Journal articles: 'Model "integrate-and-fire"'

1

Ashida, Go, and Waldo Nogueira. "Spike-Conducting Integrate-and-Fire Model." eneuro 5, no. 4 (July 2018): ENEURO.0112–18.2018. http://dx.doi.org/10.1523/eneuro.0112-18.2018.

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Gerstner, Wulfram, and Romain Brette. "Adaptive exponential integrate-and-fire model." Scholarpedia 4, no. 6 (2009): 8427. http://dx.doi.org/10.4249/scholarpedia.8427.

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Destexhe, Alain. "Conductance-Based Integrate-and-Fire Models." Neural Computation 9, no. 3 (March 1, 1997): 503–14. http://dx.doi.org/10.1162/neco.1997.9.3.503.

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A conductance-based model of Na+ and K+ currents underlying action potential generation is introduced by simplifying the quantitative model of Hodgkin and Huxley (HH). If the time course of rate constants can be approximated by a pulse, HH equations can be solved analytically. Pulse-based (PB) models generate action potentials very similar to the HH model but are computationally faster. Unlike the classical integrate-and fire (IAF) approach, they take into account the changes of conductances during and after the spike, which have a determinant influence in shaping neuronal responses. Similarities and differences among PB, IAF, and HH models are illustrated for three cases: high-frequency repetitive firing, spike timing following random synaptic inputs, and network behavior in the presence of intrinsic currents.

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Górski, Tomasz, Damien Depannemaecker, and Alain Destexhe. "Conductance-Based Adaptive Exponential Integrate-and-Fire Model." Neural Computation 33, no. 1 (January 2021): 41–66. http://dx.doi.org/10.1162/neco_a_01342.

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The intrinsic electrophysiological properties of single neurons can be described by a broad spectrum of models, from realistic Hodgkin-Huxley-type models with numerous detailed mechanisms to the phenomenological models. The adaptive exponential integrate-and-fire (AdEx) model has emerged as a convenient middle-ground model. With a low computational cost but keeping biophysical interpretation of the parameters, it has been extensively used for simulations of large neural networks. However, because of its current-based adaptation, it can generate unrealistic behaviors. We show the limitations of the AdEx model, and to avoid them, we introduce the conductance-based adaptive exponential integrate-and-fire model (CAdEx). We give an analysis of the dynamics of the CAdEx model and show the variety of firing patterns it can produce. We propose the CAdEx model as a richer alternative to perform network simulations with simplified models reproducing neuronal intrinsic properties.

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Van Pottelbergh, Tomas, Guillaume Drion, and Rodolphe Sepulchre. "Robust Modulation of Integrate-and-Fire Models." Neural Computation 30, no. 4 (April 2018): 987–1011. http://dx.doi.org/10.1162/neco_a_01065.

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By controlling the state of neuronal populations, neuromodulators ultimately affect behavior. A key neuromodulation mechanism is the alteration of neuronal excitability via the modulation of ion channel expression. This type of neuromodulation is normally studied with conductance-based models, but those models are computationally challenging for large-scale network simulations needed in population studies. This article studies the modulation properties of the multiquadratic integrate-and-fire model, a generalization of the classical quadratic integrate-and-fire model. The model is shown to combine the computational economy of integrate-and-fire modeling and the physiological interpretability of conductance-based modeling. It is therefore a good candidate for affordable computational studies of neuromodulation in large networks.

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Ascione, Giacomo, and Bruno Toaldo. "A Semi-Markov Leaky Integrate-and-Fire Model." Mathematics 7, no. 11 (October 29, 2019): 1022. http://dx.doi.org/10.3390/math7111022.

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In this paper, a Leaky Integrate-and-Fire (LIF) model for the membrane potential of a neuron is considered, in case the potential process is a semi-Markov process. Semi-Markov property is obtained here by means of the time-change of a Gauss-Markov process. This model has some merits, including heavy-tailed distribution of the waiting times between spikes. This and other properties of the process, such as the mean, variance and autocovariance, are discussed.

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Tonnelier, Arnaud, Hana Belmabrouk, and Dominique Martinez. "Event-Driven Simulations of Nonlinear Integrate-and-Fire Neurons." Neural Computation 19, no. 12 (December 2007): 3226–38. http://dx.doi.org/10.1162/neco.2007.19.12.3226.

