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- Tyrus Berry, Timothy Sauer
- 2014

Article history: Received 16 July 2014 Received in revised form 6 January 2015 Accepted 9 March 2015 Available online xxxx Communicated by Amit Singer

- Franz Hamilton, Tyrus Berry, Timothy Sauer
- Physical review. E, Statistical, nonlinear, and…
- 2015

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)

- Tyrus Berry, Franz Hamilton, Nathalia Peixoto, Timothy Sauer
- Journal of neuroscience methods
- 2012

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)

- Domenico Napoletani, Timothy Sauer
- Physical review. E, Statistical, nonlinear, and…
- 2008

Given a general physical network and measurements of node dynamics, methods are proposed for reconstructing the network topology. We focus on networks whose connections are sparse and where data are limited. Under these conditions, common in many biological networks, constrained optimization techniques based on the L1 vector norm are found to be superior… (More)

- Tyrus Berry, John Robert Cressman, Zrinka Greguric-Ferencek, Timothy Sauer
- SIAM J. Applied Dynamical Systems
- 2013

It has long been known that the method of time-delay embedding can be used to reconstruct nonlinear 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)

- Tyrus Berry, Timothy Sauer
- 2012

A necessary ingredient of an ensemble Kalman filter is covariance inflation [1], used to control filter divergence and compensate for model error. There is an ongoing search for inflation tunings that can be learned adaptively. Early in the development of Kalman filtering, Mehra [2] enabled adaptivity in the context of linear dynamics with white noise model… (More)

Methods of data assimilation are established in physical sciences and engineering for the merging of observed data with dynamical models. When the model is nonlinear, methods such as the ensemble Kalman filter have been developed for this purpose. At the other end of the spectrum, when a model is not known, the delay coordinate method introduced by Takens… (More)

- Franz Hamilton, Tyrus Berry, Nathalia Peixoto, Timothy Sauer
- Physical review. E, Statistical, nonlinear, and…
- 2013

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)

Assimilation of data with models of physical processes is a critical component of modern scientific analysis. In recent years, nonlinear versions of Kalman filtering have been developed, in addition to methods that estimate model parameters in parallel with the system state. We propose a substantial extension of these tools to deal with the specific case of… (More)

- Timothy Sauer
- Applied Mathematics and Computation
- 2011

Convergence results are presented for rank-type difference equations, whose evolution rule is defined at each step as the kth largest of p univariate difference equations. If the univariate equations are individually contractive, then the equation converges to a fixed point equal to the kth largest of the individual fixed points of the univariate equations.… (More)