How we hear what is not there: a neural mechanism for the missing fundamental illusion

Frequency-specific contributions to auditory perceptual priors: Testing the predictive-coding hypothesis

Perceptual priors formed by recent stimuli bias our immediate percept. These priors, expressing our implicit expectations, affect both high- and low-level processing stages. Yet, the nature of the inter-level interaction is unknown. Do priors operate top-down and bias low-level features toward recently experienced objects (predictive-coding hypothesis), or are low-level biases bottom-up driven and formed by local memory circuits? To decipher between these options in auditory perception, we used the "missing fundamental illusion", enabling the dissociation of low-level components from the high-level pitch. Surprisingly, in contrast to predictive coding, when the fundamental frequency was missing, pitch contraction across timbre categories was not found to the previously perceived high-level pitch, but to the physically present frequency. This bottom-up contribution of low-level memory components to perceptual priors, operating independently of recent high-level percepts, may stabilize the perceptual organization and underlie continuity between similar low-level features belonging to different object categories in the auditory modality.

Hearing as adaptive cascaded envelope interpolation

The human auditory system is designed to capture and encode sounds from our surroundings and conspecifics. However, the precise mechanisms by which it adaptively extracts the most important spectro-temporal information from sounds are still not fully understood. Previous auditory models have explained sound encoding at the cochlear level using static filter banks, but this vision is incompatible with the nonlinear and adaptive properties of the auditory system. Here we propose an approach that considers the cochlear processes as envelope interpolations inspired by cochlear physiology. It unifies linear and nonlinear adaptive behaviors into a single comprehensive framework that provides a data-driven understanding of auditory coding. It allows simulating a broad range of psychophysical phenomena from virtual pitches and combination tones to consonance and dissonance of harmonic sounds. It further predicts the properties of the cochlear filters such as frequency selectivity. Here we propose a possible link between the parameters of the model and the density of hair cells on the basilar membrane. Cascaded Envelope Interpolation may lead to improvements in sound processing for hearing aids by providing a non-linear, data-driven, way to preprocessing of acoustic signals consistent with peripheral processes.

Adaptive stochastic resonance for unknown and variable input signals

All sensors have a threshold, defined by the smallest signal amplitude that can be detected. The detection of sub-threshold signals, however, is possible by using the principle of stochastic resonance, where noise is added to the input signal so that it randomly exceeds the sensor threshold. The choice of an optimal noise level that maximizes the mutual information between sensor input and output, however, requires knowledge of the input signal, which is not available in most practical applications. Here we demonstrate that the autocorrelation of the sensor output alone is sufficient to find this optimal noise level. Furthermore, we demonstrate numerically and analytically the equivalence of the traditional mutual information approach and our autocorrelation approach for a range of model systems. We furthermore show how the level of added noise can be continuously adapted even to highly variable, unknown input signals via a feedback loop. Finally, we present evidence that adaptive stochastic resonance based on the autocorrelation of the sensor output may be a fundamental principle in neuronal systems.

From the intrinsic properties to the functional role of a neuron phenotype: an example from electric fish during signal trade-off

This review deals with the question: what is the relationship between the properties of a neuron and the role that the neuron plays within a given neural circuit? Answering this kind of question requires collecting evidence from multiple neuron phenotypes and comparing the role of each type in circuits that perform well-defined computational tasks. The focus here is on the spherical neurons in the electrosensory lobe of the electric fish Gymnotus omarorum. They belong to the one-spike-onset phenotype expressed at the early stages of signal processing in various sensory modalities and diverse taxa. First, we refer to the one-spike neuron intrinsic properties, their foundation on a low-threshold K(+) conductance, and the potential roles of this phenotype in different circuits within a comparative framework. Second, we present a brief description of the active electric sense of weakly electric fish and the particularities of spherical one-spike-onset neurons in the electrosensory lobe of G. omarorum. Third, we introduce one of the specific tasks in which these neurons are involved: the trade-off between self- and allo-generated signals. Fourth, we discuss recent evidence indicating a still-undescribed role for the one-spike phenotype. This role deals with the blockage of the pathway after being activated by the self-generated electric organ discharge and how this blockage favors self-generated electrosensory information in the context of allo-generated interference. Based on comparative analysis we conclude that one-spike-onset neurons may play several functional roles in animal sensory behavior. There are specific adaptations of the neuron's 'response function' to the circuit and task. Conversely, the way in which a task is accomplished depends on the intrinsic properties of the neurons involved. In short, the role of a neuron within a circuit depends on the neuron and its functional context.

