Aperiodic stochastic resonance in neural information processing with Gaussian colored noise

The aim of this paper is to explore the phenomenon of aperiodic stochastic resonance in neural systems with colored noise. For nonlinear dynamical systems driven by Gaussian colored noise, we prove that the stochastic sample trajectory can converge to the corresponding deterministic trajectory as noise intensity tends to zero in mean square, under global and local Lipschitz conditions, respectively. Then, following forbidden interval theorem we predict the phenomenon of aperiodic stochastic resonance in bistable and excitable neural systems. Two neuron models are further used to verify the theoretical prediction. Moreover, we disclose the phenomenon of aperiodic stochastic resonance induced by correlation time and this finding suggests that adjusting noise correlation might be a biologically more plausible mechanism in neural signal processing.     

Miniaturization of nervous systems and neurons

Miniaturized species have evolved in many animal lineages, including insects and vertebrates. Consequently, their nervous systems are constrained to fit within tiny volumes. These miniaturized nervous systems face two major challenges for information processing: noise and energy consumption. Fewer or smaller neurons with fewer molecular components will increase noise, affecting information processing and transmission. Smaller, more densely-packed neural processes will increase the density of energy consumption whilst reducing the space available for mitochondria, which supply energy. Although miniaturized nervous systems benefit from smaller distances between neurons, thus saving time, space and energy, they have also increased the space available for neural processing by expanding and contorting their nervous systems to fill any available space, sometimes at the expense of other structures. Other adaptations, such as multifunctional neurons or matched filters, may further alleviate the pressures on space within miniaturized nervous systems. Despite these adaptations, we argue that limitations on information processing are likely to affect the behaviour generated by miniaturized nervous systems.     

Neural dynamics of envelope coding

We consider the processing of narrowband signals that modulate carrier waveforms in sensory systems. The tuning of sensory neurons to the carrier frequency results in a high sensitivity to the amplitude modulations of the carrier. Recent work has revealed how specialized circuitry can extract the lower-frequency modulation associated with the slow envelope of a narrowband signal, and send it to higher brain along with the full signal. This paper first summarizes the experimental evidence for this processing in the context of electroreception, where the narrowband signals arise in the context of social communication between the animals. It then examines the mechanism of this extraction by single neurons and neural populations, using intracellular recordings and new modeling results contrasting envelope extraction and stochastic resonance. Low noise and peri-threshold stimulation are necessary to obtain a firing pattern that shows high coherence with the envelope of the input. Further, the output must be fed through a slow synapse. Averaging networks are then considered for their ability to detect, using additional noise, signals with power in the envelope bandwidth. The circuitry that does support envelope extraction beyond the primary receptors is available in many areas of the brain including cortex. The mechanism of envelope extraction and its gating by noise and bias currents is thus accessible to non-carrier-based coding as well, as long as the input to the circuit is a narrowband signal. Novel results are also presented on a more biophysical model of the receptor population, showing that it can encode a narrowband signal, but not its envelope, as observed experimentally. The model is modified from previous models by stimulus reducing contrast in order to make it sufficiently linear to agree with the experimental data.     

Spatiotemporal pattern formation in two-dimensional neural circuits: roles of refractoriness and noise

Refractoriness is one of the most fundamental states of neural firing activity, in which neurons that have just fired are unable to produce another spike, regardless of the strength of afferent stimuli. Another essential and unavoidable feature of neural systems is the existence of noise. To study the role of these essential factors in spatiotemporal pattern formation in neural systems, a spatially expended neural network model is constructed, with the dynamics of its individual neurons capturing the three most essential states of the neural firing behavior: firing, refractory and resting, and the network topology consistent with the widely observed center-surround coupling manner in the real brain. By changing the refractory period with and without noise in a systematic way in the network, it is shown numerically and analytically that without refractoriness, or when the refractory period is smaller than a certain value, the collective activity pattern of the system consists of localized, oscillating patterns. However, when the refractory period is greater than a certain value, crescent-shaped, localized propagating patterns emerge in the presence of noise. It is further illustrated that the formation of the dynamical spiking patterns is due to a symmetry breaking mechanism, refractoriness-induced symmetry breaking; that is generated by the interplay of noise and refractoriness in the network model. This refractoriness-induced symmetry breaking provides a novel perspective on the emergence of localized, spiking wave patterns or spike timing sequences as ubiquitously observed in real neural systems; it therefore suggests that refractoriness may benefit neural systems in their temporal information processing, rather than limiting the performance of neurons, as has been conventionally thought. Our results also highlight the importance of considering noise in studying spatially extended neural systems, where it may facilitate the formation of spatiotemporal order.     

