Dynamical Models for Multiplex Data
Dr. Daryl DeFord
Department of Mathematics
Dartmouth College
Abstract: Multiplex networks represent the different types of relationships that can exist between objects of interest, like the difference between social media ``friends'' and real life acquaintances. In this talk I will discuss a variety of network models for this type of data and introduce a family of dynamical operators that avoid some of the distortions introduced by the structural approaches. These new models preserve the original dynamics and interpolate the extremes of the structural models for a variety of network metrics. I will present both spectral results and applications for this family of operators in the settings of centrality metrics and spectral clustering. This process of refining and reevaluating known techniques to account for increasingly detailed data motivates many interesting pure and applied problems and I will conclude by discussing a similar methodology in the analysis entropy measures for time series.
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