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72
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 41 (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.
Synaptic background activity enhances the responsiveness of neocortical pyramidal neurons
 J
, 2000
"... You might find this additional info useful... This article cites 32 articles, 12 of which you can access for free at: ..."
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Cited by 31 (8 self)
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You might find this additional info useful... This article cites 32 articles, 12 of which you can access for free at:
Is there chaos in the brain? II. Experimental evidence and related models
 C. R. Biol
, 2003
"... The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The meth ..."
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Cited by 22 (0 self)
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The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The methods used in each of these studies have almost invariably combined the analysis of experimental data with simulations using formal models, often based on modified Huxley and Hodgkin equations and/or of the Hindmarsh and Rose models of bursting neurons. Due to technical limitations, the results of these simulations have prevailed over experimental ones in studies on the nonlinear properties of large cortical networks and higher brain functions. Yet, and although a convincing proof of chaos (as defined mathematically) has only been obtained at the level of axons, of single and coupled cells, convergent results can be interpreted as compatible with the notion that signals in the brain are distributed according to chaotic patterns at all levels of its various forms of hierarchy. This chronological account of the main landmarks of nonlinear neurosciences follows an earlier publication [Faure, Korn, C. R. Acad. Sci. Paris, Ser. III 324 (2001) 773–793] that was focused on the basic concepts of nonlinear dynamics and methods of investigations which allow chaotic processes to be distinguished from stochastic ones and on the rationale for envisioning their control using external perturbations. Here we present the data and main arguments that support the existence of chaos at all levels from the simplest to the most complex forms of organization of the nervous system.
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 19 (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.
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 systems. The SR ..."
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Cited by 17 (9 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...
Stochastic models of neuronal dynamics
, 2005
"... Cortical activity is the product of interactions among neuronal populations. Macroscopic electrophysiological phenomena are generated by these interactions. In principle, the mechanisms of these interactions afford constraints on biologically plausible models of electrophysiological responses. In ot ..."
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Cited by 13 (5 self)
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Cortical activity is the product of interactions among neuronal populations. Macroscopic electrophysiological phenomena are generated by these interactions. In principle, the mechanisms of these interactions afford constraints on biologically plausible models of electrophysiological responses. In other words, the macroscopic features of cortical activity can be modelled in terms of the microscopic behaviour of neurons. An evoked response potential (ERP) is the mean electrical potential measured from an electrode on the scalp, in response to some event. The purpose of this paper is to outline a population density approach to modelling ERPs. We propose a biologically plausible model of neuronal activity that enables the estimation of physiologically meaningful parameters from electrophysiological data. The model encompasses four basic characteristics of neuronal activity and organization: (i) neurons are dynamic units, (ii) driven by stochastic forces, (iii) organized into populations with similar biophysical properties and response characteristics and (iv) multiple populations interact to form functional networks. This leads to a formulation of population dynamics in terms of the Fokker–Planck equation. The solution of this equation is the temporal evolution of a probability density over statespace, representing the distribution of an ensemble of trajectories. Each trajectory corresponds to the changing state of a
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 10 (3 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 Trans. Nanotechnol
, 2006
"... Abstract—Electrical noise can help pulsetrain signal detection at the nanolevel. Experiments on a singlewalled carbon nanotube transistor confirmed that a threshold exhibited stochastic resonance (SR) for finitevariance and infinitevariance noise: small amounts of noise enhanced the nanotube det ..."
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Cited by 7 (6 self)
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Abstract—Electrical noise can help pulsetrain signal detection at the nanolevel. Experiments on a singlewalled carbon nanotube transistor confirmed that a threshold exhibited stochastic resonance (SR) for finitevariance and infinitevariance noise: small amounts of noise enhanced the nanotube detector’s performance. The experiments used a carbon nanotube fieldeffect transistor to detect noisy subthreshold electrical signals. Two new SR hypothesis tests in the Appendix also confirmed the SR effect in the nanotube transistor. Three measures of detector performance showed the SR effect: Shannon’s mutual information, the normalized correlation measure, and an inverted bit error rate compared the input and output discretetime random sequences. The nanotube detector had a thresholdlike input–output characteristic in its gate effect. It produced little current for subthreshold digital input voltages that fed the transistor’s gate. Three types of synchronized
Enhancement of signaltonoise ratio and phase locking for small inputs by a lowthreshold outward current in auditory neurons
 J. Neurosci
, 2002
"... Neurons possess multiple voltagedependent conductances specific for their function. To investigate how lowthreshold outward currents improve the detection of small signals in a noisy background, we recorded from gerbil medial superior olivary (MSO) neurons in vitro. MSO neurons responded phasicall ..."
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Cited by 7 (1 self)
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Neurons possess multiple voltagedependent conductances specific for their function. To investigate how lowthreshold outward currents improve the detection of small signals in a noisy background, we recorded from gerbil medial superior olivary (MSO) neurons in vitro. MSO neurons responded phasically, with a single spike to a step current injection. When bathed in dendrotoxin (DTX), most cells switched to tonic firing, suggesting that lowthreshold potassium currents (I KLT) participated in shaping these phasic responses. Neurons were stimulated with a computergenerated steady barrage of random inputs, mimicking weak synaptic conductance transients (the “noise”), together with a larger but still subthreshold postsynaptic conductance, EPSG (the “signal”). DTX reduced the signaltonoise ratio (SNR), defined as the ratio of probability to fire in response to the EPSG and the probability to fire spontaneously in response to noise. The reduction was mainly attribBecause of the temporal cues present in sound signals, the auditory nervous system provides a good opportunity to explore how multiple membrane currents influence signal integration (Trussell, 1999). The preservation of precise temporal information is crucial for coding and decoding, especially below �2 kHz in mammals. Correspondingly, brainstem auditory neurons have very fast decaying synaptic currents (Raman and Trussell, 1992; Gardner et al., 1999) and fast lowthreshold potassium currents
Stochastic resonance in continuous and spiking neuron models with levy noise. Neural Networks
 IEEE Transactions on
, 2008
"... Abstract—Levy noise can help neurons detect faint or subthreshold signals. Levy noise extends standard Brownian noise to many types of impulsive jumpnoise processes found in real and model neurons as well as in models of finance and other random phenomena. Two new theorems and the Itô calculus show ..."
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Cited by 6 (6 self)
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Abstract—Levy noise can help neurons detect faint or subthreshold signals. Levy noise extends standard Brownian noise to many types of impulsive jumpnoise processes found in real and model neurons as well as in models of finance and other random phenomena. Two new theorems and the Itô calculus show that white Levy noise will benefit subthreshold neuronal signal detection if the noise process’s scaled drift velocity falls inside an interval that depends on the threshold values. These results generalize earlier “forbidden interval ” theorems of neuronal “stochastic resonance ” (SR) or noiseinjection benefits. Global and local Lipschitz conditions imply that additive white Levy noise can increase the mutual information or bit count of several feedback neuron models that obey a general stochastic differential equation (SDE). Simulation results show that the same noise benefits still occur for some infinitevariance stable Levy noise processes even though the theorems themselves apply only to finitevariance Levy noise. The Appendix proves the two Itôtheoretic lemmas that underlie the new Levy noisebenefit theorems. Index Terms—Levy noise, jump diffusion, mutual information, neuron models, signal detection, stochastic resonance (SR). I. STOCHASTIC RESONANCE IN NEURAL SIGNAL DETECTION STOCHASTIC RESONANCE (SR) occurs when noise benefits a system rather than harms it. Small amounts of noise can often enhance some forms of nonlinear signal processing