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It has long been known that the method of time-delay embedding can be used to reconstruct non-linear dynamics from time series data. A less-appreciated fact is that the induced geometry of time-delay coordinates increasingly biases the reconstruction toward the stable directions as delays are added. This bias can be exploited, using the diffusion maps(More)
Methods for forecasting time series are a critical aspect of the understanding and control of complex networks. When the model of the network is unknown, nonparametric methods for prediction have been developed, based on concepts of attractor reconstruction pioneered by Takens and others. In this Rapid Communication we consider how to make use of a subset(More)
We develop a method from semiparametric statistics (Cox, 1972) for the purpose of tracking links and connection strengths over time in a neuronal network from spike train data. We consider application of the method as implemented in Masud and Borisyuk (2011), and evaluate its use on data generated independently of the Cox model hypothesis, in particular(More)
Mathematical models of marine populations exhibit chaotic dynamics. However, we hypothesize that in moving water, Eu-lerian sampling of spatially heterogeneous populations may obscure any deterministic signal beyond the resolving capabilities of presently available nonlinear signal processing techniques. To examine this hypothesis we created two(More)
A nonlinear data assimilation technique is applied to determine and track effective connections between ensembles of cultured spinal cord neurons measured with multielectrode arrays. The method is statistical, depending only on confidence intervals, and requiring no form of arbitrary thresholding. In addition, the method updates connection strengths(More)