Related Experiment Video
Updated: Jul 29, 2025

Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments
Published on: November 12, 2019
Design of continuous-time recurrent neural networks with piecewise-linear activation function for generation of
Norikazu Takahashi1, Tsuyoshi Yamakawa2, Yasuhiro Minetoma2
1Okayama University, 3-1-1 Tsuhima-naka, Kita-ku, Okayama, 700-8530, Japan.
Abstract:
A recurrent neural network (RNN) can generate a sequence of patterns as the temporal evolution of the output vector. This paper focuses on a continuous-time RNN model with a piecewise-linear activation function that has neither external inputs nor hidden neurons, and studies the problem of finding the parameters of the model so that it generates a given sequence of bipolar vectors. First, a sufficient condition for the model to generate the desired sequence is derived, which is expressed as a system of linear inequalities in the parameters. Next, three approaches to finding solutions of the system of linear inequalities are proposed: One is formulated as a convex quadratic programming problem and others are linear programming problems. Then, two types of sequences of bipolar vectors that can be generated by the model are presented. Finally, the case where the model generates a periodic sequence of bipolar vectors is considered, and a sufficient condition for the trajectory of the state vector to converge to a limit cycle is provided.
Related Concept Videos
Neural Circuits
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
Basic Discrete Time Signals
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
Sequence Networks of Rotating Machines
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
Basic Continuous Time Signals
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
Propagation of Action Potentials
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
Sampling Continuous Time Signal
In the...

