Discussion | Furthermore, we presented adaptations to the modulation index to account for deviations from the Poisson process assumptions. |
Discussion | Explicitly, we show its usage in an inhomogeneous Poisson process with an absolute refractory period, which dramatically alters the spectrum of real neurons. |
Discussion | The correction procedure is based on information extracted from the given spike train, and on the underlying rate function, including the deviation from the Poisson process . |
Introduction | This model is termed the inhomogeneous Poisson process when the instantaneous firing rate changes over time. |
Power spectrum of a finite inhomogeneous Poisson process | Power spectrum of a finite inhomogeneous Poisson process |
Power spectrum of a finite inhomogeneous Poisson process | The following is based on the general formulation by Pinhasi and Lurie [28]: Let's consider a Poisson process of occurring delta functions, With a non-constant and time dependent rate )L (t). |
Results | The spiking activity of oscillatory neurons can be modeled as an inhomogeneous Poisson process Whose rate Mt) is modulated by a cosine function (Fig 1A): |
Results | The power spectrum of an inhomogeneous spike train over a period (T) is (see methods: power spectrum of a finite inhomogeneous Poisson process ): |
Results | In the specific case of cosine rate modulation over a base frequency (fo) (Eq 1) the power spectrum is: (see methods: power spectrum of an inhomogeneous Poisson process with an oscillatory rate function) |
Spike train simulations | The spike trains were modeled as an inhomogeneous Poisson process , Whose rate is modulated by a 12 Hz cosine function. |
Analytical consideration of synaptic weight dynamics | The synaptic weight dynamics defined above can be rewritten as ij 7 7 of time and also using a stochastic Poisson process , synaptic weight change follows aptic weight dynamics can be analytically estimated. |
Model | For simplicity, we approximated the actiVity of external sources using a Poisson process with the constant rate 1180. |
Model | If we define the Poisson process with rate r as 6(1’), the actiVity of the external source [,4 at time tis written as sfl(t) = 6 (see Table 1 for the list of variables). |
Model | Poisson process , the spiking activity of the input neuron 1' follows p where no is the instantaneous firing rate defined with rf = vff — E qmvj, q,” is the response [421 probability for the hidden external source {4, and qb(t) = t2e‘t/9t /20t3 is the response kernel for each external event. |
Detection of artificial EPSCs immersed in fluctuating noise | We assume that postsynaptic spiking is generated by a Poisson process with a rate determined by a baseline firing rate, the recent history of the neuron’s firing, as well as input produced by presynaptic spikes (see Methods for details). |
Discussion | While these models can describe the auto and cross-correlations present in the data, neurons often have more complex nonlinear behavior [56,57] and generate spikes much more reliably than Poisson processes [58]. |
Experiment 1. Partially-defined input: Artificial EPSCs immersed in fluctuating noise | This corresponds to a neuron firing at a rate of 5Hz with more regularity (CV % 0.7) than a Poisson process . |
U | F) Dependence of the log likelihood ratios of models M1 and M2 relative to a homogeneous Poisson process on the length of data used for analysis. |
Background | The defining feature of a Poisson process is that responses in non-overlapping time bins are conditionally independent given the spike rate. |
Models with Bernoulli spiking | However, real spike trains may eXhibit more or less variability than a Poisson process [fl]. |
Models with Bernoulli spiking | The Bernoulli and discrete-time Poisson models approach the same limiting Poisson process as the bin size (and single-bin spike probability) approaches zero while the average spike rate remains constant. |