Extra Seminar Mathematics - Dr. C.Hirsch
|When:||Fr 08-03-2019 11:35 - 12:20|
Statistics and Networks: Perspectives from Neuro-, Materials and Data Science
How does the network of neurons affect learning in the human brain? How is the microstructure of a material related to its charge-transport properties? What insights do statistics of connected component and loops provide on network data? Although these questions arise in a variety of different contexts, they all fundamentally relate to the statistical modeling and the statistical analysis of random networks. In the first part of the seminar, we will catch a glimpse on the mathematical concepts and the associated statistical tools that are at the heart of these questions.
In the second part of the seminar, we focus on the problem of estimating geodesic tortuosity and constrictivity as two structural characteristics in materials science. Loosely speaking, geodesic tortuosity measures the windedness of paths whereas the notion of constrictivity captures the appearance of bottlenecks resulting from narrow passages. We propose estimators for these key characteristics and derive sufficient conditions for their consistency in large domains. In that context, a surprising link to percolation theory appears.