Preference of sensory neural coding for 1/f signals

Complexity Synchronization of Organ Networks

The transdisciplinary nature of science as a whole became evident as the necessity for the complex nature of phenomena to explain social and life science, along with the physical sciences, blossomed into complexity theory and most recently into complexitysynchronization. This science motif is based on the scaling arising from the 1/f-variability in complex dynamic networks and the need for a network of networks to exchange information internally during intra-network dynamics and externally during inter-network dynamics. The measure of complexity adopted herein is the multifractal dimension of the crucial event time series generated by an organ network, and the difference in the multifractal dimensions of two organ networks quantifies the relative complexity between interacting complex networks. Information flows from dynamic networks at a higher level of complexity to those at lower levels of complexity, as summarized in the 'complexity matching effect', and the flow is maximally efficient when the complexities are equal. Herein, we use the scaling of empirical datasets from the brain, cardiovascular and respiratory networks to support the hypothesis that complexity synchronization occurs between scaling indices or equivalently with the matching of the time dependencies of the networks' multifractal dimensions.

Scale-free dynamics in the core-periphery topography and task alignment decline from conscious to unconscious states

Scale-free physiological processes are ubiquitous in the human organism. Resting-state functional MRI studies observed the loss of scale-free dynamics under anesthesia. In contrast, the modulation of scale-free dynamics during task-related activity remains an open question. We investigate scale-free dynamics in the cerebral cortex's unimodal periphery and transmodal core topography in rest and task states during three conscious levels (awake, sedation, and anesthesia) complemented by computational modelling (Stuart-Landau model). The empirical findings demonstrate that the loss of the brain's intrinsic scale-free dynamics in the core-periphery topography during anesthesia, where pink noise transforms into white noise, disrupts the brain's neuronal alignment with the task's temporal structure. The computational model shows that the stimuli's scale-free dynamics, namely pink noise distinguishes from brown and white noise, also modulate task-related activity. Together, we provide evidence for two mechanisms of consciousness, temporo-spatial nestedness and alignment, suggested by the Temporo-Spatial Theory of Consciousness (TTC).

1/f laws found in non-human music

A compelling question at the intersection of physics, neuroscience, and evolutionary biology concerns the extent to which the brains of various species evolved to encode regularities of the physical world. It would be parsimonious and adaptive, for example, for brains to evolve an innate understanding of gravity and the laws of motion, and to be able to detect, auditorily, those patterns of noises that ambulatory creatures make when moving about the world. One such physical regularity of the world is fractal structure, generally characterized by power-law correlations or 1/f ^β spectral distributions. Such laws are found broadly in nature and human artifacts, from noise in physical systems, to coastline topography (e.g., the Richardson effect), to neuronal spike patterns. These distributions have also been found to hold for the rhythm and power spectral density of a wide array of human music, suggesting that human music incorporates regularities of the physical world that our species evolved to recognize and produce. Here we show for the first time that 1/f^β laws also govern the spectral density of a wide range of animal vocalizations (music), from songbirds, to whales, to howling wolves. We discovered this 1/f^β power-law distribution in the vocalizations within all of the 17 diverse species examined. Our results demonstrate that such power laws are prevalent in the animal kingdom, evidence that their brains have evolved a sensitivity to them as an aid in processing sensory features of the natural world.

Wired for sound: The effect of sound on the epileptic brain

Sound waves are all around us resonating at audible and inaudible frequencies. Our ability to hear is crucial in providing information and enabling interaction with our environment. The human brain generates neural oscillations or brainwaves through synchronised electrical impulses. In epilepsy these brainwaves can change and form rhythmic bursts of abnormal activity outwardly appearing as seizures. When two waveforms meet, they can superimpose onto one another forming constructive, destructive or mixed interference. The effects of audible soundwaves on epileptic brainwaves has been largely explored with music. The Mozart Sonata for Two Pianos in D major, K. 448 has been examined in a number of studies where significant clinical and methodological heterogeneity exists. These studies report variable reductions in seizures and interictal epileptiform discharges. Treatment effects of Mozart Piano Sonata in C Major, K.545 and other composer interventions have been examined with some musical exposures, for example Hayden's Symphony No. 94 appearing pro-epileptic. The underlying anti-epileptic mechanism of Mozart music is currently unknown, but interesting research is moving away from dopamine reward system theories to computational analysis of specific auditory parameters. In the last decade several studies have examined inaudible low intensity focused ultrasound as a neuro-modulatory intervention in focal epilepsy. Whilst acute and chronic epilepsy rodent model studies have consistently demonstrated an anti-epileptic treatment effect this is yet to be reported within large scale human trials. Inaudible infrasound is of concern since at present there are no reported studies on the effects of exposure to infrasound on epilepsy. Understanding the impact of infrasound on epilepsy is critical in an era where sustainable energies are likely to increase exposure.

