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There are a variety of choices to be made in both computer algebra systems (CASs) and satisfiability modulo theory (SMT) solvers which can impact performance without affecting mathematical correctness. Such choices are candidates for…

A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…

Tailoring the design of robot bodies for control purposes is implicitly performed by engineers, however, a methodology or set of tools is largely absent and optimization of morphology (shape, material properties of robot bodies, etc.) is…

Information technologies for studying physical-mathematical disciplines on base of mathematical modeling in the computer algebra system Maple are described.

The present contribution suggests the use of a multidimensional scaling (MDS) algorithm as a visualization tool for manifold-valued elements. A visualization tool of this kind is useful in signal processing and machine learning whenever…

A clear definition of system dynamics modeling can provide shared understanding and clarify the impact of the field. We introduce a set of characteristics that define quantitative system dynamics, selected to capture core philosophy,…

This paper discusses the concept of model-driven software engineering applied to the Grid application domain. As an extension to this concept, the approach described here, attempts to combine both formal architecture-centric and…

To every covering of curves, we associate several varieties having the same field of moduli and same fields of definition. We deduce examples of curves having Q (the field of rationals) as field of moduli, that admit models over any…

To increase the transparency of modern computer-aided diagnosis (CAD) systems for assessing the malignancy of lung nodules, an interpretable model based on applying the generalized additive models and the concept-based learning is proposed.…

Direct modeling is a very recent CAD paradigm that can provide unprecedented modeling flexibility. It, however, lacks the parametric capability, which is indispensable to modern CAD systems. For direct modeling to have this capability, an…

Complex systems are hard to define. Nevertheless they are more and more frequently encountered. Examples include a worldwide airline traffic management system, a global telecommunication or energy infrastructure or even the whole legacy…

Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…

Background: Despite the potential benefits of software modelling, developers have shown a considerable reluctance towards its application. There is substantial existing research studying industrial use and technical challenges of modelling.…

Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where…

Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…

Building complex software systems necessitates the use of component-based architectures. In theory, of the set of components needed for a design, only some small portion of them are "custom"; the rest are reused or refactored existing…

This chapter reviews the purpose and use of models from the field of complex systems and, in particular, the implications of trying to use models to understand or make decisions within complex situations, such as policy makers usually face.…

Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters…

This is a manifesto for DEMoS, which is a Distributed Embedded Modular System, but also a manifesto addressing the need for more inter-/cross-disciplinary mastery of working knowledge related to installing this class of systems in the real…

Compositionality is a key strategy for addressing combinatorial complexity and the curse of dimensionality. Recent work has shown that compositional solutions can be learned and offer substantial gains across a variety of domains, including…