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22
Noise in IntegrateandFire Neurons: From Stochastic Input to Escape Rates
 TO APPEAR IN NEURAL COMPUTATION.
, 1999
"... We analyze the effect of noise in integrateandfire neurons driven by timedependent input, and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for timedependent subthreshold input, diffusive noise can be replaced by escape noise with a hazard funct ..."
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Cited by 38 (6 self)
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We analyze the effect of noise in integrateandfire neurons driven by timedependent input, and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for timedependent subthreshold input, diffusive noise can be replaced by escape noise with a hazard function that has a Gaussian dependence upon the distance between the (noisefree) membrane voltage and threshold. The approximation is improved if we add to the hazard function a probability current proportional to the derivative of the voltage. Stochastic resonance in response to periodic input occurs in both noise models and exhibits similar characteristics.
Adaptive Stochastic Resonance
 Proceedings of the IEEE: special issue on intelligent signal processing
, 1998
"... This paper shows how adaptive systems can learn to add an optimal amount of noise to some nonlinear feedback systems. Noise can improve the signaltonoise ratio of many nonlinear dynamical systems. This "stochastic resonance" effect occurs in a wide range of physical and biological system ..."
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Cited by 23 (11 self)
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This paper shows how adaptive systems can learn to add an optimal amount of noise to some nonlinear feedback systems. Noise can improve the signaltonoise ratio of many nonlinear dynamical systems. This "stochastic resonance" effect occurs in a wide range of physical and biological systems. The SR effect may also occur in engineering systems in signal processing, communications, and control. The noise energy can enhance the faint periodic signals or faint broadband signals that force the dynamical systems. Most SR studies assume full knowledge of a system's dynamics and its noise and signal structure. Fuzzy and other adaptive systems can learn to induce SR based only on samples from the process. These samples can tune a fuzzy system's ifthen rules so that the fuzzy system approximates the dynamical system and its noise response. The paper derives the SR optimality conditions that any stochastic learning system should try to achieve. The adaptive system learns the SR effect as the sys...
Extracting Oscillations: Neuronal Coincidence Detection with Noisy Periodic Spike Input
, 1998
"... How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integra ..."
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Cited by 20 (6 self)
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How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integrateandfire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and we demonstrate that there is an optimal threshold. Our considerations can be used to predict from neuronal parameters whether and to what extent a neuron can act as a coincidence detector and thus can convert a temporal code into a rate code.
Neural Noise Can Explain Expansive, PowerLaw Nonlinearities In Neural Resopnse Functions
, 2002
"... Many phenomenological models of the responses of simple cells in primary visual cortex have concluded that a cell's firing rate should be given by its input raised to a power greater than one. This is known as an expansive powerlaw nonlinearity. However, intracellular recordings have shown tha ..."
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Cited by 18 (3 self)
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Many phenomenological models of the responses of simple cells in primary visual cortex have concluded that a cell's firing rate should be given by its input raised to a power greater than one. This is known as an expansive powerlaw nonlinearity. However, intracellular recordings have shown that a di#erent nonlinearity, a linearthreshold function, appears to give a good prediction of firing rate from a cell's lowpassfiltered voltage response. Using a model based on a linearthreshold function, Anderson et al. (2000) showed that voltage noise was critical to converting voltage responses with contrastinvariant orientation tuning into spiking responses with contrastinvariant tuning. We present two separate results clarifying the connection between noisesmoothed linearthreshold functions and powerlaw nonlinearities. First, we prove analytically that a powerlaw nonlinearity is the only inputoutput function that converts contrastinvariant input tuning into contrastinvariant spike tuning. Second, we examine simulations of a simple model that assumes (i) instantaneous spike rate is given by a linearthreshold function of voltage, and (ii) voltage responses include significant noise. We show that the resulting average spike rate is well described by an expansive power law of the average voltage (averaged over multiple trials), provided that average voltage remains less than about 1.5 standard deviations of the noise above threshold. Finally, we use this model to show that the noise levels recorded by Anderson et al. (2000) are consistent with the degree to which the orientation tuning of spiking responses is more sharply tuned than the orientation tuning of voltage responses. Thus, neuronal noise can robustly generate powerlaw inputoutput functions of the form freq...
Statistical Analysis of Stochastic Resonance in a Simple Setting
 Phys. Rev. E
, 1999
"... A subthreshold signal may be detected if noise is added to the data. We study a simple model, consisting of a constant signal to which at uniformly spaced times independent and identically distributed noise variables with known distribution are added. A detector records the times at which the noisy ..."
