly popular paradigm for programming with effects. A key benefit is modularity: programs with effects are defined against an interface of operations, allowing the implementation of effects to be defined and refined without changing or recompiling programs. The behavior of effects is specified using equational theories, with equational proofs inheriting the same modularity. However, higher-order operations (that take computations as arguments) break this modularity: while they can often be encoded in terms of algebraic effects, this typically breaks modularity as operations defined this way are not encapsulated in an interface, inducing changes to programs and proofs upon refinement of the implementation. In this paper, we show that syntactic overloading is a viable solution to this modularity problem by defining hefty algebras: a formal framework that captures an overloading-based semantics of higher-order effects by defining modular elaborations from higher-order effect trees into primitive algebraic effects. We demonstrate how this approach scales to define a wide range of known higher-order effects from the literature and develop modular higher-order effect theories and modular reasoning principles that build on and extend the state of the art in modular algebraic effect theories. We formalize our contributions in Agda.

Efforts to integrate intelligent chatbots into academic courses, particularly for language learning, have been gaining popularity. However, the impact of chatbot-supported collaborative learning (CL) on student engagement and English speaking skills is under-researched. This study explored the impact of utilizing intelligent chatbot–supported CL on student engagement and speaking skills of English as a foreign language (EFL) learners. It investigated how chatbot-supported CL influences student engagement and speaking skills. The experimental group was taught using chatbot-supported CL, while the control group followed conventional CL. A total of 75 first-year undergraduate students participated, with 39 students in the experimental group and 36 in the control group. Data were collected through a 14-item engagement questionnaire, a speaking test based on the IELTS speaking evaluation rubric for both groups, and a 5-item CL questionnaire administered solely to the experimental group. The data were analyzed using repeated measures analysis of variance (RM-ANOVA) and linear regression analysis. The RM-ANOVA results showed that chatbot-supported CL positively affected student engagement and speaking skills. The linear regression analysis further indicated that CL supported by intelligent chatbots influenced student engagement, which in turn significantly impacted speaking skills. The findings suggested that active engagement in CL speaking classes is crucial for improving EFL speaking skills and that intelligent chatbots can be valuable and effective tools for promoting such engagement.

This article revisits the concept of the instrument’s inherent score, exploring how musical instruments can embody a form of notation that both shapes and inspires performance. Building on earlier research (Tomás 2016; Tomás and Kaltenbrunner 2014), the study examines the historical and theoretical foundations of this idea, tracing its roots to experimental music practices of the 1960s and 1970s, particularly within the Sonic Arts Union collective. Composers such as Alvin Lucier, Gordon Mumma and Nicolas Collins have described how electronic instruments embody compositional elements, effectively functioning as scores. The paper argues that the instrument’s score emerges from the material and symbolic affordances of the instrument, mediating the performer’s engagement with its sonic and physical properties. This concept has influenced contemporary digital instrument design, where the boundary between composition and instrument becomes blurred. The study also engages with theoretical frameworks from Vilém Flusser and Friedrich Kittler, situating the instrument’s score within broader discourses on technology and embodiment. Finally, the paper explores the challenges of notating such scores, drawing parallels with choreographic practices, and concludes by emphasising the body’s central role in interpreting and enacting these inscriptions during performance.