Spike output jitter, mean firing time and coefficient of variation

Feng, Jianfeng; Brown, David W.

doi:10.1088/0305-4470/31/4/013

Cited by 29 publications

(19 citation statements)

References 28 publications

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“…Based upon further extensive numerical simulations on more realistic neuronal models, they then argued that this property of neurones provides one of the biophysical substrates necessary for exploiting the detailed timing information inherent in spike trains [2,9,10].…”

Section: Introductionmentioning

confidence: 99%

Impact of temporal variation and the balance between excitation and inhibition on the output of the perfect integrate-and-fire model

Feng

Brown

1998

Biological Cybernetics

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Abstract. We consider how the output of the perfect integrate-and-®re (I&F) model of a single neuron is aected by the properties of the input, ®rst of all by the distribution of aerent excitatory and inhibitory postsynaptic potential (EPSP, IPSP) inter-arrival times, discriminating particularly between short-and longtailed forms, and by the degree of balance between excitation and inhibition (as measured by the ratio, r, between the numbers of inhibitory and excitatory inputs). We ®nd that the coecient of variation (CV; standard deviation divided by mean) of eerent interspike interval (ISI) is an increasing function of the length of the tail of the distribution of EPSP inter-arrival times and the ratio r. There is a range of values of r in which the CV of output ISIs is between 0.5 and 1. Too tight a balance between EPSPs and IPSPs will cause the model to produce a CV outside the interval considered to correspond to the physiological range. Going to the extreme, an exact balance between EPSPs and IPSPs as considered in [24] ensures a long-tailed ISI output distribution for which the moments such as mean and variance cannot be de®ned. In this case it is meaningless to consider quantities like output jitter, CV, etc. of the eerent ISIs. The longer the tail of the input inter-arrival time distribution, the less is the requirement for balance between EPSPs and IPSPs in order to evoke output spike trains with a CV between 0.5 and 1. For a given short-tailed input distribution, the range of values of r in which the CV of eerent ISIs is between 0.5 and 1 is almost completely inside the range in which output jitter (standard deviation of eerent ISI) is greater than input jitter. Only when the CV is smaller than 0.5 or the input distribution is a long-tailed one is output less than input jitter [21]. The I&F model tends to enlarge low input jitter and reduce high input jitter. We also provide a novel theoretical framework, based upon extreme value theory in statistics, for estimating output jitter, CV and mean ®ring time. IntroductionThe integrate and ®re (I&F) model is a rudimentary model that underpins the idea of a neuron being a device which accumulates inputs until it reaches a threshold, whereupon it ®res. The model has recently been examined by several authors [1,24,25,28]. Softky and Koch [25] compared the behaviour of the model with data obtained in the visual cortex of the monkey, via theoretical calculations and numerical simulations. They found, with exclusively excitatory postsynaptic potential (EPSP) inputs, that the output of the I&F model is very regular, with the coecient of variation (CV) of the inter-spike interval (ISI, the standard deviation or so-called output jitter divided by the mean) converging to zero at a rate 1ax th p , as x th becomes large, where x th is the number of EPSPs needed to trigger a spike. Therefore, they concluded that the model cannot account for the phenomena observed in neurones in the visual cortex with a CV between 0X5 and 1X Their results cast doubt on the rate coding assu...

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Section: Introductionmentioning

confidence: 99%

Impact of temporal variation and the balance between excitation and inhibition on the output of the perfect integrate-and-fire model

Feng

Brown

1998

Biological Cybernetics

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“…It has been claimed that-at realistic levels of random synaptic input-such neurons effectively integrate a large number of random inputs to produce an output which itself is of low variability [2,6,7] as measured by the coefficient of variation of the interspike interval [CV(ISI)]. However, other studies have shown the IF neuron to be capable of nearPoisson firing at realistic levels of excitatory input over a significant range of r, the ratio of the number of inhibitory to excitatory inputs [8][9][10]. For convenience, we here use the term "near-Poisson firing" as a shorthand for the occurrence of firing patterns with 0.5 , CV͑ISI͒ , 1.…”

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“…Comparison with integrate-and-fire model: The detailed properties of IF neurons in response to stochastic synaptic input have been described by the present authors elsewhere [8][9][10]22,23]. Mean ISI takes a very wide range of values as r is varied: from 6-15 ms when r 0.1, depending on the value of N E , to 1 s when 0.7 , r , 0.9 for N E taking values between 40 and 100 (Fig.…”

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Variability of Firing of Hodgkin-Huxley and FitzHugh-Nagumo Neurons with Stochastic Synaptic Input

1999

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“…In the past few years, we have seen a large body of literature devoted to studying single neuron models with stochastic inputs (see for example Brown et al, 1999;Destexhe and Pare, 1999;Feng, 1997;Feng and Brown, 1998a;Harris and Wolpert, 1998;Konig et al, 1996;Mainen and Sejnowski, 1995;Softky and Koch, 1993;Newsome, 1994, 1998;Salinas and Sejnowski, 2000;Stevens and Zador, 1998), aiming to gain further insights into the coding problem. One popular assumption when studying neurons with stochastic inputs is that they receive synaptically correlated inputs, in contrast to conventional independent inputs (Tuckwell, 1988).…”

Section: Introductionmentioning

confidence: 99%

Effects of correlated and synchronized stochastic inputs to leaky integrator neuronal model

Feng

2003

Journal of Theoretical Biology

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We present an analysis of neuronal model behaviour with correlated synaptic inputs including the cases that correlated inputs are equivalent to exactly synchronized inputs and correlated inputs are not equivalent to exactly synchronized inputs.For the former case, * it is found that the fully (synaptically) correlated inputs assumption (see Section 1 for definition), which is used in most, if not all, theoretical and experimental work in the past few years, results in a waste of resources and might be an unrealistic assumption; * with an exactly balanced excitatory and inhibitory, and synaptically correlated input, the integrate-and-fire model simply behaves as a synchrony detector in certain parameter regions; * the well-known diffusion model, upon which most theoretical work is based, fails to approximate the model with synaptically correlated Poisson inputs. A novel way to approximate synaptically correlated Poisson inputs is then presented; * an optimization principle on neuronal models with partially (synaptically) correlated inputs is proposed, which enables us to predict microscopic structures in neuronal systems.For the latter case, * with tightly synchronized inputs (see Section 1 for definition), the model behaviour depends on its integration time of input signals and could exhibit bursting discharge. * for loosely synchronized inputs, we found that correlated inputs are equivalent to the post-spike voltage reset mechanism proposed in the literature.

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Spike output jitter, mean firing time and coefficient of variation

Cited by 29 publications

References 28 publications

Impact of temporal variation and the balance between excitation and inhibition on the output of the perfect integrate-and-fire model

Impact of temporal variation and the balance between excitation and inhibition on the output of the perfect integrate-and-fire model

Variability of Firing of Hodgkin-Huxley and FitzHugh-Nagumo Neurons with Stochastic Synaptic Input

Effects of correlated and synchronized stochastic inputs to leaky integrator neuronal model

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