Index of papers in April 2015 that mention
  • Poisson process
Ayala Matzner, Izhar Bar-Gad
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.
Poisson process is mentioned in 14 sentences in this paper.
Topics mentioned in this paper:
Naoki Hiratani, Tomoki Fukai
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(1ā€™), 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 ā€” E qmvj, q,ā€ is the response [421 probability for the hidden external source {4, and qb(t) = t2eā€˜t/9t /20t3 is the response kernel for each external event.
Poisson process is mentioned in 4 sentences in this paper.
Topics mentioned in this paper:
Ross S. Williamson, Maneesh Sahani, Jonathan W. Pillow
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.
Poisson process is mentioned in 3 sentences in this paper.
Topics mentioned in this paper: