Timothy D. Sauer

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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)
The problem of reconstructing and identifying intracellular protein signaling and biochemical networks is of critical importance in biology. We propose a mathematical approach called augmented sparse reconstruction for the identification of links among nodes of ordinary differential equation (ODE) networks, given a small set of observed trajectories with(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)
OBJECT Hydrocephalus is one of the most common brain disorders in children throughout the world. The majority of infant hydrocephalus cases in East Africa appear to be postinfectious, related to preceding neonatal infections, and are thus preventable if the microbial origins and routes of infection can be characterized. In prior microbiological work, the(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)
We examine the question whether the dimension D of a set or probability measure is the same as the dimension of its image under a typical smooth function, if the range space is at least D-dimensional. If is a Borel probability measure of bounded support in Rn with correlation dimension D, and if m D, then under almost every continuously differentiable(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)