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We examine a monoidal structure on the category of polynomial functors, defined through the operation of substituting one polynomial into another. We explain how this composition product transforms polynomials into a richer algebraic structure, enabling the modeling of more complex interactions and processes. The chapter explores the properties of this monoidal structure, how it relates to existing constructions in category theory, and its implications for understanding time evolution and dynamical behavior. We also provide examples and visual representations to clarify how substitution works in practice.
A flexible power assistive exoskeleton is proposed in this study to overcome limitations in range of motion, assistance, and comfort existing in current exoskeletons. The flexible power assistive exoskeleton is made of three springs that store energy from shoulder movements to provide assistance. It uses biomechanical models to simulate muscle forces. It is highly portable and comfortable, with only 83.29 g weight. A theoretical model was established to address the relationship between body work and output force. An evaluation system is proposed to assess the comfort effect of the assistive exoskeleton. Results show that the assistive exoskeleton can support all ranges of motion for the human upper limbs. It can offer up to 14.2% assistance. It also has a mass-to-assistance value of 120. For a comforting evaluation, its satisfaction rate reaches 93.4%. In summary, we present a highly flexible power-assisted exoskeleton with a large motion range, noticeable assistance effect, and high comfortability. This work contributes to the development of flexible assistive exoskeletons and comforting evaluation strategies for wearable devices.
We study the structure and utility of the category formed by small categories and retrofunctors. We analyze key properties of this category, such as limits, colimits, and factorizations, and explain how these structures support various forms of composition and interaction. The chapter delves into the cofree comonoid construction, exploring how it connects to familiar concepts in category theory, and extends our understanding of state-based systems. We also discuss applications of retrofunctors and demonstrate how they can be used to model complex processes in a structured way.
We formally define polynomial endofunctors on the category of sets, referring to them as polynomial functors or simply polynomials. These are constructed as sums of representable functors on the category of sets. We provide concrete examples of polynomials and highlight that the set of representable summands of a polynomial is isomorphic to the set obtained by evaluating the functor at the singleton set, which we term the positions of the polynomial. For each position, the elements of the representing set of the corresponding representable summand are called the directions. Beyond representables, we define three additional special classes of polynomials: constants, linear polynomials, and monomials. We close the chapter by offering three intuitive interpretations of positions and directions: as menus and options available to a decision-making agent, as roots and leaves of specific directed graphs called corolla forests, and as entries in two-cell spreadsheets we refer to as polyboxes.
We show that the category of comonoids, defined with respect to the composition product in the category of polynomial functors, is equivalent to a category of small categories as objects but with an interesting type of morphism called retrofunctors. Unlike traditional functors, retrofunctors operate in a forward-backward manner, offering a different kind of relationship between categories. We introduce this concept of retrofunctors, provide examples to illustrate their behavior, and explain their role in modeling state systems.
We model discrete-time dynamical systems using a specific class of lenses between polynomials whose domains are equipped with a bijection between their positions and their directions. We introduce Moore machines and deterministic state automata as key examples, showing how these morphisms describe state transitions and interactions. We also explain how to build new dynamical systems from existing ones using operations like products, parallel composition, and compositions of these maps. This chapter demonstrates how polynomial functors can be used to represent and analyze discrete-time dynamical behavior in a clear, structured way.
We describe a range of additional category-theoretic structures on the category of polynomial functors. These include concepts like adjunctions, epi-mono factorizations, and cartesian closure. We also cover limits and colimits of polynomials and explore vertical-cartesian factorizations of morphisms. The chapter highlights how these structures provide new tools for working with polynomial functors and extend their usefulness in modeling various types of interactions and constructions.
This study focuses on certain combinations of rules or conditions involving a would-be ‘provability’ or ‘truth’ predicate that would render a system of arithmetic containing them either straightforwardly inconsistent (if those predicates were assumed to be definable) or logico-semantically paradoxical (if those predicates were taken as primitive and governed by the rules in question). These two negative properties are not to be conflated; we conjecture, however, that they are complementary. Logico-semantic paradoxicality, we contend, admits of proof-theoretic analysis: the ‘disproofs’ involved do not reveal straightforward inconsistency. This is because, unlike the disproofs involved in establishing straightforward inconsistencies, these paradox-revealing ‘disproofs’ cannot be brought into normal form.
The border between metamathematical proofs of certain (constructive) impossibility results and the non-normalizable (and always constructive) disproofs engendered by semantic paradoxicality is not fully understood. The respective strategies of reasoning on each side—genuine proofs of inconsistency versus whatever kind of ‘disproof’ uncovers semantic paradoxicality—seem somehow similar. They seem to involve the same ‘lines of reasoning’. But there is an important and principled difference between them.
