Parallel processing by a homogeneous group of coupled model neurons can enhance, reduce and generate signal correlations

 Correlated activities have been proposed as correlates of flexible association and assembly coding. We addressed the basic question of how signal correlations on parallel pathways are enhanced, reduced and generated by homogeneous groups of coupled neurons, and how this depends on the input activities and their interactions with internal coupling processes. For this we simulated a fully connected group of identical impulse-coded neurons with dynamic input and threshold processes and additive or multiplicative lateral coupling. Input signals were Gaussian white noise (GWN), completely independent or partially correlated on a subgroup of the parallel inputs. We show that in states of high average spike rates input-output correlations were weak while the network could generate correlated activities of stochastic, oscillatory and rhythmic bursting types depending exclusively on lateral coupling strength. In states of low average spike rates input-output correlations were high and the network could effectively enhance or reduce differences in spatial correlation applied to its parallel inputs. The correlation differences were more pronounced with multiplicative lateral coupling than with the additive interactions commonly used. As the different modes of correlation processing emerged already by global changes in the average spike rate and lateral coupling strength, we assume that in real cortical circuits changes in correlational processing may also be induced by unspecific modulations of activation and lateral coupling. Received: 11 December 1995 / Accepted in revised form: 29 November 1996     

Neural network mosaic model for pupillary responses to spatial stimuli

A neural network mosaic model was developed to investigate the spatial-temporal properties of the human pupillary control system. It was based on the double-layer neural network model developed by Cannon and Robinson and the pupillary dual-path model developed by Sun and Stark. The neural network portion of the model received its input from a sensor array and consisted of a retina-like two-dimensional neuronal layer. The dual-path portion of the model was composed of interconnections of the neurons that formed a mosaic of AC transient and DC sustained paths. The spatial aggregates of the AC and DC signals were input to the AC and DC summing neurons, respectively. Finally, the weighted sum of the aggregate AC and DC signals provided the output for driving the pupillary response. An important property of the model was that it could adaptively learn from training samples by adjustment of the weights. The neural network mosaic model showed excellent performance in simulating both the traditional pupillary phenomena and the new spatial stimulation findings such as responses to change in stimulus pattern and shift of light spot. Moreover, the model could also be used for the diagnosis of clinical deficits and image processing in machine vision. Received: 12 December 1997 / Accepted in revised form: 22 April 1998     

A neural network study of precollicular saccadic averaging

Saccadic averaging is the phenomenon that two simultaneously presented retinal inputs result in a saccade with an endpoint located on an intermediate position between the two stimuli. Recordings from neurons in the deeper layers of the superior colliculus have revealed neural correlates of saccade averaging, indicating that it takes place at this level or upstream. Recently, we proposed a neural network for internal feedback in saccades. This neural network model is different from other models in that it suggests the possibility that averaging takes place in a stage upstream of the colliculus. The network consists of output units representing the neural map of the deeper layers of the superior colliculus and hidden layers imitating areas in the posterior parietal cortex. The deeper layers of the superior colliculus represent the motor error of a desired saccade, e.g. an eye movement to a visual target. In this article we show that averaging is an emergent property of the proposed network. When two retinal targets with different intensities are simultaneously presented to the network, the activity in the output layer represents a single motor error with a weighted average value. Our goal is to understand the mechanism of weighted averaging in this neural network. It appears that averaging in the model is caused by the linear dependence of the net input, received by the hidden units, on retinal error, independent of its retinal coding format. For nonnormalized retinal error inputs, also the nonlinearity between the net input and the activity of the hidden units plays a role in the averaging process. The averaging properties of the model are in agreement with physiological experiments if the hypothetical retinal error input map is normalized. The neural network predicts that if this normalization is overruled by electrical stimulation, averaging still takes place. However, in this case – as a consequence of the feedback task – the location of the resulting saccade depends on the initial eye position and the total intensity/current applied at the two locations. This could be a way to verify the neural network model. If the assumptions for the model are valid, a physiological implication of this paper is that averaging of saccades takes place upstream of the superior colliculus. Received: 22 June 1997 / Accepted in revised form: 19 February 1998     

Touch Interacts with Vision during Binocular Rivalry with a Tight Orientation Tuning

