Optimal stimulus and noise distributions for information transmission via suprathreshold stochastic resonance

Sensory white noise improves reading skills and memory recall in children with reading disability

BACKGROUND

Reading disability (RD) is characterized by slow and inaccurate word reading development, commonly reflecting underlying phonological problems. We have previously shown that exposure to white noise acutely improves cognitive performance in children with ADHD. The question addressed here is whether white noise exposure yields positive outcomes also for RD. There are theoretical reasons to expect such a possibility: a) RD and ADHD are two overlapping neurodevelopmental disorders and b) since prior research on white noise benefits has suggested that a central mechanism might be the phenomenon of stochastic resonance, then adding certain kinds of white noise might strengthen the signal-to-noise ratio during phonological processing and phoneme-grapheme mapping.

METHODS

The study was conducted with a group of 30 children with RD and phonological decoding difficulties and two comparison groups: one consisting of skilled readers (n = 22) and another of children with mild orthographic reading problems and age adequate phonological decoding (n = 30). White noise was presented experimentally in visual and auditory modalities, while the children performed tests of single word reading, orthographic word recognition, nonword reading, and memory recall.

RESULTS

For the first time, we show that visual and auditory white noise exposure improves some reading and memory capacities "on the fly" in children with RD and phonological decoding difficulties. By contrast, the comparison groups displayed either no benefit or a gradual decrease in performance with increasing noise. In interviews, we also found that the white noise exposure was tolerable or even preferred by many children.

CONCLUSION

These novel findings suggest that poor readers with phonological decoding difficulties may be immediately helped by white noise during reading. Future research is needed to determine the robustness, mechanisms, and long-term practical implications of the white noise benefits in children with reading disabilities.

Stochastic resonance and 'gamma band' synchronization in the human visual system

Cortical synchronization in the gamma-frequency range (above ~30.0 Hz) and the signal/noise interplay described by stochastic resonance models have been proposed as basic mechanisms in neuronal synchronization and sensory information processing, particularly in vision. Here we report an observation in humans of linear and inverted-U distributions of the electrophysiological (EEG) responses to visual contrast stimulation in the gamma band and in the low frequency components of the visual evoked responses (VER), respectively. The combination of linear and inverted-U distributions is described by a stochastic resonance model (SR). The observation needs replication in larger subjects' samples. It nevertheless adds to the available evidence of a role of gamma oscillatory signals and SR mechanisms in neuronal synchronization and visual processing. Some functional adaptation in human vision appears conceivable and further investigation is warranted.

Efficient sampling and noisy decisions

Human decisions are based on finite information, which makes them inherently imprecise. But what determines the degree of such imprecision? Here, we develop an efficient coding framework for higher-level cognitive processes in which information is represented by a finite number of discrete samples. We characterize the sampling process that maximizes perceptual accuracy or fitness under the often-adopted assumption that full adaptation to an environmental distribution is possible, and show how the optimal process differs when detailed information about the current contextual distribution is costly. We tested this theory on a numerosity discrimination task, and found that humans efficiently adapt to contextual distributions, but in the way predicted by the model in which people must economize on environmental information. Thus, understanding decision behavior requires that we account for biological restrictions on information coding, challenging the often-adopted assumption of precise prior knowledge in higher-level decision systems.

Noise Enhanced Signal Detection of Variable Detectors under Certain Constraints

In this paper, a noise enhanced binary hypothesis-testing problem was studied for a variable detector under certain constraints in which the detection probability can be increased and the false-alarm probability can be decreased simultaneously. According to the constraints, three alternative cases are proposed, the first two cases concerned minimization of the false-alarm probability and maximization of the detection probability without deterioration of one by the other, respectively, and the third case was achieved by a randomization of two optimal noise enhanced solutions obtained in the first two limit cases. Furthermore, the noise enhanced solutions that satisfy the three cases were determined whether randomization between different detectors was allowed or not. In addition, the practicality of the third case was proven from the perspective of Bayes risk. Finally, numerous examples and conclusions are presented.

