We analyze the effect of noise in integrate-and-fire neurons driven by timedependent input, and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for time-dependent sub-threshold input, diffusive noise can be replaced by escape noise with a hazard function that has a Gaussian dependence upon the distance between the (noise-free) 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.

How does a neuron vary its mean output firing rate if the input changes from random to coherent activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidence detection properties of an integrate-and-fire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, (i) we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and (ii) 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. Physik-Department der TU Munchen (T35), D-85747 Garching bei Munchen, Germany y Swiss Federal Institute of Technology, Center of Neuromimetic Systems, EPFL-DI, CH-1015 Lausanne, Switz...

This paper shows how adaptive systems can learn to add an optimal amount of noise to some nonlinear feedback systems. Noise can improve the signal-to-noise 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 if-then 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...

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 non-constant signals. AMS 1991 subject classifications. Primary 62F12; secondary 62P10. Key words and Phrases. E#cient estimator, max...

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 power-law nonlinearity. However, intracellular recordings have shown that a di#erent nonlinearity, a linear-threshold function, appears to give a good prediction of firing rate from a cell's low-pass-filtered voltage response. Using a model based on a linear-threshold function, Anderson et al. (2000) showed that voltage noise was critical to converting voltage responses with contrast-invariant orientation tuning into spiking responses with contrast-invariant tuning. We present two separate results clarifying the connection between noise-smoothed linear-threshold functions and power-law nonlinearities. First, we prove analytically that a power-law nonlinearity is the only input-output function that converts contrast-invariant input tuning into contrast-invariant spike tuning. Second, we examine simulations of a simple model that assumes (i) instantaneous spike rate is given by a linear-threshold 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 power-law input-output functions of the form freq...

Abstract—Electrical noise can help pulse-train signal detection at the nanolevel. Experiments on a single-walled carbon nanotube transistor confirmed that a threshold exhibited stochastic resonance (SR) for finite-variance and infinite-variance noise: small amounts of noise enhanced the nanotube detector’s performance. The experiments used a carbon nanotube field-effect 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 discrete-time random sequences. The nanotube detector had a threshold-like 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

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 integrate-and-fire 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 near-optimal threshold values. Fine-tuning is not necessary. Keywords: Coincidence detection, voltage threshold, coherent activity, temporal coding, rate coding, integrate-and-fire neuron Institut fur Theoretische Physik, Physik Department der TU Munchen, D-85747 Garching, Germany...

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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 integrate-fire model. When the neuron is driven by periodic input, noise optimally improves the signal-to-noise 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: Integrate-fire neuron ; Stochastic resonance ; Ornstein--Uhlenbeck 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 ...

We propose a simple theoretical structure of interacting integrate and fire neurons that can handle fast information processing, and may account for the fact that only a few neuronal spikes suffice to transmit information in the brain. Using integrate and fire neurons that are subjected to individual noise and to a common external input, we calculate their first passage time (FPT), or inter-spike interval.