scholarly journals Generalization of the Event-Based Carnevale-Hines Integration Scheme for Integrate-and-Fire Models

2009 ◽  
Vol 21 (7) ◽  
pp. 1913-1930 ◽  
Author(s):  
Ronald A. J. van Elburg ◽  
Arjen van Ooyen
Keyword(s):  
Neuron Model ◽  
Formal Proof ◽  
Integration Scheme ◽  
Synaptic Currents ◽  
General Applicability ◽  
Time Constants ◽  
Integrate And Fire ◽  
Double Exponential ◽  
Event Based ◽  
Integrate And Fire Neuron

An event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory synaptic currents and double exponential inhibitory synaptic currents has been introduced by Carnevale and Hines. However, the integration scheme imposes nonphysiological constraints on the time constants of the synaptic currents, which hamper its general applicability. This letter addresses this problem in two ways. First, we provide physical arguments demonstrating why these constraints on the time constants can be relaxed. Second, we give a formal proof showing which constraints can be abolished. As part of our formal proof, we introduce the generalized Carnevale-Hines lemma, a new tool for comparing double exponentials as they naturally occur in many cascaded decay systems, including receptor-neurotransmitter dissociation followed by channel closing. Through repeated application of the generalized lemma, we lift most of the original constraints on the time constants. Thus, we show that the Carnevale-Hines integration scheme for the integrate-and-fire model can be employed for simulating a much wider range of neuron and synapse types than was previously thought.

Critical Analysis of Two Dimensional and Four-Dimensional Spiking Neuron Models

2019 ◽  
Vol 16 (9) ◽  
pp. 3897-3905
Author(s):  
Pankaj Kumar Kandpal ◽  
Ashish Mehta
Keyword(s):  
Error Correction ◽  
Neuron Model ◽  
Learning Algorithm ◽  
Two Dimensional ◽  
Spiking Neuron ◽  
Classification Rate ◽  
Integrate And Fire ◽  
Study Results ◽  
Spiking Neuron Model ◽  
Integrate And Fire Neuron

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.

Simplicity and Efficiency of Integrate-and-Fire Neuron Models

2009 ◽  
Vol 21 (2) ◽  
pp. 353-359 ◽  
Author(s):  
Hans E. Plesser ◽  
Markus Diesmann
Keyword(s):  
Neuron Model ◽  
State Of The Art ◽  
Network Modeling ◽  
Spiking Neuron ◽  
Neuron Models ◽  
Computer Clusters ◽  
Integrate And Fire ◽  
The Past ◽  
History Of ◽  
Integrate And Fire Neuron

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.

High-order finite volume approximation for population density model based on quadratic integrate-and-fire neuron

2018 ◽  
Vol 36 (1) ◽  
pp. 84-102 ◽  
Author(s):  
Paramjeet Singh ◽  
Santosh Kumar ◽  
Mehmet Emir Koksal
Keyword(s):  
Population Density ◽  
Finite Volume ◽  
Model Equation ◽  
Neuron Model ◽  
High Order ◽  
Content Type ◽  
Integrate And Fire ◽  
Volume Approximation ◽  
Finite Volume Approximation ◽  
Integrate And Fire Neuron

PurposeThe purpose of this paper is to develop and apply a high-order numerical method based on finite volume approximation for quadratic integrate-and-fire (QIF) neuron model with the help of population density approach.Design/methodology/approachThe authors apply the population density approach for the QIF neuron model to derive the governing equation. The resulting mathematical model cannot be solved with existing analytical or numerical techniques owing to the presence of delay and advance. The numerical scheme is based along the lines of approximation: spatial discretization is performed by weighted essentially non-oscillatory (WENO) finite volume approximation (FVM) and temporal discretization are performed by strong stability-preserving explicit Runge–Kutta (SSPERK) method. Compared with existing schemes of orders 2 and 3 from the literature, the proposed scheme is found to be more efficient and it produces accurate solutions with few grid cells. In addition to this, discontinuity is added in the application of the model equation to illustrate the high performance of the proposed scheme.FindingsThe developed scheme works nicely for the simulation of the resulting model equation. The authors discussed the role of inhibitory and excitatory parts in variation of neuronal firing. The validation of the designed scheme is measured by its comparison with existing schemes in the literature. The efficiency of the designed scheme is demonstrated via numerical simulations.Practical implicationsIt is expected that the present study will be a useful tool to tackle the complex neuron model and related studies.Originality/valueThe novel aspect of this paper is the application of the numerical methods to study the modified version of leaky integrate-and-fire neuron based on a QIF neuron. The model of the current study is inspired from the base model given in Stein (1965) and modified version in Kadalbajoo and Sharma (2005) and Wang and Zhang (2014). The applicability was confirmed by taking some numerical examples.

scholarly journals Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model

2017 ◽  
Vol 90 ◽  
pp. 1-7 ◽  
Author(s):  
F.S. Borges ◽  
P.R. Protachevicz ◽  
E.L. Lameu ◽  
R.C. Bonetti ◽  
K.C. Iarosz ◽  
...  
Keyword(s):  
Neuron Model ◽  
Random Network ◽  
Firing Patterns ◽  
Integrate And Fire ◽  
Integrate And Fire Neuron
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