An equivalence relation can be constructed from a given (homogeneous, binary) relation in two steps: first, construct the smallest reflexive and transitive relation containing the given relation (the “star” of the relation) and, second, construct the largest symmetric relation that is included in the result of the first step. The fact that the final result is also reflexive and transitive (as well as symmetric), and thus an equivalence relation, is not immediately obvious, although straightforward to prove. Rather than prove that the defining properties of reflexivity and transitivity are satisfied, we establish reflexivity and transitivity constructively by exhibiting a starth root—in a way that emphasises the creative process in its construction. The resulting construction is fundamental to algorithms that determine the strongly connected components of a graph as well as the decomposition of a graph into its strongly connected components together with an acyclic graph connecting such components.

We show that the twin-width of every $n$-vertex $d$-regular graph is at most $n^{\frac{d-2}{2d-2}+o(1)}$ for any fixed integer $d \geq 2$ and that almost all $d$-regular graphs attain this bound. More generally, we obtain bounds on the twin-width of sparse Erdős–Renyi and regular random graphs, complementing the bounds in the denser regime due to Ahn, Chakraborti, Hendrey, Kim, and Oum.

Some top-down problem specifications, if executed, may compute sub-problems repeatedly. Instead, we may want a bottom-up algorithm that stores solutions of sub-problems in a table to be reused. How the table can be represented and efficiently maintained, however, can be tricky. We study a special case: computing a function ${\mathit{h}}$ taking lists as inputs such that ${\mathit{h}\;\mathit{xs}}$ is defined in terms of all immediate sublists of ${\mathit{xs}}$. Richard Bird studied this problem in 2008 and presented a concise but cryptic algorithm without much explanation. We give this algorithm a proper derivation and discovered a key property that allows it to work. The algorithm builds trees that have certain shapes—the sizes along the left spine is a prefix of a diagonal in Pascal’s triangle. The crucial function we derive transforms one diagonal to the next.

Social impact has been widely discussed by the engineering community, but studies show that there is currently little systematic consideration of the social impact of products in both academia and in industry beyond social impacts on health and safety. While Failure Mode and Effect Analysis (FMEA) is useful for evaluating health and safety risks, new developments are needed to create an FMEA-style evaluation that can be applied to a wide range of social impacts for engineered products. The authors describe necessary modifications to traditional FMEA that transform it into a tool for social impact analysis. The modification of FMEA involves the introduction of positive and negative impacts, the inclusion of discrete and continuous impacts, the consideration of various stakeholder types, and the inclusion of uncertainty in place of detectability. This modified FMEA is referred to in this paper as Social Impact Effects Analysis (SIEA). The paper describes how SIEA is performed and articulates the potential benefits of SIEA.

The advent of generative artificial intelligence (AI) models holds potential for aiding teachers in the generation of pedagogical materials. However, numerous knowledge gaps concerning the behavior of these models obfuscate the generation of research-informed guidance for their effective usage. Here, we assess trends in prompt specificity, variability, and weaknesses in foreign language teacher lesson plans generated by zero-shot prompting in ChatGPT. Iterating a series of prompts that increased in complexity, we found that output lesson plans were generally high quality, though additional context and specificity to a prompt did not guarantee a concomitant increase in quality. Additionally, we observed extreme cases of variability in outputs generated by the same prompt. In many cases, this variability reflected a conflict between outdated (e.g. reciting scripted dialogues) and more current research-based pedagogical practices (e.g. a focus on communication). These results suggest that the training of generative AI models on classic texts concerning pedagogical practices may bias generated content toward teaching practices that have been long refuted by research. Collectively, our results offer immediate translational implications for practicing and training foreign language teachers on the use of AI tools. More broadly, these findings highlight trends in generative AI output that have implications for the development of pedagogical materials across a diversity of content areas.

Let $T$ be a tree on $t$ vertices. We prove that for every positive integer $k$ and every graph $G$, either $G$ contains $k$ pairwise vertex-disjoint subgraphs each having a $T$ minor, or there exists a set $X$ of at most $t(k-1)$ vertices of $G$ such that $G-X$ has no $T$ minor. The bound on the size of $X$ is best possible and improves on an earlier $f(t)k$ bound proved by Fiorini, Joret, and Wood (2013) with some fast-growing function $f(t)$. Moreover, our proof is short and simple.