Multisensory integration is a common feature of the mammalian brain that allows it to deal more efficiently with the ambiguity of sensory input by combining complementary signals from several sensory sources. Growing evidence suggests that multisensory interactions can occur as early as primary sensory cortices. Here we present incompatible visual signals (orthogonal gratings) to each eye to create visual competition between monocular inputs in primary visual cortex where binocular combination would normally take place. The incompatibility prevents binocular fusion and triggers an ambiguous perceptual response in which the two images are perceived one at a time in an irregular alternation. One key function of multisensory integration is to minimize perceptual ambiguity by exploiting cross-sensory congruence. We show that a haptic signal matching one of the visual alternatives helps disambiguate visual perception during binocular rivalry by both prolonging the dominance period of the congruent visual stimulus and by shortening its suppression period. Importantly, this interaction is strictly tuned for orientation, with a mismatch as small as 7.5° between visual and haptic orientations sufficient to annul the interaction. These results indicate important conclusions: first, that vision and touch interact at early levels of visual processing where interocular conflicts are first detected and orientation tunings are narrow, and second, that haptic input can influence visual signals outside of visual awareness, bringing a stimulus made invisible by binocular rivalry suppression back to awareness sooner than would occur without congruent haptic input.     

Control of a one-link arm by burst signal generators

 The focus of this paper is the study of stability and point-to-point movement of a one-link arm. The sagittal arm has two musculotendon actuators, two neural oscillators that generate burst signals as motoneuron inputs, and spindles and Golgi tendon organs for extrinsic reflex feedbacks. It is shown that coactivation leads to intrinsic position and velocity feedback, and that the tendons introduce intrinsic force and rate of force feedback. In addition, the integrating effects of the tendons are studied when the actuator is constructed from a large number of identical fibers that are excited by alpha signals whose arrival times at the fiber are randomly distributed. Each of the musculotendon actuators receives two input signals – a burst signal analogous to alpha inputs and a conventional analogue signal that represents fusimotor input to the spindles. The process of combining burst signals and conventional analogue signals is studied. Simulation results show that the movement of the system with burst signals as inputs has overshoot and speed similar to the system with analogue signals. Received: 30 May 1994/Accepted in revised form: 13 January 1995     

Breakthrough to awareness: a preliminary neural network model of conscious and unconscious perception in word processing

 A neural network model is constructed to mimic the processing involved in semantic and working memory when subliminal effects are involved. These effects involve modifications of reaction time to later inputs, according to whether or not there has been conscious or unconscious processing of the earlier input. The model is constructed of two separate modules: one (a semantic memory module) allowing for processing at a semantic, but unconscious, level, and the other (a working memory module) for conscious experience. The latter module, although a replica of the earlier one, has different lateral connectivity and output function from the former. The model is shown to give a good fit to Marcel’s data on the processing of polysemous words. Further tests are suggested for the model, and a possible cortical implementation suggested. The relevance of the model to recent approaches to consciousness is also explored. Received: 7 February 1995/Accepted in revised form: 14 November 1995     

Blind noise reduction for multisensory signals using ICA and subspace filtering, with application to EEG analysis

 In many applications of signal processing, especially in communications and biomedicine, preprocessing is necessary to remove noise from data recorded by multiple sensors. Typically, each sensor or electrode measures the noisy mixture of original source signals. In this paper a noise reduction technique using independent component analysis (ICA) and subspace filtering is presented. In this approach we apply subspace filtering not to the observed raw data but to a demixed version of these data obtained by ICA. Finite impulse response filters are employed whose vectors are parameters estimated based on signal subspace extraction. ICA allows us to filter independent components. After the noise is removed we reconstruct the enhanced independent components to obtain clean original signals; i.e., we project the data to sensor level. Simulations as well as real application results for EEG-signal noise elimination are included to show the validity and effectiveness of the proposed approach. Received: 6 November 2000 / Accepted in revised form: 12 November 2001     