Emerging concepts for the dynamical organization of resting-state activity in the brain

A broad body of experimental work has demonstrated that apparently spontaneous brain activity is not random. At the level of large-scale neural systems, as measured with functional MRI (fMRI), this ongoing activity reflects the organization of a series of highly coherent functional networks. These so-called resting-state networks (RSNs) closely relate to the underlying anatomical connectivity but cannot be understood in those terms alone. Here we review three large-scale neural system models of primate neocortex that emphasize the key contributions of local dynamics, signal transmission delays and noise to the emerging RSNs. We propose that the formation and dissolution of resting-state patterns reflects the exploration of possible functional network configurations around a stable anatomical skeleton.     

Experimental and theoretical approaches to conscious processing

Recent experimental studies and theoretical models have begun to address the challenge of establishing a causal link between subjective conscious experience and measurable neuronal activity. The present review focuses on the well-delimited issue of how an external or internal piece of information goes beyond nonconscious processing and gains access to conscious processing, a transition characterized by the existence of a reportable subjective experience. Converging neuroimaging and neurophysiological data, acquired during minimal experimental contrasts between conscious and nonconscious processing, point to objective neural measures of conscious access: late amplification of relevant sensory activity, long-distance cortico-cortical synchronization at beta and gamma frequencies, and "ignition" of a large-scale prefronto-parietal network. We compare these findings to current theoretical models of conscious processing, including the Global Neuronal Workspace (GNW) model according to which conscious access occurs when incoming information is made globally available to multiple brain systems through a network of neurons with long-range axons densely distributed in prefrontal, parieto-temporal, and cingulate cortices. The clinical implications of these results for general anesthesia, coma, vegetative state, and schizophrenia are discussed.     

Information processing in neural networks by means of controlled dynamic regimes

This paper is concerned with the modeling of neural systems regarded as information processing entities. I investigate the various dynamic regimes that are accessible in neural networks considered as nonlinear adaptive dynamic systems. The possibilities of obtaining steady, oscillatory or chaotic regimes are illustrated with different neural network models. Some aspects of the dependence of the dynamic regimes upon the synaptic couplings are examined. I emphasize the role that the various regimes may play to support information processing abilities. I present an example where controlled transient evolutions in a neural network, are used to model the regulation of motor activities by the cerebellar cortex.     

Computational models of schizophrenia and dopamine modulation in the prefrontal cortex

Computational neuroscience models can be used to understand the diminished stability and noisy neurodynamical behaviour of prefrontal cortex networks in schizophrenia. These neurodynamical properties can be captured by simulated neural networks with randomly spiking neurons that introduce noise into the system and produce trial-by-trial variation of postsynaptic potentials. Theoretical and experimental studies have aimed to understand schizophrenia in relation to noise and signal-to-noise ratio, which are promising concepts for understanding the symptoms that characterize this heterogeneous illness. Simulations of biologically realistic neural networks show how the functioning of NMDA (N-methyl-D-aspartate), GABA (gamma-aminobutyric acid) and dopamine receptors is connected to the concepts of noise and variability, and to related neurophysiological findings and clinical symptoms in schizophrenia.     

Bio-Inspired Electromagnetic Protection Based on Neural Information Processing

Electronic systems are vulnerable in electromagnetic interference environment. Although many solutions are adopted to solve this problem, for example shielding, filtering and grounding, noise is still introduced into the circuit inevitably. What impresses us is the biological nervous system with a vital property of robustness in noisy environment. Some mechanisms, such as neuron population coding, degeneracy and parallel distributed processing, are believed to partly explain how the nervous system counters the noise and component failure. This paper proposes a novel concept of bio-inspired electromagnetic protec- tion making reference to the characteristic of neural information processing. A bionic model is presented here to mimic neuron populations to transform the input signal into neural pulse signal. In the proposed model, neuron provides a dynamic feedback to the adjacent one according to the concept of synaptic plasticity. A simple neural circuitry is designed to verify the rationality of the bio-inspired model for electromagnetic protection. The experiment results display that bio-inspired electromagnetic pro- tection model has more power to counter the interference and component failure.     

Threshold fatigue and information transfer

Neurons in vivo must process sensory information in the presence of significant noise. It is thus plausible to assume that neural systems have developed mechanisms to reduce this noise. Theoretical studies have shown that threshold fatigue (i.e. cumulative increases in the threshold during repetitive firing) could lead to noise reduction at certain frequencies bands and thus improved signal transmission as well as noise increases and decreased signal transmission at other frequencies: a phenomenon called noise shaping. There is, however, no experimental evidence that threshold fatigue actually occurs and, if so, that it will actually lead to noise shaping. We analyzed action potential threshold variability in intracellular recordings in vivo from pyramidal neurons in weakly electric fish and found experimental evidence for threshold fatigue: an increase in instantaneous firing rate was on average accompanied by an increase in action potential threshold. We show that, with a minor modification, the standard Hodgkin–Huxley model can reproduce this phenomenon. We next compared the performance of models with and without threshold fatigue. Our results show that threshold fatigue will lead to a more regular spike train as well as robustness to intrinsic noise via noise shaping. We finally show that the increased/reduced noise levels due to threshold fatigue correspond to decreased/increased information transmission at different frequencies. Action Editor: David Golomb     