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Event-driven strategies have been used to simulate spiking neural networks exactly. Previous work is limited to linear integrate-and-fire neurons. In this note, we extend event-driven schemes to a class of nonlinear integrate-and-fire models. Results are presented for the quadratic integrate-and-fire model with instantaneous or exponential synaptic currents. Extensions to conductance-based currents and exponential integrate-and-fire neurons are discussed.

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Zador, Anthony M., and Barak A. Pearlmutter. "VC Dimension of an Integrate-and-Fire Neuron Model." Neural Computation 8, no. 3 (April 1996): 611–24. http://dx.doi.org/10.1162/neco.1996.8.3.611.

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We compute the VC dimension of a leaky integrate-and-fire neuron model. The VC dimension quantifies the ability of a function class to partition an input pattern space, and can be considered a measure of computational capacity. In this case, the function class is the class of integrate-and-fire models generated by varying the integration time constant T and the threshold θ, the input space they partition is the space of continuous-time signals, and the binary partition is specified by whether or not the model reaches threshold at some specified time. We show that the VC dimension diverges only logarithmically with the input signal bandwidth N. We also extend this approach to arbitrary passive dendritic trees. The main contributions of this work are (1) it offers a novel treatment of computational capacity of this class of dynamic system; and (2) it provides a framework for analyzing the computational capabilities of the dynamic systems defined by networks of spiking neurons.

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Breen, Barbara J., William C. Gerken, and Robert J. Butera. "Hybrid Integrate-and-Fire Model of a Bursting Neuron." Neural Computation 15, no. 12 (December 1, 2003): 2843–62. http://dx.doi.org/10.1162/089976603322518768.

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We present a reduction of a Hodgkin-Huxley (HH)—style bursting model to a hybridized integrate-and-fire (IF) formalism based on a thorough bifurcation analysis of the neuron's dynamics. The model incorporates HH-style equations to evolve the subthreshold currents and includes IF mechanisms to characterize spike events and mediate interactions between the subthreshold and spiking currents. The hybrid IF model successfully reproduces the dynamic behavior and temporal characteristics of the full model over a wide range of activity, including bursting and tonic firing. Comparisons of timed computer simulations of the reduced model and the original model for both single neurons and moderate lysized networks (n ≤ 500) show that this model offers improvement in computational speed over the HH-style bursting model.

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10

Robert, M. E. "Integrate-and-Fire Model for Electrically Stimulated Nerve Cell." IEEE Transactions on Biomedical Engineering 53, no. 4 (April 2006): 756–58. http://dx.doi.org/10.1109/tbme.2006.870209.

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Buonocore, A., L. Caputo, E. Pirozzi, and L. M. Ricciardi. "On a Stochastic Leaky Integrate-and-Fire Neuronal Model." Neural Computation 22, no. 10 (October 2010): 2558–85. http://dx.doi.org/10.1162/neco_a_00023.

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The leaky integrate-and-fire neuronal model proposed in Stevens and Zador ( 1998 ), in which time constant and resting potential are postulated to be time dependent, is revisited within a stochastic framework in which the membrane potential is mathematically described as a gauss-diffusion process. The first-passage-time probability density, miming in such a context the firing probability density, is evaluated by either the Volterra integral equation of Buonocore, Nobile, and Ricciardi ( 1987 ) or, when possible, by the asymptotics of Giorno, Nobile, and Ricciardi ( 1990 ). The model examined here represents an extension of the classic leaky integrate-and-fire one based on the Ornstein-Uhlenbeck process in that it is in principle compatible with the inclusion of some other physiological characteristics such as relative refractoriness. It also allows finer tuning possibilities in view of its accounting for certain qualitative as well as quantitative features, such as the behavior of the time course of the membrane potential prior to firings and the computation of experimentally measurable statistical descriptors of the firing time: mean, median, coefficient of variation, and skewness. Finally, implementations of this model are provided in connection with certain experimental evidence discussed in the literature.