Bilateral matching of frequency tuning in neural cross-correlators of the owl

Sound localization requires comparison between the inputs to the left and right ears. One important aspect of this comparison is the differences in arrival time to each side, also called interaural time difference (ITD). A prevalent model of ITD detection, consisting of delay lines and coincidence-detector neurons, was proposed by Jeffress (J Comp Physiol Psychol 41:35–39, 1948). As an extension of the Jeffress model, the process of detecting and encoding ITD has been compared to an effective cross-correlation between the input signals to the two ears. Because the cochlea performs a spectrotemporal decomposition of the input signal, this cross-correlation takes place over narrow frequency bands. Since the cochlear tonotopy is arranged in series, sounds of different frequencies will trigger neural activity with different temporal delays. Thus, the matching of the frequency tuning of the left and right inputs to the cross-correlator units becomes a ‘timing’ issue. These properties of auditory transduction gave theoretical support to an alternative model of ITD-detection based on a bilateral mismatch in frequency tuning, called the ‘stereausis’ model. Here we first review the current literature on the owl’s nucleus laminaris, the equivalent to the medial superior olive of mammals, which is the site where ITD is detected. Subsequently, we use reverse correlation analysis and stimulation with uncorrelated sounds to extract the effective monaural inputs to the cross-correlator neurons. We show that when the left and right inputs to the cross-correlators are defined in this manner, the computation performed by coincidence-detector neurons satisfies conditions of cross-correlation theory. We also show that the spectra of left and right inputs are matched, which is consistent with predictions made by the classic model put forth by Jeffress. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

Relative spike timing in stochastic oscillator networks of the Hermissenda eye

The role of relative spike timing on sensory coding and stochastic dynamics of small pulse-coupled oscillator networks is investigated physiologically and mathematically, based on the small biological eye network of the marine invertebrate Hermissenda. Without network interactions, the five inhibitory photoreceptors of the eye network exhibit quasi-regular rhythmic spiking; in contrast, within the active network, they display more irregular spiking but collective network rhythmicity. We investigate the source of this emergent network behavior first analyzing the role of relative input to spike–timing relationships in individual cells. We use a stochastic phase oscillator equation to model photoreceptor spike sequences in response to sequences of inhibitory current pulses. Although spike sequences can be complex and irregular in response to inputs, we show that spike timing is better predicted if relative timing of spikes to inputs is accounted for in the model. Further, we establish that greater noise levels in the model serve to destroy network phase-locked states that induce non-monotonic stimulus rate-coding, as predicted in Butson and Clark (J Neurophysiol 99:146–154, 2008a; J Neurophysiol 99:155–165, 2008b). Hence, rate-coding can function better in noisy spiking cells relative to non-noisy cells. We then study how relative input to spike–timing dynamics of single oscillators contribute to network-level dynamics. Relative timing interactions in the network sharpen the stimulus window that can trigger a spike, affecting stimulus encoding. Also, we derive analytical inter-spike interval distributions of cells in the model network, revealing that irregular Poisson-like spike emission and collective network rhythmicity are emergent properties of network dynamics, consistent with experimental observations. Our theoretical results generate experimental predictions about the nature of spike patterns in the Hermissenda eye.     

A neural network model for the intersensory coordination involved in goal-directed movements

A neural network model for a sensorimotor system, which was developed to simulate oriented movements in man, is presented. It is composed of a formal neural network comprising two layers: a sensory layer receiving and processing sensory inputs, and a motor layer driving a simulated arm. The sensory layer is an extension of the topological network previously proposed by Kohonen (1984). Two kinds of sensory modality, proprioceptive and exteroceptive, are used to define the arm position. Each sensory cell receives proprioceptive inputs provided by each arm-joint together with the exteroceptive inputs. This sensory layer is therefore a kind of associative layer which integrates two separate sensory signals relating to movement coding. It is connected to the motor layer by means of adaptive synapses which provide a physical link between a motor activity and its sensory consequences. After a learning period, the spatial map which emerges in the sensory layer clearly depends on the sensory inputs and an associative map of both the arm and the extra-personal space is built up if proprioceptive and exteroceptive signals are processed together. The sensorimotor transformations occuring in the junctions linking the sensory and motor layers are organized in such a manner that the simulated arm becomes able to reach towards and track a target in extra-personal space. Proprioception serves to determine the final arm posture adopted and to correct the ongoing movement in cases where changes in the target location occur. With a view to developing a sensorimotor control system with more realistic salient features, a robotic model was coupled with the formal neural network. This robotic implementation of our model shows the capacity of formal neural networks to control the displacement of mechanical devices.     

