Encoding Chaos in Neural Spike Trains

Richardson, Kristen A.; Imhoff, Thomas T.; Grigg, Peter; Collins, James J.

doi:10.1103/physrevlett.80.2485

Cited by 26 publications

(11 citation statements)

References 19 publications

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“…In neural systems (real and modeled) driven by chaotic and by random stimuli, it has been shown that the determinism in the driving signal is retained (as assessed by predictability) after passing through simple neural dynamics and an embedding procedure (20,23). Thus it has been demonstrated that important dynamic information is conserved in a state-space reconstruction of discrete-time data.…”

Section: Methodsmentioning

confidence: 99%

Random walks, random sequences, and nonlinear dynamics in human optokinetic nystagmus

Trillenberg

Gross²,

Shelhamer

2001

Journal of Applied Physiology

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Optokinetic nystagmus (OKN) is a reflexive eye movement with target-following slow phases (SP) alternating with oppositely directed fast phases (FP). We measured the following from OKN in three humans: FP beginning and ending positions, amplitudes, and intervals and SP amplitudes and velocities. We sought to predict future values of each parameter on the basis of past values, using state-space representation of the sequence (time-delay embedding) and local second-order approximation of trajectories. Predictability is an indication of determinism: this approach allows us to investigate the relative contributions of random and deterministic dynamics in OKN. FP beginning and ending positions showed good predictability, but SP velocity was less predictable. FP and SP amplitudes and FP intervals had little or no predictability. FP beginnings and endings were as predictable as randomized versions that retain linear autocorrelation; this is typical of random walks. Predictability of FP intervals did not change under random rearrangement, which is characteristic of a random process. Only linear determinism was demonstrated; nonlinear interactions may exist that would not be detected by our present approach.

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Section: Methodsmentioning

confidence: 99%

Random walks, random sequences, and nonlinear dynamics in human optokinetic nystagmus

Trillenberg

Gross²,

Shelhamer

2001

Journal of Applied Physiology

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“…It is an intriguing problem whether ISI reconstruction of a deterministic input is applicable to real biological neurons which are certainly more complex in dynamics than the integrate-and-®re model. The validity of the ISI reconstruction has been tested by numerical simulations for neuron models of various complexities (Racicot and Longtin 1997), by the eect of noise (Lindner et al 1998), and by physiological data of in vitro rat cutaneous mechanoreceptors (Richardson et al 1998). There has also been an attempt at reconstruction using threshold-crossing intervals (Janson et al 1998).…”

Section: Introductionmentioning

confidence: 99%

Analysis of neural spike trains with interspike interval reconstruction

Suzuki

Aihara

Murakami

et al. 2000

Biological Cybernetics

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As a method for the analysis of neural spike trains, we examine fundamental characteristics of interspike interval (ISI) reconstruction theoretically with a leaky-integrator neuron model and experimentally with cricket wind receptor cells. Both the input to the leaky integrator and the stimulus to the wind receptor cells are the time series generated from the Rossler system. By numerical analysis of the leaky integrator, it is shown that, even if ISI reconstruction is possible, sometimes the entire structure of the Rössler attractor may not be reconstructed with ISI reconstruction. For analysis of the in vivo physiological responses of cricket wind receptor cells, we apply ISI reconstruction, nonlinear prediction and the surrogate data method to the experimental data. As a result of the analysis, it is found that there is a significant deterministic structure in the spike trains. By this analysis of physiological data, it is also shown that, even if ISI reconstruction is possible, the entire attractor may not be reconstructed.

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“…This can be seen by comparison with Figure 3. Figure 8 shows an example of input signal reconstruction which estimates I input using ISI vectors of the described in Equation 15. We used a time delay T = 1, an embedding dimension d E = 7, and a local linear map for H(y(j)).…”

Section: Numerical Resultsmentioning

confidence: 99%

Reading Neural Encodings using Phase Space Methods

Tumer¹

2003

Perspectives and Problems in Nolinear Science

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Environmental signals sensed by nervous systems are often represented in spike trains carried from sensory neurons to higher neural functions where decisions and functional actions occur. Information about the environmental stimulus is contained (encoded) in the train of spikes. We show how to "read" the encoding using state space methods of nonlinear dynamics. We create a mapping from spike signals which are output from the neural processing system back to an estimate of the analog input signal. This mapping is realized locally in a reconstructed state space embodying both the dynamics of the source of the sensory signal and the dynamics of the neural circuit doing the processing. We explore this idea using a Hodgkin-Huxley conductance based neuron model and input from a low dimensional dynamical system, the Lorenz system. We show that one may accurately learn the dynamical input/output connection and estimate with high precision the details of the input signals from spike timing output alone. This form of "reading the neural code" has a focus on the neural circuitry as a dynamical system and emphasizes how one interprets the dynamical degrees of freedom in the neural circuit as they transform analog environmental information into spike trains.

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Encoding Chaos in Neural Spike Trains

Cited by 26 publications

References 19 publications

Random walks, random sequences, and nonlinear dynamics in human optokinetic nystagmus

Random walks, random sequences, and nonlinear dynamics in human optokinetic nystagmus

Analysis of neural spike trains with interspike interval reconstruction

Reading Neural Encodings using Phase Space Methods

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