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Jolivet, Renaud, Timothy J. Lewis, and Wulfram Gerstner. "Generalized Integrate-and-Fire Models of Neuronal Activity Approximate Spike Trains of a Detailed Model to a High Degree of Accuracy." Journal of Neurophysiology 92, no. 2 (August 2004): 959–76. http://dx.doi.org/10.1152/jn.00190.2004.

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We demonstrate that single-variable integrate-and-fire models can quantitatively capture the dynamics of a physiologically detailed model for fast-spiking cortical neurons. Through a systematic set of approximations, we reduce the conductance-based model to 2 variants of integrate-and-fire models. In the first variant (nonlinear integrate-and-fire model), parameters depend on the instantaneous membrane potential, whereas in the second variant, they depend on the time elapsed since the last spike [Spike Response Model (SRM)]. The direct reduction links features of the simple models to biophysical features of the full conductance-based model. To quantitatively test the predictive power of the SRM and of the nonlinear integrate-and-fire model, we compare spike trains in the simple models to those in the full conductance-based model when the models are subjected to identical randomly fluctuating input. For random current input, the simple models reproduce 70–80 percent of the spikes in the full model (with temporal precision of ±2 ms) over a wide range of firing frequencies. For random conductance injection, up to 73 percent of spikes are coincident. We also present a technique for numerically optimizing parameters in the SRM and the nonlinear integrate-and-fire model based on spike trains in the full conductance-based model. This technique can be used to tune simple models to reproduce spike trains of real neurons.

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Feng, Jianfeng, and David Brown. "Impact of Correlated Inputs on the Output of the Integrate-and-Fire Model." Neural Computation 12, no. 3 (March 1, 2000): 671–92. http://dx.doi.org/10.1162/089976600300015745.

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For the integrate-and-fire model with or without reversal potentials, we consider how correlated inputs affect the variability of cellular output. For both models, the variability of efferent spike trains measured by coefficient of variation (CV) of the interspike interval is a nondecreasing function of input correlation. When the correlation coefficient is greater than 0.09, the CV of the integrate-and-fire model without reversal potentials is always above 0.5, no matter how strong the inhibitory inputs. When the correlation coefficient is greater than 0.05, CV for the integrate- and-fire model with reversal potentials is always above 0.5, independent of the strength of the inhibitory inputs. Under a given condition on correlation coefficients, we find that correlated Poisson processes can be decomposed into independent Poisson processes. We also develop a novel method to estimate the distribution density of the first passage time of the integrate-and-fire model.

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PRIGNANO, LUCE, OLEGUER SAGARRA, PABLO M. GLEISER, and ALBERT DIAZ-GUILERA. "SYNCHRONIZATION OF MOVING INTEGRATE AND FIRE OSCILLATORS." International Journal of Bifurcation and Chaos 22, no. 07 (July 2012): 1250179. http://dx.doi.org/10.1142/s0218127412501799.

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We present a model of integrate and fire oscillators that move on a plane. The phase of the oscillators evolves linearly in time and when it reaches a threshold value they fire choosing their neighbors according to a certain interaction range. Depending on the velocity of the ballistic motion and the average number of neighbors each oscillator fires to, we identify different regimes shown in a phase diagram. We characterize these regimes by means of novel parameters as the accumulated number of contacted neighbors.

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Plesser, Hans E., and Markus Diesmann. "Simplicity and Efficiency of Integrate-and-Fire Neuron Models." Neural Computation 21, no. 2 (February 2009): 353–59. http://dx.doi.org/10.1162/neco.2008.03-08-731.

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Lovelace and Cios ( 2008 ) recently proposed a very simple spiking neuron (VSSN) model for simulations of large neuronal networks as an efficient replacement for the integrate-and-fire neuron model. We argue that the VSSN model falls behind key advances in neuronal network modeling over the past 20 years, in particular, techniques that permit simulators to compute the state of the neuron without repeated summation over the history of input spikes and to integrate the subthreshold dynamics exactly. State-of-the-art solvers for networks of integrate-and-fire model neurons are substantially more efficient than the VSSN simulator and allow routine simulations of networks of some 105 neurons and 109 connections on moderate computer clusters.

