Related papers: A progression ring for interfaces of instruction s…
Polynomial functors model systems with interfaces: each polynomial specifies the outputs a system can produce and, for each output, the inputs it accepts. The bicategory $\mathbb{O}\mathbf{rg}$ of dynamic organizations…
Message Sequence Charts & Sequence Diagrams are graphical models that represent the behavior of distributed and concurrent systems via the scheduling of discrete and local emission and reception events. We propose an Interaction Language…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
We investigate a graphical representation of session invocation interdependency in order to prove progress for the pi-calculus with sessions under the usual session typing discipline. We show that those processes whose associated dependency…
Contract-based design is a promising methodology for taming the complexity of developing sophisticated systems. A formal contract distinguishes between assumptions, which are constraints that the designer of a component puts on the…
Correctness of concurrent objects is defined in terms of safety properties such as linearizability, sequential consistency, and quiescent consistency, and progress properties such as wait-, lock-, and obstruction-freedom. These properties,…
This paper describes a design that can be used for Explainable AI. The lower level is a nested ensemble of patterns created by self-organisation. The upper level is a hierarchical tree, where nodes are linked through individual concepts, so…
Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes,…
We focus on working on incidence rings, a class of (possibly infinite) matrix rings indexed by ordered sets. Some general properties about them are given, including how they are always the inverse limit of finite matrix rings, giving a…
We propose a categorical framework for processes which interact bidirectionally with both an environment and a 'controller'. Examples include open learners, in which the controller is an optimiser such as gradient descent, and an approach…
In this work, we aim to establish a strong connection between two significant bodies of machine learning research: continual learning and sequence modeling. That is, we propose to formulate continual learning as a sequence modeling problem,…
The development of many highly dynamic environments, like pervasive environments, introduces the possibility to use geographically close-related services. Dynamically integrating and unintegrating these services in running applications is a…
Building on the classroom framework in Heath et al. (2025), this paper proposes FLARE v2 as a recursive, semiotically informed account of how program meaning can be described across abstraction scales in common teaching languages. It…
A notion of a coring extension is defined and it is related to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable…
We develop an interface-modeling framework for quality and resource management that captures configurable working points of hardware and software components in terms of functionality, resource usage and provision, and quality indicators…
The paper studies sequential reasoning over graph-structured data, which stands as a fundamental task in various trending fields like automated math problem solving and neural graph algorithm learning, attracting a lot of research interest.…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
Interface specifications play an important role in component-based software development. An interface theory is a formal framework supporting composition, refinement and compatibility of interface specifications. We present different…
In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a…
Many mathematical objects can be represented as functors from finitely-presented categories $\mathsf{C}$ to $\mathsf{Set}$. For instance, graphs are functors to $\mathsf{Set}$ from the category with two parallel arrows. Such functors are…