However, the stochastic nature of neuronal activity leads to severe biases in the estimation of these oscillations in single unit spike trains .

Different biological and experimental factors cause the spike train to differentially reflect its underlying oscillatory rate function.

estimationWe introduce a novel objective measure, the "modulation index", which overcomes these biases, and enables reliable detection of oscillations from spike trains and a direct estima-tion of the oscillation magnitude.

In this manuscript, we expose major biases and distortions which arise from the quantification of neuronal spike train oscillations.

detectionNext, following a formulation of the distortions, we introduce a novel objective measure, the "modulation index", which overcomes these biases, and enables a reliable de-tection of oscillations from spike trains and a direct estimation of the oscillation magnitude.

Analysis of the power spectrum is a common method for identifying enhanced (or reduced) oscillations in neuronal data, and is widely used on a variety of brain signals spanning multiple orders of magnitude, such as electroencephalograms (EEG), local field potentials (LFP), multiunit activity (MUA), single unit spike trains and cellular membrane potentials [5—8].

The time of occurrence of action potentials emitted by a single neuron; i.e., single unit spike trains , are a major source of neurophysiological data stemming from both intracellular and extracellular recordings.

These neuronal spike trains may be viewed as a stochastic point process where a discrete event represents each action potential [9].

To separately control the correlations within and between the pre-synaptic pools of the striatal neurons, we extended the multiple-interaction process (MIP) model of correlated ensemble of Poisson type spike trains [12, 23].

The MIP model generates correlations by copying spikes from a spike train (the mother spike train) with a fixed probability (the copy probability, which determined the resulting correlation) to the individual spike trains .

By making many convergent connections using the ‘lossy synapse’ we can mimic the random copying of spikes from the mother spike train to the children process.

The spike trains in each pre-synaptic pool are themselves correlated With a correlation coefficient W. For such pooled random variables, Bedenbaugh and Gerstein [22] derived the following relationship: where p12 is the correlation coefficient between the two pools of the pre-synaptic neurons, 11 is the size of each pre-synaptic pool.

Intuitively we can understand this relationship between B and W in the following way: Imagine two pools of identical spike trains, but with individual spikes trains uncorrelated to each other (i.e.

In this case, the average correlations between the two pools will be small because each spike train has only copy in the other pool, while being uncorrelated with all others.

The empirical Bernoulli information is strictly greater than the estimated single-spike (or “Poisson”) information for a binary spike train that is not all zeros or ones, since To > 0 and these spike absences are neglected by the single-spike information measure.

Quantifying MID information loss for binary spike trains .

Thus, for example, if 20% of the bins in a binary spike train contain a spike, the standard MID estimator will necessarily neglect at least 10% of the total mutual information.

However, real spike trains may eXhibit more or less variability than a Poisson process [fl].

Despite the diversity and variability of input spike trains , neurons can learn and represent specific information during developmental processes and according to specific task requirements.

In reality, however, there would be crosstalk noise among input spike trains caused by the interference of external sources.

In the model used by those authors, the synaptic weight matrix is treated as a hyper parameter and estimated by considering the maximum likelihood estimation of input spike trains .