Stochastic resonance in a single neuron model: theory and analog simulation

Non-invasive brain stimulation and vision rehabilitation: a clinical perspective

Non-invasive brain stimulation techniques allow targeted modulation of brain regions and have emerged as a promising tool for vision rehabilitation. This review presents an overview of studies that have examined the use of non-invasive brain stimulation techniques for improving vision and visual functions. A description of the proposed neural mechanisms that underpin non-invasive brain stimulation effects is also provided. The clinical implications of non-invasive brain stimulation in vision rehabilitation are examined, including their safety, effectiveness, and potential applications in specific conditions such as amblyopia, post-stroke hemianopia, and central vision loss associated with age-related macular degeneration. Additionally, the future directions of research in this field are considered, including the need for larger and more rigorous clinical trials to validate the efficacy of these techniques. Overall, this review highlights the potential for brain stimulation techniques as a promising avenue for improving visual function in individuals with impaired vision and underscores the importance of continued research in this field.

Role of asymmetry and external noise in the development and synchronization of oscillations in the analog Hopfield neural networks with time delay

The analog Hopfield neural network with time delay and random connections has been studied for its similarities in activity to human electroencephalogram and its usefulness in other areas of the applied sciences such as speech recognition, image analysis, and electrocardiogram modeling. Our goal here is to understand the mechanisms that affect the rhythmic activity in the neural network and how the addition of a Gaussian noise contributes to the network behavior. The neural network studied is composed of ten identical neurons. We investigated the excitatory and inhibitory networks with symmetric (square matrix) and asymmetric (triangular matrix) connections. The differential equations that model the network are solved numerically using the stochastic second-order Runge-Kutta method. Without noise, the neural networks with symmetric and asymmetric matrices possessed different synchronization properties: fully connected networks were synchronized both in time and in amplitude, while asymmetric networks were synchronized in time only. Saturation outputs of the excitatory neural networks do not depend on the time delay, whereas saturation oscillation amplitudes of inhibitory networks increase with the time delay until the steady state. The addition of the Gaussian noise is shown to significantly amplify small-amplitude oscillations, dramatically accelerates the rate of amplitude growth to saturation, and changes synchronization properties of the neural network outputs.

How synaptic strength, short-term plasticity, and input synchrony contribute to neuronal spike output

Neurons integrate from thousands of synapses whose strengths span an order of magnitude. Intriguingly, in mouse neocortex, the few 'strong' synapses are formed between similarly tuned cells, suggesting they determine spiking output. This raises the question of how other computational primitives, including 'background' activity from the many 'weak' synapses, short-term plasticity, and temporal factors contribute to spiking. We used paired recordings and extracellular stimulation experiments to map excitatory postsynaptic potential (EPSP) amplitudes and paired-pulse ratios of synaptic connections formed between pyramidal neurons in layer 2/3 (L2/3) of barrel cortex. While net short-term plasticity was weak, strong synaptic connections were exclusively depressing. Importantly, we found no evidence for clustering of synaptic properties on individual neurons. Instead, EPSPs and paired-pulse ratios of connections converging onto the same cells spanned the full range observed across L2/3, which critically constrains theoretical models of cortical filtering. To investigate how different computational primitives of synaptic information processing interact to shape spiking, we developed a computational model of a pyramidal neuron in the excitatory L2/3 circuitry, which was constrained by our experiments and published in vivo data. We found that strong synapses were substantially depressed during ongoing activation and their ability to evoke correlated spiking primarily depended on their high temporal synchrony and high firing rates observed in vivo. However, despite this depression, their larger EPSP amplitudes strongly amplified information transfer and responsiveness. Thus, our results contribute to a nuanced framework of how cortical neurons exploit synergies between temporal coding, synaptic properties, and noise to transform synaptic inputs into spikes.

Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter P, which controls STDP, on the characteristic rewiring frequency parameter F, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing P (which enhances the weakening effect of STDP on synaptic weights) and decreasing F (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter τ_{c} has some appropriate values. (ii) Increasing the synaptic time delay τ_{c} induces multiple CR (MCR)-the occurrence of multiple peaks in the degree of coherence as τ_{c} changes-in small-world and random networks, with MCR becoming more pronounced at smaller values of P and F. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

Dynamic peripheral nerve stimulation can produce cortical activation similar to punctate mechanical stimuli

During contact, phasic and tonic responses provide feedback that is used for task performance and perceptual processes. These disparate temporal dynamics are carried in peripheral nerves, and produce overlapping signals in cortex. Using longitudinal intrafascicular electrodes inserted into the median nerve of a nonhuman primate, we delivered composite stimulation consisting of onset and release bursts to capture rapidly adapting responses and sustained stochastic stimulation to capture the ongoing response of slowly adapting receptors. To measure the stimulation's effectiveness in producing natural responses, we monitored the local field potential in somatosensory cortex. We compared the cortical responses to peripheral nerve stimulation and vibrotactile/punctate stimulation of the fingertip, with particular focus on gamma band (30-65 Hz) responses. We found that vibrotactile stimulation produces consistently phase locked gamma throughout the duration of the stimulation. By contrast, punctate stimulation responses were phase locked at the onset and release of stimulation, but activity maintained through the stimulation was not phase locked. Using these responses as guideposts for assessing the response to the peripheral nerve stimulation, we found that constant frequency stimulation produced continual phase locking, whereas composite stimulation produced gamma enhancement throughout the stimulus, phase locked only at the onset and release of the stimulus. We describe this response as an "Appropriate Response in the gamma band" (ARγ), a trend seen in other sensory systems. Our demonstration is the first shown for intracortical somatosensory local field potentials. We argue that this stimulation paradigm produces a more biomimetic response in somatosensory cortex and is more likely to produce naturalistic sensations for readily usable neuroprosthetic feedback.