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

This is the third essay advocating the use the (non-integer) fractional calculus (FC) to capture the dynamics of complex networks in the twilight of the Newtonian era. Herein, the focus is on drawing a distinction between networks described by monfractal time series extensively discussed in the prequels and how they differ in function from multifractal time series, using physiological phenomena as exemplars. In prequel II, the network effect was introduced to explain how the collective dynamics of a complex network can transform a many-body non-linear dynamical system modeled using the integer calculus (IC) into a single-body fractional stochastic rate equation. Note that these essays are about biomedical phenomena that have historically been improperly modeled using the IC and how fractional calculus (FC) models better explain experimental results. This essay presents the biomedical entailment of the FC, but it is not a mathematical discussion in the sense that we are not concerned with the formal infrastucture, which is cited, but we are concerned with what that infrastructure entails. For example, the health of a physiologic network is characterized by the width of the multifractal spectrum associated with its time series, and which becomes narrower with the onset of certain pathologies. Physiologic time series that have explicitly related pathology to a narrowing of multifractal time series include but are not limited to heart rate variability (HRV), stride rate variability (SRV) and breath rate variability (BRV). The efficiency of the transfer of information due to the interaction between two such complex networks is determined by their relative spectral width, with information being transferred from the network with the broader to that with the narrower width. A fractional-order differential equation, whose order is random, is shown to generate a multifractal time series, thereby providing a FC model of the information exchange between complex networks. This equivalence between random fractional derivatives and multifractality has not received the recognition in the bioapplications literature we believe it warrants.

On the scaling properties of oscillatory modes with balanced energy

Animal bodies maintain themselves with the help of networks of physiological processes operating over a wide range of timescales. Many physiological signals are characterized by 1/f scaling where the amplitude is inversely proportional to frequency, presumably reflecting the multi-scale nature of the underlying network. Although there are many general theories of such scaling, it is less clear how they are grounded on the specific constraints faced by biological systems. To help understand the nature of this phenomenon, we propose to pay attention not only to the geometry of scaling processes but also to their energy. The first key assumption is that physiological action modes constitute thermodynamic work cycles. This is formalized in terms of a theoretically defined oscillator with dissipation and energy-pumping terms. The second assumption is that the energy levels of the physiological action modes are balanced on average to enable flexible switching among them. These ideas were addressed with a modelling study. An ensemble of dissipative oscillators exhibited inverse scaling of amplitude and frequency when the individual oscillators' energies are held equal. Furthermore, such ensembles behaved like the Weierstrass function and reproduced the scaling phenomenon. Finally, the question is raised whether this kind of constraint applies both to broadband aperiodic signals and periodic, narrow-band oscillations such as those found in electrical cortical activity.

Linking space-time correlations for a class of self-organized critical systems

The hypothesis of self-organized criticality explains the existence of long-range "space-time" correlations, observed inseparably in many natural dynamical systems. A simple link between these correlations is yet unclear, particularly in fluctuations at an "external drive" timescale. As an example, we consider a class of sandpile models displaying nontrivial correlations. We apply the scaling method and determine spatial cross-correlation by establishing a relationship between local and global temporal correlations. We find that the spatial cross-correlation decays in a power-law manner with an exponent γ=1-δ, where δ characterizes a scaling of the total power of the global temporal process with the system size.

Modality-specific tracking of attention and sensory statistics in the human electrophysiological spectral exponent

A hallmark of electrophysiological brain activity is its 1/f-like spectrum - power decreases with increasing frequency. The steepness of this 'roll-off' is approximated by the spectral exponent, which in invasively recorded neural populations reflects the balance of excitatory to inhibitory neural activity (E:I balance). Here, we first establish that the spectral exponent of non-invasive electroencephalography (EEG) recordings is highly sensitive to general (i.e., anaesthesia-driven) changes in E:I balance. Building on the EEG spectral exponent as a viable marker of E:I, we then demonstrate its sensitivity to the focus of selective attention in an EEG experiment during which participants detected targets in simultaneous audio-visual noise. In addition to these endogenous changes in E:I balance, EEG spectral exponents over auditory and visual sensory cortices also tracked auditory and visual stimulus spectral exponents, respectively. Individuals' degree of this selective stimulus-brain coupling in spectral exponents predicted behavioural performance. Our results highlight the rich information contained in 1/f-like neural activity, providing a window into diverse neural processes previously thought to be inaccessible in non-invasive human recordings.

