The talk will present our research at the Biomedical Cybernetics Group that I established about three years ago in Technical University Dresden. We adopt a transdisciplinary approach integrating information theory, machine learning and network science to investigate the physics of adaptive processes that characterize complex interacting systems at different scales, from molecules to ecosystems, with a particular attention to biology and medicine, and a new emerging interest for the analysis of complex big data in economy and finance. Our theoretical effort is to translate advanced mathematical paradigms typically adopted in theoretical physics (such as topology, network and manifold theory) to characterize many-body interactions in complex systems. We apply the theoretical frameworks we invent in the mission to develop computational tools for systems and network analysis. In particular, we deal with: prediction of wiring in networks and multiscale-combinatorial marker design for quantification of topological modifications in complex networks. Our attention for precision biomedicine is aim to subjects with important impact from the economical point of few such as development of tools for disease biomarker discovery, drug repositioning and combinatorial drug therapy.
This talk will focus on three main theoretical innovation. Firstly, Minimum Curvilinearity, which is a theory for topological estimation of nonlinear relations in high-dimensional data (or in complex networks) and its relevance for applications in big data. The new topic on the impact of Minimum Curvilinearity for network embedding in the hyperbolic space will be also treated, and the idea to develop quantitative markers in the latent geometry space will be introduced. Secondly, we will discuss the Local Community Paradigm (LCP), which is a theory proposed to model local-topology-dependent link-growth in complex networks and therefore it is useful to devise topological methods for link prediction in monopartite and bipartite networks such as product-consumer networks. Finally, we will discuss the importance of a new model we developed for the detection of rich-clubs in complex networks and the relevance of this topic for analysis of complex systems in biological, social and economic sciences.