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This chapter is about Métayer’s polygraphic homology of ω-categories. This homology theory was first defined in the following way: the polygraphic homology of an ω-category is the homology of the abelianization of any of its polygraphic replacements. Métayer then showed with Lafont that for every monoid, considered as an ω-category, its polygraphic homology coincides with its classical homology as a monoid. This result was then generalized to 1-categories by Guetta. In this chapter, it is proven that the polygraphic homology is the left derived functor of a linearization functor from the category of ω-categories to the category of chain complexes, respectively endowed with ω-equivalences and quasi-isomorphisms.
In this chapter, a notion of Tietze transformation for 2-polygraphs is introduced, consisting of elementary operations on 2-polygraphs that preserve the presented category, such that any two finite 2-polygraphs presenting the same category can be transformed into one another by applying such transformations. By using Tietze transformations, the goal is to turn a given presentation of a category into another one that possesses better computational properties. In particular, the Knuth-Bendix completion procedure applies those transformations to turn a presentation into a confluent one. Convergent presentations lead to a solution of the word problem: for those, the equivalence between two words is immediately decided by comparing their normal forms.To tackle the word problem for an arbitrary presentation, a good strategy consists in trying to transform it into a convergent one by using Tietze transformations. From this point of view, a natural question arises as to whether a finite presentation of a category with decidable word problem can always be turned into a convergent one by applying Tietze transformations: this problem is called "universality of convergent presentations".
Various factors are considered when designing a floorplan layout, including the plan’s outer boundary, room shape and size, adjacency, privacy, and circulation space, among others. While graph-theoretic approaches have proven effective for floorplan generation, existing algorithms generally focus on defining the boundary of the plan or different room shapes, lacking the investigation of designing circulation space within a floorplan. However, the circulation design in architectural planning is a crucial factor that affects the functionality and efficiency of areas within a building. This paper presents a graph-theoretic approach for integrating circulation within a floorplan. In this study, we use plane graphs to represent floorplans and develop graph algorithms to incorporate various types of circulation within a floorplan as follows:
i. The first phase generates a spanning circulation, that is, a corridor leading to each room using a circulation graph.
ii. Subsequently, using an approximation algorithm, the circulation space is minimized, that is, generation of minimum circulation space covering all the rooms, thereby enhancing space utilization in the floorplan.
iii. Furthermore, customized circulations are generated to cater to user preferences, distinguishing between public and private spaces within the floorplan.
In addition to the theoretical framework, we have implemented our algorithms in Python and developed a user-friendly graphical interface (GUI), enabling seamless integration of our algorithms into architectural design processes.
This appendix gives some examples of presentations of 2-categories by 3-polygraphs. In many examples, the presented 2-categories are in fact monoidal categories and, actually, PROs.
This paper proposes a LiDAR-inertial odometry (LIO) based on the dynamic voxel merging and smoothing method, DV-LIO. In this approach, a local map management mechanism based on feature distribution is introduced to unify the features of similar adjacent voxels through dynamic merging and segmentation, thereby improving the perceptual consistency of environmental features. Moreover, a novel noise detector that performs noise detection and incremental filtering by evaluating the consistency of voxel features is designed to further reduce local map noise and improve mapping accuracy while ensuring real-time algorithm performance. Meanwhile, to ensure the computational efficiency of the LIO system, a point cache is set for each voxel, which allows the voxel to be updated incrementally and intermittently. The proposed method is extensively evaluated on datasets gathered over various environments, including campus, park, and unstructured gardens.
Understanding and tracking societal discourse around essential governance challenges of our times is crucial. One possible heuristic is to conceptualize discourse as a network of actors and policy beliefs.
Here, we present an exemplary and widely applicable automated approach to extract discourse networks from large volumes of media data, as a bipartite graph of organizations and beliefs connected by stance edges. Our approach leverages various natural language processing techniques, alongside qualitative content analysis. We combine named entity recognition, named entity linking, supervised text classification informed by close reading, and a novel stance detection procedure based on large language models.
We demonstrate our approach in an empirical application tracing urban sustainable transport discourse networks in the Swiss urban area of Zürich over 12 years, based on more than one million paragraphs extracted from slightly less than two million newspaper articles.
We test the internal validity of our approach. Based on evaluations against manually automated data, we find support for what we call the window validity hypothesis of automated discourse network data gathering. The internal validity of automated discourse network data gathering increases if inferences are combined over sliding time windows.
Our results show that when leveraging data redundancy and stance inertia through windowed aggregation, automated methods can recover basic structure and higher-level structurally descriptive metrics of discourse networks well. Our results also demonstrate the necessity of creating high-quality test sets and close reading and that efforts invested in automation should be carefully considered.
Upper extremity rehabilitation robots have become crucial in stroke rehabilitation due to their high durability, repeatability, and task-specific capabilities. A significant challenge in assessing the comfort performance of these robots is accurately calculating the human-robot interaction forces. In this study, a four-degree-of-freedom (4-DOF) upper extremity rehabilitation robot mechanism, kinematically compatible with the human upper limb, is proposed. Based on this mechanism, an algorithm for estimating human-robot interaction forces is developed using Newton-Euler dynamics. A prototype of the proposed robot is constructed, and a series of comparative experiments are carried out to validate the feasibility of the proposed force estimation approach. The results indicate that the proposed method reliably predicts interaction forces with minimal deviation from experimental data, demonstrating its potential for application in upper limb rehabilitation robots. This work provides a foundation for future studies focused on comfort evaluation and optimization of rehabilitation robots, with significant practical implications for improving patient rehabilitation outcomes.
This paper explores the evolution of the concept of peace in the context of a globalized and digitalized 21st century, proposing a novel vision that shifts from viewing peace as a thing or a condition, to understanding peace as dynamic and relational process that emerges through human interactions. Building on - yet also going beyond - traditional definitions of peace as something to be found through inner reflection (virtue ethics), as the product of reason, contracts and institutions (Enlightenment philosophy), and as the absence of different forms of violence (modern peace research), this paper introduces a new meso-level theory on networks, emphasizing the importance of connections, interactions and relationships in the physical and online worlds. The paper is structured around three main objectives: conceptualizing relational peace in terms of the quantity and quality of interactions, mapping these interactions into networks of peace, and examining how these networks interact with their environment, including the influence of digital transformation and artificial intelligence. By integrating insights from ethical and peace research literature, the paper makes theoretical, conceptual, and methodological contributions towards understanding peace as an emergent property of human behavior. Through this innovative approach, the paper aims to provide clarity on how peace (and violence) emerges through interactions and relations in an increasingly networked and digitalized global society, offering a foundation for future empirical research and concerted policy action in this area. It highlights the need for bridging normative and descriptive sciences to better understand and promote peace in the digital age.