Modality-specific tracking of attention and sensory statistics in the human electrophysiological spectral exponent

A hallmark of electrophysiological brain activity is its 1/f-like spectrum - power decreases with increasing frequency. The steepness of this 'roll-off' is approximated by the spectral exponent, which in invasively recorded neural populations reflects the balance of excitatory to inhibitory neural activity (E:I balance). Here, we first establish that the spectral exponent of non-invasive electroencephalography (EEG) recordings is highly sensitive to general (i.e., anaesthesia-driven) changes in E:I balance. Building on the EEG spectral exponent as a viable marker of E:I, we then demonstrate its sensitivity to the focus of selective attention in an EEG experiment during which participants detected targets in simultaneous audio-visual noise. In addition to these endogenous changes in E:I balance, EEG spectral exponents over auditory and visual sensory cortices also tracked auditory and visual stimulus spectral exponents, respectively. Individuals' degree of this selective stimulus-brain coupling in spectral exponents predicted behavioural performance. Our results highlight the rich information contained in 1/f-like neural activity, providing a window into diverse neural processes previously thought to be inaccessible in non-invasive human recordings.

Music in epilepsy: Predicting the effects of the unpredictable

Epilepsy is the most common serious neurological disorder in the world. Despite medical and surgical treatment, many individuals continue to have seizures, suggesting adjunctive management strategies are required. Promising effects of daily listening to Mozart K.448 on reducing seizure frequency in individuals with epilepsy have been demonstrated. In our recent randomized control study, we reported the positive effect of daily listening to Mozart K.448 on reducing seizures compared to daily listening to a control piece with an identical power spectrum to the Mozart piece yet devoid of rhythmic structure. Despite the promising effect of listening to Mozart K.448 on reducing seizure in individuals with epilepsy, the mechanism(s) underlying such an effect is largely unknown. In this paper, we specifically review how auditory stimulation alters brain dynamics, in addition to computational approaches to define the structural features of classical music, to then propose a plausible mechanism for the underlying anti-convulsant effects of listening to Mozart K.448. We review the evidence demonstrating that some Mozart pieces in addition to compositions from other composers such as Joplin contain less predictable rhythmic structure in comparison with other composers such as Beethoven. We propose through both entrainment and 1/f resonance mechanisms that listening to musical pieces containing the least predictable rhythmic structure, might reduce the self similarity of brain activity which in turn modulates low frequency power, situating the brain in a more "noise like" state and away from brain dynamics that can lead to seizures.

The neuroaesthetics of architectural spaces

People in developed countries spend over 90% of their time in built environments. Yet, we know little about its pervasive and often hidden effects on our mental state and our brain. Despite growing interest in the neuroscience of architecture, much of this scholarship has been descriptive. The typical approach is to map knowledge of the brain onto constructs important to architecture. For a programmatic line of research, how might descriptive neuroarchitecture be transformed into an experimental science? We review the literature outlining how one might consider experimental architecture first by examining the role of natural features in architectural settings. We then turn to the human experience of occupants, and hypothesized that aesthetic responses to architectural interiors reduce to key psychological dimensions. Conducting Psychometric Network Analysis (PNA) and Principal Components Analysis (PCA) on responses to curated images, we identified three components: coherence (ease of organizing and comprehending a scene), fascination (informational richness and generated interest), and hominess (personal ease and comfort). Coherence and fascination are well-established dimensions for natural scenes. Hominess was a new dimension related to architectural interiors. Central to all three communities in the PNA was emotional valence. We also reanalyzed data from an earlier fMRI study in which participants made beauty and approach-avoidance decisions while viewing the same images. Regardless of task, the degree of fascination covaried with neural activity in the right lingual gyrus. In contrast, coherence covaried with neural activity in the left inferior occipital gyrus only when participants judged beauty, and hominess covaried with neural activity in the left cuneus only when they made approach-avoidance decisions. The visual brain harbours hidden sensitivities to architectural interiors that are captured by the dimensions of coherence, fascination, and hominess. These findings represent first steps towards an experimental neuroarchitecture.

Untangling the wires: development of sparse, distributed connectivity in the mushroom body calyx

Appropriate perception and representation of sensory stimuli pose an everyday challenge to the brain. In order to represent the wide and unpredictable array of environmental stimuli, principle neurons of associative learning regions receive sparse, combinatorial sensory inputs. Despite the broad role of such networks in sensory neural circuits, the developmental mechanisms underlying their emergence are not well understood. As mammalian sensory coding regions are numerically complex and lack the accessibility of simpler invertebrate systems, we chose to focus this review on the numerically simpler, yet functionally similar, Drosophila mushroom body calyx. We bring together current knowledge about the cellular and molecular mechanisms orchestrating calyx development, in addition to drawing insights from literature regarding construction of sparse wiring in the mammalian cerebellum. From this, we formulate hypotheses to guide our future understanding of the development of this critical perceptual center.

Autonomous Development of Active Binocular and Motion Vision Through Active Efficient Coding

We present a model for the autonomous and simultaneous learning of active binocular and motion vision. The model is based on the Active Efficient Coding (AEC) framework, a recent generalization of classic efficient coding theories to active perception. The model learns how to efficiently encode the incoming visual signals generated by an object moving in 3-D through sparse coding. Simultaneously, it learns how to produce eye movements that further improve the efficiency of the sensory coding. This learning is driven by an intrinsic motivation to maximize the system's coding efficiency. We test our approach on the humanoid robot iCub using simulations. The model demonstrates self-calibration of accurate object fixation and tracking of moving objects. Our results show that the model keeps improving until it hits physical constraints such as camera or motor resolution, or limits on its internal coding capacity. Furthermore, we show that the emerging sensory tuning properties are in line with results on disparity, motion, and motion-in-depth tuning in the visual cortex of mammals. The model suggests that vergence and tracking eye movements can be viewed as fundamentally having the same objective of maximizing the coding efficiency of the visual system and that they can be learned and calibrated jointly through AEC.

The Impact of Frequency Scale on the Response Sensitivity and Reliability of Cortical Neurons to 1/fβ Input Signals

What type of principle features intrinsic inside of the fluctuated input signals could drive neurons with the maximal excitations is one of the crucial neural coding issues. In this article, we examined both experimentally and theoretically the cortical neuronal responsivity (including firing rate and spike timing reliability) to input signals with different intrinsic correlational statistics (e.g., white-type noise, showed 1/f⁰ power spectrum, pink noise 1/f, and brown noises 1/f²) and different frequency ranges. Our results revealed that the response sensitivity and reliability of cortical neurons is much higher in response to 1/f noise stimuli with long-term correlations than 1/f⁰ with short-term correlations for a broad frequency range, and also higher than 1/f² for all frequency ranges. In addition, we found that neuronal sensitivity diverges to opposite directions for 1/f noise comparing with 1/f⁰ white noise as a function of cutoff frequency of input signal. As the cutoff frequency is progressively increased from 50 to 1,000 Hz, the neuronal responsiveness increased gradually for 1/f noise, while decreased exponentially for white noise. Computational simulations of a general cortical model revealed that, neuronal sensitivity and reliability to input signal statistics was majorly dominated by fast sodium inactivation, potassium activation, and membrane time constants.

Critical synchronization and 1/f noise in inhibitory/excitatory rich-club neural networks

In recent years, diverse studies have reported that different brain regions, which are internally densely connected, are also highly connected to each other. This configuration seems to play a key role in integrating and interchanging information between brain areas. Also, changes in the rich-club connectivity and the shift from inhibitory to excitatory behavior of hub neurons have been associated with several diseases. However, there is not a clear understanding about the role of the proportion of inhibitory/excitatory hub neurons, the dynamic consequences of rich-club disconnection, and hub inhibitory/excitatory shifts. Here, we study the synchronization and temporal correlations in the neural Izhikevich model, which comprises excitatory and inhibitory neurons located in a scale-free hierarchical network with rich-club connectivity. We evaluated the temporal autocorrelations and global synchronization dynamics displayed by the system in terms of rich-club connectivity and hub inhibitory/excitatory population. We evaluated the synchrony between pairs of sets of neurons by means of the global lability synchronization, based on the rate of change in the total number of synchronized signals. The results show that for a wide range of excitatory/inhibitory hub ratios the network displays 1/f dynamics with critical synchronization that is concordant with numerous health brain registers, while a network configuration with a vast majority of excitatory hubs mostly exhibits short-term autocorrelations with numerous large avalanches. Furthermore, rich-club connectivity promotes the increase of the global lability of synchrony and the temporal persistence of the system.

Speed-Selectivity in Retinal Ganglion Cells is Sharpened by Broad Spatial Frequency, Naturalistic Stimuli

Motion detection represents one of the critical tasks of the visual system and has motivated a large body of research. However, it remains unclear precisely why the response of retinal ganglion cells (RGCs) to simple artificial stimuli does not predict their response to complex, naturalistic stimuli. To explore this topic, we use Motion Clouds (MC), which are synthetic textures that preserve properties of natural images and are merely parameterized, in particular by modulating the spatiotemporal spectrum complexity of the stimulus by adjusting the frequency bandwidths. By stimulating the retina of the diurnal rodent, Octodon degus with MC we show that the RGCs respond to increasingly complex stimuli by narrowing their adjustment curves in response to movement. At the level of the population, complex stimuli produce a sparser code while preserving movement information; therefore, the stimuli are encoded more efficiently. Interestingly, these properties were observed throughout different populations of RGCs. Thus, our results reveal that the response at the level of RGCs is modulated by the naturalness of the stimulus - in particular for motion - which suggests that the tuning to the statistics of natural images already emerges at the level of the retina.

Long-Term Activity Dynamics of Single Neurons and Networks

The firing rate of neuronal spiking in vitro and in vivo significantly varies over extended timescales, characterized by long-memory processes and complex statistics, and appears in spontaneous as well as evoked activity upon repeated stimulus presentation. These variations in response features and their statistics, in face of repeated instances of a given physical input, are ubiquitous in all levels of brain-behavior organization. They are expressed in single neuron and network response variability but even appear in variations of subjective percepts or psychophysical choices and have been described as stemming from history-dependent, stochastic, or rate-determined processes.But what are the sources underlying these temporally rich variations in firing rate? Are they determined by interactions of the nervous system as a whole, or do isolated, single neurons or neuronal networks already express these fluctuations independent of higher levels? These questions motivated the application of a method that allows for controlled and specific long-term activation of a single neuron or neuronal network, isolated from higher levels of cortical organization.This chapter highlights the research done in cultured cortical networks to study (1) the inherent non-stationarity of neuronal network activity, (2) single neuron response fluctuations and underlying processes, and (3) the interface layer between network and single cell, the non-stationary efficacy of the ensemble of synapses impinging onto the observed neuron.

When Coordinating Finger Tapping to a Variable Beat the Variability Scaling Structure of the Movement and the Cortical BOLD Signal are Both Entrained to the Auditory Stimuli

Rhythmic actions are characterizable as a repeating invariant pattern of movement together with variability taking the form of cycle-to-cycle fluctuations. Variability in behavioral measures is atypically random, and often exhibits serial temporal dependencies and statistical self-similarity in the scaling of variability magnitudes across timescales. Self-similar (i.e. fractal) variability scaling is evident in measures of both brain and behavior. Variability scaling structure can be quantified via the scaling exponent (α) from detrended fluctuation analysis (DFA). Here we study the task of coordinating thumb-finger tapping to the beats of constructed auditory stimuli. We test the hypothesis that variability scaling evident in tap-to-tap intervals as well as in the fluctuations of cortical hemodynamics will become entrained to (i.e. drawn toward) manipulated changes in the variability scaling of a stimulus's beat-to-beat intervals. Consistent with this hypothesis, manipulated changes of the exponent α of the experimental stimuli produced corresponding changes in the exponent α of both tap-to-tap intervals and cortical hemodynamics. The changes in hemodynamics were observed in both motor and sensorimotor cortical areas in the contralateral hemisphere. These results were observed only for the longer timescales of the detrended fluctuation analysis used to measure the exponent α. These findings suggest that complex auditory stimuli engage both brain and behavior at the level of variability scaling structures.

Detecting change in stochastic sound sequences

Our ability to parse our acoustic environment relies on the brain's capacity to extract statistical regularities from surrounding sounds. Previous work in regularity extraction has predominantly focused on the brain's sensitivity to predictable patterns in sound sequences. However, natural sound environments are rarely completely predictable, often containing some level of randomness, yet the brain is able to effectively interpret its surroundings by extracting useful information from stochastic sounds. It has been previously shown that the brain is sensitive to the marginal lower-order statistics of sound sequences (i.e., mean and variance). In this work, we investigate the brain's sensitivity to higher-order statistics describing temporal dependencies between sound events through a series of change detection experiments, where listeners are asked to detect changes in randomness in the pitch of tone sequences. Behavioral data indicate listeners collect statistical estimates to process incoming sounds, and a perceptual model based on Bayesian inference shows a capacity in the brain to track higher-order statistics. Further analysis of individual subjects' behavior indicates an important role of perceptual constraints in listeners' ability to track these sensory statistics with high fidelity. In addition, the inference model facilitates analysis of neural electroencephalography (EEG) responses, anchoring the analysis relative to the statistics of each stochastic stimulus. This reveals both a deviance response and a change-related disruption in phase of the stimulus-locked response that follow the higher-order statistics. These results shed light on the brain's ability to process stochastic sound sequences.

Investigating the impact of electrical stimulation temporal distribution on cortical network responses

Background

The brain is continuously targeted by a wealth of stimuli with complex spatio-temporal patterns and has presumably evolved in order to cope with those inputs in an optimal way. Previous studies investigating the response capabilities of either single neurons or intact sensory systems to external stimulation demonstrated that stimuli temporal distribution is an important, if often overlooked, parameter.

Results

In this study we investigated how cortical networks plated over micro-electrode arrays respond to different stimulation sequences in which inter-pulse intervals followed a 1/f^β distribution, for different values of β ranging from 0 to ∞. Cross-correlation analysis revealed that network activity preferentially synchronizes with external input sequences featuring β closer to 1 and, in any case, never for regular (i.e. fixed-frequency) stimulation sequences. We then tested the interplay between different average stimulation frequencies (based on the intrinsic firing/bursting frequency of the network) for two selected values of β, i.e. 1 (scale free) and ∞ (regular). In general, we observed no preference for stimulation frequencies matching the endogenous rhythms of the network. Moreover, we found that in case of regular stimulation the capability of the network to follow the stimulation sequence was negatively correlated to the absolute stimulation frequency, whereas using scale-free stimulation cross-correlation between input and output sequences was independent from average input frequency.

Conclusions

Our results point out that the preference for a scale-free distribution of the stimuli is observed also at network level and should be taken into account in designing more efficient protocols for neuromodulation purposes.

