Lapicque’s 1907 paper: from frogs to integrate-and-fire

@article{Brunel2007Lapicques1P,
  title={Lapicque’s 1907 paper: from frogs to integrate-and-fire},
  author={Nicolas J.-B. Brunel and Mark C. W. van Rossum},
  journal={Biological Cybernetics},
  year={2007},
  volume={97},
  pages={337-339}
}
Exactly 100 years ago, Louis Lapicque published a paper on the excitability of nerves that is often cited in the context of integrate-and-fire neurons. We discuss Lapicque’s contributions along with a translation of the original publication. 

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References

SHOWING 1-10 OF 16 REFERENCES
A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties
  • A. Burkitt
  • Physics, Computer Science
  • Biological Cybernetics
  • 2006
TLDR
This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses, and focuses on the mathematical methods that allow the output spike distribution to be analyzed. Expand
A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input
  • A. Burkitt
  • Computer Science, Medicine
  • Biological Cybernetics
  • 2006
TLDR
The focus of this review is upon the mathematical techniques that give the time distribution of output spikes, namely stochastic differential equations and the Fokker–Planck equation. Expand
RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON.
TLDR
Quantitative methods for the study of the statistical properties of spontaneously occurring spike trains from single neurons suggest a number of descriptive mathematical models that can describe a wide range of neuronal activity in terms of two parameters. Expand
Dynamics of Encoding in a Population of Neurons
  • B. Knight
  • Computer Science, Medicine
  • The Journal of general physiology
  • 1972
A simple encoder model, which is a reasonable idealization from known electrophysiological properties, yields a population in which the variation of the firing rate with time is a perfect replica ofExpand
Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting
TLDR
This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition, providing a link between the two disciplines. Expand
A THEORETICAL ANALYSIS OF NEURONAL VARIABILITY.
  • R. Stein
  • Mathematics, Medicine
  • Biophysical journal
  • 1965
TLDR
The assumptions of the model are relaxed and the effects of such experimentally found phenomena as relative refractory and supernormal periods, adaptation, potentiation, and rhythmic slow potentials are discussed. Expand
The Relationship between the Firing Rate of a Single Neuron and the Level of Activity in a Population of Neurons
  • B. Knight
  • Biology, Medicine
  • The Journal of general physiology
  • 1972
TLDR
The experiment confirms the theoretical prediction that under appropriate conditions an enlarged resonant response should appear in the activity of the neuron population, near the frequency at which there is minimum modulation in the instantaneous rate of a single neuron. Expand
Georges Weiss' Fundamental Law of Electrostimulation Is 100 Years Old
  • W. Irnich
  • Psychology, Medicine
  • Pacing and clinical electrophysiology : PACE
  • 2002
TLDR
Georges Weiss made many contributions to physiology, but his main field of interest was electrophysiology, and there were no measuring technology available at that time to measure the quantity of devices with short‐lasting pulses in the millisecond range. Expand
Excitation and Accommodation in Nerve
When an electric current is passed through a living excitable tissue it changes the “condition” of the tissue in such a way that, if the change be in the right direction and great enough, excitationExpand
ON THE INTENSITY-TIME RELATIONS FOR STIMULATION BY ELECTRIC CURRENTS. I
  • H. A. Blair
  • Physics, Medicine
  • The Journal of general physiology
  • 1932
TLDR
Experimental data are discussed and are shown to agree satisfactorily with the derived formulae for stimulation both at the anode and cathode for stimulation by direct currents using the following hypotheses. Expand
...
1
2
...