scholarly journals A simple model for low variability in neural spike trains

2018 ◽  
Author(s):  
Ulisse Ferrari ◽  
Stéphane Deny ◽  
Olivier Marre ◽  
Thierry Mora
Keyword(s):  
Simple Model ◽  
Spike Train ◽  
Spike Trains ◽  
Firing Rates ◽  
Repeated Stimulus ◽  
Neural Noise ◽  
Poisson Models ◽  
Neural Spike ◽  
Neural Spike Trains ◽  
Two Parameters

Neural noise sets a limit to information transmission in sensory systems. In several areas, the spiking response (to a repeated stimulus) has shown a higher degree of regularity than predicted by a Poisson process. However, a simple model to explain this low variability is still lacking. Here we introduce a new model, with a correction to Poisson statistics, which can accurately predict the regularity of neural spike trains in response to a repeated stimulus. The model has only two parameters, but can reproduce the observed variability in retinal recordings in various conditions. We show analytically why this approximation can work. In a model of the spike emitting process where a refractory period is assumed, we derive that our simple correction can well approximate the spike train statistics over a broad range of firing rates. Our model can be easily plugged to stimulus processing models, like Linear-nonlinear model or its generalizations, to replace the Poisson spike train hypothesis that is commonly assumed. It estimates the amount of information transmitted much more accurately than Poisson models in retinal recordings. Thanks to its simplicity this model has the potential to explain low variability in other areas.

scholarly journals A Simple Model for Low Variability in Neural Spike Trains

2018 ◽  
Vol 30 (11) ◽  
pp. 3009-3036 ◽  
Author(s):  
Ulisse Ferrari ◽  
Stéphane Deny ◽  
Olivier Marre ◽  
Thierry Mora
Keyword(s):  
Simple Model ◽  
Spike Train ◽  
Spike Trains ◽  
Firing Rates ◽  
Repeated Stimulus ◽  
Neural Noise ◽  
Poisson Models ◽  
Neural Spike ◽  
Neural Spike Trains ◽  
Two Parameters

Neural noise sets a limit to information transmission in sensory systems. In several areas, the spiking response (to a repeated stimulus) has shown a higher degree of regularity than predicted by a Poisson process. However, a simple model to explain this low variability is still lacking. Here we introduce a new model, with a correction to Poisson statistics, that can accurately predict the regularity of neural spike trains in response to a repeated stimulus. The model has only two parameters but can reproduce the observed variability in retinal recordings in various conditions. We show analytically why this approximation can work. In a model of the spike-emitting process where a refractory period is assumed, we derive that our simple correction can well approximate the spike train statistics over a broad range of firing rates. Our model can be easily plugged to stimulus processing models, like a linear-nonlinear model or its generalizations, to replace the Poisson spike train hypothesis that is commonly assumed. It estimates the amount of information transmitted much more accurately than Poisson models in retinal recordings. Thanks to its simplicity, this model has the potential to explain low variability in other areas.

The Time-Rescaling Theorem and Its Application to Neural Spike Train Data Analysis

2002 ◽  
Vol 14 (2) ◽  
pp. 325-346 ◽  
Author(s):  
Emery N. Brown ◽  
Riccardo Barbieri ◽  
Valérie Ventura ◽  
Robert E. Kass ◽  
Loren M. Frank
Keyword(s):  
Probability Theory ◽  
Data Analysis ◽  
Spike Train ◽  
Point Process ◽  
Goodness Of Fit ◽  
Spike Trains ◽  
Neural Spike ◽  
Neural Spike Train ◽  
Neural Spike Trains ◽  
Spike Train Data

Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model's validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a well-known result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers, inhomogeneous Poisson, inhomogeneous gamma, and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity. To help make the logic behind the time-rescaling theorem more accessible to researchers in neuroscience, we present a proof using only elementary probability theory arguments.We also show how the theorem may be used to simulate a general point process model of a spike train. Our paradigm makes it possible to compare parametric and histogram-based neural spike train models directly. These results suggest that the time-rescaling theorem can be a valuable tool for neural spike train data analysis.

Correlation between neural spike trains increases with firing rate

Nature ◽  
2007 ◽  
Vol 448 (7155) ◽  
pp. 802-806 ◽  
Author(s):  
Jaime de la Rocha ◽  
Brent Doiron ◽  
Eric Shea-Brown ◽  
Krešimir Josić ◽  
Alex Reyes
Keyword(s):  
Firing Rate ◽  
Spike Trains ◽  
Neural Spike ◽  
Neural Spike Trains

scholarly journals The Neuroid revisited: A heuristic approach to model neural spike trains

2017 ◽  
Vol 33 (4) ◽  
pp. 331-343
Author(s):  
Erick Javier Argüello Prada ◽  
Ignacio Antonio Buscema Arteaga ◽  
Antonio José D’Alessandro Martínez
Keyword(s):  
Spike Trains ◽  
Heuristic Approach ◽  
Neural Spike ◽  
Neural Spike Trains

Bursts and recurrences of bursts in the spike trains of spontaneously active striate cortex neurons

1985 ◽  
Vol 53 (4) ◽  
pp. 926-939 ◽  
Author(s):  
C. R. Legendy ◽  
M. Salcman
Keyword(s):  
Standard Deviation ◽  
Spike Train ◽  
Striate Cortex ◽  
Quantitative Measure ◽  
Spike Trains ◽  
Spike Rate ◽  
Occurrence Rate ◽  
Implanted Electrodes ◽  
Firing Rates ◽  
The Mean

Simultaneous recordings were made from small collections (2-7) of spontaneously active single units in the striate cortex of unanesthetized cats, by means of chronically implanted electrodes. The recorded spike trains were computer scanned for bursts of spikes, and the bursts were catalogued and studied. The firing rates of the neurons ranged from 0.16 to 32 spikes/s; the mean was 8.9 spikes/s, the standard deviation 7.0 spikes/s. Bursts of spikes were assigned a quantitative measure, termed Poisson surprise (S), defined as the negative logarithm of their probability in a random (Poisson) spike train. Only bursts having S greater than 10, corresponding to an occurrence rate of about 0.01 bursts/1,000 spikes in a random spike train, were considered to be of interest. Bursts having S greater than 10 occurred at a rate of about 5-15 bursts/1,000 spikes, or about 1-5 bursts/min. The rate slightly increased with spike rate; averaging about 2 bursts/min for neurons having 3 spikes/s and about 4.5 bursts/min for neurons having 30 spikes/s. About 21% of the recorded units emitted significantly fewer bursts than the rest (below 1 burst/1,000 spikes). The percentage of these neurons was independent of spike rate. The spike rate during bursts was found to be about 3-6 times the average spike rate; about the same for longer as for shorter bursts. Bursts typically contained 10-50 spikes and lasted 0.5-2.0 s. When the number of spikes in the successively emitted bursts was listed, it was found that in some neurons these numbers were not distributed at random but were clustered around one or more preferred values. In this sense, bursts occasionally "recurred" a few times in a few minutes. The finding suggests that neurons are highly reliable. When bursts of two or more simultaneously recorded neurons were compared, the bursts often appeared to be temporally close, especially between pairs of neurons recorded by the same electrode; but bursts seldom started and ended simultaneously on two channels. Recurring bursts emitted by one neuron were occasionally accompanied by time-locked recurring bursts by other neurons.

Automatic speech recognition with neural spike trains

2005 ◽  
Author(s):  
Marcus Holmberg ◽  
David Gelbart ◽  
Ulrich Ramacher ◽  
Werner Hemmert
Keyword(s):  
Speech Recognition ◽  
Automatic Speech Recognition ◽  
Spike Trains ◽  
Neural Spike ◽  
Neural Spike Trains
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