Short term depression unmasks the ghost frequency

Short Term Plasticity (STP) has been shown to exist extensively in synapses throughout the brain. Its function is more or less clear in the sense that it alters the probability of synaptic transmission at short time scales. However, it is still unclear what effect STP has on the dynamics of neural networks. We show, using a novel dynamic STP model, that Short Term Depression (STD) can affect the phase of frequency coded input such that small networks can perform temporal signal summation and determination with high accuracy. We show that this property of STD can readily solve the problem of the ghost frequency, the perceived pitch of a harmonic complex in absence of the base frequency. Additionally, we demonstrate that this property can explain dynamics in larger networks. By means of two models, one of chopper neurons in the Ventral Cochlear Nucleus and one of a cortical microcircuit with inhibitory Martinotti neurons, it is shown that the dynamics in these microcircuits can reliably be reproduced using STP. Our model of STP gives important insights into the potential roles of STP in self-regulation of cortical activity and long-range afferent input in neuronal microcircuits.

Ghost resonance in the chaotic Chua's circuit

We experimentally investigate the ghost resonance phenomenon in the electronic circuit of Chua operating in the chaotic regime. The circuit can be stimulated to jump between two single-scroll attractors by an external periodic signal with an amplitude above an intrinsic threshold. For subthreshold signals, jumps between the chaotic attractors can be promoted by a superposed white noise. We show that the circuit output can exhibit a well-defined ghost resonance signature, i.e., a resonance on a frequency that is absent in a multicomponent input signal, when the amplitudes of the input components are properly related. Further, we show that ghost resonance can be induced by the Chua's circuit's own chaotic dynamics when it is driven by a suprathreshold multicomponent signal without the need of an external noise source.

Coherence depression in stochastic excitable systems with two-frequency forcing

We study the response of two generic neuron models, the leaky integrate-and-fire (LIF) model and the leaky integrate-and-fire model with dynamic threshold (LIFDT) (i.e., with memory) to a stimulus consisting of two sinusoidal drives with incommensurate frequency, an amplitude modulation ("envelope") noise and a relatively weak additive noise. Spectral and coherence analysis of responses to such naturalistic stimuli reveals how the LIFDT model exhibits better correlation between modulation and spike train even in the presence of both noises. However, a resonance-induced synchrony, occurring when the beat frequency between the sinusoids is close to the intrinsic neuronal firing rate, decreases the coherence in the dynamic threshold case. Under suprathreshold conditions, the modulation noise simultaneously decreases the linear spectral coherence between the spikes and the whole stimulus, as well as between spikes and the stimulus envelope. Our study shows that the coefficient of variation of the envelope fluctuations is positively correlated with the degree of coherence depression. As the coherence function quantifies the linear information transmission, our findings indicate that under certain conditions, a transmission loss results when an excitable system with adaptive properties encodes a beat with frequency in the vicinity of its mean firing rate.

Japanese Knowledge Creation and the Fundamental Illusion Theory: A Fresh Look

We propose the fundamental illusion theory to explain knowledge creation based on Japanese companies. This theory is a hearing illusion which explains that when two tones occur together a third lower pitched tone is heard, but this last perceived pitch is a frequency (fundamental) for which there is no actual source vibration. If we make an analogy between fundamental frequency and knowledge, between tones occurring together and learning + culture + leadership, we have a new management model.

Spike train statistics for consonant and dissonant musical accords in a simple auditory sensory model

The phenomena of dissonance and consonance in a simple auditory sensory model composed of three neurons are considered. Two of them, here so-called sensory neurons, are driven by noise and subthreshold periodic signals with different ratio of frequencies, and its outputs plus noise are applied synaptically to a third neuron, so-called interneuron. We present a theoretical analysis with a probabilistic approach to investigate the interspike intervals statistics of the spike train generated by the interneuron. We find that tones with frequency ratios that are considered consonant by musicians produce at the third neuron inter-firing intervals statistics densities that are very distinctive from densities obtained using tones with ratios that are known to be dissonant. In other words, at the output of the interneuron, inharmonious signals give rise to blurry spike trains, while the harmonious signals produce more regular, less noisy, spike trains. Theoretical results are compared with numerical simulations.

