arXiv subjects

Jochen Fiedler

Publications and source records attributed to Jochen Fiedler.

5 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↗

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↗

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↗

arXiv2023

Starker Effekt von Schnelltests (Strong effect of rapid tests)

This article is a reproduction of a Fraunhofer ITWM report from 28 June 2021 on the contribution of various non-pharmaceutical measures in breaking the 3rd Corona wave in Germany. The main finding is that testing contributed more to the containment of the pandemic in this phase than vaccination or contact restrictions. The analysis is based on a new epidemiological cohort model that represents testing, vaccination and contact restrictions by time-varying rates of detection, vaccination and contacts, respectively. Only the effectiveness of different vaccines is taken from the literature. All other parameters are automatically identified in such a way that the simulated and the published incidences and death rates match. Among these parameters are incubation time, mean duration of the infectious phase, mortality rate, as well as two contact rates and one detection rate per week. Note that we can reconstruct such a high number of parameters only because we assume that the weekly wave patterns in new infections follow real infection dynamics, periodically driven by high contact rates on weekdays and lower ones on weekends. Usually, people assume that the weekly wave patterns are just reporting artefacts and that weekly mean values are the finest usable data. One focus of the paper is to quantify the increase in detection rate due to the introduction of rapid testing in schools. For this purpose, we compare federal states that differ in the start of school tests and Easter holidays. There is a clear temporal correlation with the identified detection rates. Finally, we compare the effect of the individual non-pharmaceutical measures by replacing one by one the fitted rates of detection, vaccination and contacts by neutral ones. The increase in the simulated number of actually infected persons measures the effect of the measure ignored.

q-bio.OT↗

arXiv2014

From Fourier to Gegenbauer: Dimension walks on spheres

We show that the even- resp. odd-dimensional Schoenberg coefficients in Gegenbauer expansions of isotropic positive definite functions on the d-sphere can be expressed as linear combinations of Fourier resp. Legendre coefficients, and we give closed form expressions for the coefficients involved in these expansions.

math.ST↗