arXiv subjects

Marco Reidelbach

Publications and source records attributed to Marco Reidelbach.

7 recordsLinked to original sources

arXiv2026

MathModDB: A Database for Mathematical Models

When researchers need a mathematical model for a research problem, they face a fragmented landscape: relevant formulas, quantities, assumptions, and model variants are scattered across publications and domain-specific conventions. The Mathematical Models Database (MathModDB) addresses this challenge by providing a curated knowledge graph for mathematical models, deployed on the MaRDI Portal as part of the German National Research Data Infrastructure (NFDI). Building on ontology designs presented in earlier work, this paper focuses on MathModDB as a publicly available service. It addresses researchers who use mathematical models in their work -- whether in applied mathematics, engineering, or the natural sciences. We describe its deployment on the Wikibase-powered MaRDI Portal, report on its current scale, and demonstrate its practical use through a walkthrough of an electric discharge modeling use case from plasma physics. We further discuss the ecosystem around MathModDB, including its connection to the MathAlgoDB knowledge graph for numerical algorithms and the MaRDMO documentation tool.

cs.DL↗

arXiv2026

Boolean Algebra -- Driven Sepsis Diagnosis

Sepsis remains a diagnostic challenge due to its heterogeneous molecular signatures and complex immune responses. In this study, we develop a logical data analysis framework based on Boolean polynomial rings. This method constructs an ideal $\mathcal{I}$ of selection criteria that isolate empty subsets of previously analyzed patient data. This approach enables the derivation of interpretable classification rules based on biomarker profiles. We demonstrate that logical data analysis identifies distinct logical patterns for positive and negative sepsis classification. For instance, elevated levels of GLP-1 and MyD88 are associated with septic states in our dataset, whereas high TRAIL and low MyD88 concentrations may suggest a non-septic condition. Importantly, a new way to integrate expert knowledge to filter out potential overfitting or dataset-specific artifacts is shown. Our findings highlight the utility of logics in generating transparent, biologically plausible rules for a data-based and expert-based understanding of sepsis. Moreover, we show how data analysis can benefit from algebraic structures.

math.RA↗

arXiv2025

MaRDMO: Future Gateway to FAIR Mathematical Data

Mathematical research data plays a crucial role across scientific disciplines, yet its documentation and dissemination remain challenging due to the lack of standardized research data management practices. The MaRDMO Plugin addresses these challenges by integrating mathematical models, algorithms, and interdisciplinary workflows into the established framework of the Research Data Management Organiser (RDMO). Built on FAIR principles, MaRDMO enables structured documentation and retrieval of mathematical research data through guided questionnaires. It connects to multiple knowledge graphs, including MathModDB, MathAlgoDB, and the MaRDI Portal. Users can document and search for models, algorithms, and workflows via dynamic selection interfaces that also leverage other sources such as Wikidata. The plugin facilitates the export to the individual MaRDI services, ensuring data quality through automated validation. By embedding mathematical research data management into the widely adopted RDMO platform, MaRDMO represents a significant step toward making mathematical research data more findable, accessible, and reusable.

cs.HC↗

arXiv2024

Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics

Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this research data FAIR, two previously distinct ontologies were merged and extended, becoming a living knowledge graph. The link between the two ontologies is established by introducing computational tasks, as they occur in modeling, corresponding to algorithmic tasks. Moreover, controlled vocabularies are incorporated and a new class, distinguishing base quantities from specific use case quantities, was introduced. Also, both models and algorithms can now be enriched with metadata. Subject-specific metadata is particularly relevant here, such as the symmetry of a matrix or the linearity of a mathematical model. This is the only way to express specific workflows with concrete models and algorithms, as the feasible solution algorithm can only be determined if the mathematical properties of a model are known. We demonstrate this using two examples from different application areas of applied mathematics. In addition, we have already integrated over 250 research assets from applied mathematics into our knowledge graph.

cs.AI↗

arXiv2024

Towards a FAIR Documentation of Workflows and Models in Applied Mathematics

Modeling-Simulation-Optimization workflows play a fundamental role in applied mathematics. The Mathematical Research Data Initiative, MaRDI, responded to this by developing a FAIR and machine-interpretable template for a comprehensive documentation of such workflows. MaRDMO, a Plugin for the Research Data Management Organiser, enables scientists from diverse fields to document and publish their workflows on the MaRDI Portal seamlessly using the MaRDI template. Central to these workflows are mathematical models. MaRDI addresses them with the MathModDB ontology, offering a structured formal model description. Here, we showcase the interaction between MaRDMO and the MathModDB Knowledge Graph through an algebraic modeling workflow from the Digital Humanities. This demonstration underscores the versatility of both services beyond their original numerical domain.

cs.AI↗

arXiv2023

Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines

In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data, the Mathematical Research Data Initiative has developed, merged and implemented ontologies and knowledge graphs. This contributes to making mathematical research data FAIR by introducing semantic technology and documenting the mathematical foundations accordingly. Using the concrete example of microfracture analysis of porous media, it is shown how the knowledge of the underlying mathematical model and the corresponding numerical algorithms for its solution can be represented by the ontologies.

cs.AI↗

arXiv2022

Research-Data Management Planning in the German Mathematical Community

In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring research-data management plans to mathematicians' research processes and discuss their usage all along the data life cycle.

math.HO↗