Minimal models of multidimensional computations

The multidimensional computations performed by many biological systems are often characterized with limited information about the correlations between inputs and outputs. Given this limitation, our approach is to construct the maximum noise entropy response function of the system, leading to a closed-form and minimally biased model consistent with a given set of constraints on the input/output moments; the result is equivalent to conditional random field models from machine learning. For systems with binary outputs, such as neurons encoding sensory stimuli, the maximum noise entropy models are logistic functions whose arguments depend on the constraints. A constraint on the average output turns the binary maximum noise entropy models into minimum mutual information models, allowing for the calculation of the information content of the constraints and an information theoretic characterization of the system's computations. We use this approach to analyze the nonlinear input/output functions in macaque retina and thalamus; although these systems have been previously shown to be responsive to two input dimensions, the functional form of the response function in this reduced space had not been unambiguously identified. A second order model based on the logistic function is found to be both necessary and sufficient to accurately describe the neural responses to naturalistic stimuli, accounting for an average of 93% of the mutual information with a small number of parameters. Thus, despite the fact that the stimulus is highly non-Gaussian, the vast majority of the information in the neural responses is related to first and second order correlations. Our results suggest a principled and unbiased way to model multidimensional computations and determine the statistics of the inputs that are being encoded in the outputs.     

Noise affects the shape of female preference functions for acoustic signals

The shape of female mate preference functions influences the speed and direction of sexual signal evolution. However, the expression of female preferences is modulated by interactions between environmental conditions and the female's sensory processing system. Noise is an especially relevant environmental condition because it interferes directly with the neural processing of signals. Although noise is therefore likely a significant force in the evolution of communication systems, little is known about its effects on preference function shape. In the grasshopper Chorthippus biguttulus, female preferences for male calling song characteristics are likely to be affected by noise because its auditory system is sensitive to fine temporal details of songs. We measured female preference functions for variation in male song characteristics in several levels of masking noise and found strong effects of noise on preference function shape. The overall responsiveness to signals in noise generally decreased. Preference strength increased for some signal characteristics and decreased for others, largely corresponding to expectations based on neurophysiological studies of acoustic signal processing. These results suggest that different signal characteristics will be favored under different noise conditions, and thus that signal evolution may proceed differently depending on the extent and temporal patterning of environmental noise.     

Visual threshold is set by linear and nonlinear mechanisms in the retina that mitigate noise: how neural circuits in the retina improve the signal-to-noise ratio of the single-photon response

In sensory biology, a major outstanding question is how sensory receptor cells minimize noise while maximizing signal to set the detection threshold. This optimization could be problematic because the origin of both the signals and the limiting noise in most sensory systems is believed to lie in stimulus transduction. Signal processing in receptor cells can improve the signal-to-noise ratio. However, neural circuits can further optimize the detection threshold by pooling signals from sensory receptor cells and processing them using a combination of linear and nonlinear filtering mechanisms. In the visual system, noise limiting light detection has been assumed to arise from stimulus transduction in rod photoreceptors. In this context, the evolutionary optimization of the signal-to-noise ratio in the retina has proven critical in allowing visual sensitivity to approach the limits set by the quantal nature of light. Here, we discuss how noise in the mammalian retina is mitigated to allow for highly sensitive night vision.     

Finding the way with a noisy brain

Successful navigation is fundamental to the survival of nearly every animal on earth, and achieved by nervous systems of vastly different sizes and characteristics. Yet surprisingly little is known of the detailed neural circuitry from any species which can accurately represent space for navigation. Path integration is one of the oldest and most ubiquitous navigation strategies in the animal kingdom. Despite a plethora of computational models, from equational to neural network form, there is currently no consensus, even in principle, of how this important phenomenon occurs neurally. Recently, all path integration models were examined according to a novel, unifying classification system. Here we combine this theoretical framework with recent insights from directed walk theory, and develop an intuitive yet mathematically rigorous proof that only one class of neural representation of space can tolerate noise during path integration. This result suggests many existing models of path integration are not biologically plausible due to their intolerance to noise. This surprising result imposes significant computational limitations on the neurobiological spatial representation of all successfully navigating animals, irrespective of species. Indeed, noise-tolerance may be an important functional constraint on the evolution of neuroarchitectural plans in the animal kingdom.     