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16

Brette, Romain. "Exact Simulation of Integrate-and-Fire Models with Synaptic Conductances." Neural Computation 18, no. 8 (August 2006): 2004–27. http://dx.doi.org/10.1162/neco.2006.18.8.2004.

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Computational neuroscience relies heavily on the simulation of large networks of neuron models. There are essentially two simulation strategies: (1) using an approximation method (e.g., Runge-Kutta) with spike times binned to the time step and (2) calculating spike times exactly in an event-driven fashion. In large networks, the computation time of the best algorithm for either strategy scales linearly with the number of synapses, but each strategy has its own assets and constraints: approximation methods can be applied to any model but are inexact; exact simulation avoids numerical artifacts but is limited to simple models. Previous work has focused on improving the accuracy of approximation methods. In this article, we extend the range of models that can be simulated exactly to a more realistic model: an integrate-and-fire model with exponential synaptic conductances.

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Merzon, Liya, Tatiana Malevich, Georgiy Zhulikov, Sofia Krasovskaya, and W. Joseph MacInnes. "Temporal Limitations of the Standard Leaky Integrate and Fire Model." Brain Sciences 10, no. 1 (December 27, 2019): 16. http://dx.doi.org/10.3390/brainsci10010016.

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Itti and Koch’s Saliency Model has been used extensively to simulate fixation selection in a variety of tasks from visual search to simple reaction times. Although the Saliency Model has been tested for its spatial prediction of fixations in visual salience, it has not been well tested for their temporal accuracy. Visual tasks, like search, invariably result in a positively skewed distribution of saccadic reaction times over large numbers of samples, yet we show that the leaky integrate and fire (LIF) neuronal model included in the classic implementation of the model tends to produce a distribution shifted to shorter fixations (in comparison with human data). Further, while parameter optimization using a genetic algorithm and Nelder–Mead method does improve the fit of the resulting distribution, it is still unable to match temporal distributions of human responses in a visual task. Analysis of times for individual images reveal that the LIF algorithm produces initial fixation durations that are fixed instead of a sample from a distribution (as in the human case). Only by aggregating responses over many input images do they result in a distribution, although the form of this distribution still depends on the input images used to create it and not on internal model variability.

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18

Feng, Jianfeng. "Origin of firing varibility of the integrate-and-fire model." Neurocomputing 26-27 (June 1999): 117–22. http://dx.doi.org/10.1016/s0925-2312(99)00006-5.

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Tsigkri-DeSmedt, N. D., J. Hizanidis, P. Hövel, and A. Provata. "Multi-chimera States in the Leaky Integrate-and-Fire Model." Procedia Computer Science 66 (2015): 13–22. http://dx.doi.org/10.1016/j.procs.2015.11.004.

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Abbott, L. F. "Lapicque’s introduction of the integrate-and-fire model neuron (1907)." Brain Research Bulletin 50, no. 5-6 (November 1999): 303–4. http://dx.doi.org/10.1016/s0361-9230(99)00161-6.

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21

Bezzi, Michele, Thierry Nieus, Olivier J.-M. Coenen, and Egidio D'Angelo. "An integrate-and-fire model of a cerebellar granule cell." Neurocomputing 58-60 (June 2004): 593–98. http://dx.doi.org/10.1016/j.neucom.2004.01.100.

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22

Feng, Jianfeng. "Is the integrate-and-fire model good enough?—a review." Neural Networks 14, no. 6-7 (July 2001): 955–75. http://dx.doi.org/10.1016/s0893-6080(01)00074-0.

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23

Naud, Richard, Nicolas Marcille, Claudia Clopath, and Wulfram Gerstner. "Firing patterns in the adaptive exponential integrate-and-fire model." Biological Cybernetics 99, no. 4-5 (November 2008): 335–47. http://dx.doi.org/10.1007/s00422-008-0264-7.

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Ditlevsen, Susanne, and Priscilla Greenwood. "The Morris–Lecar neuron model embeds a leaky integrate-and-fire model." Journal of Mathematical Biology 67, no. 2 (May 24, 2012): 239–59. http://dx.doi.org/10.1007/s00285-012-0552-7.