Our emotions do not always surface into our awareness, making it difficult to manage them and communicate them to others. Even when emotions do not reach our awareness, they still express themselves as physiological changes, often unperceived by ourselves and others. To aid in emotion self-regulation and increase the bandwidth of emotion communication, I designed a programmable affective sleeve that translates physiological aspects of emotions into material haptic action. The affective sleeve has been developed as a case study for Affective Matter. Affective Matter suggests a method for human-material interaction that enhances health and wellbeing.

I first discuss the three foundations of Affective Matter underlying the design of the affective sleeve: Embodiment, Entrainment, and Material Intelligence. I then proceed to the methods and results of an exploratory study I developed and conducted that tests the psychophysiological impact of the sleeve on 36 participants. The study results suggest that the pace of the affective sleeve’s haptic action can be programmed to regulate the wearer’s breathing pace to either have a calming or a stimulating impact on the wearer. The results also show varied affective responses to distinct haptic stimuli. Discussion of the results suggests future research directions and therapeutic applications for the benefit of individuals with mental health and neurodevelopmental disorders.

The path planning and obstacle-crossing motion planning of cable trench inspection robots are essential for achieving automated inspection. To improve path planning efficiency and obstacle navigation in complex environments, an enhanced global path planning algorithm based on the A* algorithm has been developed, combined with an improved Dynamic Window Approach (DWA) for local path planning. For unavoidable obstacles, a specific obstacle-crossing motion planning strategy has been formulated. The enhanced A* algorithm improves efficiency and safety through adaptive neighborhood expansion and the elimination of redundant path points. The improved DWA algorithm enables real-time dynamic obstacle avoidance in local path planning. The simulation results on a $20 \times 20$ grid map indicate that the improved A* algorithm reduces the number of nodes by 58.4% and shortens the path length by 6.1% compared to the traditional A* algorithm, demonstrating significant advantages over other conventional path planning algorithms. In the simulation experiments integrating global and local path planning, the enhanced A* algorithm combined with the improved DWA algorithm reduces the path length by 3.2% on the $20 \times 20$ grid map compared to the integration with the traditional DWA algorithm. On the $30 \times 30$ grid maps with different obstacle configurations, the path lengths are reduced by 3.5% and 3.6%, respectively. In the obstacle-crossing experiments, the robot successfully overcame obstacles of 10 cm and 20 cm in height. The proposed path planning algorithm and obstacle-crossing motion planning strategy hold substantial application potential in complex environments, offering reliable technical support for cable trench inspection robots.

Remote center-of-motion (RCM) manipulators are a key issue in minimally invasive surgeries (MIS). The existing RCM parallel mechanisms (PMs) can only generate RCM motion based on the invariant RCM. To provide mobility for RCM, this paper designed a new family of RCM PMs with movable RCM that features a double-stage topological structure. Drawing mainly on configuration evolution and Lie-group, a general approach is proposed to design double-stage PMs with movable RCM. Feasible limbs for 2R1T RCM motion are enumerated and used to construct the secondary PM. Type synthesis of the primary PMs that realize movable RCM is accomplished based on the method presented. Different connection styles between the two stages that ensure the geometrical conditions of RCM motion are designed. Using different connection styles, double-stage PMs with movable RCM are constructed. These new RCM PMs can realize precise positioning of RCM by taking advantage of the primary PMs, which indicates their potential application prospects in MIS.

This paper introduces a sophisticated trajectory capture and playback mechanism for collaborative robots, aimed at enhancing accuracy and operational efficiency through several innovative techniques. The Ju-Gibbs attitude quaternion is utilized for enhanced kinematic modeling across multi-axis systems, which simplifies variables, reduces dimensions, and enhances symbolic clarity, thus surpassing the limitations of traditional rotation vectors and unit quaternions. A new sliding filter is developed to effectively reduce noise and optimize trajectory details more efficiently. Additionally, an automated mechanism is implemented for adjusting the sampling rate and removing static data points at the trajectory’s start and end, further refining data collection accuracy. These advancements have been successfully replicated on the Kuka robot LBR iiwa 7 R800, demonstrating the practical applicability of the solutions in real-world settings.