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Cited by 13 (4 self)
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A subthreshold signal may be detected if noise is added to the data. We study a simple model, consisting of a constant signal to which at uniformly spaced times independent and identically distributed noise variables with known distribution are added. A detector records the times at which the noisy signal exceeds a threshold. There is an optimal noise level, called stochastic resonance. We explore the detectability of the signal in a system with one or more detectors, with di#erent thresholds. We use a statistical detectability measure, the asymptotic variance of the best estimator of the signal from the thresholded data, or equivalently, the Fisher information in the data. In particular, we determine optimal configurations of detectors, varying the distances between the thresholds and the signal, as well as the noise level. The approach generalizes to nonconstant signals. AMS 1991 subject classifications. Primary 62F12; secondary 62P10. Key words and Phrases. E#cient estimator, max...
NoiseEnhanced Detection of Subthreshold Signals with Carbon Nanotubes
 IEEE Transactions on Nanotechnology
, 2006
"... ..."
How the Threshold of a Neuron Determines its Capacity for Coincidence Detection
, 1998
"... Coherent oscillatory activity of a population of neurons is thought to be a vital feature of temporal coding in the brain. We focus on the question of whether a single neuron can transform a spike code into a rate code. More precisely, how does a neuron vary its mean output firing rate, if its in ..."
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Cited by 5 (2 self)
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Coherent oscillatory activity of a population of neurons is thought to be a vital feature of temporal coding in the brain. We focus on the question of whether a single neuron can transform a spike code into a rate code. More precisely, how does a neuron vary its mean output firing rate, if its input changes from random to coherent? We investigate the coincidence detection properties of an integrateandfire neuron in dependence upon internal parameters and input statistics. In particular, we show how coincidence detection depends on the membrane time constant and the threshold. Furthermore, we demonstrate that there is an optimal threshold for coincidence detection and that there is a broad range of nearoptimal threshold values. Finetuning is not necessary. Keywords: Coincidence detection, voltage threshold, coherent activity, temporal coding, rate coding, integrateandfire neuron Institut fur Theoretische Physik, Physik Department der TU Munchen, D85747 Garching, Germany...
Bandpass Properties of IntegrateFire Neurons
 Neurocomputing
, 1999
"... There is mounting experimental evidence that the nervous system utilizes neural noise to improve sensory signal transmission. Here, we investigate the response properties of a noisy neuron using an integratefire model. When the neuron is driven by periodic input, noise optimally improves the signal ..."
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Cited by 2 (0 self)
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There is mounting experimental evidence that the nervous system utilizes neural noise to improve sensory signal transmission. Here, we investigate the response properties of a noisy neuron using an integratefire model. When the neuron is driven by periodic input, noise optimally improves the signaltonoise ratio of the elicited spike train, if the driving frequency is in a certain range. This phenomenon, called bona fide stochastic resonance, is analyzed in a Markov chain formalism which avoids implausible assumptions made in earlier studies. The bandpass property of the transmission function of the neuron may explain why certain oscillation frequencies are prevalent in cortex. Key words: Integratefire neuron ; Stochastic resonance ; OrnsteinUhlenbeck process ; Markov chain 1 Introduction There is mounting experimental evidence that the nervous system utilizes the noise ubiquitous in neurons to improve sensory signal transmission [10,18,3,11]. Here, we consider neural noise from ...
Informationtheoretic measures improved by noise in nonlinear systems
 Proc. 14th Int. Conf. on Math. Theory of Networks
, 2000
"... signal, noise. Stochastic resonance is a phenomenon whereby the transmission of a signal by certain nonlinear systems can be improved by addition of noise. We propose a brief overview of this effect, together with an extension based on informationtheoretic concepts. We analyze various conditions of ..."
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Cited by 2 (0 self)
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signal, noise. Stochastic resonance is a phenomenon whereby the transmission of a signal by certain nonlinear systems can be improved by addition of noise. We propose a brief overview of this effect, together with an extension based on informationtheoretic concepts. We analyze various conditions of nonlinear transmission where the input–output Shannon mutual information, the input–output Kullback divergence, or the input–output Fisher information can receive improvement from noise addition, demonstrating different forms of noiseenhanced transmission. 1 Stochastic resonance phenomenon When a linear system couples linearly a signal and a noise, generally the noise acts as a nuisance spoiling the signal.