Synchronization of stochastic bistable systems by biperiodic signals

We study the nonlinear response of a noisy bistable system to a biperiodic signal through experiments with an electronic circuit (Schmitt trigger). The signal we use is a biharmonic one, i.e., a superposition of low and high frequency harmonic components. It is shown that the mean switching frequency (MSF) of the system can be locked at both low and high frequencies. Moreover, the phenomenon of MSF locking at the lower frequency can be induced and enhanced by the higher frequency excitation. Thus high frequency bias can control synchronization at the low frequency.

Phantom reflexes: Muscle contractions at a frequency not physically present in the input stimuli

In the motor system, the periodic stimulation of one Ia-afferent input produces reflex muscle contractions at the input frequency. However, we observed that when two Ia monosynaptic reflex-afferent inputs are involved the periodic muscle contractions may occur at a frequency physically not present in the afferent inputs even when these inputs are sub-threshold. How can the muscles respond with such phantom reflex contractions at a frequency physically absent in the sub-threshold Ia-afferent input stimuli? Here we provide an explanation for this phenomenon in the cat spinal cord, that we termed "ghost motor response". We recorded monosynaptic reflexes in the L7 ventral root, intracellular potentials in the motoneurons, and the associated muscular contractions elicited by stimulation of the lateral and medial gastrocnemius nerves. By stimulating with periodic pulses of sub-threshold intensities and distinct frequencies of 2 and 3 Hz the lateral and medial gastrocnemius nerves, respectively, we observed monosynaptic responses and phantom reflex muscle contractions occurring at the fundamental frequency (1 Hz), which was absent in the input stimuli. Thus we observed a reflex ghost motor response at a frequency not physically present in the inputs. We additionally studied the inharmonic case for sub-threshold stimuli and observed muscular contractions occurring at much lower frequencies, which were also conspicuously absent in the inputs. This is the first experimental evidence of a phantom reflex response in the nervous system. The observed behavior was modeled by numerical simulations of a pool of neurons subjected to two different input pulses.

Ghost resonance in a pool of heterogeneous neurons

We numerically study the subharmonic response of a heterogeneous pool of neurons to a pair of independent inputs. The neurons are stimulated with periodic pulse trains of frequencies f(1)=2 Hz and f(2)=3 Hz, and with inharmonic pulses whose frequencies f(1) and f(2) are equally shifted an amount Delta f. When both inputs are subthreshold, we find that the neurons respond at a frequency equal to f(2)-f(1) in the harmonic situation (Delta f=0), that increases linearly with Delta f in the inharmonic case. Thus the neurons detect a frequency not present in the input; this effect is termed "ghost resonance". When one of the inputs is slightly suprathreshold the ghost resonance persists, but responses related with the frequency of the suprathreshold input also emerge. This behavior must be taken into account in experimental studies of signal integration and coincidence detection by neuronal pools.

An auditory neural correlate suggests a mechanism underlying holistic pitch perception

Current theories of auditory pitch perception propose that cochlear place (spectral) and activity timing pattern (temporal) information are somehow combined within the brain to produce holistic pitch percepts, yet the neural mechanisms for integrating these two kinds of information remain obscure. To examine this process in more detail, stimuli made up of three pure tones whose components are individually resolved by the peripheral auditory system, but that nonetheless elicit a holistic, "missing fundamental" pitch percept, were played to human listeners. A technique was used to separate neural timing activity related to individual components of the tone complexes from timing activity related to an emergent feature of the complex (the envelope), and the region of the tonotopic map where information could originate from was simultaneously restricted by masking noise. Pitch percepts were mirrored to a very high degree by a simple combination of component-related and envelope-related neural responses with similar timing that originate within higher-frequency regions of the tonotopic map where stimulus components interact. These results suggest a coding scheme for holistic pitches whereby limited regions of the tonotopic map (spectral places) carrying envelope- and component-related activity with similar timing patterns selectively provide a key source of neural pitch information. A similar mechanism of integration between local and emergent object properties may contribute to holistic percepts in a variety of sensory systems.

