Reliable Logic Circuit Elements that Exploit Nonlinearity in the Presence of a Noise Floor

Murali, K.; Sinha, Sudeshna; Ditto, William L.; Bulsara, Adi R.

doi:10.1103/physrevlett.102.104101

Cited by 208 publications

(145 citation statements)

References 12 publications

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“…Noise provides a critical barrier for the development of sensitive electronic and mechanical devices, particularly at the nanoscale [2,3]. Increasingly, researchers are focusing on exploring innovative, non-traditional device design and control strategies that exploit the ambient noise [4][5][6][7][8][9][10][11]. In this regard, there are clear advantages to understanding how nature has managed to harness noise in a setting whose primary (apparent) function is to manage information.…”

Section: Introductionmentioning

confidence: 99%

Neuron dynamics in the presence of1/fnoise

Sobie

Babul²,

Sousa³

2011

Phys. Rev. E

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Interest in understanding the interplay between noise and the response of a non-linear device cuts across disciplinary boundaries. It is as relevant for unmasking the dynamics of neurons in noisy environments as it is for designing reliable nanoscale logic circuit elements and sensors. Most studies of noise in non-linear devices are limited to either time-correlated noise with a Lorentzian spectrum (of which the white noise is a limiting case) or just white noise. We use analytical theory and numerical simulations to study the impact of the more ubiquitous "natural" noise with a 1/f frequency spectrum. Specifically, we study the impact of the 1/f noise on a leaky integrate and fire model of a neuron. The impact of noise is considered on two quantities of interest to neuron function: The spike count Fano factor and the speed of neuron response to a small step-like stimulus. For the perfect (non-leaky) integrate and fire model, we show that the Fano factor can be expressed as an integral over noise spectrum weighted by a (low pass) filter function given by F(t, f ) = sinc 2 (πf t). This result elucidates the connection between low frequency noise and disorder in neuron dynamics. Under 1/f noise, spike dynamics lacks a characteristic correlation time, inducing the leaky and non-leaky models to exhibit non-ergodic behavior and Fano factor increasing logarithmically as a function of time. We compare our results to experimental data of single neurons in vivo [M.C. Teich, C. Heneghan, S.B. Lowen, T. Ozaki, and E. Kaplan, Journal of the Optical Society of America A 14, 529 (1997)], and show how the 1/f noise model provides much better agreement than the usual approximations based on Lorentzian noise. The low frequency noise, however, complicates the case for information coding scheme based on interspike intervals by introducing variability in the neuron response time. On a positive note, the neuron response time to a step stimulus is, remarkably, nearly optimal in the presence of 1/f noise. An explanation of this effect elucidates how the brain can take advantage of noise to prime a subset of the neurons to respond almost instantly to sudden stimuli.

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Section: Introductionmentioning

confidence: 99%

Neuron dynamics in the presence of1/fnoise

Sobie

Babul²,

Sousa³

2011

Phys. Rev. E

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“…These include stochastic resonance (SR) [1][2][3][4][5], noise-induced linearization [6], noise-enhanced stability [7], and noise-assisted logic operations [8]. The response is obviously correlated with the nonlinearity and noise characteristics, and understanding this relationship has been a key issue in both science and engineering.…”

Section: Introductionmentioning

confidence: 99%

Design and characterization of nonlinear functions for the transmission of a small signal with non-Gaussian noise

2013

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We design nonlinear functions for the transmission of a small signal with non-Gaussian noise and perform experiments to characterize their responses. Using statistical design theory [A. Ichiki and Y. Tadokoro, Phys. Rev. E 88, 012124 (2013)], a static nonlinear function is estimated from the probability density function of the given noise in order to maximize the signal-to-noise ratio of the output. Using an electronic system that implements the optimized nonlinear function, we confirm the recovery of a small signal from a signal with non-Gaussian noise. In our experiment, the non-Gaussian noise is a mixture of Gaussian noises. A similar technique is also applied to the optimization of the threshold value of the function. We find that, for non-Gaussian noise, the response of the optimized nonlinear systems is better than that of the linear system.

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“…In nonlinear systems the interplay of bistability and noise can result in non-trivial noise-induced effects that can potentially be exploited for applications [1]. A recent example is the numerical demonstration of the implementation of a stochastic logic gate using a vertical-cavity surface-emitting laser (VCSEL) by exploiting the interplay of polarization bistability and noise [2].…”

Section: Introductionmentioning

confidence: 99%

All optical implementation of a stochastic logic gate using a VCSEL with external optical injection

Perrone

Masoller

Vilaseca

2011

2011 Fifth Rio De La Plata Workshop on Laser Dynamics and Nonlinear Photonics

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Abstract-We perform numerical simulations of the dynamics of two VCSELs optically coupled in a master-slave configuration. We show that the interplay of nonlinearity and spontaneous emission noise can yield logic behavior, and the emergent outcome of such system is a reliable logic gate. Specifically in our case represents an all-optical logic gate, with the logic input encoded in the strength of the light injected in the slave laser by the master laser, and the fast and robust response decoded from the polarization state of the light emitted by the slave laser.

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Reliable Logic Circuit Elements that Exploit Nonlinearity in the Presence of a Noise Floor

Cited by 208 publications

References 12 publications

Neuron dynamics in the presence of1/fnoise

Neuron dynamics in the presence of1/fnoise

Design and characterization of nonlinear functions for the transmission of a small signal with non-Gaussian noise

All optical implementation of a stochastic logic gate using a VCSEL with external optical injection

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