Tim Sauer

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We developed a modern numerical approach to the multivariate linear discrimination of Fisher from 1936 based upon singular value decomposition that is sufficiently stable to permit widespread application to spatiotemporal neuronal patterns. We demonstrate this approach on an old problem in neuroscience--whether seizures have distinct dynamical states as(More)
Long time series of monosynaptic Ia-afferent to alpha-motoneuron reflexes were recorded in the L7 or S1 ventral roots in the cat. Time series were collected before and after spinalization at T13 during constant amplitude stimulations of group Ia muscle afferents in the triceps surae muscle nerves. Using autocorrelation to analyze the linear correlation in(More)
Long time series of Schaffer collateral to CA1 pyramidal cell presynaptic volleys (stratum radiatum) and population spikes (stratum pyramidale) were evoked (driven) in rat hippocampal slices. From the driven CA1 region in normal [K+] perfusate, both population spike amplitude and an input-output function consisting of population spike amplitude divided by(More)
OBJECTIVE To discriminate seizures from interictal dynamics based on multivariate synchrony measures, and to identify dynamics of a pre-seizure state. METHODS A linear discriminator was constructed from two different measures of synchronization: cross-correlation and phase synchronization. We applied this discriminator to a sequence of seizures recorded(More)
An approach to discriminating deterministic versus stochastic dynamics from neuronal data is presented. Direct tests for determinism are emphasized, as well as using time series with clear physical correlates measured from small ensembles of neurons. Surrogate data are used to provide null hypotheses that the dynamics in our data could be accounted for by(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)
In this paper, we utilize techniques from the theory of nonlinear dynamical systems to define a notion of embedding estimators. More specifically, we use delay-coordinates embeddings of sets of coefficients of the measured signal (in some chosen frame) as a data mining tool to separate structures that are likely to be generated by signals belonging to some(More)
— We propose a new method for fitting model parameters to the neural spike train obtained from an experimental neuron. Due to the uncertainty associated with measuring the accurate voltage in a noisy environment, it is essential to develop methods that rely solely on the interspike intervals (ISI). Existing techniques do not provide a smooth and continuous(More)
The increasing need of knowledge in the treatment of brain diseases has driven a huge interest in understanding the phenomenon of neural spiking. Researchers have successfully been able to create mathematical models which, with specific parameters, are able to reproduce the experimental neuronal responses. The spiking activity is characterized using spike(More)