Auditory, tactile, and multimodal noise reduce balance variability

Auditory and somatosensory white noise can stabilize standing balance. However, the differential effects of auditory and tactile noise stimulation on balance are unknown. Prior work on unimodal noise stimulation showed gains in balance with white noise through the auditory and tactile modalities separately. The current study aims to examine whether multimodal noise elicits similar responses to unimodal noise. We recorded the postural sway of healthy young adults who were presented with continuous white noise through the auditory or tactile modalities and through a combination of both (multimodal condition) using a wearable device. Our results replicate previous work that showed that auditory or tactile noise reduces sway variability with and without vision. Additionally, we show that multimodal noise also reduces the variability of sway. Analysis of different frequency bands of sway is typically used to separate open-loop exploratory (< 0.3 Hz) and feedback-driven (> 0.3 Hz) sway. We performed this analysis and showed that unimodal and multimodal white noise affected postural sway variability similarly in both timescales. These results support that the sensory noise effects on balance are robust across unimodal and multimodal conditions and can affect both mechanisms of sway represented in the frequency spectrum. In future work, the parameters of acoustic/tactile manipulation should be optimized for the most effective balance stabilization, and multimodal therapies should be explored for older adults with typical age-related balance instabilities.

Pulse-frequency-dependent resonance in a population of pyramidal neuron models

Stochastic resonance is known as a phenomenon whereby information transmission of weak signal or subthreshold stimuli can be enhanced by additive random noise with a suitable intensity. Another phenomenon induced by applying deterministic pulsatile electric stimuli with a pulse frequency, commonly used for deep brain stimulation (DBS), was also shown to improve signal-to-noise ratio in neuron models. The objective of this study was to test the hypothesis that pulsatile high-frequency stimulation could improve the detection of both sub- and suprathreshold synaptic stimuli by tuning the frequency of the stimulation in a population of pyramidal neuron models. Computer simulations showed that mutual information estimated from a population of neural spike trains displayed a typical resonance curve with a peak value of the pulse frequency at 80-120 Hz, similar to those utilized for DBS in clinical situations. It is concluded that a "pulse-frequency-dependent resonance" (PFDR) can enhance information transmission over a broad range of synaptically connected networks. Since the resonance frequency matches that used clinically, PFDR could contribute to the mechanism of the therapeutic effect of DBS.

Correlation Technologies for Emerging Wireless Applications

In this article, we introduce correlation technologies both at RF/mmWave and baseband frequencies. At RF and mmWave frequencies, power-spectra and energy-spectra metrics are introduced for measuring the power-density of mobile devices and systems. New ASIC-embedded smart connectors are developed for bringing correlation-based signal processing close to antenna modules. At baseband frequencies, DSP-based convolutional accelerators are proposed for fast and accurate measurement of EVM (error vector magnitude) using correlation technologies. Porting of the DSP-based convolutional accelerators into advanced fully depleted silicon-on-insulator (FDSOI)-based ASIC platforms for co-integration with adaptive RF/mmWave front-end modules will enable real-time extraction of auto-correlation and cross-correlation functions of stochastic signals. Perspectives for optically synchronized interferometric-correlation technologies are drawn for accurate measurements in noisy environments of stochastic EM fields using power-spectra and energy-spectra metrics. Adoption of correlation technologies will foster new paradigms relative to interactions of humans with smart devices and systems in randomly fluctuating environments. The resulting new paradigms will open new possibilities in communication theory for properly combining and reconciling information signal theory (Shannon information-based entropy) and physical information theory (statistical-physics-based entropy) into a unified framework.

When Noise meets Chaos: Stochastic Resonance in Neurochaos Learning

Chaos and Noise are ubiquitous in the Brain. Inspired by the chaotic firing of neurons and the constructive role of noise in neuronal models, we for the first time connect chaos, noise and learning. In this paper, we demonstrate Stochastic Resonance (SR) phenomenon in Neurochaos Learning (NL). SR manifests at the level of a single neuron of NL and enables efficient subthreshold signal detection. Furthermore, SR is shown to occur in single and multiple neuronal NL architecture for classification tasks - both on simulated and real-world spoken digit datasets, and in architectures with 1D chaotic maps as well as Hindmarsh-Rose spiking neurons. Intermediate levels of noise in neurochaos learning enable peak performance in classification tasks thus highlighting the role of SR in AI applications, especially in brain inspired learning architectures.

Necessary Conditions for Reliable Propagation of Slowly Time-Varying Firing Rate

Reliable propagation of slow-modulations of the firing rate across multiple layers of a feedforward network (FFN) has proven difficult to capture in spiking neural models. In this paper, we explore necessary conditions for reliable and stable propagation of time-varying asynchronous spikes whose instantaneous rate of changes-in fairly short time windows [20-100] msec-represents information of slow fluctuations of the stimulus. Specifically, we study the effect of network size, level of background synaptic noise, and the variability of synaptic delays in an FFN with all-to-all connectivity. We show that network size and the level of background synaptic noise, together with the strength of synapses, are substantial factors enabling the propagation of asynchronous spikes in deep layers of an FFN. In contrast, the variability of synaptic delays has a minor effect on signal propagation.

Mechanisms underlying gain modulation in the cortex

Cortical gain regulation allows neurons to respond adaptively to changing inputs. Neural gain is modulated by internal and external influences, including attentional and arousal states, motor activity and neuromodulatory input. These influences converge to a common set of mechanisms for gain modulation, including GABAergic inhibition, synaptically driven fluctuations in membrane potential, changes in cellular conductance and changes in other biophysical neural properties. Recent work has identified GABAergic interneurons as targets of neuromodulatory input and mediators of state-dependent gain modulation. Here, we review the engagement and effects of gain modulation in the cortex. We highlight key recent findings that link phenomenological observations of gain modulation to underlying cellular and circuit-level mechanisms. Finally, we place these cellular and circuit interactions in the larger context of their impact on perception and cognition.

Multiplicative noise is beneficial for the transmission of sensory signals in simple neuron models

We study simple integrate-and-fire type models with multiplicative noise and consider the transmission of a weak and slow signal, i.e. a signal that evokes a small modulation of the instantaneous firing rate on time scales that are much larger than the membrane time scale and the mean interspike interval. The specific question of interest is whether and how the state-dependence of the noise can be optimized with respect to information transmission. First, in a simple model in which the noise intensity varies linearly with the state variable, we show analytically that multiplicative fluctuations may benefit the signal transfer and we elucidate the mechanism for this improvement. In a conductance-based integrate-and-fire model with synaptically filtered shot-noise input, we show by means of extended numerical simulations that also in a biophysically more relevant situation, multiplicative noise can enhance the signal-to-noise ratio. Our results shed light on a so far unexplored aspect of stochastic signal transmission in neural systems.

Random pulse induced synchronization and resonance in uncoupled non-identical neuron models

Random pulses contribute to stochastic resonance in neuron models, whereas common random pulses cause stochastic-synchronized excitation in uncoupled neuron models. We studied concurrent phenomena contributing to phase synchronization and stochastic resonance following induction by a weak common random pulse in uncoupled non-identical Hodgkin-Huxley type neuron models. The common random pulse was selected from a gamma distribution and the degree of synchronization depended on the corresponding shape parameter. Specifically, a low shape parameter of the weak random pulse induced well-synchronized spiking in uncoupled neuron models, whereas a high shape parameter of the weak random pulse or a weak periodic pulse caused low degrees of synchronization. These were improved by concurrent inputs of periodic and random pulses with high shape parameters. Finally, the output pulse was synchronized with the periodic pulse, and the common random pulse revealed periodic responses in the present neuron models.

Modeling effects of neural fluctuations and inter-scale interactions

One of the greatest challenges to science, in particular, to neuroscience, is to understand how processes at different levels of organization are related to each other. In connection with this problem is the question of the functional significance of fluctuations, noise, and chaos. This paper deals with three related issues: (1) how processes at different organizational levels of neural systems might be related, (2) the functional significance of non-linear neurodynamics, including oscillations, chaos, and noise, and (3) how computational models can serve as useful tools in elucidating these types of issues. In order to capture and describe phenomena at different micro (molecular), meso (cellular), and macro (network) scales, the computational models need to be of appropriate complexity making use of available experimental data. I exemplify by two major types of computational models, those of Hans Braun and colleagues and those of my own group, which both aim at bridging gaps between different levels of neural systems. In particular, the constructive role of noise and chaos in such systems is modelled and related to functions, such as sensation, perception, learning/memory, decision making, and transitions between different (un-)conscious states. While there is, in general, a focus on upward causation, I will also discuss downward causation, where higher level activity may affect the activity at lower levels, which should be a condition for any functional role of consciousness and free will, often considered to be problematic to science.

On the complex dynamics of savanna landscapes

Simple mathematical models can exhibit rich and complex behaviors. Prototypical examples of these drawn from biology and other disciplines have provided insights that extend well beyond the situations that inspired them. Here, we explore a set of simple, yet realistic, models for savanna-forest vegetation dynamics based on minimal ecological assumptions. These models are aimed at understanding how vegetation interacts with both climate (a primary global determinant of vegetation structure) and feedbacks with chronic disturbances from fire. The model includes three plant functional types-grasses, savanna trees, and forest trees. Grass and (when they allow grass to persist in their subcanopy) savanna trees promote the spread of fires, which in turn, demographically limit trees. The model exhibits a spectacular range of behaviors. In addition to bistability, analysis reveals (i) that diverse cyclic behaviors (including limit and homo- and heteroclinic cycles) occur for broad ranges of parameter space, (ii) that large shifts in landscape structure can result from endogenous dynamics and not just from external drivers or from noise, and (iii) that introducing noise into this system induces resonant and inverse resonant phenomena, some of which have never been previously observed in ecological models. Ecologically, these results raise questions about how to evaluate complicated dynamics with data. Mathematically, they lead to classes of behaviors that are likely to occur in other models with similar structure.

How does transient signaling input affect the spike timing of postsynaptic neuron near the threshold regime: an analytical study

The noisy threshold regime, where even a small set of presynaptic neurons can significantly affect postsynaptic spike-timing, is suggested as a key requisite for computation in neurons with high variability. It also has been proposed that signals under the noisy conditions are successfully transferred by a few strong synapses and/or by an assembly of nearly synchronous synaptic activities. We analytically investigate the impact of a transient signaling input on a leaky integrate-and-fire postsynaptic neuron that receives background noise near the threshold regime. The signaling input models a single strong synapse or a set of synchronous synapses, while the background noise represents a lot of weak synapses. We find an analytic solution that explains how the first-passage time (ISI) density is changed by transient signaling input. The analysis allows us to connect properties of the signaling input like spike timing and amplitude with postsynaptic first-passage time density in a noisy environment. Based on the analytic solution, we calculate the Fisher information with respect to the signaling input’s amplitude. For a wide range of amplitudes, we observe a non-monotonic behavior for the Fisher information as a function of background noise. Moreover, Fisher information non-trivially depends on the signaling input’s amplitude; changing the amplitude, we observe one maximum in the high level of the background noise. The single maximum splits into two maximums in the low noise regime. This finding demonstrates the benefit of the analytic solution in investigating signal transfer by neurons.

Stochastic resonance improves vision in the severely impaired

We verified whether a stochastic resonance paradigm (SR), with random interference (“noise”) added in optimal amounts, improves the detection of sub-threshold visual information by subjects with retinal disorder and impaired vision as it does in the normally sighted. Six levels of dynamic, zero-mean Gaussian noise were added to each pixel of images (13 contrast levels) in which alphabet characters were displayed against a uniform gray background. Images were presented with contrast below the subjective threshold to 14 visually impaired subjects (age: 22–53 yrs.). The fraction of recognized letters varied between 0 and 0.3 at baseline and increased in all subjects when noise was added in optimal amounts; peak recognition ranged between 0.2 and 0.8 at noise sigmas between 6 and 30 grey scale values (GSV) and decreased in all subjects at noise levels with sigma above 30 GSV. The results replicate in the visually impaired the facilitation of visual information processing with images presented in SR paradigms that has been documented in sighted subjects. The effect was obtained with low-level image manipulation and application appears readily possible: it would enhance the efficiency of today vision-improving aids and help in the development of the visual prostheses hopefully available in the future.

Brownian Optogenetic-Noise-Photostimulation on the Brain Amplifies Somatosensory-Evoked Field Potentials

Stochastic resonance (SR) is an inherent and counter-intuitive mechanism of signal-to-noise ratio (SNR) facilitation in biological systems associated with the application of an intermediate level of noise. As a first step to investigate in detail this phenomenon in the somatosensory system, here we examined whether the direct application of noisy light on pyramidal neurons from the mouse-barrel cortex expressing a light-gated channel channelrhodopsin-2 (ChR2) can produce facilitation in somatosensory evoked field potentials. Using anesthetized Thy1-ChR2-YFP transgenic mice, and a new neural technology, that we called Brownian optogenetic-noise-photostimulation (BONP), we provide evidence for how BONP directly applied on the barrel cortex modulates the SNR in the amplitude of whisker-evoked field potentials (whisker-EFP). In all transgenic mice, we found that the SNR in the amplitude of whisker-EFP (at 30% of the maximal whisker-EFP) exhibited an inverted U-like shape as a function of the BONP level. As a control, we also applied the same experimental paradigm, but in wild-type mice, as expected, we did not find any facilitation effects. Our results show that the application of an intermediate intensity of BONP on the barrel cortex of ChR2 transgenic mice amplifies the SNR of somatosensory whisker-EFPs. This result may be relevant to explain the improvements found in sensory detection in humans produced by the application of transcranial-random-noise-stimulation (tRNS) on the scalp.

Noise Improves Visual Motion Discrimination via a Stochastic Resonance-Like Phenomenon

The stochastic resonance (SR) is a phenomenon in which adding a moderate amount of noise can improve the signal-to-noise ratio and performance of non-linear systems. SR occurs in all sensory modalities including the visual system in which noise can enhance contrast detection sensitivity and the perception of ambiguous figures embedded in static scenes. Here, we explored how adding background white pixel-noise to a random dot motion (RDM) stimulus produced changes in visual motion discrimination in healthy human adults. We found that, although the average reaction times (RTs) remained constant, an intermediate level of noise improved the subjects’ ability to discriminate motion direction in the RDM task. The psychophysical responses followed an inverted U-like function of the input noise, whereas the incorrect responses with short RTs did not exhibit such modulation by external noise. Moreover, by applying stimulus and noisy signals to different eyes, we found that the SR phenomenon occurred presumably in the primary visual cortex, where these two signals first converge. Our results suggest that a SR-like phenomenon mediates the improvement of visual motion perception in the RDM task.

Spintronic Nanodevices for Bioinspired Computing

Bioinspired hardware holds the promise of low-energy, intelligent, and highly adaptable computing systems. Applications span from automatic classification for big data management, through unmanned vehicle control, to control for biomedical prosthesis. However, one of the major challenges of fabricating bioinspired hardware is building ultra-high-density networks out of complex processing units interlinked by tunable connections. Nanometer-scale devices exploiting spin electronics (or spintronics) can be a key technology in this context. In particular, magnetic tunnel junctions (MTJs) are well suited for this purpose because of their multiple tunable functionalities. One such functionality, non-volatile memory, can provide massive embedded memory in unconventional circuits, thus escaping the von-Neumann bottleneck arising when memory and processors are located separately. Other features of spintronic devices that could be beneficial for bioinspired computing include tunable fast nonlinear dynamics, controlled stochasticity, and the ability of single devices to change functions in different operating conditions. Large networks of interacting spintronic nanodevices can have their interactions tuned to induce complex dynamics such as synchronization, chaos, soliton diffusion, phase transitions, criticality, and convergence to multiple metastable states. A number of groups have recently proposed bioinspired architectures that include one or several types of spintronic nanodevices. In this paper, we show how spintronics can be used for bioinspired computing. We review the different approaches that have been proposed, the recent advances in this direction, and the challenges toward fully integrated spintronics complementary metal-oxide-semiconductor (CMOS) bioinspired hardware.

Reverse stochastic resonance in a hippocampal CA1 neuron model

Stochastic resonance (SR) is a ubiquitous and counter- intuitive phenomenon whereby the addition of noise to a non-linear system can improve the detection of sub-threshold signals. The "signal" is normally periodic or deterministic whereas the "noise" is normally stochastic. However, in neural systems, signals are often stochastic. Moreover, periodic signals are applied near neurons to control neural excitability (i.e. deep brain stimulation). We therefore tested the hypothesis that a quasi-periodic signal applied to a neural network could enhance the detection of a stochastic neural signal (reverse stochastic resonance). Using computational methods, a CA1 hippocampal neuron was simulated and a Poisson distributed subthreshold synaptic input ("signal") was applied to the synaptic terminals. A periodic or quasi periodic pulse train at various frequencies ("noise") was applied to an extracellular electrode located near the neuron. The mutual information and information transfer rate between the output and input of the neuron were calculated. The results display the signature of stochastic resonance with information transfer reaching a maximum value for increasing power (or frequency) of the "noise". This result shows that periodic signals applied extracellularly can improve the detection of subthreshold stochastic neural signals. The optimum frequency (110 Hz) is similar to that used in patients with Parkinson's suggesting that this phenomenon could play a role in the therapeutic effect of high frequency stimulation.

A review of methods for identifying stochastic resonance in simulations of single neuron models

Stochastic resonance (SR) is said to be observed when the presence of noise in a nonlinear system enables an output signal from the system to better represent some feature of an input signal than it does in the absence of noise. The effect has been observed in models of individual neurons, and in experiments performed on real neural systems. Despite the ubiquity of biophysical sources of stochastic noise in the nervous system, however, it has not yet been established whether neuronal computation mechanisms involved in performance of specific functions such as perception or learning might exploit such noise as an integral component, such that removal of the noise would diminish performance of these functions. In this paper we revisit the methods used to demonstrate stochastic resonance in models of single neurons. This includes a previously unreported observation in a multicompartmental model of a CA1-pyramidal cell. We also discuss, as a contrast to these classical studies, a form of 'stochastic facilitation', known as inverse stochastic resonance. We draw on the reviewed examples to argue why new approaches to studying 'stochastic facilitation' in neural systems need to be developed.

Noise-aided logic in an electronic analog of synthetic genetic networks

We report the experimental verification of noise-enhanced logic behaviour in an electronic analog of a synthetic genetic network, composed of two repressors and two constitutive promoters. We observe good agreement between circuit measurements and numerical prediction, with the circuit allowing for robust logic operations in an optimal window of noise. Namely, the input-output characteristics of a logic gate is reproduced faithfully under moderate noise, which is a manifestation of the phenomenon known as Logical Stochastic Resonance. The two dynamical variables in the system yield complementary logic behaviour simultaneously. The system is easily morphed from AND/NAND to OR/NOR logic.

Effects of time delay and random rewiring on the stochastic resonance in excitable small-world neuronal networks

The effects of time delay and rewiring probability on stochastic resonance and spatiotemporal order in small-world neuronal networks are studied in this paper. Numerical results show that, irrespective of the pacemaker introduced to one single neuron or all neurons of the network, the phenomenon of stochastic resonance occurs. The time delay in the coupling process can either enhance or destroy stochastic resonance on small-world neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of the pacemaker. More importantly, it is found that the small-world topology can significantly affect the stochastic resonance on excitable neuronal networks. For small time delays, increasing the rewiring probability can largely enhance the efficiency of pacemaker-driven stochastic resonance. We argue that the time delay and the rewiring probability both play a key role in determining the ability of the small-world neuronal network to improve the noise-induced outreach of the localized subthreshold pacemaker.

Effects of time delay on the stochastic resonance in small-world neuronal networks

The effects of time delay on stochastic resonance in small-world neuronal networks are investigated. Without delay, an intermediate intensity of additive noise is able to optimize the temporal response of the neural system to the subthreshold periodic signal imposed on all neurons constituting the network. The time delay in the coupling process can either enhance or destroy stochastic resonance of neuronal activity in the small-world network. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of weak external forcing. It is found that the delay-induced multiple stochastic resonances are most efficient when the forcing frequency is close to the global-resonance frequency of each individual neuron. Furthermore, the impact of time delay on stochastic resonance is largely independent of the small-world topology, except for resonance peaks. Considering that information transmission delays are inevitable in intra- and inter-neuronal communication, the presented results could have important implications for the weak signal detection and information propagation in neural systems.

Relation between optimal nonlinearity and non-Gaussian noise: enhancing a weak signal in a nonlinear system

In the study of stochastic resonance, it is often mentioned that nonlinearity can enhance a weak signal embedded in noise. In order to give a systematic proof of the signal enhancement in nonlinear systems, we derive an optimal nonlinearity that maximizes a signal-to-noise ratio (SNR). The obtained optimal nonlinearity yields the maximum unbiased signal estimation performance, which is known in the context of information theory. It is found that a linear system is optimal for a Gaussian noise, but for a non-Gaussian noise, there exist nonlinear systems that can achieve an SNR higher than that obtained from linear systems. This analysis refers to a system subjected to an additive non-Gaussian noise with a small signal input.

Stochastic resonance with a mixture of sub-and supra-threshold stimuli in a population of neuron models

This paper presents a novel type of stochastic resonance (SR) with a mixture of sub- and supra-threshold stimuli in a population of neuron models beyond regular SR and Supra-threshold SR (SSR) phenomena. We investigate through computer simulations if the novel type of SR can be observed or not, using the mutual information (MI) estimated from a population of neural spike trains as an index of information transmission. Computer simulations showed that the MI had a typical type of SR curves, even when the balance between sub-and supra-threshold stimuli was varied, suggesting the novel type of SR. Moreover, the peak of MI increased as the balance of supra-threshold stimuli got stronger, i.e., as the situation was getting close to the SSR from the regular SR. This finding could accelerate our understanding about how fluctuations play a role in processing information carried by a mixture of sub-and supra-threshold stimuli.

Introduction to Focus Issue: nonlinear and stochastic physics in biology

Frank Moss was a leading figure in the study of nonlinear and stochastic processes in biological systems. His work, particularly in the area of stochastic resonance, has been highly influential to the interdisciplinary scientific community. This Focus Issue pays tribute to Moss with articles that describe the most recent advances in the field he helped to create. In this Introduction, we review Moss's seminal scientific contributions and introduce the articles that make up this Focus Issue.

Stochastic resonance on a modular neuronal network of small-world subnetworks with a subthreshold pacemaker

We study the phenomenon of stochastic resonance on a modular neuronal network consisting of several small-world subnetworks with a subthreshold periodic pacemaker. Numerical results show that the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the intensity of additive spatiotemporal noise. This effect of pacemaker-driven stochastic resonance of the system depends extensively on the local and the global network structure, such as the intra- and inter-coupling strengths, rewiring probability of individual small-world subnetwork, the number of links between different subnetworks, and the number of subnetworks. All these parameters play a key role in determining the ability of the network to enhance the noise-induced outreach of the localized subthreshold pacemaker, and only they bounded to a rather sharp interval of values warrant the emergence of the pronounced stochastic resonance phenomenon. Considering the rather important role of pacemakers in real-life, the presented results could have important implications for many biological processes that rely on an effective pacemaker for their proper functioning.

Integration and transmission of distributed deterministic neural activity in feed-forward networks

A ten layer feed-forward network characterized by diverging/converging patterns of projection between successive layers of regular spiking (RS) neurons is activated by an external spatiotemporal input pattern fed to Layer 1 in presence of stochastic background activities fed to all layers. We used three dynamical systems to derive the external input spike trains including the temporal information, and three types of neuron models for the network, i.e. either a network formed either by neurons modeled by exponential integrate-and-fire dynamics (RS-EIF, Fourcaud-Trocmé et al., 2003), or by simple spiking neurons (RS-IZH, Izhikevich, 2004) or by multiple-timescale adaptive threshold neurons (RS-MAT, Kobayashi et al., 2009), given five intensities for the background activity. The assessment of the temporal structure embedded in the output spike trains was carried out by detecting the preferred firing sequences for the reconstruction of de-noised spike trains (Asai and Villa, 2008). We confirmed that the RS-MAT model is likely to be more efficient in integrating and transmitting the temporal structure embedded in the external input. We observed that this structure could be propagated not only up to the 10th layer but in some cases it was retained better beyond the 4th downstream layers. This study suggests that diverging/converging network structures, by the propagation of synfire activity, could play a key role in the transmission of complex temporal patterns of discharges associated to deterministic nonlinear activity. This article is part of a Special Issue entitled Neural Coding.

Enhancement of information transmission of sub-threshold signals applied to distal positions of dendritic trees in hippocampal CA1 neuron models with stochastic resonance

Stochastic resonance (SR) has been shown to enhance the signal-to-noise ratio and detection of low level signals in neurons. It is not yet clear how this effect of SR plays an important role in the information processing of neural networks. The objective of this article is to test the hypothesis that information transmission can be enhanced with SR when sub-threshold signals are applied to distal positions of the dendrites of hippocampal CA1 neuron models. In the computer simulation, random sub-threshold signals were presented repeatedly to a distal position of the main apical branch, while the homogeneous Poisson shot noise was applied as a background noise to the mid-point of a basal dendrite in the CA1 neuron model consisting of the soma with one sodium, one calcium, and five potassium channels. From spike firing times recorded at the soma, the mutual information and information rate of the spike trains were estimated. The simulation results obtained showed a typical resonance curve of SR, and that as the activity (intensity) of sub-threshold signals increased, the maximum value of the information rate tended to increased and eventually SR disappeared. It is concluded that SR can play a key role in enhancing the information transmission of sub-threshold stimuli applied to distal positions on the dendritic trees.

Stochastic resonance can enhance information transmission of supra-threshold neural signals

Stochastic resonance (SR) has been shown to improve detection of sub-threshold signals with additive uncor-related background noise, not only in a single hippocampal CA1 neuron model, but in a population of hippocampal CA1 neuron models (Array-Enhanced Stochastic Resonance; AESR). However, most of the information in the CNS is transmitted through supra-threshold signals and the effect of stochastic resonance in neurons on these signals is unknown. Therefore, we investigate through computer simulations whether information transmission of supra-threshold input signal can be improved by uncorrelated noise in a population of hippocampal CA1 neuron models by supra-threshold stochastic resonance (SSR). The mutual information was estimated as an index of information transmission via total and noise entropies from the inter-spike interval (ISI) histograms of the spike trains generated by gathering each of spike trains in a population of hippocampal CA1 neuron models at N = 1, 2, 4, 10, 20 and 50. It was shown that the mutual information was maximized at a specific amplitude of uncorrelated noise, i.e., a typical curve of SR was observed when the number of neurons was greater than 10 with SSR. However, SSR did not affect the information transfer with a small number of neurons. In conclusion, SSR may play an important role in processing information such as memory formation in a population of hippocampal neurons.

Synaptic noise and physiological coupling generate high-frequency oscillations in a hippocampal computational model

There is great interest in the role of coherent oscillations in the brain. In some cases, high-frequency oscillations (HFOs) are integral to normal brain function, whereas at other times they are implicated as markers of epileptic tissue. Mechanisms underlying HFO generation, especially in abnormal tissue, are not well understood. Using a physiological computer model of hippocampus, we investigate random synaptic activity (noise) as a potential initiator of HFOs. We explore parameters necessary to produce these oscillations and quantify the response using the tools of stochastic resonance (SR) and coherence resonance (CR). As predicted by SR, when noise was added to the network the model was able to detect a subthreshold periodic signal. Addition of basket cell interneurons produced two novel SR effects: 1) improved signal detection at low noise levels and 2) formation of coherent oscillations at high noise that were entrained to harmonics of the signal frequency. The periodic signal was then removed to study oscillations generated only by noise. The combined effects of network coupling and synaptic noise produced coherent, periodic oscillations within the network, an example of CR. Our results show that, under normal coupling conditions, synaptic noise was able to produce gamma (30-100 Hz) frequency oscillations. Synaptic noise generated HFOs in the ripple range (100-200 Hz) when the network had parameters similar to pathological findings in epilepsy: increased gap junctions or recurrent synaptic connections, loss of inhibitory interneurons such as basket cells, and increased synaptic noise. The model parameters that generated these effects are comparable with published experimental data. We propose that increased synaptic noise and physiological coupling mechanisms are sufficient to generate gamma oscillations and that pathologic changes in noise and coupling similar to those in epilepsy can produce abnormal ripples.

Error-probability noise benefits in threshold neural signal detection

Five new theorems and a stochastic learning algorithm show that noise can benefit threshold neural signal detection by reducing the probability of detection error. The first theorem gives a necessary and sufficient condition for such a noise benefit when a threshold neuron performs discrete binary signal detection in the presence of additive scale-family noise. The theorem allows the user to find the optimal noise probability density for several closed-form noise types that include generalized Gaussian noise. The second theorem gives a noise-benefit condition for more general threshold signal detection when the signals have continuous probability densities. The third and fourth theorems reduce this noise benefit to a weighted-derivative comparison of signal probability densities at the detection threshold when the signal densities are continuously differentiable and when the noise is symmetric and comes from a scale family. The fifth theorem shows how collective noise benefits can occur in a parallel array of threshold neurons even when an individual threshold neuron does not itself produce a noise benefit. The stochastic gradient-ascent learning algorithm can find the optimal noise value for noise probability densities that do not have a closed form.

Enhancement of information transmission with stochastic resonance in hippocampal CA1 neuron network

Stochastic resonance (SR) has been shown to improve the detection of subthreshold neural signals in uncorrelated noise. It is yet unclear if and how interactions within a population of neurons can improve information processing in neural networks. In this paper, we investigate the effect of the number of neurons on information transmission in an array of hippocampal CA1 neuron models, i.e., array-enhanced SR (AESR). In computer simulations, the sub-threshold synaptic current (signal) generated by a filtered homogeneous Poisson process was applied to a distal position in each of the apical dendrites, while the background synaptic currents (uncorrelated noise) were presented to a proximal or middle point in each of the dendrites. The transmembrane potentials were recorded at one of the somas in the array of CA1 neuron models, in order to find spike firings and likewise to estimate the total and noise entropies calculated from those spike firing times. The results show that the information rate estimated at the population of the CA1 neuron models is maximized at a specific amplitude of uncorrelated noise, implying AESR. The results further show that the maximum information rate is increased as the number of neurons is increased. It is concluded that AESR can be an important role in information processing is neural systems and that the AESR is modulated by the number of neurons within the network.

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.

Stochastic resonance can induce oscillation in a recurrent Hodgkin-Huxley neuron model with added Gaussian noise

Stochastic resonance (SR) has been shown to enhance the signal to noise ratio or detection of signals in neurons. It has not been clear yet if SR can play an important role in information processing in neural networks. In this paper, we test the hypothesis through computer simulations that SR can induce an oscillation phenomenon in a recurrent neural network with added Gaussian noise in which the recurrent model is constructed by four Hodgkin-Huxley (HH) neuron models. Each HH neuron model is driven by Gaussian noise and sub-threshold excitatory synaptic currents with an alpha function from another HH neuron model, and the action potentials (spike firings) of each HH neuron model are transferred to the other HH neuron model via sub-threshold synaptic currents. From spike firing times recorded, the inter spike interval (ISI) histogram was generated, and the periodicity of spike firings was detected from the ISI histogram at each HH neuron model. The results show that the probability of spike firings in the oscillation period (about 50 ms or 20 Hz) increases as the standard deviation (S.D.) of the Gaussian white noise increases, and reach a maximum value at a specific S.D. of the Gaussian white noise, implying that SR can improve sub-threshold synaptic transmission in the recurrent HH neuron model. It is concluded that an oscillation (20 Hz) can be induced by adding Gaussian white noise at lower amplitudes with intrinsic characteristics in the recurrent HH neuron model, while another oscillation (100 Hz) can be generated by the noise at greater amplitudes with extrinsic characteristics.