The radical innovation design (RID) comparator is an unprecedented method for design comparison. It overcomes the limitations of traditional methods with a nuanced, structured approach that emphasizes detailed analysis over simple grading. At its core, the RID comparator employs a novel ontology based on the RID building blocks, enabling a precise alignment of activities and solutions. This alignment is deepened through the innovative “quantities of pain” metric, a tool that allows for a refined evaluation and comparison of solutions, facilitating the calculation of effectiveness indicators in a data-driven manner. The true impact of the method is demonstrated through an industrial use case on solutions for cleaning solar panels. The RID comparator demonstrates its practical efficacy in addressing complex, multifactorial design challenges, by constructing a cognitive model of the cleaning activity not only encapsulating the myriad aspects of the design problem but also generating a wealth of discussion and consensus-building among stakeholders. The resultant cognitive model serves as a pivotal tool in redefining the process of generating innovation briefs, deeply rooted in the actual needs and constraints of real-world scenarios. In essence, the RID comparator method significantly enhances the efficiency and quality of innovation processes, particularly in complex industrial contexts.

This paper aims to explore alternative representations of the physical architecture using its real-world sensory data through artificial neural networks (ANNs). In the project developed for this research, a detailed 3-D point cloud model is produced by scanning a physical structure with LiDAR. Then, point cloud data and mesh models are divided into parts according to architectural references and part-whole relationships with various techniques to create datasets. A deep learning model is trained using these datasets, and new 3-D models produced by deep generative models are examined. These new 3-D models, which are embodied in different representations, such as point clouds, mesh models, and bounding boxes, are used as a design vocabulary, and combinatorial formations are generated from them.

This article examines the National Health Data Network (RNDS), the platform launched by the Ministry of Health in Brazil as the primary tool for its Digital Health Strategy 2020–2028, including innovation aspects. The analysis is made through two distinct frameworks: Right to health and personal data protection in Brazil. The first approach is rooted in the legal framework shaped by Brazil’s trajectory on health since 1988, marked by the formal acknowledgment of the Right to health and the establishment of the Unified Health System, Brazil’s universal access health system, encompassing public healthcare and public health actions. The second approach stems from the repercussions of the General Data Protection Law, enacted in 2018 and the inclusion of Right to personal data protection in Brazilian’s Constitution. This legislation, akin to the EU’s General Data Protection Regulations, addressed the gap in personal data protection in Brazil and established principles and rules for data processing. The article begins by explanting the two approaches, and then it provides a brief history of health informatics policies in Brazil, leading to the current Digital Health Strategy and the RNDS. Subsequently, it delves into an analysis of the RNDS through the lenses of the two aforementioned approaches. In the final discussion sections, the article attempts to extract lessons from the analyses, particularly in light of ongoing discussions such as the secondary use of data for innovation in the context of different interpretations about innovation policies.

Turbulent flows are chaotic and multi-scale dynamical systems, which have large numbers of degrees of freedom. Turbulent flows, however, can be modeled with a smaller number of degrees of freedom when using an appropriate coordinate system, which is the goal of dimensionality reduction via nonlinear autoencoders. Autoencoders are expressive tools, but they are difficult to interpret. This article aims to propose a method to aid the interpretability of autoencoders. First, we introduce the decoder decomposition, a post-processing method to connect the latent variables to the coherent structures of flows. Second, we apply the decoder decomposition to analyze the latent space of synthetic data of a two-dimensional unsteady wake past a cylinder. We find that the dimension of latent space has a significant impact on the interpretability of autoencoders. We identify the physical and spurious latent variables. Third, we apply the decoder decomposition to the latent space of wind-tunnel experimental data of a three-dimensional turbulent wake past a bluff body. We show that the reconstruction error is a function of both the latent space dimension and the decoder size, which are correlated. Finally, we apply the decoder decomposition to rank and select latent variables based on the coherent structures that they represent. This is useful to filter unwanted or spurious latent variables or to pinpoint specific coherent structures of interest. The ability to rank and select latent variables will help users design and interpret nonlinear autoencoders.