Coding of time-dependent stimuli in homogeneous and heterogeneous neural populations

We compare the information transmission of a time-dependent signal by two types of uncoupled neuron populations that differ in their sources of variability: i) a homogeneous population whose units receive independent noise and ii) a deterministic heterogeneous population, where each unit exhibits a different baseline firing rate ('disorder'). Our criterion for making both sources of variability quantitatively comparable is that the interspike-interval distributions are identical for both systems. Numerical simulations using leaky integrate-and-fire neurons unveil that a non-zero amount of both noise or disorder maximizes the encoding efficiency of the homogeneous and heterogeneous system, respectively, as a particular case of suprathreshold stochastic resonance. Our findings thus illustrate that heterogeneity can render similarly profitable effects for neuronal populations as dynamic noise. The optimal noise/disorder depends on the system size and the properties of the stimulus such as its intensity or cutoff frequency. We find that weak stimuli are better encoded by a noiseless heterogeneous population, whereas for strong stimuli a homogeneous population outperforms an equivalent heterogeneous system up to a moderate noise level. Furthermore, we derive analytical expressions of the coherence function for the cases of very strong noise and of vanishing intrinsic noise or heterogeneity, which predict the existence of an optimal noise intensity. Our results show that, depending on the type of signal, noise as well as heterogeneity can enhance the encoding performance of neuronal populations.

Energy-efficient neural information processing in individual neurons and neuronal networks

Brains are composed of networks of an enormous number of neurons interconnected with synapses. Neural information is carried by the electrical signals within neurons and the chemical signals among neurons. Generating these electrical and chemical signals is metabolically expensive. The fundamental issue raised here is whether brains have evolved efficient ways of developing an energy-efficient neural code from the molecular level to the circuit level. Here, we summarize the factors and biophysical mechanisms that could contribute to the energy-efficient neural code for processing input signals. The factors range from ion channel kinetics, body temperature, axonal propagation of action potentials, low-probability release of synaptic neurotransmitters, optimal input and noise, the size of neurons and neuronal clusters, excitation/inhibition balance, coding strategy, cortical wiring, and the organization of functional connectivity. Both experimental and computational evidence suggests that neural systems may use these factors to maximize the efficiency of energy consumption in processing neural signals. Studies indicate that efficient energy utilization may be universal in neuronal systems as an evolutionary consequence of the pressure of limited energy. As a result, neuronal connections may be wired in a highly economical manner to lower energy costs and space. Individual neurons within a network may encode independent stimulus components to allow a minimal number of neurons to represent whole stimulus characteristics efficiently. This basic principle may fundamentally change our view of how billions of neurons organize themselves into complex circuits to operate and generate the most powerful intelligent cognition in nature. © 2017 Wiley Periodicals, Inc.

The Role of Visual Noise in Influencing Mental Load and Fatigue in a Steady-State Motion Visual Evoked Potential-Based Brain-Computer Interface

As a spatial selective attention-based brain-computer interface (BCI) paradigm, steady-state visual evoked potential (SSVEP) BCI has the advantages of high information transfer rate, high tolerance to artifacts, and robust performance across users. However, its benefits come at the cost of mental load and fatigue occurring in the concentration on the visual stimuli. Noise, as a ubiquitous random perturbation with the power of randomness, may be exploited by the human visual system to enhance higher-level brain functions. In this study, a novel steady-state motion visual evoked potential (SSMVEP, i.e., one kind of SSVEP)-based BCI paradigm with spatiotemporal visual noise was used to investigate the influence of noise on the compensation of mental load and fatigue deterioration during prolonged attention tasks. Changes in α, θ, θ + α powers, θ/α ratio, and electroencephalography (EEG) properties of amplitude, signal-to-noise ratio (SNR), and online accuracy, were used to evaluate mental load and fatigue. We showed that presenting a moderate visual noise to participants could reliably alleviate the mental load and fatigue during online operation of visual BCI that places demands on the attentional processes. This demonstrated that noise could provide a superior solution to the implementation of visual attention controlling-based BCI applications.

Comparing Auditory Noise Treatment with Stimulant Medication on Cognitive Task Performance in Children with Attention Deficit Hyperactivity Disorder: Results from a Pilot Study

Background: Recent research has shown that acoustic white noise (80 dB) can improve task performance in people with attention deficits and/or Attention Deficit Hyperactivity Disorder (ADHD). This is attributed to the phenomenon of stochastic resonance in which a certain amount of noise can improve performance in a brain that is not working at its optimum. We compare here the effect of noise exposure with the effect of stimulant medication on cognitive task performance in ADHD. The aim of the present study was to compare the effects of auditory noise exposure with stimulant medication for ADHD children on a cognitive test battery. A group of typically developed children (TDC) took the same tests as a comparison.

Methods: Twenty children with ADHD of combined or inattentive subtypes and twenty TDC matched for age and gender performed three different tests (word recall, spanboard and n-back task) during exposure to white noise (80 dB) and in a silent condition. The ADHD children were tested with and without central stimulant medication.