The cellular basis for parallel neural transmission of a high-frequency stimulus and its low-frequency envelope

Sensory stimuli often have rich temporal and spatial structure. One class of stimuli that are common to visual and auditory systems and, as we show, the electrosensory system are signals that contain power in a narrow range of temporal (or spatial) frequencies. Characteristic of this class of signals is a slower variation in their amplitude, otherwise known as an envelope. There is evidence suggesting that, in the visual cortex, both narrowband stimuli and their envelopes are coded for in separate and parallel streams. The implementation of this parallel transmission is not well understood at the cellular level. We have identified the cellular basis for the parallel transmission of signal and envelope in the electrosensory system: a two-cell network consisting of an interneuron connected to a pyramidal cell by means of a slow synapse. This circuit could, in principle, be implemented in the auditory or visual cortex by the previously identified biophysics of cortical interneurons.

Ghost stochastic resonance with distributed inputs in pulse-coupled electronic neurons

We study experimentally the phenomenon of ghost stochastic resonance in pulse-coupled excitable systems, for input signals distributed among different elements. Specifically, two excitable electronic circuits are driven by different sinusoidal signals that produce periodic spikes at distinct frequencies. Their outputs are sent to a third circuit that processes these spiking signals and is additionally perturbed by noise. When the input signals are harmonics of a certain fundamental (that is not present in the inputs) the processing circuit exhibits, for an optimal amount of noise, a resonant response at the frequency of the missing fundamental (ghost frequency). In contrast with the standard case in which the signals being directly integrated are sinusoidal, this behavior relies here on a coincidence-detection mechanism. When the input signals are homogeneously shifted in frequency, the processing circuit responds with pulse packages composed of spikes at a frequency that depends linearly on the frequency shift. Expressions for the dependence of the package period and duration on the frequency shift and spike width, respectively, are obtained. These results provide an experimental verification of a recently proposed mechanism of binaural pitch perception.

Ghost stochastic resonance in vertical-cavity surface-emitting lasers: experiment and theory

We study the polarization response of a vertical-cavity surface-emitting laser, driven simultaneously by noise and two (or more) weak periodic signals. In the bistable regime, we observe experimentally the occurrence of stochastic resonance at a frequency that is absent in the input driving signal. The presence of this so-called ghost resonance is confirmed theoretically.

Noise-assisted transport on symmetric periodic substrates

The rectification of a massive Brownian particle moving on a periodic substrate can be achieved in the absence of spatial asymmetry, by having recourse to (at least) two periodic, zero-mean input signals. We determine the relevant drift current under diverse operation conditions, namely, additive and multiplicative couplings, adiabatic and fast oscillating drives, and propagating substrate modulations. Distinct rectification mechanisms result from the interplay of noise and commensuration of the input frequencies, mediated through the nonlinearity of the substrate. These mechanisms are then extended to characterize soliton transport along a directed multistable chain. As the side-wise soliton diffusion is ultimately responsible for the transverse diffusion of such chains, our approach provides a full account of the Brownian motion of both pointlike and linear objects on a periodic substrate.

Neural mechanism for binaural pitch perception via ghost stochastic resonance

We present a physiologically plausible binaural mechanism for the perception of the pitch of complex sounds via ghost stochastic resonance. In this scheme, two neurons are driven by noise and a different periodic signal each (with frequencies f(1)=kf(0) and f(2)=(k+1)f(0), where k>1), and their outputs (plus noise) are applied synaptically to a third neuron. Our numerical results, using the Morris-Lecar neuron model with chemical synapses explicitly considered, show that intermediate noise levels enhance the response of the third neuron at frequencies close to f(0), as in the cases previously described of ghost resonance. For the case of an inharmonic combination of inputs (f(1)=kf(0)+Deltaf and f(2)=(k+1)f(0)+Deltaf) noise is also seen to enhance the rates of most probable spiking for the third neuron at a frequency f(r)=f(0)+[Deltaf(k+12)]. In addition, we show that similar resonances can be observed as a function of the synaptic time constant. The suggested ghost-resonance-based stochastic mechanism can thus arise either at the peripheral level or at a higher level of neural processing in the perception of pitch.

Coupling-mediated ghost resonance in mutually injected lasers

We experimentally and numerically study the phenomenon of ghost resonance in coupled nonlinear systems. Two mutually injected semiconductor lasers are externally perturbed in their pump currents by two respective periodic signals of different frequencies f(1) and f(2). For small amplitudes of the external modulations, the two laser intensities display synchronized optical pulses, in the form of dropout events occurring at irregular times. By adjusting the amplitude and frequencies of the driving signals, the system exhibits a ghost resonance in the dropout appearance at a frequency f(r) not present in the distributed inputs.