Selected Publications

Traditionally, network analysis is based on local properties of ver- tices, like their degree or clustering, and their statistical behavior across the network in question. This paper develops an approach which is different in two respects: We investigate edge-based properties, and we define global characteristics of networks directly. More concretely, we start with Forman’s notion of the Ricci curvature of a graph, or more generally, a polyhedral complex. This will allow us to pass from a graph as representing a network to a polyhedral complex for instance by filling in triangles into connected triples of edges and to investigate the resulting effect on the curvature. This is insightful for two reasons: First, we can define a curvature flow in order to asymptotically simplify a network and reduce it to its essentials. Second, using a construction of Bloch which yields a discrete Gauß-Bonnet theorem, we have the Euler characteristic of a network as a global characteristic. These two aspects beautifully merge in the sense that the asymptotic properties of the curvature flow are indicated by that Euler characteristic.
In J. Compl. Net., 2017.

Projects

Curvature-based Network Analysis

Forman-Ricci curvature and discrete geometric flows for a curvature-based analysis of complex networks.

Event Classification with CNNs

Convolutional Neural Networks for Event Classification at LHC’s ATLAS experiment.

Functional Analysis of Gene Networks

Efficient tools for functional characterization of gene networks.

Geometric Aspects in Machine Learing

Understanding and Learning the Geometry of Data.

Modeling Brain Disorders with Hopfield Networks

Neural networks model for effects of brain disorders on associative memory.

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