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Kandpal, Pankaj Kumar, and Ashish Mehta. "Critical Analysis of Two Dimensional and Four-Dimensional Spiking Neuron Models." Journal of Computational and Theoretical Nanoscience 16, no. 9 (September 1, 2019): 3897–905. http://dx.doi.org/10.1166/jctn.2019.8268.

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In the present article, two-dimensional “Spiking Neuron Model” is being compared with the fourdimensional “Integrate-and-fire Neuron Model” (IFN) using error correction back propagation learning algorithm (error correction learning). A comparative study has been done on the basis of several parameters like iteration, execution time, miss-classification rate, number of iterations etc. The authors choose the five-bit parity problem and Iris classification problem for the present study. Results of simulation express that both the models are capable to perform classification task. But single spiking neuron model having two-dimensional phenomena is less complex than Integrate-fire-neuron, produces better results. On the contrary, the classification performance of single ingrate-and-fire neuron model is not very poor but due to complex four-dimensional architecture, miss-classification rate is higher than single spiking neuron model, it means Integrate-and-fire neuron model is less capable than spiking neuron model to solve classification problems.

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Feng, Jianfeng, David Brown, Gang Wei, and Brunello Tirozzi. "Detectable and undetectable input signals for the integrate-and-fire model." Journal of Physics A: Mathematical and General 34, no. 8 (February 19, 2001): 1637–48. http://dx.doi.org/10.1088/0305-4470/34/8/310.

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Touboul, Jonathan, and Romain Brette. "Dynamics and bifurcations of the adaptive exponential integrate-and-fire model." Biological Cybernetics 99, no. 4-5 (November 2008): 319–34. http://dx.doi.org/10.1007/s00422-008-0267-4.

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Rudd, Michael E., and Lawrence G. Brown. "Noise Adaptation in Integrate-and-Fire Neurons." Neural Computation 9, no. 5 (July 1, 1997): 1047–69. http://dx.doi.org/10.1162/neco.1997.9.5.1047.

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The statistical spiking response of an ensemble of identically prepared stochastic integrate-and-fire neurons to a rectangular input current plus gaussian white noise is analyzed. It is shown that, on average, integrate-and-fire neurons adapt to the root-mean-square noise level of their input. This phenomenon is referred to as noise adaptation. Noise adaptation is characterized by a decrease in the average neural firing rate and an accompanying decrease in the average value of the generator potential, both of which can be attributed to noise-induced resets of the generator potential mediated by the integrate-and-fire mechanism. A quantitative theory of noise adaptation in stochastic integrate-and-fire neurons is developed. It is shown that integrate-and-fire neurons, on average, produce transient spiking activity whenever there is an increase in the level of their input noise. This transient noise response is either reduced or eliminated over time, depending on the parameters of the model neuron. Analytical methods are used to prove that nonleaky integrate-and-fire neurons totally adapt to any constant input noise level, in the sense that their asymptotic spiking rates are independent of the magnitude of their input noise. For leaky integrate-and-fire neurons, the long-run noise adaptation is not total, but the response to noise is partially eliminated. Expressions for the probability density function of the generator potential and the first two moments of the potential distribution are derived for the particular case of a nonleaky neuron driven by gaussian white noise of mean zero and constant variance. The functional significance of noise adaptation for the performance of networks comprising integrate-and-fire neurons is discussed.

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Casti, A. R. R., A. Omurtag, A. Sornborger, E. Kaplan, B. Knight, J. Victor, and L. Sirovich. "A Population Study of Integrate-and-Fire-or-Burst Neurons." Neural Computation 14, no. 5 (May 1, 2002): 957–86. http://dx.doi.org/10.1162/089976602753633349.

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Any realistic model of the neuronal pathway from the retina to the visual cortex (V1) must account for the burstingbehavior of neurons in the lateral geniculate nucleus (LGN). A robust but minimal model, the integrate- and-fire-or-burst (IFB) model, has recently been proposed for individual LGN neurons. Based on this, we derive a dynamic population model and study a population of such LGN cells. This population model, the first simulation of its kind evolving in a two-dimensional phase space, is used to study the behavior of bursting populations in response to diverse stimulus conditions.

