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Background: Contract-based Design (CbD) is a valuable methodology for software design that allows annotation of code and architectural components with contracts, thereby enhancing clarity and reliability in software development. It…

One of the goals of Software design is to model a system in such a way that it is reused. Actively reusing designs or code allows taking advantage of the investment made on reusable components. However development of domain specific…

This is an overview of the idea of a crossed module. For a group, the triple that consists of the group, its group of automorphisms, and the canonical homomorphism from the group to its group of automorphisms constitutes a crossed module.…

Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…

Requirements engineering plays a critical role in developing software systems. One of the most difficult tasks in this process is identifying functional requirements. A critical problem in many projects is missing requirements until late in…

The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…

A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can…

Diffusion models are learning pattern-learning systems to model and sample from data distributions with three functional components namely the forward process, the reverse process, and the sampling process. The components of diffusion…

A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional…

Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring…

The theory of spin models intersects with condensed matter physics, complex systems, graph theory, combinatorial optimization, computational complexity and neural networks. Many ensuing applications rely on the fact that complicated spin…

This paper presents a SysML-based approach to enhance functional and software development process within an industrial context. The recent changes in technology such as electromobility and increased automation in heavy construction…

We investigate the use of an extension of rule-based modelling for cellular signalling to create a structured space of model variants. This enables the incremental development of rule sets that start from simple mechanisms and which, by a…

This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…

With the widespread adoption of Computer-Aided Design(CAD) drawings in engineering, architecture, and industrial design, the ability to accurately interpret and analyze these drawings has become increasingly critical. Among various…

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…

In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case of line…

The nature of Systems of Systems (SoSs), large complex systems composed of independent, geographically distributed and continuously evolving constituent systems, means that faults are unavoidable. Previous work on defining contractual…

In a multi-modeling based approach, the system under development is described by several models that represent various perspectives and concerns. Obviously, these partial representations are less complex than the global model, but they need…

How can the complexity of ML-enabled systems be managed effectively? The goal of this research is to investigate how complexity affects ML-Enabled Systems (MLES). To address this question, this research aims to introduce a metrics-based…