Related papers: Category Theory and Model-Driven Engineering: From…
A model is a simplified representation of portion of reality that hides a system s nonessential characteristics. It provides a means for reducing complexity as well as visualization and communication and a basis for building it. Most models…
Machine Learning (ML) provides important techniques for classification and predictions. Most of these are black-box models for users and do not provide decision-makers with an explanation. For the sake of transparency or more validity of…
Quantum mechanics/molecular mechanics (QM/MM) hybrid models allow one to address chemical phenomena in complex molecular environments. Whereas this modeling approach can cope with a large system size at moderate computational costs, the…
The paper introduces a novel framework based on category theory to enhance the explainability of artificial intelligence systems, particularly focusing on word embeddings. Key topics include the construction of categories $\mathcal{L}_T$…
The work presented in this paper is related to the area of Situational Method Engineering (SME) which focuses on project-specific method construction. We propose a faceted framework to understand and classify issues in system development…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…
Certainly, the success of the Unified Modeling Language (UML) as the de facto standard for modeling software systems does not imply closing the door on scientific exploration or experimentation with modeling in the field. Continuing studies…
The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
The advent of data-driven science in the 21st century brought about the need for well-organized structured data and associated infrastructure able to facilitate the applications of Artificial Intelligence and Machine Learning. We present an…
In this paper, we report some on-going focused research, but are further keen to set it in the context of a proposed bigger picture, as follows. There is a certain depressing pattern about the attitude of industry to spreadsheet error…
Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete…
Eight categorical soundness and completeness theorems are established within the framework of algebraic theories. Exactly six of the eight deduction systems exhibit complete semantics within the cartesian monoidal category of sets. The…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can…
Mathematical models are vital to the field of metrology, playing a key role in the derivation of measurement results and the calculation of uncertainties from measurement data, informed by an understanding of the measurement process. These…
Two established approaches to engineer adaptive systems are architecture-based adaptation that uses a Monitor-Analysis-Planning-Executing (MAPE) loop that reasons over architectural models (aka Knowledge) to make adaptation decisions, and…
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…
Machine learning (ML)-based solutions are rapidly changing the landscape of many fields, including structural engineering. Despite their promising performance, these approaches are usually only demonstrated as proof-of-concept in structural…
Model predictive control (MPC) is an optimal control technique which involves solving a sequence of constrained optimization problems across a given time horizon. In this paper, we introduce a category theoretic framework for constructing…