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Choi, Hyung Wooc, Seong Eun Maeng, and Jae Woo Lee. "Self-organized criticality of a simple integrate-and-fire neural model." Journal of the Korean Physical Society 60, no. 4 (February 2012): 657–59. http://dx.doi.org/10.3938/jkps.60.657.

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Sharma, Dipty, Paramjeet Singh, Ravi P. Agarwal, and Mehmet Emir Koksal. "Numerical Approximation for Nonlinear Noisy Leaky Integrate-and-Fire Neuronal Model." Mathematics 7, no. 4 (April 21, 2019): 363. http://dx.doi.org/10.3390/math7040363.

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We consider a noisy leaky integrate-and-fire (NLIF) neuron model. The resulting nonlinear time-dependent partial differential equation (PDE) is a Fokker-Planck Equation (FPE) which describes the evolution of the probability density. The finite element method (FEM) has been proposed to solve the governing PDE. In the realistic neural network, the irregular space is always determined. Thus, FEM can be used to tackle those situations whereas other numerical schemes are restricted to the problems with only a finite regular space. The stability of the proposed scheme is also discussed. A comparison with the existing Weighted Essentially Non-Oscillatory (WENO) finite difference approximation is also provided. The numerical results reveal that FEM may be a better scheme for the solution of such types of model problems. The numerical scheme also reduces computational time in comparison with time required by other schemes.

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Lansky, Petr, Laura Sacerdote, and Cristina Zucca. "Optimum signal in a diffusion leaky integrate-and-fire neuronal model." Mathematical Biosciences 207, no. 2 (June 2007): 261–74. http://dx.doi.org/10.1016/j.mbs.2006.08.027.

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Feng, Jianfeng. "Behaviors of Spike Output Jitter in the Integrate-and-Fire Model." Physical Review Letters 79, no. 22 (December 1, 1997): 4505–8. http://dx.doi.org/10.1103/physrevlett.79.4505.

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Pressley, Joanna, and Todd W. Troyer. "Temporal processing in the exponential integrate-and-fire model is nonlinear." Neurocomputing 69, no. 10-12 (June 2006): 1076–80. http://dx.doi.org/10.1016/j.neucom.2005.12.049.

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Marcille, Nicolas, Claudia Clopath, Rajnish Ranjan, Shaul Druckmann, Felix Schuermann, Henry Markram, and Wulfram Gerstner. "Predicting neuronal activity with an adaptive exponential integrate-and-fire model." BMC Neuroscience 8, Suppl 2 (2007): P121. http://dx.doi.org/10.1186/1471-2202-8-s2-p121.

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Churilov, Alexander N., John Milton, and Elvira R. Salakhova. "An integrate-and-fire model for pulsatility in the neuroendocrine system." Chaos: An Interdisciplinary Journal of Nonlinear Science 30, no. 8 (August 2020): 083132. http://dx.doi.org/10.1063/5.0010553.

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Feng, Jianfeng, Hilary Buxton, and Yingchun Deng. "Training the integrate-and-fire model with the informax principle: I." Journal of Physics A: Mathematical and General 35, no. 10 (March 4, 2002): 2379–94. http://dx.doi.org/10.1088/0305-4470/35/10/304.

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Lansky, Petr, Pavel Sanda, and Jufang He. "The parameters of the stochastic leaky integrate-and-fire neuronal model." Journal of Computational Neuroscience 21, no. 2 (July 28, 2006): 211–23. http://dx.doi.org/10.1007/s10827-006-8527-6.

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Jaras, Ismael, Taiki Harada, Marcos E. Orchard, Pedro E. Maldonado, and Rodrigo C. Vergara. "Extending the integrate‐and‐fire model to account for metabolic dependencies." European Journal of Neuroscience 54, no. 4 (July 16, 2021): 5249–60. http://dx.doi.org/10.1111/ejn.15326.

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Brette, Romain. "Exact Simulation of Integrate-and-Fire Models with Exponential Currents." Neural Computation 19, no. 10 (October 2007): 2604–9. http://dx.doi.org/10.1162/neco.2007.19.10.2604.