Results: In the spanboard- and the word recall tasks, but not in the 2-back task, white noise exposure led to significant improvements for both non-medicated and medicated ADHD children. No significant effects of medication were found on any of the three tasks.

Conclusion: This pilot study shows that exposure to white noise resulted in a task improvement that was larger than the one with stimulant medication thus opening up the possibility of using auditory noise as an alternative, non-pharmacological treatment of cognitive ADHD symptoms.

Differences in Speech Recognition Between Children with Attention Deficits and Typically Developed Children Disappear When Exposed to 65 dB of Auditory Noise

The most common neuropsychiatric condition in the in children is attention deficit hyperactivity disorder (ADHD), affecting ∼6–9% of the population. ADHD is distinguished by inattention and hyperactive, impulsive behaviors as well as poor performance in various cognitive tasks often leading to failures at school. Sensory and perceptual dysfunctions have also been noticed. Prior research has mainly focused on limitations in executive functioning where differences are often explained by deficits in pre-frontal cortex activation. Less notice has been given to sensory perception and subcortical functioning in ADHD. Recent research has shown that children with ADHD diagnosis have a deviant auditory brain stem response compared to healthy controls. The aim of the present study was to investigate if the speech recognition threshold differs between attentive and children with ADHD symptoms in two environmental sound conditions, with and without external noise. Previous research has namely shown that children with attention deficits can benefit from white noise exposure during cognitive tasks and here we investigate if noise benefit is present during an auditory perceptual task. For this purpose we used a modified Hagerman’s speech recognition test where children with and without attention deficits performed a binaural speech recognition task to assess the speech recognition threshold in no noise and noise conditions (65 dB). Results showed that the inattentive group displayed a higher speech recognition threshold than typically developed children and that the difference in speech recognition threshold disappeared when exposed to noise at supra threshold level. From this we conclude that inattention can partly be explained by sensory perceptual limitations that can possibly be ameliorated through noise exposure.

Energy-efficient population coding constrains network size of a neuronal array system

We consider the open issue of how the energy efficiency of the neural information transmission process, in a general neuronal array, constrains the network size, and how well this network size ensures the reliable transmission of neural information in a noisy environment. By direct mathematical analysis, we have obtained general solutions proving that there exists an optimal number of neurons in the network, where the average coding energy cost (defined as energy consumption divided by mutual information) per neuron passes through a global minimum for both subthreshold and superthreshold signals. With increases in background noise intensity, the optimal neuronal number decreases for subthreshold signals and increases for suprathreshold signals. The existence of an optimal number of neurons in an array network reveals a general rule for population coding that states that the neuronal number should be large enough to ensure reliable information transmission that is robust to the noisy environment but small enough to minimize energy cost.

Enhanced brain signal variability in children with autism spectrum disorder during early childhood

Extensive evidence shows that a core neurobiological mechanism of autism spectrum disorder (ASD) involves aberrant neural connectivity. Recent advances in the investigation of brain signal variability have yielded important information about neural network mechanisms. That information has been applied fruitfully to the assessment of aging and mental disorders. Multiscale entropy (MSE) analysis can characterize the complexity inherent in brain signal dynamics over multiple temporal scales in the dynamics of neural networks. For this investigation, we sought to characterize the magnetoencephalography (MEG) signal variability during free watching of videos without sound using MSE in 43 children with ASD and 72 typically developing controls (TD), emphasizing early childhood to older childhood: a critical period of neural network maturation. Results revealed an age‐related increase of brain signal variability in a specific timescale in TD children, whereas atypical age‐related alteration was observed in the ASD group. Additionally, enhanced brain signal variability was observed in children with ASD, and was confirmed particularly for younger children. In the ASD group, symptom severity was associated region‐specifically and timescale‐specifically with reduced brain signal variability. These results agree well with a recently reported theory of increased brain signal variability during development and aberrant neural connectivity in ASD, especially during early childhood. Results of this study suggest that MSE analytic method might serve as a useful approach for characterizing neurophysiological mechanisms of typical‐developing and its alterations in ASD through the detection of MEG signal variability at multiple timescales. Hum Brain Mapp 37:1038–1050, 2016. © 2015 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Different effects of adding white noise on cognitive performance of sub-, normal and super-attentive school children

OBJECTIVES

Noise often has detrimental effects on performance. However, because of the phenomenon of stochastic resonance (SR), auditory white noise (WN) can alter the "signal to noise" ratio and improve performance. The Moderate Brain Arousal (MBA) model postulates different levels of internal "neural noise" in individuals with different attentional capacities. This in turn determines the particular WN level most beneficial in each individual case-with one level of WN facilitating poor attenders but hindering super-attentive children. The objective of the present study is to find out if added WN affects cognitive performance differently in children that differ in attention ability.

METHODS

Participants were teacher-rated super- (N = 25); normal- (N = 29) and sub-attentive (N = 36) children (aged 8 to 10 years). Two non-executive function (EF) tasks (a verbal episodic recall task and a delayed verbal recognition task) and two EF tasks (a visuo-spatial working memory test and a Go-NoGo task) were performed under three WN levels. The non-WN condition was only used to control for potential differences in background noise in the group testing situations.

RESULTS

There were different effects of WN on performance in the three groups-adding moderate WN worsened the performance of super-attentive children for both task types and improved EF performance in sub-attentive children. The normal-attentive children's performance was unaffected by WN exposure. The shift from moderate to high levels of WN had little further effect on performance in any group.

SIGNIFICANCE

The predicted differential effect of WN on performance was confirmed. However, the failure to find evidence for an inverted U function challenges current theories. Alternative explanations are discussed. We propose that WN therapy should be further investigated as a possible non-pharmacological treatment for inattention.

Noise-enhanced nonlinear response and the role of modular structure for signal detection in neuronal networks

We show that sensory noise can enhance the nonlinear response of neuronal networks, and when delivered together with a weak signal, it improves the signal detection by the network. We reveal this phenomenon in neuronal networks that are in a dynamical state preceding a saddle-node bifurcation corresponding to the appearance of sustained network oscillations. In this state, even a weak subthreshold pulse can evoke a large-amplitude oscillation of neuronal activity. The signal-to-noise ratio reaches a maximum at an optimum level of sensory noise, manifesting stochastic resonance (SR) at the population level. We demonstrate SR by use of simulations and numerical integration of rate equations in a cortical model. Using this model, we mimic the experiments of Gluckman et al. [Phys. Rev. Lett. 77, 4098 (1996)PRLTAO0031-900710.1103/PhysRevLett.77.4098] that have given evidence of SR in mammalian brain. We also study neuronal networks in which neurons are grouped in modules and every module works in the regime of SR. We find that even a few modules can strongly enhance the reliability of signal detection in comparison with the case when a modular organization is absent.

Channel-noise-induced stochastic facilitation in an auditory brainstem neuron model

Neuronal membrane potentials fluctuate stochastically due to conductance changes caused by random transitions between the open and closed states of ion channels. Although it has previously been shown that channel noise can nontrivially affect neuronal dynamics, it is unknown whether ion-channel noise is strong enough to act as a noise source for hypothesized noise-enhanced information processing in real neuronal systems, i.e., "stochastic facilitation". Here we demonstrate that biophysical models of channel noise can give rise to two kinds of recently discovered stochastic facilitation effects in a Hodgkin-Huxley-like model of auditory brainstem neurons. The first, known as slope-based stochastic resonance (SBSR), enables phasic neurons to emit action potentials that can encode the slope of inputs that vary slowly relative to key time constants in the model. The second, known as inverse stochastic resonance (ISR), occurs in tonically firing neurons when small levels of noise inhibit tonic firing and replace it with burstlike dynamics. Consistent with previous work, we conclude that channel noise can provide significant variability in firing dynamics, even for large numbers of channels. Moreover, our results show that possible associated computational benefits may occur due to channel noise in neurons of the auditory brainstem. This holds whether the firing dynamics in the model are phasic (SBSR can occur due to channel noise) or tonic (ISR can occur due to channel noise).

Control strategies for underactuated neural ensembles driven by optogenetic stimulation

Motivated by experiments employing optogenetic stimulation of cortical regions, we consider spike control strategies for ensembles of uncoupled integrate and fire neurons with a common conductance input. We construct strategies for control of spike patterns, that is, multineuron trains of action potentials, up to some maximal spike rate determined by the neural biophysics. We emphasize a constructive role for parameter heterogeneity, and find a simple rule for controllability in pairs of neurons. In particular, we determine parameters for which common drive is not limited to inducing synchronous spiking. For large ensembles, we determine how the number of controllable neurons varies with the number of observed (recorded) neurons, and what collateral spiking occurs in the full ensemble during control of the subensemble. While complete control of spiking in every neuron is not possible with a single input, we find that a degree of subensemble control is made possible by exploiting dynamical heterogeneity. As most available technologies for neural stimulation are underactuated, in the sense that the number of target neurons far exceeds the number of independent channels of stimulation, these results suggest partial control strategies that may be important in the development of sensory neuroprosthetics and other neurocontrol applications.