Electronic supplementary material

The online version of this article (doi:10.1186/s12868-017-0366-z) contains supplementary material, which is available to authorized users.

A novel mechanism of cone photoreceptor adaptation

An animal’s ability to survive depends on its sensory systems being able to adapt to a wide range of environmental conditions, by maximizing the information extracted and reducing the noise transmitted. The visual system does this by adapting to luminance and contrast. While luminance adaptation can begin at the retinal photoreceptors, contrast adaptation has been shown to start at later stages in the retina. Photoreceptors adapt to changes in luminance over multiple time scales ranging from tens of milliseconds to minutes, with the adaptive changes arising from processes within the phototransduction cascade. Here we show a new form of adaptation in cones that is independent of the phototransduction process. Rather, it is mediated by voltage-gated ion channels in the cone membrane and acts by changing the frequency response of cones such that their responses speed up as the membrane potential modulation depth increases and slow down as the membrane potential modulation depth decreases. This mechanism is effectively activated by high-contrast stimuli dominated by low frequencies such as natural stimuli. However, the more generally used Gaussian white noise stimuli were not effective since they did not modulate the cone membrane potential to the same extent. This new adaptive process had a time constant of less than a second. A critical component of the underlying mechanism is the hyperpolarization-activated current, I_h, as pharmacologically blocking it prevented the long- and mid- wavelength sensitive cone photoreceptors (L- and M-cones) from adapting. Consistent with this, short- wavelength sensitive cone photoreceptors (S-cones) did not show the adaptive response, and we found they also lacked a prominent I_h. The adaptive filtering mechanism identified here improves the information flow by removing higher-frequency noise during lower signal-to-noise ratio conditions, as occurs when contrast levels are low. Although this new adaptive mechanism can be driven by contrast, it is not a contrast adaptation mechanism in its strictest sense, as will be argued in the Discussion.

An animal’s ability to survive depends on its ability to adapt to a wide range of light conditions, by maximizing the information flow through the retina. Here, we show a new form of adaptation in cone photoreceptors that helps them optimize the information they transmit by adjusting their response kinetics to better match the visual conditions. The adaptive mechanism we describe is independent of the cone phototransduction process and is instead mediated by membrane processes in which the hyperpolarization-activated current, I_h, plays a critical role. Consistent with the critical role of this current, we also found that cones sensitive to short wavelengths lacked a prominent I_h current and did not show this new form of adaptation. As voltage-dependent processes underlie the adaptational mechanism, it is only apparent when the stimuli are able to sufficiently modulate the membrane potential of cones. This happens with natural stimuli, which are able to deliver high levels of “effective” contrast. However, even though this new adaptive mechanism can be driven by contrast, we argue in the Discussion that in its strictest sense it is not a contrast adaptation mechanism per se.

Enhanced functional connectivity properties of human brains during in-situ nature experience

In this study, we investigated the impacts of in-situ nature and urban exposure on human brain activities and their dynamics. We randomly assigned 32 healthy right-handed college students (mean age = 20.6 years, SD = 1.6; 16 males) to a 20 min in-situ sitting exposure in either a nature (n = 16) or urban environment (n = 16) and measured their Electroencephalography (EEG) signals. Analyses revealed that a brief in-situ restorative nature experience may induce more efficient and stronger brain connectivity with enhanced small-world properties compared with a stressful urban experience. The enhanced small-world properties were found to be correlated with “coherent” experience measured by Perceived Restorativeness Scale (PRS). Exposure to nature also induces stronger long-term correlated activity across different brain regions with a right lateralization. These findings may advance our understanding of the functional activities during in-situ environmental exposures and imply that a nature or nature-like environment may potentially benefit cognitive processes and mental well-being.

Nonergodic complexity management

Linear response theory, the backbone of nonequilibrium statistical physics, has recently been extended to explain how and why nonergodic renewal processes are insensitive to simple perturbations, such as in habituation. It was established that a permanent correlation results between an external stimulus and the response of a complex system generating nonergodic renewal processes, when the stimulus is a similar nonergodic process. This is the principle of complexity management, whose proof relies on ensemble distribution functions. Herein we extend the proof to the nonergodic case using time averages and a single time series, hence making it usable in real life situations where ensemble averages cannot be performed because of the very nature of the complex systems being studied.

