# Prof. Zoltan Toroczkai from NDU presented today a NEST seminar entitled: "The physics of network inference" hosted by Prof. Gyorgy Korniss

Prof. Toroczkai discussed Jaynes’s maximum entropy method that provides a family of principled models that allow the prediction of a system’s properties as constrained by empirical data (observables). However, their use is often hindered by the degeneracy problem characterized by spontaneous symmetry breaking, where predictions fail. In the talk Prof. Toroczkai showed that degeneracy appears when the corresponding density of states function is not log-concave, which is typically the consequence of nonlinear relationships between the constraining observables. This phenomenon was illustrated on several examples, including complex networks, combinatorics and classical spin systems. Exploiting these nonlinear relationships the speaker then proposed a solution to the degeneracy problem for a large class of systems via non-linear transformations that render the density of states function log-concave. The effectiveness of the method was demonstrated on real-world network data. Finally, the implications of these findings on the relationship between the geometrical properties of the density of states function and phase transitions in physical systems such as magnetic spin systems and the van der Waals gas were discussed.

Short bio fo the speaker:

Zoltan Toroczkai is a professor in the Department of Physics and a concurrent professor in the Department of Computer Science and Engineering at University of Notre Dame. He is a Fellow of the American Physical Society. His research interests lie in the areas of statistical physics, nonlinear dynamical systems and mathematical physics with applications to complex networks, foundations of computing and neuroscience.