Principles and practice of information theory
Principles and practice of information theory
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
Differences in spiking patterns among cortical neurons
Neural Computation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Information Geometry of Interspike Intervals in Spiking Neurons
Neural Computation
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Probability and Random Processes for Electrical and Computer Engineers
Probability and Random Processes for Electrical and Computer Engineers
Neural Computation
Information Theory and Network Coding
Information Theory and Network Coding
Capacity of a single spiking neuron channel
Neural Computation
Capacity analysis for integrate-and-fire neurons with descending action potential thresholds
IEEE Transactions on Information Theory - Special issue on information theory in molecular biology and neuroscience
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A neuroscience-based mathematical model of how a neuron stochastically processes data and communicates information is introduced and analyzed. Call the neuron in question "neuron j", or just "j". The information j transmits approximately describes the time-varying intensity of the excitation j is continuously experiencing from neural spike trains delivered to its synapses by thousands of other neurons. Neuron j "encodes" this excitation history into a sequence of time instants at which it generates neural spikes of its own. By propagating these spikes along its axon, j acts as a multiaccess, partially degraded broadcast channel with thousands of input and output terminals that employs a time-continuous version of pulse position modulation. The mathematical model features three parameters, m, κ, and b, which largely characterize j as an engine of computation and communication. Each set of values of these parameters corresponds to a long term maximization of the bits j conveys to its targets per joule it expends doing so, which is achieved by distributing the random duration between successive spikes j generates according to a gamma pdf with parameters κ and b and distributing b/A according to a beta probability density with parameters κ and m - κ, where A is the random intensity of the effectively Poisson process of spikes that arrive to the union of all of j's synapses at a randomly chosen time instant.