The results of Section 3.1 of the 2017 paper “Isomorphism Theorems between Models of Mixed Choice” need an additional assumption when $\bullet$ is “$1$.” If $\bullet$ is nothing or “$\leq 1$,” no change is needed. Also, the mistake only applies to the angelic cases, namely to the maps $r_{{\mathtt {A}}{\mathtt {P}}}$ and $s^\bullet _{{\mathtt {A}}{\mathtt {P}}}$; the demonic cases $r_{{\mathtt {D}}{\mathtt {P}}}$ and $s^\bullet _{{\mathtt {D}}{\mathtt {P}}}$ are unaffected. If $\bullet$ is “$1$,” and in the angelic cases, instead of just assuming that $\mathcal L X$ is locally convex, we need to additionally assume that $X$ is compact, or that $\mathcal L X$ is locally convex-compact, sober, and topological – for example, if $X$ is core-compact – or that $X$ is LCS-complete, namely, a homeomorph of a $G_\delta$ subspace of a locally compact sober space.

We develop the theory of limits and colimits in $\infty$-categories within the synthetic framework of simplicial homotopy type theory established by Riehl and Shulman. We also show that in this setting, the limit of a family of spaces can be computed as a dependent product.

Consulting dictionaries during writing requires time and cognitive resources. ColloCaid, a writing assistance prototype freely available online, was designed to minimize the cognitive strain on writers by embedding a collocation database within the writing environment. Usability surveys have shown ColloCaid can indeed help. In this study, we go beyond user perceptions. Using authentic excerpts of student academic writing by 27 advanced L2 English speakers, we analysed (1) the lexical coverage of the tool, (2) the collocation changes prompted by the tool, (3) the reasons behind decisions to revise collocations, (4) the effect of revisions prompted by ColloCaid, and (5) the participants’ perceptions of using the tool to revise authentic writing assignments. Our findings indicate that ColloCaid offered good academic collocation coverage, that the participants tended to accept its collocation prompts with discernment, and that the revisions made resulted in more fluent texts overall.

Human–machine compatibility and collaborative control for stroke patients utilizing lower limb rehabilitation robots have attracted considerable research attention. As a highly human–machine-coupled system, ensuring adequate compliance and safety is fundamental to efficient and comfortable rehabilitation. Therefore, this paper first quantifies human–machine contact interactions, proposes a human–machine coupling dynamics modeling method, and identifies the robot’s dynamic inertia parameters and human lower limb parameters. Second, a dual closed-loop controller for the rehabilitation robot is designed. Based on the bottom position control, an adaptive admittance control algorithm is proposed that employs the root-mean-square propagation (RMSprop) algorithm to tune the adaptive gain. In rehabilitation training, the controller can adaptively adjust the admittance parameters according to the human–machine interaction force to achieve responsiveness to the dynamic changes of the human–machine system. The experimental results of the control system show that the human–machine cooperative control performance is significantly improved, the maximum joint angle error is reduced by more than 40.9%, and the maximum human–machine interaction force is reduced by more than 19.4%.

Rehabilitation treatment is often labor-intensive and time-consuming, but it also lacks quantitative and objective assessment. With regard to the matter of balance rehabilitation machines, the continuous advancement of parallel robot technology provides new solutions for balance rehabilitation. However, these robots have inherent limitations, including a confined workspace, excessive height, a complex structure, and unstable movement due to singularity in workspace. Therefore, this study presents a new 3-2PUS double-triangular construction mechanism with six degrees of freedom for use in balance rehabilitation therapy. First, the forward and inverse kinematic models are established, and then the Newton–Raphson method is employed to resolve the forward kinematics. Subsequently, the velocity model is analyzed and its singular configuration is determined. Finally, the workspace of the 3-2PUS parallel mechanism is delineated, and the findings indicate that its structure is compact and that the workspace is free of singularities. This ensures that the rehabilitative devices will remain stable throughout the rehabilitation process, thus preventing any additional injuries that might otherwise result from unstable movement. To validate the study of the full parallel mechanism, a series of simulations is conducted using computational analysis software. Based on the analysis results, a prototype of a balance rehabilitation parallel manipulator is presented.

This paper introduces Choice Trees (CTrees), a monad for modeling nondeterministic, recursive, and impure programs in Rocq. Inspired by Xia et al.’s ((2019) Proc. ACM Program. Lang. 4(POPL)) ITrees, this novel data structure embeds computations into coinductive trees with three kinds of nodes: external events, internal steps, and delayed branching. This structure allows us to provide shallow embedding of denotational models with nondeterministic choice in the style of ccs, while recovering an inductive LTS view of the computation. CTrees leverage a vast collection of bisimulation and refinement tools well-studied on LTSs, with respect to which we establish a rich equational theory. We connect CTrees to the ITrees infrastructure by showing how a monad morphism embedding the former into the latter permits using CTrees to implement nondeterministic effects. We demonstrate the utility of CTrees by using them to model concurrency semantics in two case studies: ccs and cooperative multithreading.