Noise induced oscillations in recurrent neural networks

It has been shown that oscillations can be generated by additive Gaussian white noise in a recurrent Hodgkin-Huxley neuron model. Type 1 oscillation was induced with Stochastic Resonance (SR) by additive Gaussian noise at lower amplitudes, while Type 2 oscillation was observed at higher amplitudes. However, the mechanism of Type 2 oscillation is not clear. In this article, we test the hypothesis through computer simulations that the period of the Type 2 oscillation can be affected by temperature in a recurrent neural network in which the recurrent model is constructed by four Hodgkin-Huxley (HH) neuron models. Each HH neuron model is driven by Gaussian noise and sub-threshold excitatory synaptic currents with an alpha function from another HH neuron model, and the action potentials (spike firings) of each HH neuron model are transferred to the other HH neuron model via sub-threshold synaptic currents. From spike firing times recorded, the inter spike interval (ISI) histogram was generated, and the periodicity of spike firings was detected from the ISI histogram at each HH neuron model. The results show that the probability of spike firings in the Type1 oscillation is maximized at a specific standard deviation (S.D.) of the Gaussian white noise with SR at 6.3, 15.0 and 25.0 degrees C, while the period of the Type 2 oscillation depends on temperature. It is concluded that the Type1 oscillation can be induced by additive Gaussian white noise on the basis of a synaptic delay in the recurrent HH neuron model, whereas ISIs of the Type 2 oscillation may be determined by refractory periods of HH neuron models.

Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force

We identify an unconventional route to the creation of a strange nonchaotic attractor (SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal (square wave) force as one of the quasiperiodic forces through numerical and experimental studies. We find that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square-wave-type force. The bubbles then enlarge and get increasingly wrinkled as a function of the control parameter. Finally, the bubbles get extremely wrinkled (while the remaining parts of the strands of the torus remain largely unaffected) resulting in the creation of the SNA; we term this the bubbling route to the SNA. We characterize and confirm this creation from both experimental and numerical data using maximal Lyapunov exponents and their variance, Poincaré maps, Fourier amplitude spectra, and spectral distribution functions. We also strongly confirm the creation of a SNA via the bubbling route by the distribution of the finite-time Lyapunov exponents.

Enhancement of information transmission with stochastic resonance in hippocampal CA1 neuron models: effects of noise input location

Stochastic resonance (SR) has been shown to enhance the signal to noise ratio or detection of signals in neurons. It is not yet clear how this effect of SR on the signal to noise ratio affects signal processing in neural networks. In this paper, we investigate the effects of the location of background noise input on information transmission in a hippocampal CA1 neuron model. In the computer simulation, random sub-threshold spike trains (signal) generated by a filtered homogeneous Poisson process were presented repeatedly to the middle point of the main apical branch, while the homogeneous Poisson shot noise (background noise) was applied to a location of the dendrite in the hippocampal CA1 model consisting of the soma with a sodium, a calcium, and five potassium channels. The location of the background noise input was varied along the dendrites to investigate the effects of background noise input location on information transmission. The computer simulation results show that the information rate reached a maximum value for an optimal amplitude of the background noise amplitude. It is also shown that this optimal amplitude of the background noise is independent of the distance between the soma and the noise input location. The results also show that the location of the background noise input does not significantly affect the maximum values of the information rates generated by stochastic resonance.

Enhancement of information transmission with stochastic resonance in hippocampal CA1 neuron models

Stochastic resonance (SR) has been shown to enhance the signal to noise ratio or detection of signals in neurons. It is not yet clear how this effect of SR on the signal to noise ratio affects signal processing in neural networks. In this paper, we test the hypothesis that SR can improve information transmission in the hippocampus. From spike firing times recorded at the soma, the inter spike intervals were generated and then "total" and "noise" entropies were estimated to obtain the mutual information and information rate of the spike trains. The results show that the information rate reached a maximum value at a specific amplitude of the background noise, implying that the stochastic resonance can improve the information transmission in the CA1 neuron model. Furthermore, the results also show that the effect of stochastic resonance tended to decrease as the intensity of the random sub-threshold spike trains (signal) (more than 20 l/s) approached to that of the background noise (100 l/s). In conclusion, the computation results that the stochastic resonance can improve information processing in the hippocampal CA1 neuron model in which the intensity of the random sub-threshold spike trains was set at 5-20 l/s.

Information transmission in hippocampal CA1 neuron models in the presence of poisson shot noise: the case of periodic sub-threshold spike trains

This article presents an analysis of the information transmission of periodic sub-threshold spike trains in a hippocampal CA1 neuron model in the presence of a homogeneous Poisson shot noise. In the computer simulation, periodic sub-threshold spike trains were presented repeatedly to the midpoint of the main apical branch, while the homogeneous Poisson shot noise was applied to the mid-point of a basal dendrite in the CA1 neuron model consisting of the soma with one sodium, one calcium, and five potassium channels. From spike firing times recorded at the soma, the inter spike intervals were generated and then the probability, p(T), of the inter-spike interval histogram corresponding to the spike interval, r, of the periodic input spike trains was estimated to obtain an index of information transmission. In the present article, it is shown that at a specific amplitude of the homogeneous Poisson shot noise, p(T) was found to be maximized, as well as the possibility to encode the periodic sub-threshold spike trains became greater. It was implied that setting the amplitude of the homogeneous Poisson shot noise to the specific values which maximize the information transmission might contribute to efficiently encoding the periodic sub-threshold spike trains by utilizing the stochastic resonance.