Entropy of labeled versus unlabeled networks.

The structure of a network is an unlabeled graph, yet graphs in most models of complex networks are labeled by meaningless random integers. Is the associated labeling noise always negligible, or can it overpower the network-structural signal? To address this question, we introduce and consider the sparse unlabeled versions of popular network models and compare their entropy against the original labeled versions. We show that labeled and unlabeled Erdős-Rényi graphs are entropically equivalent, even though their degree distributions are very different.

Parameterless detection of liquid-liquid interfaces with sub-micron resolution in single-molecule localization microscopy.

Hypothesis: Knowing the exact location of soft interfaces, such as between water and oil, is essential to the study of nanoscale wetting phenomena. Recently, iPAINT was used to visualize soft interfaces in situ with minimal invasiveness, but computing the exact location of the interface remains challenging. We propose a new method to determine the interface with high accuracy.

Phase transitions for scaling of structural correlations in directed networks.

Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e., models that generate uncorrelated scale-free networks.