Research @ TRA 1 Modelling
Research profile, topics, projects

Research Profile TRA Modelling

At the core of the TRA Modelling is mathematics, which provides a universal tool and language for all quantitative sciences. A central challenge for computer science lies in improving data-driven methods for the creation of intelligent models of complex systems. While previous scientific ages have focused on the understanding of individual parts of nature, it is one of the biggest challenges of our time to understand how these parts interact. This yields an understanding of how the increasingly complex systems around us actually work.

In the TRA Modelling, researchers from a broad range of disciplines such as applied mathematics, computer sciences, quantitative economics, life science/medicine, and agricultural science create models that not only describe complex systems, but are able to analyze their behavior. This is achieved by the interaction of mathematical modelling, classical observational methods, data analytics, data simulation and creative spirit.

Research
© TRA Modelling

Self-Concept

The TRA Modeling deliberately addresses a broad, open spectrum of transdisciplinary topics. It is affiliated with the Cluster of Excellence Hausdorff Center for Mathematics (HCM)11 and further cooperates with researchers from the Clusters of Excellence ImmunoSensation222 and PhenoRob33 as well as the b-it (Bonn-Aachen International Center for Information Technology)44, the Fraunhofer Institute SCAI 55or the Max-Planck-Institute for Mathematics66.

Besides the traditional cooperation of Bonns economists and mathematicians, topics of the Interdisciplinary Research Units Mathematics and life sciences77, the cooperation between the Research Institute for Discrete Mathematics with IBM for more than 30 years as well as the associated research area „combinatorial optimization, complexity, and chip design“88 at the interface of mathematics, computer science and engineering or the SFB 1060 - The Mathematics of Emergent Effects99 at the interface of mathematics and physics have to be mentioned..

While initially built around the core fields of mathematics and computer science applied to quantitative economics, the TRA's focus meanwhile developed towards further highly promising application fields such as life sciences/medicine, geodesy, and chemical engineering10.

Research Focus & Sub-Schemes

In a participatory bottom-up process, the TRA recently sharpened its research profile and identified three (naturally overlapping) sub-schemes of active and highly promising research collaborations:

  • “Mathematics, Computational Biology & Medicine”
    Applied Mathematics / Computational Science / Life Science / Medicine
    Exemplary research methods: data analysis in the field of cell sequencing, neuroscience, modelling of clinical and pharmacological data
  • “Computer and Data Science for Economics”
    Applied Mathematics / Computational Science / Quantitative Economics
    Exemplary research methods: data analysis and machine learning applied to economics and econometrics, algorithmic economics
  • “Data Analytics and Algorithm Engineering”
    Applied Mathematics / Computational Science / Agricultural Science / Engineering
    Exemplary research methods: (predictive) data analytics and/or algorithm engineering for Earth observation data, environmental or meteorological data
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© TRA Modelling
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© TRA Modelling

Example: Mathematics and Life Science

Quantitative analysis and the generation of large data sets in life sciences have steadily increased since the 1990s. This is often associated with the desire to use already existing data sets to make predictions about biological processes. The research fields of Biomathematics & Computational Life Sciences combine mathematical modeling and experimental methods in order to achieve this. For its success, true inter- and transdisciplinary research approaches are imperative.
 
The Clusters of Excellence Hausdorff Center for Mathematics and ImmunoSensation2 have taken a pioneering role in this field at the University of Bonn through Interdisciplinary Research Units. Also within the TRA Modelling and the TRA Life & Health, research at the interface mathematics, computer science and life sciences is getting established.

Example: Mathematical Modelling & Computational Science in Economics and Life Science

Decision-making involves risk and uncertainties. In pandemic times, the complexity of uncertainties and influencing factors that come together from different areas become even more apparent:  Computer-based models used by epidemiologists to predict the effects of distancing rules on the spread of viruses involve uncertainties such as the evolving incidence number. When economists investigate the effect of the pandemic on markets, they have to deal with uncertainties about price elasticities. The forecasts of financial experts involve uncertainties on stock price development. Factors that are relevant for the transmission of viruses and their influence can vary greatly between groups of people - both at the biomedical and socioeconomic levels. The coronavirus pandemic thus shows that major societal challenges and the associated complex questions cannot be answered by one scientific discipline alone. It is necessary to combine the expertise, findings and models from different disciplines to overcome the shortcomings of fragile implications and to identify knowledge gaps.