Using sensory weighting to model the influence of canal,otolith and visual cues on spatial orientation and eye movements

 The sensory weighting model is a general model of sensory integration that consists of three processing layers. First, each sensor provides the central nervous system (CNS) with information regarding a specific physical variable. Due to sensor dynamics, this measure is only reliable for the frequency range over which the sensor is accurate. Therefore, we hypothesize that the CNS improves on the reliability of the individual sensor outside this frequency range by using information from other sensors, a process referred to as “frequency completion.” Frequency completion uses internal models of sensory dynamics. This “improved” sensory signal is designated as the “sensory estimate” of the physical variable. Second, before being combined, information with different physical meanings is first transformed into a common representation; sensory estimates are converted to intermediate estimates. This conversion uses internal models of body dynamics and physical relationships. Third, several sensory systems may provide information about the same physical variable (e.g., semicircular canals and vision both measure self-rotation). Therefore, we hypothesize that the “central estimate” of a physical variable is computed as a weighted sum of all available intermediate estimates of this physical variable, a process referred to as “multicue weighted averaging.” The resulting central estimate is fed back to the first two layers. The sensory weighting model is applied to three-dimensional (3D) visual–vestibular interactions and their associated eye movements and perceptual responses. The model inputs are 3D angular and translational stimuli. The sensory inputs are the 3D sensory signals coming from the semicircular canals, otolith organs, and the visual system. The angular and translational components of visual movement are assumed to be available as separate stimuli measured by the visual system using retinal slip and image deformation. In addition, both tonic (“regular”) and phasic (“irregular”) otolithic afferents are implemented. Whereas neither tonic nor phasic otolithic afferents distinguish gravity from linear acceleration, the model uses tonic afferents to estimate gravity and phasic afferents to estimate linear acceleration. The model outputs are the internal estimates of physical motion variables and 3D slow-phase eye movements. The model also includes a smooth pursuit module. The model matches eye responses and perceptual effects measured during various motion paradigms in darkness (e.g., centered and eccentric yaw rotation about an earth-vertical axis, yaw rotation about an earth-horizontal axis) and with visual cues (e.g., stabilized visual stimulation or optokinetic stimulation). Received: 20 September 2000 / Accepted in revised form: 28 September 2001     

Functionality of divergence and convergence in a model of the insect olfactory system

Recent studies have shown that the insect olfactory system uses a spatio-temporal encoding of odours in the population of projection neurons in the antennal lobe, and suggest that the information thus coded is spread across a large population of Kenyon cells in the mushroom bodies. At this stage, the temporal part of the code might be transformed into a spatial code, especially via the temporally sensitive mechanisms of paired–pulse facilitation and feedback inhibition with its possible associated rebound. We explore here a simple model of the olfactory system using a three–layer network of formal neurons, comprising a fixed number (three) of projection and inhibitory neurons, but a variable number of Kenyon cells. We show how enlarging the divergence of the network (i.e. the ratio between the number of Kenyon cells to the number of input – projection – neurons) alters the number of different output spatial states in response to a fixed set of spatio-temporal inputs, and may therefore improve its effectiveness in discriminating between these inputs. Such enlarged divergence also reduces the variation of this effectiveness among random realisations of the network connectivity. Our model shows that the discriminative effectiveness first increases with the divergence, and then plateaus for a divergence factor of ∼20. The maximal average number of different outputs was 470.2, which was computed from some simulations with random realisations of connectivity and with a set of 512 possible inputs. The discriminative effectiveness of the network is sensitive to paired-pulse facilitation, and especially to inhibition with rebound. Received: 6 April 2001 / Accepted in revised form: 8 April 2002     

An olfactory neuronal network for vapor recognition in an artificial nose

Odorant sensitivity and discrimination in the olfactory system appear to involve extensive neural processing of the primary sensory inputs from the olfactory epithelium. To test formally the functional consequences of such processing, we implemented in an artificial chemosensing system a new analytical approach that is based directly on neural circuits of the vertebrate olfactory system. An array of fiber-optic chemosensors, constructed with response properties similar to those of olfactory sensory neurons, provide time-varying inputs to a computer simulation of the olfactory bulb (OB). The OB simulation produces spatiotemporal patterns of neuronal firing that vary with vapor type. These patterns are then recognized by a delay line neural network (DLNN). In the final output of these two processing steps, vapor identity is encoded by the spatial patterning of activity across units in the DLNN, and vapor intensity is encoded by response latency. The OB-DLNN combination thus separates identity and intensity information into two distinct codes carried by the same output units, enabling discrimination among organic vapors over a range of input signal intensities. In addition to providing a well-defined system for investigating olfactory information processing, this biologically based neuronal network performs better than standard feed-forward neural networks in discriminating vapors when small amounts of training data are used. Received: 30 June 1997 / Accepted in revised form: 12 January 1998     

Synaptic transmission in sympathetic vasoconstrictor pathways and its modification after injuries