This difference will be emphasized throughout our discussion of certain arithmetical impossibility results, and closely related semantic paradoxes. The proof-theoretic criterion for paradoxicality is that in the case of paradoxes (as opposed to genuine inconsistencies) the apparent ‘disproofs’ that use the rules stipulated for the primitive predicates in question cannot be brought into normal form. In proof-theoretic terminology: their reduction sequences do not terminate. This means that cut fails for languages generating paradox. But cut holds for the language of arithmetic. It follows that the paradox-generating primitive predicates of a semantically closed language cannot be defined in arithmetical terms. For, if they could be, then they could be replaced by their definitions within the paradoxical disproofs, and the resulting disproofs would be normalizable.
Workspace analysis is a crucial step in designing any robotic system and ensuring its safe operation. This article analyzes the workspace of a six degree-of-freedom (6-DOF) hybrid robot, which includes two separate modules with parallel architectures placed above each other. The upper module is a 4-DOF Delta-type parallel mechanism, and the lower module is a 2-DOF rotary mechanism with a circular rail. With this design, the hybrid robot represents a relative manipulation system, and workspace analysis is performed in the relative motion of the modules. This approach differs from other similar studies that combine the workspaces determined for each module independently, and we propose a method and derive results more suitable for practical use. To solve the workspace analysis problem, the paper develops a discretization-based approach, which considers all mechanical constraints. These constraints include joint constraints of each module and link interference between the modules. To analyze this interference, we apply the Gilbert–Johnson–Keerthi algorithm and represent the links as convex polytopes. Multiple numerical examples illustrate the developed techniques and show the translation and orientation workspaces of the robot for various relative configurations of its modules. Computer-aided-design simulations validate the proposed theoretical algorithms. The results demonstrate that the link interference between the modules, often ignored in other works, limits the workspace and should be considered for the proper workspace evaluation and design of similar hybrid robots.
Maximising creativity requires an enriched imagination that uses all five senses. This study explored the effects of a reduced visual–auditory multisensory stimuli environment on creativity. Nineteen participants took the Alternative Uses Test (AUT) under the nine decreased visual–auditory multisensory stimuli conditions. Fluency and originality were evaluated as a part of the creativity assessment. The number of ideas from the AUT determined the fluency level, and the three judges’ evaluations determined originality. A study on associative conceptual network analysis explored the word associations of selected nouns from the AUT under nine reduced visual–auditory multisensory stimuli experimental conditions, revealing outdegree centrality scores to evaluate creative potential. The results suggest that the decreasing visual stimuli inhibit fluency whereas auditory stimuli do not, and that originality is enhanced when stimuli are reduced, whether visual or auditory, unless there is a notable divergence between the visual and auditory conditions. These results highlight the importance of perceptual focus and cognitive load regulation in fostering creative potential.
The paper proposes and studies new classical, type-free theories of truth and determinateness with unprecedented features. The theories are fully compositional, strongly classical (namely, their internal and external logics are both classical), and feature a defined determinateness predicate satisfying desirable and widely agreed principles. The theories capture a conception of truth and determinateness according to which the generalizing power associated with the classicality and full compositionality of truth is combined with the identification of a natural class of sentences—the determinate ones—for which clear-cut semantic rules are available. Our theories can also be seen as the classical closures of Kripke–Feferman truth: their $\omega $-models, which we precisely pin down, result from including in the extension of the truth predicate the sentences that are satisfied by a Kripkean closed-off fixed-point model. The theories compare to recent theories proposed by Fujimoto and Halbach, featuring a primitive determinateness predicate. In the paper we show that our theories entail all principles of Fujimoto and Halbach’s theories, and are proof-theoretically equivalent to Fujimoto and Halbach’s $\mathsf {CD}^{+}$. We also show establish some negative results on Fujimoto and Halbach’s theories: such results show that, unlike what happens in our theories, the primitive determinateness predicate prevents one from establishing clear and unrestricted semantic rules for the language with type-free truth.
Generative artificial intelligence (GenAI) has been heralded by some as a transformational force in education. It is argued to have the potential to reduce inequality and democratize the learning experience, particularly in the Global South. Others warn of the dangers of techno-solutionism, dehumanization of learners, and a widening digital divide. The reality, as so often, may be more complicated than this juxtaposition suggests. In our study, we investigated the ways in which GenAI can contribute to independent language learning in the context of Pakistan. We were particularly interested in the roles of five variables that have been shown to be particularly salient in this and similar contexts: learners’ Generative Artificial Intelligence-mediated Informal Digital Learning of English (GenAI-IDLE) participation, AI Literacy, Foreign Language Enjoyment (FLE) and Foreign Language Boredom (FLB), and their second language Willingness to Communicate (L2 WTC). Employing a structural equation modelling approach, we surveyed 359 Pakistani English as a foreign language (EFL) learners to investigate their interrelationships between variables. The results demonstrate that EFL learners’ GenAI-IDLE activity directly and positively influences AI literacy and FLE. Students’ AI literacy and FLE play a chain-mediating role in the relationship between GenAI-IDLE participation and L2 WTC. However, FLB lacks predictive power over L2 WTC. We discuss the implications of these results for language learning, in particular in low-resource contexts.
