Shot noise, weak convergence and diffusion approximations

Tamborrino, Massimiliano; Lánský, Petr

doi:10.1016/j.physd.2021.132845

Cited by 7 publications

(2 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, note that our approach is distinct from those adopted in recent computational and theoretical works [94][95][96][97] as our focus is on the derivation of exact formulas with explicit dependence on inputs numbers, sizes and correlations. Importantly, the moment expressions obtained in the diffusion and effective-timeconstant approximations can be recovered within our framework by making the two independent assumptions that (i) synaptic weights are small, i.e., w e,1 , w i, 1 1 and that (ii) input synchrony can be neglected , i.e.…”

Section: B Moment Analysismentioning

confidence: 99%

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

Becker

Priebe

et al. 2023

Preprint

View full text Add to dashboard Cite

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects post-spiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime only yields realistic subthreshold variability (voltage variance ≅ 4-9mV2) when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

show abstract

Section: B Moment Analysismentioning

confidence: 99%

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

Becker

Priebe

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…An Ornstein-Uhlenbeck (ou) process is a classical linear autoregressive model [13]. For the simplest 1D case it has a stationary probability density function (pdf), an autocorrelation function (acf) which decays exponentially, and its statistical moments are known explicitly [11]. Owing to their convenience, ou processes have been widely used in scientific and engineering applications, including but not limited to insurance [6], environmental engineering [14], and flood analysis [10].…”

Section: Introductionmentioning

confidence: 99%

Fitting a superposition of Ornstein–Uhlenbeck process to time series of discharge in a perennial river environment

Yoshioka

2022

ANZIAMJ

View full text Add to dashboard Cite

Classical Ornstein–Uhlenbeck (ou) processes are Lévy-driven linear stochastic models with exponentially decaying autocorrelation functions which do not always fit more slowly decaying real time series data. A superposition of ou processes (known as a supou process) is proposed to overcome this issue for application to river discharge time series data. The discharge data has a sub-exponential autocorrelation function and this is captured by the supou process based on the mean reversion speed generated by a Gamma distribution. All the parameters of the supou process are identified by matching the autocorrelation and the first to fourth statistical moments of the discharge data. The empirical and modelled histograms of the discharge data are comparable with each other. References O. E. Barndorff-Nielsen. Superposition of Ornstein–Uhlenbeck type processes. Theory Prob. Appl. 45.2 (2001), pp. 175–194. doi: 10.1137/S0040585X97978166 O. E. Barndorff-Nielsen, F. E. Benth, and A. E. D. Veraart. Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes. Bernoulli 19.3 (2013), pp. 803–845. doi: 10.3150/12-BEJ476 O. E. Barndorff-Nielsen and N. N. Leonenko. Burgers’ turbulence problem with linear or quadratic external potential. J. Appl. Prob. 42.2 (2001), pp. 550–565. url: http://www.jstor.org/stable/30040809 J. Beran, Y. Feng, S. Ghosh, and R. Kulik. Long-Memory Processes. Springer-Verlag, Berlin, Heidelberg, 2016. doi: 10.1007/978-3-642-35512-7 F. Fuchs and R. Stelzer. Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model. ESAIM: Prob. Stat. 17 (2013), pp. 455–471. doi: 10.1051/ps/2011158 Y. Kabanov and S. Pergamenshchikov. Ruin probabilities for a Lévy-driven generalised Ornstein–Uhlenbeck process. Fin. Stoch. 24.1 (2020), pp. 39–69. doi: 10.1007/s00780-019-00413-3 R. Kawai and H. Masuda. On simulation of tempered stable random variates. J. Comput. Appl. Math. 235.8 (2011), pp. 2873–2887. doi: 10.1016/j.cam.2010.12.014 S. Pelacani and F. G. Schmitt. Scaling properties of the turbidity and streamflow time series at two different locations of an intra-Apennine stream: Case study. J. Hydro. 603.B (2021), p. 126943. doi: 10.1016/j.jhydrol.2021.126943 R. Stelzer, T. Tosstorff, and M. Wittlinger. Moment based estimation of supOU processes and a related stochastic volatility model. Stat. Risk Model. 32.1 (2015), pp. 1–24. doi: 10.1515/strm-2012-1152 S. Suweis, E. Bertuzzo, G. Botter, A. Porporato, I. Rodriguez-Iturbe, and A. Rinaldo. Impact of stochastic fluctuations in storage-discharge relations on streamflow distributions. Water Resource. Res. 46.3 (2010), W03517. doi: 10.1029/2009WR008038 M. Tamborrino and P. Lansky. Shot noise, weak convergence and diffusion approximations. Physica D: Nonlinear Phenomena 418 (2021), p. 132845. doi: 10.1016/j.physd.2021.132845 E. Taufer and N. Leonenko. Simulation of Lévy-driven Ornstein–Uhlenbeck processes with given marginal distribution. In: Comput. Stat. Data Anal. 53.6 (2009), pp. 2427–2437. doi: 10.1016/j.csda.2008.02.026 C. Van Den Broeck. On the relation between white shot noise, Gaussian white noise, and the dichotomic Markov process. J. Stat. Phys. 31 (1983), pp. 467–483. doi: 10.1007/BF01019494 H. Yoshioka and Y. Yoshioka. Designing cost-efficient inspection schemes for stochastic streamflow environment using an effective Hamiltonian approach. Opt. Eng. (2021), pp. 1–33. doi: 10.1007/s11081-021-09655-7

show abstract

Signal-to-noise ratio gain of an adaptive neuron model with Gamma renewal synaptic input

Kang,

Fu,

Chen

2022

Acta Mech. Sin.

View full text Add to dashboard Cite

Shot noise, weak convergence and diffusion approximations

Cited by 7 publications

References 39 publications

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

Fitting a superposition of Ornstein–Uhlenbeck process to time series of discharge in a perennial river environment

Signal-to-noise ratio gain of an adaptive neuron model with Gamma renewal synaptic input

Contact Info

Product

Resources

About