Resonance phenomena in discrete systems with bichromatic input signal

We undertake a detailed numerical study of the twin phenomena of stochastic and vibrational resonance in a discrete model system in the presence of bichromatic input signal. A two parameter cubic map is used as the model that combines the features of both bistable and threshold settings. Our analysis brings out several interesting results, such as, the existence of a cross over behaviour from vibrational to stochastic resonance and the possibility of using stochastic resonance as a filter for the selective detection/transmission of the component frequencies in a composite signal. The study also reveals a fundamental difference between the bistable and threshold mechanisms with respect to amplification of a multi signal input.Comment: 17 pages, 16 figures, submitted to European Physical Journa

Noise-enhanced computation in a model of a cortical column

Varied sensory systems use noise in order to enhance detection of weak signals. It has been conjectured in the literature that this effect, known as stochastic resonance, may take place in central cognitive processes such as the memory retrieval of arithmetical multiplication. We show in a simplified model of cortical tissue, that complex arithmetical calculations can be carried out and are enhanced in the presence of a stochastic background. The performance is shown to be positively correlated to the susceptibility of the network, defined as its sensitivity to a variation of the mean of its inputs. For nontrivial arithmetic tasks such as multiplication, stochastic resonance is an emergent property of the microcircuitry of the model network

Representation of acoustic communication signals by insect auditory receptor neurons

Despite their simple auditory systems, some insect species recognize certain temporal aspects of acoustic stimuli with an acuity equal to that of vertebrates; however, the underlying neural mechanisms and coding schemes are only partially understood. In this study, we analyze the response characteristics of the peripheral auditory system of grasshoppers with special emphasis on the representation of species-specific communication signals. We use both natural calling songs and artificial random stimuli designed to focus on two low-order statistical properties of the songs: their typical time scales and the distribution of their modulation amplitudes. Based on stimulus reconstruction techniques and quantified within an information-theoretic framework, our data show that artificial stimuli with typical time scales of >40 msec can be read from single spike trains with high accuracy. Faster stimulus variations can be reconstructed only for behaviorally relevant amplitude distributions. The highest rates of information transmission (180 bits/sec) and the highest coding efficiencies (40%) are obtained for stimuli that capture both the time scales and amplitude distributions of natural songs. Use of multiple spike trains significantly improves the reconstruction of stimuli that vary on time scales <40 msec or feature amplitude distributions as occur when several grasshopper songs overlap. Signal-to-noise ratios obtained from the reconstructions of natural songs do not exceed those obtained from artificial stimuli with the same low-order statistical properties. We conclude that auditory receptor neurons are optimized to extract both the time scales and the amplitude distribution of natural songs. They are not optimized, however, to extract higher-order statistical properties of the song-specific rhythmic patterns

Stochastic resonance in electrical circuits—II: Nonconventional stochastic resonance.

Stochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treate

Outlook for detection of GW inspirals by GRB-triggered searches in the Advanced detector era

Short, hard gamma-ray bursts (GRBs) are believed to originate from the coalescence of two neutron stars (NSs) or a NS and a black hole (BH). If this scenario is correct, then short GRBs will be accompanied by the emission of strong gravitational waves (GWs), detectable by GW observatories such as LIGO, Virgo, KAGRA, and LIGO-India. As compared with blind, all-sky, all-time GW searches, externally triggered searches for GW counterparts to short GRBs have the advantages of both significantly reduced detection threshold due to known time and sky location and enhanced GW amplitude because of face-on orientation. Based on the distribution of signal-to-noise ratios in candidate compact binary coalescence events in the most recent joint LIGO-Virgo data, our analytic estimates, and our Monte Carlo simulations, we find an effective sensitive volume for GRB-triggered searches that is about 2 times greater than for an all-sky, all-time search. For NS-NS systems, a jet angle of 20 degrees, a gamma-ray satellite field of view of 10% of the sky, and priors with generally precessing spin, this doubles the number of NS-NS short-GRB and NS-BH short-GRB associations, to ~3-4% of all detections of NS-NSs and NS-BHs. We also investigate the power of tests for statistical excesses in lists of subthreshold events, and show that these are unlikely to reveal a subthreshold population until finding GW associations to short GRBs is already routine. Finally, we provide useful formulas for calculating the prior distribution of GW amplitudes from a compact binary coalescence, for a given GW detector network and given sky location.Comment: 14 pages, 4 figures, published in PRD; this version includes changes in final copyedited articl

Environmental Noise and Nonlinear Relaxation in Biological Systems

We analyse the effects of environmental noise in three different biological systems: (i) mating behaviour of individuals of \emph{Nezara viridula} (L.) (Heteroptera Pentatomidae); (ii) polymer translocation in crowded solution; (iii) an ecosystem described by a Verhulst model with a multiplicative L\'{e}vy noise.Comment: 32 pages; In "Ecological Modeling" by Ed. Wen-Jun Zhang. ISBN: 978-1-61324-567-5. - Nova Science Publishers, New York, 201

What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations—e.g., random noise—cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being “suboptimal”. Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significantly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the “neural code”. Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise—via stochastic resonance or otherwise—than if it did. We also challenge neuroscientists and biologists, both computational and experimental, to embrace a very broad definition of stochastic resonance in terms of signal-processing “noise benefits”, and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology