NS Seminar

Date and Location

Apr 13, 2018 - 1:00pm to 2:00pm
Bldg 434, room 122

Abstract

Exploring the structure and function of temporal networks with dynamic graphlets (presented by Taom Sakal, Department of Ecology, Evolution, and Marine Biology)

Y. Hulovatyy, H. Chen, T. Milenković; Exploring the structure and function of temporal networks with dynamic graphlets, Bioinformatics, Volume 31, Issue 12, 15 June 2015, Pages i171–i180, https://doi.org/10.1093/bioinformatics/btv227

Motivation: With increasing availability of temporal real-world networks, how to efficiently study these data? One can model a temporal network as a single aggregate static network, or as a series of time-specific snapshots, each being an aggregate static network over the corresponding time window. Then, one can use established methods for static analysis on the resulting aggregate network(s), but losing in the process valuable temporal information either completely, or at the interface between different snapshots, respectively. Here, we develop a novel approach for studying a temporal network more explicitly, by capturing inter-snapshot relationships.
Results: We base our methodology on well-established graphlets (subgraphs), which have been proven in numerous contexts in static network research. We develop new theory to allow for graphlet-based analyses of temporal networks. Our new notion of dynamic graphlets is different from existing dynamic network approaches that are based on temporal motifs (statistically significant subgraphs). The latter have limitations: their results depend on the choice of a null network model that is required to evaluate the significance of a subgraph, and choosing a good null model is non-trivial. Our dynamic graphlets overcome the limitations of the temporal motifs. Also, when we aim to characterize the structure and function of an entire temporal network or of individual nodes, our dynamic graphlets outperform the static graphlets. Clearly, accounting for temporal information helps. We apply dynamic graphlets to temporal age-specific molecular network data to deepen our limited knowledge about human aging.

 

Persistent homology of time-dependent functional networks constructed from coupled time series (presented by Rachel Redberg, Computer Science)

arXiv:1605.00562v3 [q-bio.QM] 3 Dec 2016

We use topological data analysis to study “functional networks” that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results. Our first example uses time-series output from networks of coupled Kuramoto oscillators. Our second example consists of biological data in the form of functional magnetic resonance imaging (fMRI) data that was acquired from human subjects during a simple motor-learning task in which subjects were monitored on three days in a five-day period. With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can sometimes play a more vital role than persistence in the interpretation of topological features, even though conventionally the latter is used to distinguish between signal and noise. We find that persistent homology can detect differences in synchronization patterns in our data sets over time, giving insight both on changes in community structure in the networks and on increased synchronization between brain regions that form loops in a functional network during motor learning. For the motor-learning data, persistence landscapes also reveal that on average the majority of changes in the network loops take place on the second of the three days of the learning process.