We prove that the satisfaction relation $\mathcal {N}\models \varphi [\vec a]$ of first-order logic is not absolute between models of set theory having the structure $\mathcal {N}$ and the formulas $\varphi $ all in common. Two models of set theory can have the same natural numbers, for example, and the same standard model of arithmetic $\left \langle {\mathbb N},{+},{\cdot },0,1, <\right \rangle $, yet disagree on their theories of arithmetic truth; two models of set theory can have the same natural numbers and the same arithmetic truths, yet disagree on their truths-about-truth, at any desired level of the iterated truth-predicate hierarchy; two models of set theory can have the same natural numbers and the same reals, yet disagree on projective truth; two models of set theory can have the same $\left \langle {H}_{\omega _2},{\in }\right \rangle $ or the same rank-initial segment $\left \langle {V}_\delta ,{\in }\right \rangle $, yet disagree on which assertions are true in these structures.

On the basis of these mathematical results, we argue that a philosophical commitment to the determinateness of the theory of truth for a structure cannot be seen as a consequence solely of the determinateness of the structure in which that truth resides. The determinate nature of arithmetic truth, for example, is not a consequence of the determinate nature of the arithmetic structure ${\mathbb N}=\{\,{0,1,2,\ldots }\,\}$ itself, but rather, we argue, is an additional higher-order commitment requiring its own analysis and justification.

Water resources from the Indus Basin sustain over 270 million people. However, water security in this region is threatened by climate change. This is especially the case for the upper Indus Basin, where most frozen water reserves are expected to decrease significantly by the end of the century, leaving rainfall as the main driver of river flow. However, future precipitation estimates from global climate models differ greatly for this region. To address this uncertainty, this paper explores the feasibility of using probabilistic machine learning to map large-scale circulation fields, better represented by global climate models, to local precipitation over the upper Indus Basin. More specifically, Gaussian processes are trained to predict monthly ERA5 precipitation data over a 15-year horizon. This paper also explores different Gaussian process model designs, including a non-stationary covariance function to learn complex spatial relationships in the data. Going forward, this approach could be used to make more accurate predictions from global climate model outputs and better assess the probability of future precipitation extremes.

European asylum policy still has a long way to go to better address protection challenges. This paper presents data and visualizations that should help improve responsibility-sharing and solidarity between states. We developed an interactive cartographic tool to map the distribution of refugees in Europe. Besides the observed geographic distribution of asylum seekers and beneficiaries of the temporary protection status, our tool allows for the calculation of a theoretical distribution between countries based on different criteria. The tool is an interactive visualization created with the software “Tableau Desktop.” The original data was collected from Eurostat and the World Bank, before being processed by the research team with the Extract Transform Load (ETL) utility “Tableau Prep” and made available through the Tableau Desktop application. The actual number of asylum applications lodged in country A can thus be compared with the number that would be proportional to that country’s population within Europe in combination with three other criteria. Maps of observed and theoretical reallocations can thus be produced based on population size, area, unemployment rate, economic prosperity or a mix of these factors. The number of refugees received is represented by a red semicircle while the “equitable” number in proportion to given criteria is represented by a grey semicircle. Our database not only allows geographical analysis of the drivers of refugee distribution in Europe, but it also provides the population and policymakers with a solid basis for discussing responsibility-sharing schemes, such as those envisaged in the new EU Asylum Pact of 2024.

The emergence of large language models has significantly expanded the use of natural language processing (NLP), even as it has heightened exposure to adversarial threats. We present an overview of adversarial NLP with an emphasis on challenges, policy implications, emerging areas, and future directions. First, we review attack methods and evaluate the vulnerabilities of popular NLP models. Then, we review defense strategies that include adversarial training. We describe major policy implications, identify key trends, and suggest future directions, such as the use of Bayesian methods to improve the security and robustness of NLP systems.

The integration of artificial intelligence (AI)-driven technologies into peace dialogues offers both innovative possibilities and critical challenges for contemporary peacebuilding practice. This article proposes a context-sensitive taxonomy of digital deliberation tools designed to guide the selection and adaptation of AI-assisted platforms in conflict-affected environments. Moving beyond static typologies, the framework accounts for variables such as scale, digital literacy, inclusivity, security, and the depth of AI integration. By situating digital peace dialogues within broader peacebuilding and digital democracy frameworks, the article examines how AI can enhance participation, scale deliberation, and support knowledge synthesis, —while also highlighting emerging concerns around algorithmic bias, digital exclusion, and cybersecurity threats. Drawing on case studies involving the United Nations (UN) and civil society actors, the article underscores the limitations of one-size-fits-all approaches and makes the case for hybrid models that balance AI capabilities with human facilitation to foster trust, legitimacy, and context-responsive dialogue. The analysis contributes to peacebuilding scholarship by engaging with the ethics of AI, the politics of digital diplomacy, and the sustainability of technological interventions in peace processes. Ultimately, the study argues for a dynamic, adaptive approach to AI integration, continuously attuned to the ethical, political, and socio-cultural dimensions of peacebuilding practice.