Collaboration: Open Source Economics and TRA
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© TRA Modelling / from research project by Jan-Henrik Haunert

Example: Mathematical Modelling & Data Analytics in Geodesy

Many fields of modern geodesy can be seen as interdisciplinary data-driven science with applications such as understanding risks to society or sustainable pathways for human development. In times of climate change and climate disasters as flooding on the one hand and digitalization and big data on the other, interaction between these areas is urgently needed. Researchers in this field work with a large variety of spatial-temporal data sets and create models and measurements on sea level height, the increase and decrease of the world’s oceans or ocean circulation dynamics. To solve the required tasks, it is necessary to combine expertise from applied and numerical mathematics, applied statistics, scientific computing, and applied informatics in agricultural science.

News from TRA projects/initiatives
Mathematics meets Life Sciences

The tremendous advances made in experimental life sciences in recent years provide a wealth of data on how organisms function. To gain biomedical knowledge from these data, both mathematical modeling and numerical analysis techniques in conjunction with experimental data are essential. At a joint symposium of the Clusters of Excellence Hausdorff Center for Mathematics and ImmunoSensation2 as well as the Transdisciplinary Research Areas "Modelling" and "Life and Health" of the University of Bonn, the professors working at the interfaces and their colleagues presented their research and invited to participate.

What factors impact the spread of viruses?

Many different factors are responsible for the spread of infectious diseases. What is known is that the spread process depends essentially on the infectiousness of the pathogen and the immune response of the host, but also on human behavior. This relates, for example, to the extent to which distance regulations are observed. Less often considered, however, is the fact that the factors and their influence can vary greatly between groups of people - both at the biomedical and socioeconomic levels. Mathematicians, physicians and economists now want to take a closer look at this so-called inter-individual variability in a joint collaboration project of the University of Bonn and the University Hospital Munich. The goal is to determine new factors that are relevant for the transmission or containment of SARS-CoV-2 viruses. The German Research Foundation (DFG) is funding the project with several hundred thousand euros, of which 270,000 euros will go to Bonn.

Mathematical Epidemiologist Elba Raimundéz won the Pfizer Poster Prize for Covid19-Modelling.

Mathematical Epidemiologist Elba Raimundéz won the Pfizer Poster Prize for Covid19-Modelling at the 2021 Annual Meeting of the Society for Mathematical Biology. Her work addresses the limitations of publicly available case numbers for epidemiological modeling demonstrated on data of the COVID-19 outbreak in Wuhan. This work motivated another collaborative research initiative on parameter and prediction uncertainties, which is currently funded by the TRA Modelling.

Funded Projects

Current funding takes place for projects at the interfaces of geodesy and computer sciences, mathematics and life sciences/medicine, economics and computer sciences, as well as mathematics, computer sciences and linguistics.

Funding for Initiatives (by AD)

  • "CiliaQ, Digitalization of software applications"; Contact: Prof. Dagmar Wachten
  • "Transdisciplinary research portfolio, uncertainty quantification, and robust decisions - Initiating a transdisciplinary research program"; Contact: Prof. Philipp Eisenhauer (Koordinator), Prof. Jan Hasenauer, JProf. Lena Janys, Dr. Daniel Oeltz & Dilan Pathirana, PhD

Start-up Funding for Projects (by AD):

  • „Algorithmic Data Analytics for Geodesy”; Contact: Prof. Petra Mutzel & Prof. Jan-Henrik Haunert
  • „Establishment of computational methods for spatially-resolved deep profiling of biological tissues”; Contact: Prof. Jan Hasenauer, Prof. Michael Hölzel & Prof. Marieta Toma
  • „UNCOVer: Uncertainty Quantification of COVID-19 Epidemiological Models”; Contact: Dr. Dilan Pathirana & Elba Raimúndez Álvarez
  • "Naproche - Natural Language Proof Checking" / "Naproche for Teaching"; Contact: Prof. Peter Koepke
  • "Assessing the separate and synergistic effects of amyloid and tau on human brain activity using a computational model of brain oscillations"; Contact: Dr. Xenia Kobeleva
  • "Practical Characterization of Self-Assembling Optical Systems by Joint Forward and Inverse Modelling"; Contact: Prof. Matthias Hullin
  • "MaxCut & Binary Quadratic Programming"; Contact: Dr. Sven Mallach
  • "Development of Continuous Spatio-Temporal Finite Element Based Models for Sea Surface Approximation"; Contact: Dr. Jan Martin Brockmann

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