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A B S T R A C T Ensemble Kalman filtering was developed as a way to assimilate observed data to track the current state in a computational model. In this paper we show that the ensemble approach makes possible an additional benefit: the timing of observations, whether they occur at the assimilation time or at some earlier or later time, can be effectively… (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)

Simulations play a crucial role in the modern study of physical systems. A major open question for long dynamical simulations of physical processes is the role of discretization and truncation errors in the outcome. A general mechanism is described that can cause extremely small noise inputs to result in errors in simulation statistics that are several… (More)

- Tyrus Berry, Timothy Sauer
- 2012

A B S T R A C T A necessary ingredient of an ensemble Kalman filter (EnKF) is covariance inflation, 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 (1970, 1972) enabled adaptivity in the context of linear… (More)

Data assimilation in dynamical networks is intrinsically challenging. A method is introduced for the tracking of heterogeneous networks of oscillators or excitable cells in a nonstationary environment, using a homogeneous model network to expedite the accurate reconstruction of parameters and unobserved variables. An implementation using ensemble Kalman… (More)

We quantify observability in small (3 node) neuronal networks as a function of 1) the connection topology and symmetry, 2) the measured nodes, and 3) the nodal dynamics (linear and nonlinear). We find that typical observability metrics for 3 neuron motifs range over several orders of magnitude, depending upon topology, and for motifs containing symmetry the… (More)

A general methodology is described for constructing systems that have a slowly converging Lyapunov exponent near zero, based on one-dimensional maps with chaotic attractors. In certain parameter ranges, these relatively simple systems display the properties of intermittent dynamics known as chaotic itinerancy. We show that in addition to the local… (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)