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Neural networks can be simulated exactly using event-driven strategies, in which the algorithm advances directly from one spike to the next spike. It applies to neuron models for which we have (1) an explicit expression for the evolution of the state variables between spikes and (2) an explicit test on the state variables that predicts whether and when a spike will be emitted. In a previous work, we proposed a method that allows exact simulation of an integrate-and-fire model with exponential conductances, with the constraint of a single synaptic time constant. In this note, we propose a method, based on polynomial root finding, that applies to integrate-and-fire models with exponential currents, with possibly many different synaptic time constants. Models can include biexponential synaptic currents and spike-triggered adaptation currents.

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Salinas, Emilio, and Terrence J. Sejnowski. "Integrate-and-Fire Neurons Driven by Correlated Stochastic Input." Neural Computation 14, no. 9 (September 1, 2002): 2111–55. http://dx.doi.org/10.1162/089976602320264024.

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Neurons are sensitive to correlations among synaptic inputs. However, analytical models that explicitly include correlations are hard to solve analytically, so their influence on a neuron's response has been difficult to ascertain. To gain some intuition on this problem, we studied the firing times of two simple integrate-and-fire model neurons driven by a correlated binary variable that represents the total input current. Analytic expressions were obtained for the average firing rate and coefficient of variation (a measure of spike-train variability) as functions of the mean, variance, and correlation time of the stochastic input. The results of computer simulations were in excellent agreement with these expressions. In these models, an increase in correlation time in general produces an increase in both the average firing rate and the variability of the output spike trains. However, the magnitude of the changes depends differentially on the relative values of the input mean and variance: the increase in firing rate is higher when the variance is large relative to the mean, whereas the increase in variability is higher when the variance is relatively small. In addition, the firing rate always tends to a finite limit value as the correlation time increases toward infinity, whereas the coefficient of variation typically diverges. These results suggest that temporal correlations may play a major role in determining the variability as well as the intensity of neuronal spike trains.

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Paninski, Liam, Jonathan W. Pillow, and Eero P. Simoncelli. "Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Encoding Model." Neural Computation 16, no. 12 (December 1, 2004): 2533–61. http://dx.doi.org/10.1162/0899766042321797.

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We examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy, leaky, integrate-and-fire spike generation mechanism. This model provides a biophysically more realistic alternative to models based on Poisson (memoryless) spike generation, and can effectively reproduce a variety of spiking behaviors seen in vivo. We describe the maximum likelihood estimator for the model parameters, given only extracellular spike train responses (not intracellular voltage data). Specifically, we prove that the log-likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques. We develop an efficient algorithm for computing the maximum likelihood solution, demonstrate the effectiveness of the resulting estimator with numerical simulations, and discuss a method of testing the model's validity using time-rescaling and density evolution techniques.

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Burak, Yoram, Sam Lewallen, and Haim Sompolinsky. "Stimulus-Dependent Correlations in Threshold-Crossing Spiking Neurons." Neural Computation 21, no. 8 (August 2009): 2269–308. http://dx.doi.org/10.1162/neco.2009.07-08-830.

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Abstract:

We consider a threshold-crossing spiking process as a simple model for the activity within a population of neurons. Assuming that these neurons are driven by a common fluctuating input with gaussian statistics, we evaluate the cross-correlation of spike trains in pairs of model neurons with different thresholds. This correlation function tends to be asymmetric in time, indicating a preference for the neuron with the lower threshold to fire before the one with the higher threshold, even if their inputs are identical. The relationship between these results and spike statistics in other models of neural activity is explored. In particular, we compare our model with an integrate-and-fire model in which the membrane voltage resets following each spike. The qualitative properties of spike cross-correlations, emerging from the threshold-crossing model, are similar to those of bursting events in the integrate-and-fire model. This is particularly true for generalized integrate-and-fire models in which spikes tend to occur in bursts, as observed, for example, in retinal ganglion cells driven by a rapidly fluctuating visual stimulus. The threshold-crossing model thus provides a simple, analytically tractable description of event onsets in these neurons.

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Koyama, Shinsuke, and Robert E. Kass. "Spike Train Probability Models for Stimulus-Driven Leaky Integrate-and-Fire Neurons." Neural Computation 20, no. 7 (July 2008): 1776–95. http://dx.doi.org/10.1162/neco.2008.06-07-540.

