Lori Ziegelmeier

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  Using Topology to Measure Dynamics of Time-Varying Systems
  Lori Ziegelmeier
  A time-varying collection of metric spaces as formed, for example, by a moving school of fish or flock of birds, can contain a vast amount of information. There is sometimes a need to simplify or summarize the dynamic behavior, and recently, topological tools have been applied to this purpose. One such method is a crocker plot, a 2-dimensional image that displays the (non-persistent but varying with scale) topological information at all times simultaneously. We use this method to perform exploratory data analysis and investigate parameter recovery in the collective motion model of D’Orsogna et al. (2006). Then, we use it to choose between unbiased correlated random walk models of Nilsen et al. (2013) that describe motion tracking experiments on pea aphids. Finally, we discuss an extension of the crocker plot that is persistent and equivalent to the information in a vineyard and hence, inherits the nice stability properties of vineyards. For some purposes, the information in a vineyard is more accessible when instead displayed in this new manner.