Bulbocortical interplay in olfactory information processing via synchronous oscillations

Emergence of synchronous oscillatory activity is an inherent feature of the olfactory systems of insects, mollusks and mammals. A class of simple computational models of the mammalian olfactory system consisting of olfactory bulb and olfactory cortex is constructed to explore possible roles of the related neural circuitry in olfactory information processing via synchronous oscillations. In the models, the bulbar neural circuitry is represented by a chain of oscillators and that of cortex is analogous to an associative memory network with horizontal synaptic connections. The models incorporate the backprojection from cortical units to the bulbar oscillators in particular ways. They exhibit rapid and robust synchronous oscillations in the presence of odorant stimuli, while they show either nonoscillatory states or propagating waves in the absence of stimuli, depending on the values of model parameters. In both models, the backprojection is shown to enhance the establishment of large-scale synchrony. The results suggest that the modulation of neural activity through centrifugal inputs may play an important role at the early stage of cortical information processing.     

Electrical coupling of photoreceptors in retinal network models

The spatial width of photoreceptor receptive fields affects the processing of signals in neural networks of the retina. This effect has been examined using the simple recurrent and non-recurrent network models, where lateral interaction strength was adjusted to approximate a prescribed receptive field profile. The results indicate that the optimal performance of the networks is obtained with photoreceptor receptive fields wider than the ganglion cell separation. It is thus concluded that while electrical coupling of photoreceptors in the retina reduces the intrinsic noise in the system, it also improves the sampling efficiency of the laterally coupled neural network of the retina.     

A comparative study of pattern synchronization detection between neural signals using different cross-entropy measures

Cross-approximate entropy (X-ApEn) and cross-sample entropy (X-SampEn) have been employed as bivariate pattern synchronization measures for characterizing interdependencies between neural signals. In this study, we proposed a new measure, cross-fuzzy entropy (X-FuzzyEn), to describe the synchronicity of patterns. The performances of three statistics were first quantitatively tested using five different coupled systems including both deterministic and stochastic models, i.e., coupled broadband noises, Lorenz–Lorenz, Rossler–Rossler, Rossler–Lorenz, and neural mass model. All the measures were compared with each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise. The three measures were then applied to a real-life problem, pattern synchronization analysis of left and right hemisphere rat electroencephalographic (EEG) signals. Both simulated and real EEG data analysis results showed that the X-FuzzyEn provided an improved evaluation of bivariate series pattern synchronization and could be more conveniently and powerfully applied to different neural dynamical systems contaminated by noise.     

New strategies for improving speech enhancement

We describe two design strategies that could substantially improve the performance of speech enhancement systems. Results from a preliminary study of pulse recovery are presented to illustrate the potential benefits of such strategies. The first strategy is a direct application of a non-linear, adaptive signal processing approach for recovery of speech in noise. The second strategy optimizes performance by maximizing the enhancement system's ability to evoke target speech percepts. This approach may lead to better performance because the design is optimized on a measure directly related to the ultimate goal of speech enhancement: accurate communication of the speech percept. In both systems, recently developed ‘neural network’ learning algorithms can be used to determine appropriate parameters for enhancement processing.     

Automated refinement and inference of analytical models for metabolic networks

The reverse engineering of metabolic networks from experimental data is traditionally a labor-intensive task requiring a priori systems knowledge. Using a proven model as a test system, we demonstrate an automated method to simplify this process by modifying an existing or related model--suggesting nonlinear terms and structural modifications--or even constructing a new model that agrees with the system's time series observations. In certain cases, this method can identify the full dynamical model from scratch without prior knowledge or structural assumptions. The algorithm selects between multiple candidate models by designing experiments to make their predictions disagree. We performed computational experiments to analyze a nonlinear seven-dimensional model of yeast glycolytic oscillations. This approach corrected mistakes reliably in both approximated and overspecified models. The method performed well to high levels of noise for most states, could identify the correct model de novo, and make better predictions than ordinary parametric regression and neural network models. We identified an invariant quantity in the model, which accurately derived kinetics and the numerical sensitivity coefficients of the system. Finally, we compared the system to dynamic flux estimation and discussed the scaling and application of this methodology to automated experiment design and control in biological systems in real time.     

Information coding by ensembles of resonant neurons

In the present paper, we propose a novel neural procedure for signal processing and coding based on the subthreshold oscillations and resonance of the neural membrane potential that could be used by real neurons to perform frequency spectra analysis and information coding of incoming signals. Taking into account the biophysical properties of the neural membranes, we note that the subthreshold resonant behaviour they exhibit can be used to analyse incoming signals and represent them in the frequency domain. We study the reliability of the representation of signals depending on the biophysical parameters of the neurons, the fault-tolerance of this coding scheme and its robustness against noise and in the presence of spikes. The principal characteristics of our system are the use of the physical phenomenon of neural resonance (rarely considered in the literature for signal coding); it fits well with the biophysical parameters of most neurons that exhibit subthreshold oscillations; it is compatible with experimental data; and it can be easily integrated in a more general model of information processing and coding that includes communication between neurons based on spikes.