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Abstract:

Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike train data in important ways, but they are not very easy to apply to the analysis of spike train data. Instead, statistical methods based on point process models of spike trains provide a wide range of data-analytical techniques. Two simplified point process models have been introduced in the literature: the time-rescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (m-IMI) model. In this letter we investigate the extent to which the TRRP and m-IMI models are able to fit spike trains produced by stimulus-driven leaky integrate-and-fire (LIF) neurons. With a constant stimulus, the LIF spike train is a renewal process, and the m-IMI and TRRP models will describe accurately the LIF spike train variability. With a time-varying stimulus, the probability of spiking under all three of these models depends on both the experimental clock time relative to the stimulus and the time since the previous spike, but it does so differently for the LIF, m-IMI, and TRRP models. We assessed the distance between the LIF model and each of the two empirical models in the presence of a time-varying stimulus. We found that while lack of fit of a Poisson model to LIF spike train data can be evident even in small samples, the m-IMI and TRRP models tend to fit well, and much larger samples are required before there is statistical evidence of lack of fit of the m-IMI or TRRP models. We also found that when the mean of the stimulus varies across time, the m-IMI model provides a better fit to the LIF data than the TRRP, and when the variance of the stimulus varies across time, the TRRP provides the better fit.

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Dumont, G., J. Henry, and C. O. Tarniceriu. "Noisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model." Journal of Mathematical Biology 73, no. 6-7 (April 4, 2016): 1413–36. http://dx.doi.org/10.1007/s00285-016-1002-8.

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Hayashi, Tatsuya, Tetsuji Tokihiro, Hiroki Kurihara, Fumimasa Nomura, and Kenji Yasuda. "Integrate and fire model with refractory period for synchronization of two cardiomyocytes." Journal of Theoretical Biology 437 (January 2018): 141–48. http://dx.doi.org/10.1016/j.jtbi.2017.10.008.

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Akhmet, M. U. "Self-synchronization of the integrate-and-fire pacemaker model with continuous couplings." Nonlinear Analysis: Hybrid Systems 6, no. 1 (February 2012): 730–40. http://dx.doi.org/10.1016/j.nahs.2011.07.003.

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48

Zhang, Xuedong, and Laurel H. Carney. "Response Properties of an Integrate-and-Fire Model That Receives Subthreshold Inputs." Neural Computation 17, no. 12 (December 1, 2005): 2571–601. http://dx.doi.org/10.1162/089976605774320584.

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Abstract:

A computational technique is described for calculation of the inter-spike interval and poststimulus time histograms for the responses of an integrate-and-fire model to arbitrary inputs. The effects of the model parameters on the response statistics were studied systematically. Specifically, the probability distribution of the membrane potential was calculated as a function of time, and the mean interspike interval and PST histogram were calculated for arbitrary inputs. For stationary inputs, the regularity of the output was studied in detail for various model parameters. For nonstationary inputs, the effects of the model parameters on the output synchronization index were explored. The results show that enhanced synchronization in response to low-frequency stimuli required a large number (n > 25) of weak inputs. Irregular responses and a linear input-output rate relationship required strong (but subthreshold) inputs with a small time constant. A model cell with mixed-amplitude synaptic inputs can respond to stationary inputs irregularly and have enhanced synchronization to nonstationary inputs that are phase-locked to low-frequency inputs. Both of these response properties have been reported for some cells in the ventral cochlear nucleus in the auditory brainstem.

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Ng, Danny, MokSiew -Ying, Chan Siow -Cheng, and Goh Sing -Yau. "Simulation of Ultra-slow Oscillations Using the Integrate and Fire Neuron Model." Engineering 04, no. 10 (2012): 65–67. http://dx.doi.org/10.4236/eng.2012.410b017.

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Nomura, Ryota, Ying-Zong Liang, Kenji Morita, Kantaro Fujiwara, and Tohru Ikeguchi. "Threshold-varying integrate-and-fire model reproduces distributions of spontaneous blink intervals." PLOS ONE 13, no. 10 (October 30, 2018): e0206528. http://dx.doi.org/10.1371/journal.pone.0206528.

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Journal articles on the topic 'Model "integrate-and-fire"'

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