The discharge of vasoconstrictor pathways arising in the CNS is largely unmodified as it passes through the sympathetic ganglia to the vasculature. The underlying synaptic events have been revealed by intracellular recordings from sympathetic paravertebral ganglion cells in the course of ongoing and reflex activity in anesthetized animals, first made in Skok’s Laboratory in Kyiv (Ukraine). Each preganglionic neuron diverges to contact a number of post-ganglionic neurons, on each of which several pre-ganglionic inputs converge. However, only suprathreshold “strong,” or “dominant” synapses are effective in transmitting the CNS signals. Strong synapses differ from the other subthreshold “weak,” or “accessory” inputs: (a) excitatory synaptic currents are >1 nA in their amplitude, (b) 3 to ≈>30 times more quanta of acetylcholine are released, (c) pre-synaptic Ca²⁺ entry through channels resistant to all-known antagonists triggers acetylcholine release, and (d) post-synaptic Ca²⁺ entry boosts and prolongs the nicotinic current. While the majority of postganglionic neurons have only one strong input, a proportion receives two or, rarely, three such inputs. In cells with multiple strong inputs, an equivalent number of discrete Ca²⁺ currents can be evoked at distinct foci electrically distant from the soma, suggesting that each strong input has a unique dendritic association with a cluster of Ca²⁺ channels. When strong preganglionic inputs are destroyed, residual weak synapses sprout and rapidly restore the suprathreshold connections. While much remains to be discovered about how strong synapses are established, their high safety factor ensures the wide and secure distribution of vasoconstrictor command signals from the CNS. Neirofiziologiya/Neurophysiology, Vol. 39, Nos. 4/5, pp. 294–301, July–October, 2007.     

Rectification of correlation by a sigmoid nonlinearity

We investigated the normalized autocovariance (correlation coefficient) function of the output of an erf( ) function nonlinearity subject to non-zero mean Gaussian noise input. When the sigmoid is wide compared to the input, or the input mean is close to the midpoint of the sigmoid, the output correlation coefficient function is very close to the input correlation coefficient function. When the noise mean and variance are such that there is a significant probability of operating in the saturation region and the sigmoid is not too flat, the correlation coefficient output function is less than that of the input. This difference is much greater when the correlation coefficient is negative than when it is positive. The sigmoid partially rectifies the correlation coefficient function. The analysis does not depend on the spectral properties of the input noise. All that is required is that the input at times t and (t+τ) be jointly Gaussian with the same mean and autocovariance. The analysis therefore applies equally well to the case of two identical sigmoids with jointly Gaussian inputs. This correlational rectification could help explain the parameter sensitivity of "neural network" models. If biological neurons share this property it could explain why few negative correlations between spike trains have been observed. Received: 1 July 1992/Accepted in revised form: 6 July 1993     

Effects of spinal recurrent inhibition on motoneuron short-term synchronization

Spinal recurrent inhibition linking skeleto- motoneurons (α-MNs) via Renshaw cells (RCs) has been variously proposed to increase or decrease tendencies toward synchronous discharges between α-MNs. This controversy is not easy to settle experimentally in animal or human paradigms because RCs receive, in addition to excitatory input from α-MNs, many other modulating influences which may change their mode of operation. Computer simulations help to artificially isolate the recurrent inhibitory circuit and thus to study its effects on α-MN synchronization under conditions not achievable in natural experiments. We present here such a study which was designed to specifically test the following hypothesis. Since many α-MNs excite any particular Renshaw cell, which in turn inhibits many α-MNs, this convergence–divergence pattern establishes a random network whose random discharge patterns inject uncorrelated noise into α-MNs, and this noise counteracts any synchronization potentially arising from other sources, e.g., common inputs (Adam et al. in Biol Cybern 29:229–235, 1978). We investigated the short-term synchronization of α-MNs with two types of excitatory input signals to α-MNs (random and sinusoidally modulated random patterns). The main results showed that, while recurrent inhibitory inputs to different α-MNs were indeed different, recurrent inhibition (1) exerted rather small effects on the modulation of α-MN discharge, (2) tended to increase the short-term synchronization of α-MN discharge, and (3) did not generate secondary peaks in α-MN-α-MN cross-correlograms associated with α-MN rhythmicity.     