Complete exploration of design spaces is often computationally prohibitive. Classical search methods offer a solution but are limited by challenges like local optima and an inability to traverse dislocated design spaces. Quantum computing (QC) offers a potential solution by leveraging quantum phenomena to achieve computational speed-ups. However, the practical capability of current QC platforms to deliver these advantages remains unclear. To investigate this, we apply and compare two quantum approaches – the Gate-Based Grover’s algorithm and quantum annealing (QA) – to a generic tile placement problem. We benchmark their performance on real quantum hardware (IBM and D-Wave, respectively) against a classical brute-force search. QA on D-Wave’s hardware successfully produced usable results, significantly outperforming a classical brute-force approach (0.137 s vs 14.8 s) at the largest scale tested. Conversely, Grover’s algorithm on IBM’s gate-based hardware was dominated by noise and failed to yield solutions. While successful, the QA results exhibited a hardware-induced bias, where equally optimal solutions were not returned with the same probability (coefficient of variation: 0.248–0.463). These findings suggest that for near-term engineering applications, QA shows more immediate promise than current gate-based systems. This study’s contribution is a direct comparison of two physically implemented quantum approaches, offering practical insights, reformulation examples and clear recommendations on the utilisation of QC in engineering design.
Disability and inclusivity are progressive topics that have evolved in response to societal experiences, as evidenced by the social model of disability, which has been endorsed as a replacement for the conventional individual model of disability. However, many still regard disability as an individual rather than an environmental problem, which fosters stigmatization of people with disabilities. Addressing this requires deeper knowledge to inform experience design that raises awareness of disability and the importance of social inclusion. The authors conducted a co-design experiment focusing on how to fill the communication gap between deaf and hearing people. Six teams, each comprising one deaf and two hearing participants, were observed to identify the salient characteristics of two contrastive approaches: LESS, a deaf-oriented audio environment with decreased audio stimuli, and MORE, a hearing-oriented audio environment with no decreased auditory stimuli. The results were cross-analyzing quantitative and qualitative data with interaction mapping. The analysis found that the LESS approach helps people feel no barriers, while the MORE approach enables them to challenge prior understandings of the issue. This study will contribute to designing an experience-based awareness-raising activity, suggesting where the gap exists and how it should be filled in the context of diversity, equity and inclusion.
In many economies, youth unemployment rates over the past two decades have exceeded 10 percentage points, highlighting that not all youth successfully transition successfully from schooling to employment. Equally disturbing are the high rates of young adults not observed in employment, education, or training, a rate commonly referred to as “NEET.” There is not a single pathway for successful transitions. Understanding these pathways and the influences of geographic location, employment opportunities, and family and community characteristics that contribute to positive transitions is crucial. While abundant data exists to support this understanding, it is often siloed and not easily combined to inform schools, communities, and policymakers about effective strategies and necessary changes. Researchers prefer working with datasets, while many stakeholders favor results presented through storytelling and visualizations. This paper introduces YouthView, an innovative online platform designed to provide comprehensive insights into youth transition challenges and opportunities. YouthView integrates information from datasets on youth disadvantage indicators, employment, skills demand, and job vacancy at regional levels. The platform features two modes: a guided storytelling mode with selected visualizations, and an open-ended suite of exploratory dashboards for in-depth data analysis. This dual approach enables policymakers, community organizations, and education providers to gain a nuanced understanding of the challenges faced by different communities. By illuminating spatial patterns, socioeconomic disparities, and relationships between disadvantage factors and labor market dynamics, YouthView facilitates informed decision-making and the development of targeted interventions, ultimately contributing to improved youth economic outcomes and expanded opportunities in areas of greatest need.
Extreme precipitation events are projected to increase both in frequency and intensity due to climate change. High-resolution climate projections are essential to effectively model the convective phenomena responsible for severe precipitation and to plan any adaptation and mitigation action. Existing numerical methods struggle with either insufficient accuracy in capturing the evolution of convective dynamical systems, due to the low resolution, or are limited by the excessive computational demands required to achieve kilometre-scale resolution. To fill this gap, we propose a novel deep learning regional climate model (RCM) emulator called graph neural networks for climate downscaling (GNN4CD) to estimate high-resolution precipitation. The emulator is innovative in architecture and training strategy, using graph neural networks (GNNs) to learn the downscaling function through a novel hybrid imperfect framework. GNN4CD is initially trained to perform reanalysis to observation downscaling and then used for RCM emulation during the inference phase. The emulator is able to estimate precipitation at very high resolution both in space ($ 3 $km) and time ($ 1 $h), starting from lower-resolution atmospheric data ($ \sim 25 $km). Leveraging the flexibility of GNNs, we tested its spatial transferability in regions unseen during training. The model trained on northern Italy effectively reproduces the precipitation distribution, seasonal diurnal cycles, and spatial patterns of extreme percentiles across all of Italy. When used as an RCM emulator for the historical, mid-century, and end-of-century time slices, GNN4CD shows the remarkable ability to capture the shifts in precipitation distribution, especially in the tail, where changes are most pronounced.