This study addresses how AI-generated images of war are changing the making of memory. Instead of asking how AI-generated images affect individual recall, we focus on how they communicate specific representations, recognising that such portrayals can cultivate particular assumptions and beliefs. Drawing on memory of the multitude, visual social semiotics, and cultivation/desensitisation theories, we analyse how visual generative AI mediates the representation of the Russia-Ukraine war. Our corpus includes 200 images of the Russia-Ukraine war generated from 23 prompts across proprietary and open-source visual generative AI systems. The findings indicate that visual generative AI tends to present a sanitised view of the war. Critical aspects, such as death, injury, and suffering of children and refugees are often excluded. Furthermore, a disproportional focus on urban areas misrepresents the full scope of the war. Visual generative AI, we argue, introduces a new dimension to memory making in that it blends documentation with speculative fiction by synthesising the multitude embedded within the visual memory of war archives, historical biases, representational limitations, and commercial risk aversion. By foregrounding the socio-technical and discursive dimensions of synthetic war content, this study contributes to an interdisciplinary dialogue on collective memory at the intersection of visual communication studies, media studies, and memory studies by providing empirical insights into how generative AI mediates the visual representation of war through human-archival-mechanistic entanglements.

Digital Tools are reshaping how Engineering Design data and information are produced, processed, used, reused, shared, and stored. The Digital Thread prioritizes the flow of design data and information, promoting effective collaboration and process efficiency. While literature showcases the immense application and capability of taking a Digital Thread approach to Product Design, best practices, key features, and benefits of successful implementations remain scarce. Reviewing and understanding successful implementations can assist researchers and practitioners in making informed decisions to effectively implement Digital Threads in their product design processes. This article addresses this gap by reporting a post hoc review of a collaborative Research & Development project that developed and implemented a Digital Thread approach to the design of hydrogen composite pressure vessels. A thematic analysis of the project’s reports and interviews with members of the project team was performed to identify the key features that expedite and improve the design process through an effective Digital Thread implementation. The post hoc review offers valuable insights – in the form of six feature benefits, four potential implementation challenges, three possible extensions, and four best practice recommendations – for companies looking to adopt and implement a Digital Thread approach to their design process.

Given $n$ convex bodies in the Euclidean space $\mathbb{R}^d$, we can find their volume polynomial which is a homogeneous polynomial of degree $d$ in $n$ variables. We consider the set of homogeneous polynomials of degree $d$ in $n$ variables that can be represented as the volume polynomial of any such given convex bodies. This set is a subset of the set of Lorentzian polynomials. Using our knowledge of operations that preserve the Lorentzian property, we give a complete classification of the cases for $(n,d)$ when the two sets are equal.

This paper presents a novel control framework for achieving collision-free trajectory tracking in tractor-trailer mobile robots (TTMRs) within both static and dynamic environments. This study addresses the challenges posed by nonholonomic constraints and kinematic coupling inherent in TTMR systems. An inverse kinematic control strategy, augmented with pure integral controllers, is proposed to ensure precise trajectory tracking. The control framework is further enhanced using three obstacle avoidance approaches: two customized artificial potential field (APF) approaches and a novel path planning mode (PPM) for continuous-time trajectory adjustment. APF methods, applied for the first time to TTMR trajectory tracking, incorporate gravitational and repulsive forces to guide the robot away from obstacles, whereas PPM dynamically generates a semi-circular trajectory when the robot approaches an obstacle. Case studies validate the effectiveness of the proposed strategy in accurate trajectory tracking and safe obstacle avoidance. Comparative analyses highlight the superior performance of PPM in managing complex environments.

Although ‘in-the-wild’ technology testing provides an important opportunity to collect evidence about the performance of new technologies in real world deployment environments, such tests may themselves cause harm and wrongfully interfere with the rights of others. This paper critically examines real-world AI testing, focusing on live facial recognition technology (FRT) trials by European law enforcement agencies (in London, Wales, Berlin, and Nice) undertaken between 2016 and 2020, which serve as a set of comparative case studies. We argue that there is an urgent need for a clear framework of principles to govern real-world AI testing, which is currently a largely ungoverned ‘wild west’ without adequate safeguards or oversight. We propose a principled framework to ensure that these tests are undertaken in an epistemically, ethically, and legally responsible manner, thereby helping to ensure that such tests generate sound, reliable evidence while safeguarding the human rights and other vital interests of others. Although the case studies of FRT testing were undertaken prior to the passage of the EU’s AI Act, we suggest that these three kinds of responsibility should provide the foundational anchor points to inform the design and conduct of real-world testing of high-risk AI systems pursuant to Article 60 of the AI Act.

The hard-core model has as its configurations the independent sets of some graph instance $G$. The probability distribution on independent sets is controlled by a ‘fugacity’ $\lambda \gt 0$, with higher $\lambda$ leading to denser configurations. We investigate the mixing time of Glauber (single-site) dynamics for the hard-core model on restricted classes of bounded-degree graphs in which a particular graph $H$ is excluded as an induced subgraph. If $H$ is a subdivided claw then, for all $\lambda$, the mixing time is $O(n\log n)$, where $n$ is the order of $G$. This extends a result of Chen and Gu for claw-free graphs. When $H$ is a path, the set of possible instances is finite. For all other $H$, the mixing time is exponential in $n$ for sufficiently large $\lambda$, depending on $H$ and the maximum degree of $G$.