Synchronous firing of antennal-lobe projection neurons encodes the behaviorally effective ratio of sex-pheromone components in male Manduca sexta

Olfactory stimuli that are essential to an animal's survival and reproduction are often complex mixtures of volatile organic compounds in characteristic proportions. Here, we investigated how these proportions are encoded in the primary olfactory processing center, the antennal lobe, of male Manduca sexta moths. Two key components of the female's sex pheromone, present in an approximately 2:1 ratio, are processed in each of two neighboring glomeruli in the macroglomerular complex (MGC) of males of this species. In wind-tunnel flight experiments, males exhibited behavioral selectivity for ratios approximating the ratio released by conspecific females. The ratio between components was poorly represented, however, in the firing-rate output of uniglomerular MGC projection neurons (PNs). PN firing rate was mostly insensitive to the ratio between components, and individual PNs did not exhibit a preference for a particular ratio. Recording simultaneously from pairs of PNs in the same glomerulus, we found that the natural ratio between components elicited the most synchronous spikes, and altering the proportion of either component decreased the proportion of synchronous spikes. The degree of synchronous firing between PNs in the same glomerulus thus selectively encodes the natural ratio that most effectively evokes the natural behavioral response to pheromone.

Musical rhythm spectra from Bach to Joplin obey a 1/f power law

Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/f(β) power law across 16 subgenres and 40 composers, with β ranging from ∼0.5-1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.

1/f Noise in human color vision: the role of S-cone signals

We examine the functional role of S-cone signals on reaction time (RT) variability in human color vision. Stimuli were selected along red-green and blue-yellow cardinal directions and at random directions in the isoluminant plane of the color space. Trial-to-trial RT variability was not statistically independent but correlated across experimental conditions and exhibited 1/f noise spectra with an exponent close to unity in most of the cases. Regarding contrast coding, 1/f noise for random chromatic stimuli at isoluminance was similar to that for achromatic stimuli, thus suggesting that S-cone signals reduce variability of higher order color mechanisms. If we regard spatial coding, the effect of S-cone density in the retina on RT variability was investigated. The magnitude of 1/f noise at 16 min of arc (S-cone free zone) was higher than at 90 min of arc in the blue-yellow channel, and it was similar for the red-green channel. The results suggest that S-cone signals are beneficial and they modulate 1/f noise spectra at postreceptoral stages. The implications related to random multiplicative processes as a possible source of 1/f noise and the optimal information processing in color vision are discussed.

Cellular-resolution population imaging reveals robust sparse coding in the Drosophila mushroom body

Sensory stimuli are represented in the brain by the activity of populations of neurons. In most biological systems, studying population coding is challenging since only a tiny proportion of cells can be recorded simultaneously. Here we used two-photon imaging to record neural activity in the relatively simple Drosophila mushroom body (MB), an area involved in olfactory learning and memory. Using the highly sensitive calcium indicator GCaMP3, we simultaneously monitored the activity of >100 MB neurons in vivo (∼5% of the total population). The MB is thought to encode odors in sparse patterns of activity, but the code has yet to be explored either on a population level or with a wide variety of stimuli. We therefore imaged responses to odors chosen to evaluate the robustness of sparse representations. Different odors activated distinct patterns of MB neurons; however, we found no evidence for spatial organization of neurons by either response probability or odor tuning within the cell body layer. The degree of sparseness was consistent across a wide range of stimuli, from monomolecular odors to artificial blends and even complex natural smells. Sparseness was mainly invariant across concentrations, largely because of the influence of recent odor experience. Finally, in contrast to sensory processing in other systems, no response features distinguished natural stimuli from monomolecular odors. Our results indicate that the fundamental feature of odor processing in the MB is to create sparse stimulus representations in a format that facilitates arbitrary associations between odor and punishment or reward.

Learning with a network of competing synapses

Competition between synapses arises in some forms of correlation-based plasticity. Here we propose a game theory-inspired model of synaptic interactions whose dynamics is driven by competition between synapses in their weak and strong states, which are characterized by different timescales. The learning of inputs and memory are meaningfully definable in an effective description of networked synaptic populations. We study, numerically and analytically, the dynamic responses of the effective system to various signal types, particularly with reference to an existing empirical motor adaptation model. The dependence of the system-level behavior on the synaptic parameters, and the signal strength, is brought out in a clear manner, thus illuminating issues such as those of optimal performance, and the functional role of multiple timescales.

Global properties of natural scenes shape local properties of human edge detectors

Visual cortex analyzes images by first extracting relevant details (e.g., edges) via a large array of specialized detectors. The resulting edge map is then relayed to a processing pipeline, the final goal of which is to attribute meaning to the scene. As this process unfolds, does the global interpretation of the image affect how local feature detectors operate? We characterized the local properties of human edge detectors while we manipulated the extent to which the statistical properties of the surrounding image conformed to those encountered in natural vision. Although some aspects of local processing were unaffected by contextual manipulations, we observed significant alterations in the operating characteristics of the detector which were solely attributable to a higher-level semantic interpretation of the scene, unrelated to lower-level aspects of image statistics. Our results suggest that it may be inaccurate to regard early feature detectors as operating outside the domain of higher-level vision; although there is validity in this approach, a full understanding of their properties requires the inclusion of knowledge-based effects specific to the statistical regularities found in the natural environment.

