Tim Conrad, Stefan Klus, Gregoire Montavon
Kateryna Melnyk (FU)
01.01.2019 – 31.12.2021
Only about 1 out of 10 cells in our body is actually a human cell. We are colonized by a diverse community of bacteria, archaea and viruses, jointly referred to as the microbiome (or microbiota). They have a strong influence on our health and are sometimes even called our second genome. Catalyzed by digitalization in the health-system and new high-throughput omics technologies, research on the human microbiome has grown exponentially in recent years and. has significantly increased our understanding about the role that these microbes play for our health and their connection to major diseases.
It has also been found that although the constitution of the microbiome is constantly changing throughout our lives (in response to environmental factors and other stimuli), a healthy human microbiome (i.e., a healthy community composition) can be considered as a meta-stable state lying in a minimum of some ecological stability landscape. Most studies aiming at understanding these dynamics, however, are focused on statistical constitution analysis, omitting more complex interactions.
The goal of this project is to develop new mathematical methods to allow a better understanding of complex systems modeled by time-evolving networks. With the aid of these methods, we will study microbiome interactions and the dynamic processes behind them.
We suggest two new approaches for analyzing time-evolving and high-dimensional graphs:
We developed a kernel-based method – GraphKKE that is capable of learning embeddings of time-evolving graphs preserving temporal changes in a low-dimensional space. The method is based on the spectral analysis of transfer operators, such as the Perron–Frobenius or Koopman operator in a reproducing kernel Hilbert space.
(a) Learning transfer operators using graph kernels, where k(·, ·) is a graph kernel and Kk is the Koopman operator. (b) In the learned embedding space it is possible to detect metastable states and to determine distinct substructures.
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