Related papers: Category-Theoretic Foundations of "STCLang: State …

We establish a connection between tangles, a concept from structural graph theory that plays a central role in Robertson and Seymour's graph minor project, and hierarchical clustering. Tangles cannot only be defined for graphs, but in fact…

This paper provides a blueprint for the construction of a symplectic $(A_\infty,2)$-category, $\mathsf{Symp}$. We develop two ways of encoding the information in $\mathsf{Symp}$ -- one topological, one algebraic. The topological encoding is…

In this article, we propose a Category Theory approach to (syntactic) interoperability between linguistic tools. The resulting category consists of textual documents, including any linguistic annotations, NLP tools that analyze texts and…

This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…

Web applications underpin much of modern digital life, yet building scalable and consistent cloud applications remains difficult, requiring expertise across cloud computing, distributed systems, databases, and software engineering. These…

Sleep stage classification is crucial for detecting patients' health conditions. Existing models, which mainly use Convolutional Neural Networks (CNN) for modelling Euclidean data and Graph Convolution Networks (GNN) for modelling…

We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and St\"ark for reasoning about hierarchical…

We introduce a notion of dynamics in the setting of Segal topos, by considering the Segal category of stacks $\mathcal{X} = \text{dAff}_{\mathcal{C}}^{\, \sim, \tau}$ on a Segal category $\text{dAff}_{\mathcal{C}}=$…

Masked diffusion language models (MDLMs) enable parallel decoding by predicting all masked positions at each denoising step, yet existing training-free samplers usually decide which positions to commit at token-level granularity. We revisit…

We introduce a set of state access patterns suitable for managing state in embarrassingly parallel computations on streams. The state access patterns are useful to model typical stream parallel applications. We present a classification of…

This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The clustering algorithm extracts the splitting information either from trajectories, first or second derivatives. Initial partition is based on gap…

We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…

Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…

In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…

Metal-organic frameworks (MOFs) are porous, crystalline materials with high surface area, adjustable porosity, and structural tunability, making them ideal for diverse applications. However, traditional experimental and computational…

The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…

Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we…

Although the cloud has reached a state of robustness, the burden of using its resources falls on the shoulders of programmers who struggle to keep up with ever-growing cloud infrastructure services and abstractions. As a result, state…

The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on…

Stock and flow diagrams are already an important tool in epidemiology, but category theory lets us go further and treat these diagrams as mathematical entities in their own right. In this chapter we use communicable disease models created…