Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence
Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence
Elements of information theory
Elements of information theory
Probability
Signal processing with alpha-stable distributions and applications
Signal processing with alpha-stable distributions and applications
Fuzzy engineering
Generating gamma variates by a modified rejection technique
Communications of the ACM
IEEE Transactions on Signal Processing
2005 Special Issue: Stochastic resonance in noisy spiking retinal and sensory neuron models
Neural Networks - 2005 Special issue: IJCNN 2005
Nonlinear signal detection from an array of threshold devices for non-Gaussian noise
Digital Signal Processing
Detection of Weak Signals by Emotion-Derived Stochastic Resonance
SAB '08 Proceedings of the 10th international conference on Simulation of Adaptive Behavior: From Animals to Animats
Stochastic resonance in sequential detectors
IEEE Transactions on Signal Processing
Adaptive fuzzy priors for Bayesian inference
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Neural signal-detection noise benefits based on error probability
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Noise enhanced hypothesis-testing in the restricted Bayesian framework
IEEE Transactions on Signal Processing
Stochastic resonance in binary composite hypothesis-testing problems in the Neyman-Pearson framework
Digital Signal Processing
Noise-enhanced clustering and competitive learning algorithms
Neural Networks
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Stochastic resonance occurs when noise improves how a nonlinear system performs. This paper presents two general stochastic-resonance theorems for threshold neurons that process noisy Bernoulli input sequences. The performance measure is Shannon mutual information. The theorems show that small amounts of independent additive noise can increase the mutual information of threshold neurons if the neurons detect subthreshold signals. The first theorem shows that this stochastic-resonance effect holds for all finite-variance noise probability density functions that obey a simple mean constraint that the user can control. A corollary shows that this stochastic-resonance effect occurs for the important family of (right-sided) gamma noise. The second theorem shows that this effect holds for all infinite-variance noise types in the broad family of stable distributions. Stable bell curves can model extremely impulsive noise environments. So the second theorem shows that this stochastic-resonance effect is robust against violent fluctuations in the additive noise process.