Growth of stochastic resonance in neuronal ensembles with the input signal intensity

The presence of noise can improve the response of certain nonlinear systems to input signals through the effects of stochastic resonance (SR). The optimal noise intensity for SR is proportional to the signal frequency if the signal is periodic, but proportional to the signal intensity if the signal is aperiodic. Here, we demonstrate using linear response theory that the optimal noise intensity for SR is necessarily dependent on the signal intensity even if the signal is periodic. We also demonstrate that the SR curves grow according to the signal intensity from a bell-shaped curve to a plateau, resulting in the emergence of SR without tuning. In particular, we present a theoretical analysis indicating that the SR peak shifts with the signal intensity due to the scaling of the stationary neuronal firings. The growth of SR may serve as a useful design principle for many noise-exploiting applications.

The effects of background white noise on memory performance in inattentive school children

Background

Noise is typically conceived of as being detrimental for cognitive performance; however, a recent computational model based on the concepts of stochastic resonance and dopamine related internal noise postulates that a moderate amount of auditive noise benefit individuals in hypodopaminergic states. On the basis of this model we predicted that inattentive children would be enhanced by adding background white noise while attentive children's performance would deteriorate.

Methods

Fifty-one secondary school pupils carried out an episodic verbal free recall test in two noise conditions. In the high noise condition, verb-noun sentences were presented during auditory background noise (white noise, 78 dB), and in the low noise condition sentences were presented without noise.

Results

Exposure to background noise improved performance for inattentive children and worsened performance for attentive children and eliminated episodic memory differences between attentive and inattentive school children.

Conclusions

Consistent with the model, our data show that cognitive performance can be moderated by external background white noise stimulation in a non-clinical group of inattentive participants. This finding needs replicating in a larger sample using more noise levels but if replicated has great practical applications by offering a non-invasive way to improve school results in children with attentional problems.

Signal acquisition via polarization modulation in single photon sources

A simple model system is introduced for demonstrating how a single photon source might be used to transduce classical analog information. The theoretical scheme results in measurements of analog source samples that are (i) quantized in the sense of analog-to-digital conversion and (ii) corrupted by random noise that is solely due to the quantum uncertainty in detecting the polarization state of each photon. This noise is unavoidable if more than 1 bit per sample is to be transmitted and we show how it may be exploited in a manner inspired by suprathreshold stochastic resonance. The system is analyzed information theoretically, as it can be modeled as a noisy optical communication channel, although unlike classical Poisson channels, the detector's photon statistics are binomial. Previous results on binomial channels are adapted to demonstrate numerically that the classical information capacity, and thus the accuracy of the transduction, increases logarithmically with the square root of the number of photons, N. Although the capacity is shown to be reduced when an additional detector nonideality is present, the logarithmic increase with N remains.

Information capacity of stochastic pooling networks is achieved by discrete inputs

Stochastic pooling networks (SPN) are sensor networks where multiple sensors make independently noisy and compressed measurements of the same information source, which are combined via pooling. Examples of SPNs range from nanoelectronics to biological sensory neurons. Here it is shown that optimal information transmission in SPNs with nodes that quantize to a finite number of states requires the input signal distribution to be discrete. This is illustrated numerically for a simple SPN consisting of N binary-quantizing sensors. The resultant information capacity is shown to be independent of the noise distribution when the signal distribution can be freely chosen, but to imply an optimal noise distribution if the signal distribution is fixed. While larger than the best performance of previously studied continuously valued input signals, the capacity does not scale faster than the previous best result of log_{2}(sqrt[N]) bits per channel use. It is also shown that a plot of the optimal input distribution contains bifurcations as N increases, and that suprathreshold stochastic resonance occurs when the mutual information is determined for a suboptimal noise distribution.

Maximally informative stimuli and tuning curves for sigmoidal rate-coding neurons and populations

A general method for deriving maximally informative sigmoidal tuning curves for neural systems with small normalized variability is presented. The optimal tuning curve is a nonlinear function of the cumulative distribution function of the stimulus and depends on the mean-variance relationship of the neural system. The derivation is based on a known relationship between Shannon's mutual information and Fisher information, and the optimality of Jeffrey's prior. It relies on the existence of closed-form solutions to the converse problem of optimizing the stimulus distribution for a given tuning curve. It is shown that maximum mutual information corresponds to constant Fisher information only if the stimulus is uniformly distributed. As an example, the case of sub-Poisson binomial firing statistics is analyzed in detail.