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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)
We study a general physical network consisting of a collection of response systems with complex nonlinear dynamics, influenced by a common driver. The goal is to reconstruct dynamics, regular or chaotic, that are common to all of the response systems, working from simultaneous time series measured at the responses systems only. A fundamental theorem is(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)
Observability and controllability are vitally important in networks, but almost all of the present theory was developed for linear networks without symmetries. To advance beyond the study of such generic networks, we quantify observability and controllability in small (3 node) nonlinear neuronal networks as a function of 1) the connection topology and(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)