Graphlets in Multiplex Networks.

We develop graphlet analysis for multiplex networks and discuss how this analysis can be extended to multilayer and multilevel networks as well as to graphs with node and/or link categorical attributes. The analysis has been adapted for two typical examples of multiplexes: economic trade data represented as a 957-plex network and 75 social networks each represented as a 12-plex network. We show that wedges (open triads) occur more often in economic trade networks than in social networks, indicating the tendency of a country to produce/trade of a product in local structure of triads which are not closed. Moreover, our analysis provides evidence that the countries with small diversity tend to form correlated triangles. Wedges also appear in the social networks, however the dominant graphlets in social networks are triangles (closed triads). If a multiplex structure indicates a strong tie, the graphlet analysis provides another evidence for the concepts of strong/weak ties and structural holes. In contrast to Granovetter's seminal work on the strength of weak ties, in which it has been documented that the wedges with only strong ties are absent, here we show that for the analyzed 75 social networks, the wedges with only strong ties are not only present but also significantly correlated.

Measurement-oriented deep-learning workflow for improved segmentation of myelin and axons in high-resolution images of human cerebral white matter.

BACKGROUND: Standard segmentation of high-contrast electron micrographs (EM) identifies myelin accurately but does not translate easily into measurements of individual axons and their myelin, even in cross-sections of parallel fibers. We describe automated segmentation and measurement of each myelinated axon and its sheath in EMs of arbitrarily oriented human white matter from autopsies. NEW METHODS: Preliminary segmentation of myelin, axons and background by machine learning, using selected filters, precedes automated correction of systematic errors. Final segmentation is done by a deep neural network (DNN). Automated measurement of each putative fiber rejects measures encountering pre-defined artifacts and excludes fibers failing to satisfy pre-defined conditions. RESULTS: Improved segmentation of three sets of 30 annotated images each (two sets from human prefrontal white matter and one from human optic nerve) is achieved with a DNN trained only with a subset of the first set from prefrontal white matter. Total number of myelinated axons identified by the DNN differed from expert segmentation by 0.2%, 2.9%, and -5.1%, respectively. G-ratios differed by 2.96%, 0.74% and 2.83%. Intraclass correlation coefficients between DNN and annotated segmentation were mostly >0.9, indicating nearly interchangeable performance. COMPARISON WITH EXISTING METHOD(S): Measurement-oriented studies of arbitrarily oriented fibers from central white matter are rare. Published methods are typically applied to cross-sections of fascicles and measure aggregated areas of myelin sheaths and axons, allowing estimation only of average g-ratio. CONCLUSIONS: Automated segmentation and measurement of axons and myelin is complex. We report a feasible approach that has so far proven comparable to manual segmentation.