Usage data on research outputs such as books and journals is well established in the scholarly community. Yet, as research impact is derived from a broader set of scholarly outputs, such as data, code, and multimedia, more holistic usage and impact metrics could inform national innovation and research policy. While usage data reporting standards, such as Project COUNTER, provide the basis for shared statistics reporting practice, mandated access to publicly funded research has increased the demand for impact metrics and analytics. In this context, stakeholders are exploring how to scaffold and strengthen shared infrastructure to better support the trusted, multistakeholder exchange of usage data across a variety of outputs. In April 2023, a workshop on Exploring National Infrastructure for Public Access and Impact Reporting supported by the United States (US) National Science Foundation (NSF) explored these issues. This paper contextualizes the resources shared and recommendations generated in the workshop.

We consider the performance of Glauber dynamics for the random cluster model with real parameter $q\gt 1$ and temperature $\beta \gt 0$. Recent work by Helmuth, Jenssen, and Perkins detailed the ordered/disordered transition of the model on random $\Delta$-regular graphs for all sufficiently large $q$ and obtained an efficient sampling algorithm for all temperatures $\beta$ using cluster expansion methods. Despite this major progress, the performance of natural Markov chains, including Glauber dynamics, is not yet well understood on the random regular graph, partly because of the non-local nature of the model (especially at low temperatures) and partly because of severe bottleneck phenomena that emerge in a window around the ordered/disordered transition. Nevertheless, it is widely conjectured that the bottleneck phenomena that impede mixing from worst-case starting configurations can be avoided by initialising the chain more judiciously. Our main result establishes this conjecture for all sufficiently large $q$ (with respect to $\Delta$). Specifically, we consider the mixing time of Glauber dynamics initialised from the two extreme configurations, the all-in and all-out, and obtain a pair of fast mixing bounds which cover all temperatures $\beta$, including in particular the bottleneck window. Our result is inspired by the recent approach of Gheissari and Sinclair for the Ising model who obtained a similar flavoured mixing-time bound on the random regular graph for sufficiently low temperatures. To cover all temperatures in the RC model, we refine appropriately the structural results of Helmuth, Jenssen and Perkins about the ordered/disordered transition and show spatial mixing properties ‘within the phase’, which are then related to the evolution of the chain.

For coherent systems with components and active redundancies having heterogeneous and dependent lifetimes, we prove that the lifetime of system with redundancy at component level is stochastically larger than that with redundancy at system level. In particular, in the setting of homogeneous components and redundancy lifetimes linked by an Archimedean survival copula, we develop sufficient conditions for the reversed hazard rate order, the hazard rate order and the likelihood ratio order between two system lifetimes, respectively. The present results substantially generalize some related results in the literature. Several numerical examples are presented to illustrate the findings as well.

Can trust norms within the African moral system support data gathering for Generative AI (GenAI) development in African society? Recent developments in the field of large language models, such as GenAI, including models like ChatGPT and Midjourney, have identified a common issue with these GenAI models known as “AI hallucination,” which involves the presentation of misinformation as facts along with its potential downside of facilitating public distrust in AI performance. In the African context, this paper frames unsupportive data-gathering norms as a contributory factor to issues such as AI hallucination and investigates the following claims. First, this paper explores the claim that knowledge in the African context exists in both esoteric and exoteric forms, incorporating such diverse knowledge as data could imply that a GenAI tailored for Africa may have unlimited accessibility across all contexts. Second, this paper acknowledges the formidable challenge of amassing a substantial volume of data, which encompasses esoteric information, requisite for the development of a GenAI model, positing that the establishment of a foundational framework for data collection, rooted in trust norms that is culturally resonant, has the potential to engender trust dynamics between data providers and collectors. Lastly, this paper recommends that trust norms in the African context require recalibration to align with contemporary social progress, while preserving their core values, to accommodate innovative data-gathering methodologies for a GenAI tailored to the African setting. This paper contributes to how trust culture within the African context, particularly in the domain of GenAI for African society, propels the development of Afro-AI technologies.