Neural adaptation facilitates oscillatory responses to static inputs in a recurrent network of ON and OFF cells

We investigate the role of adaptation in a neural field model, composed of ON and OFF cells, with delayed all-to-all recurrent connections. As external spatially profiled inputs drive the network, ON cells receive inputs directly, while OFF cells receive an inverted image of the original signals. Via global and delayed inhibitory connections, these signals can cause the system to enter states of sustained oscillatory activity. We perform a bifurcation analysis of our model to elucidate how neural adaptation influences the ability of the network to exhibit oscillatory activity. We show that slow adaptation encourages input-induced rhythmic states by decreasing the Andronov–Hopf bifurcation threshold. We further determine how the feedback and adaptation together shape the resonant properties of the ON and OFF cell network and how this affects the response to time-periodic input. By introducing an additional frequency in the system, adaptation alters the resonance frequency by shifting the peaks where the response is maximal. We support these results with numerical experiments of the neural field model. Although developed in the context of the circuitry of the electric sense, these results are applicable to any network of spontaneously firing cells with global inhibitory feedback to themselves, in which a fraction of these cells receive external input directly, while the remaining ones receive an inverted version of this input via feedforward di-synaptic inhibition. Thus the results are relevant beyond the many sensory systems where ON and OFF cells are usually identified, and provide the backbone for understanding dynamical network effects of lateral connections and various forms of ON/OFF responses.     

Modeling complex tone perception: grouping harmonics with combination-sensitive neurons

 Perception of complex communication sounds is a major function of the auditory system. To create a coherent percept of these sounds the auditory system may instantaneously group or bind multiple harmonics within complex sounds. This perception strategy simplifies further processing of complex sounds and facilitates their meaningful integration with other sensory inputs. Based on experimental data and a realistic model, we propose that associative learning of combinations of harmonic frequencies and nonlinear facilitation of responses to those combinations, also referred to as “combination-sensitivity,” are important for spectral grouping. For our model, we simulated combination sensitivity using Hebbian and associative types of synaptic plasticity in auditory neurons. We also provided a parallel tonotopic input that converges and diverges within the network. Neurons in higher-order layers of the network exhibited an emergent property of multifrequency tuning that is consistent with experimental findings. Furthermore, this network had the capacity to “recognize” the pitch or fundamental frequency of a harmonic tone complex even when the fundamental frequency itself was missing. Received: 6 October 2001 / Accepted in revised form: 21 January 2002     

Combined Hebbian development of geniculocortical and lateral connectivity in a model of primary visual cortex

We present a network model of visual map development in layer 4 of primary visual cortex. Our model comprises excitatory and inhibitory spiking neurons. The input to the network consists of correlated spike trains to mimick the activity of neurons in the lateral geniculate nucleus (LGN). An activity-driven Hebbian learning mechanism governs the development of both the network's lateral connectivity and feedforward projections from LGN to cortex. Plasticity of inhibitory synapses has been included into the model so as to control overall cortical activity. Even without feedforward input, Hebbian modification of the excitatory lateral connections can lead to the development of an intracortical orientation map. We have found that such an intracortical map can guide the development of feedforward connections from LGN to cortical simple cells so that the structure of the final feedforward orientation map is predetermined by the intracortical map. In a scenario in which left- and right-eye geniculocortical inputs develop sequentially one after the other, the resulting maps are therefore very similar, provided the intracortical connectivity remains unaltered. This may explain the outcome of so-called reverse lid-suture experiments, where animals are reared so that both eyes never receive input at the same time, but the orientation maps measured separately for the two eyes are nevertheless nearly identical. Received: 20 December 1999 / Accepted in revised form: 9 June 2000     

Frequency sensitivity in Hodgkin–Huxley systems

 The frequency sensitivity of weak periodic signal detection has been studied via numerical simulations for both a single neuron and a neuronal network. The dependence of the critical amplitude of the signal upon its frequency and a resonance between the intrinsic oscillations of a neuron and the signal could account for the frequency sensitivity. In the presence of both a subthreshold periodic signal and noise, the signal-to-noise ratio (SNR) of the output of either a single neuron or a neuronal network present the typical characteristics of stochastic resonance. In particular, there exists a frequency-sensitive range of 30–100 Hz, and for signals with frequencies within this range the SNRs have large values. This implies that the system under consideration (a single neuron or a neuronal network) is more sensitive to the detection of periodic signals, and the frequency sensitivity may be of a functional significance to signal processing. Received: 26 October 1999 / Accepted in revised form: 25 July 2000