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Lecture# Nonlinear Integrate-and-Fire Model

Description

This lecture covers the reduction of a two-dimensional neuron model to one dimension, focusing on the Nonlinear Integrate-and-Fire Model. It discusses the separation of time scales, the stimulus impact, and the stability of fixed points. The Exponential Integrate-and-Fire Model is also presented, derived from Hodgkin-Huxley equations. The lecture explores the sparse activity in vivo, the prediction of spike initiation times, and subthreshold voltage in neuronal modeling.

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In MOOCs (2)

Instructor

Neuronal Dynamics - Computational Neuroscience of Single Neurons

The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail.

Neuronal Dynamics - Computational Neuroscience of Single Neurons

The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail.

Related concepts (47)

Biological neuron model

Biological neuron models, also known as a spiking neuron models, are mathematical descriptions of the properties of certain cells in the nervous system that generate sharp electrical potentials across their cell membrane, roughly one millisecond in duration, called action potentials or spikes (Fig. 2). Since spikes are transmitted along the axon and synapses from the sending neuron to many other neurons, spiking neurons are considered to be a major information processing unit of the nervous system.

Computational neuroscience

Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system. Computational neuroscience employs computational simulations to validate and solve mathematical models, and so can be seen as a sub-field of theoretical neuroscience; however, the two fields are often synonymous.

Neuron

Within a nervous system, a neuron, neurone, or nerve cell is an electrically excitable cell that fires electric signals called action potentials across a neural network. Neurons communicate with other cells via synapses - specialized connections that commonly use minute amounts of chemical neurotransmitters to pass the electric signal from the presynaptic neuron to the target cell through the synaptic gap. The neuron is the main component of nervous tissue in all animals except sponges and placozoa.

Dimensionality reduction

Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with).

Threshold voltage

The threshold voltage, commonly abbreviated as Vth or VGS(th), of a field-effect transistor (FET) is the minimum gate-to-source voltage (VGS) that is needed to create a conducting path between the source and drain terminals. It is an important scaling factor to maintain power efficiency. When referring to a junction field-effect transistor (JFET), the threshold voltage is often called pinch-off voltage instead.

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