Spiking Dynamics Observed in Three Neurons




Perera, Kevin

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A leaky integrate and fire (LIF) model is a basic mathematical model designed to simulate a neuron. The simplicity and relative ease with which network architectures can be constructed using patterns of LIF neurons make it a common choice for modeling. The RC circuit is used as the basis of the model. By way of algebraic manipulation, we can solve I(t) = (u(t)–u(rest)/R + C*du/dt, where u-u(rest) is the voltage across the resistor. The product of C*du/dt is the capacitive current. Through integration and Ohm’s Law, we can derive membrane potential in a linear differential equation[1]. Delgado et al. aims to model the membrane potential of the LIF neuron through a random process known as Ornstein-Uhlenbeck. Through the random variable Tf, we can predict the time between neuron firings. We can find an estimator of the average firing rate of the neuron[2]. The Nengo framework is an open-source neural modeling architecture leveraged across Python and the TensorFlow libraries, which are used for developing artificial intelligence models. Using LIF neurons, it is possible to create a high-level model of the brain[3]. More attention is spent by the modeler to conceptualize neural architecture; however, the drawback to using the software is that we are unable to manipulate dynamics on the neuron-to-neuron scale, making Nengo more appropriate for large scale modeling.




Perera, Kevin. Spiking Dynamics Observed in Three Neurons, 2019.