Statistical coding and decoding of heartbeat intervals

The heart integrates neuroregulatory messages into specific bands of frequency, such that the overall amplitude spectrum of the cardiac output reflects the variations of the autonomic nervous system. This modulatory mechanism seems to be well adjusted to the unpredictability of the cardiac demand, maintaining a proper cardiac regulation. A longstanding theory holds that biological organisms facing an ever-changing environment are likely to evolve adaptive mechanisms to extract essential features in order to adjust their behavior. The key question, however, has been to understand how the neural circuitry self-organizes these feature detectors to select behaviorally relevant information. Previous studies in computational perception suggest that a neural population enhances information that is important for survival by minimizing the statistical redundancy of the stimuli. Herein we investigate whether the cardiac system makes use of a redundancy reduction strategy to regulate the cardiac rhythm. Based on a network of neural filters optimized to code heartbeat intervals, we learn a population code that maximizes the information across the neural ensemble. The emerging population code displays filter tuning proprieties whose characteristics explain diverse aspects of the autonomic cardiac regulation, such as the compromise between fast and slow cardiac responses. We show that the filters yield responses that are quantitatively similar to observed heart rate responses during direct sympathetic or parasympathetic nerve stimulation. Our findings suggest that the heart decodes autonomic stimuli according to information theory principles analogous to how perceptual cues are encoded by sensory systems.

Neuron dynamics in the presence of 1/f noise

Interest in understanding the interplay between noise and the response of a nonlinear device cuts across disciplinary boundaries. It is as relevant for unmasking the dynamics of neurons in noisy environments as it is for designing reliable nanoscale logic circuit elements and sensors. Most studies of noise in nonlinear devices are limited to either time-correlated noise with a Lorentzian spectrum (of which the white noise is a limiting case) or just white noise. We use analytical theory and numerical simulations to study the impact of the more ubiquitous "natural" noise with a 1/f frequency spectrum. Specifically, we study the impact of the 1/f noise on a leaky integrate and fire model of a neuron. The impact of noise is considered on two quantities of interest to neuron function: The spike count Fano factor and the speed of neuron response to a small steplike stimulus. For the perfect (nonleaky) integrate and fire model, we show that the Fano factor can be expressed as an integral over noise spectrum weighted by a (low-pass) filter function given by F(t,f)=sinc(2)(πft). This result elucidates the connection between low-frequency noise and disorder in neuron dynamics. Under 1/f noise, spike dynamics lacks a characteristic correlation time, inducing the leaky and nonleaky models, to exhibit nonergodic behavior and the Fano factor, increasing logarithmically as a function of time. We compare our results to experimental data of single neurons in vivo [Teich, Heneghan, Lowen, Ozaki, and Kaplan, J. Opt. Soc. Am. A 14, 529 (1997)] and show how the 1/f noise model provides much better agreement than the usual approximations based on Lorentzian noise. The low-frequency noise, however, complicates the case for an information-coding scheme based on interspike intervals by introducing variability in the neuron response time. On a positive note, the neuron response time to a step stimulus is, remarkably, nearly optimal in the presence of 1/f noise. An explanation of this effect elucidates how the brain can take advantage of noise to prime a subset of the neurons to respond almost instantly to sudden stimuli.

Fractal physiology and the fractional calculus: a perspective

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks.

1/f 2 Characteristics and isotropy in the fourier power spectra of visual art, cartoons, comics, mangas, and different categories of photographs

Art images and natural scenes have in common that their radially averaged (1D) Fourier spectral power falls according to a power-law with increasing spatial frequency (1/f(2) characteristics), which implies that the power spectra have scale-invariant properties. In the present study, we show that other categories of man-made images, cartoons and graphic novels (comics and mangas), have similar properties. Further on, we extend our investigations to 2D power spectra. In order to determine whether the Fourier power spectra of man-made images differed from those of other categories of images (photographs of natural scenes, objects, faces and plants and scientific illustrations), we analyzed their 2D power spectra by principal component analysis. Results indicated that the first fifteen principal components allowed a partial separation of the different image categories. The differences between the image categories were studied in more detail by analyzing whether the mean power and the slope of the power gradients from low to high spatial frequencies varied across orientations in the power spectra. Mean power was generally higher in cardinal orientations both in real-world photographs and artworks, with no systematic difference between the two types of images. However, the slope of the power gradients showed a lower degree of mean variability across spectral orientations (i.e., more isotropy) in art images, cartoons and graphic novels than in photographs of comparable subject matters. Taken together, these results indicate that art images, cartoons and graphic novels possess relatively uniform 1/f(2) characteristics across all orientations. In conclusion, the man-made stimuli studied, which were presumably produced to evoke pleasant and/or enjoyable visual perception in human observers, form a subset of all images and share statistical properties in their Fourier power spectra. Whether these properties are necessary or sufficient to induce aesthetic perception remains to be investigated.

Beyond the death of linear response: 1/f optimal information transport

Nonergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We show that it is possible to go beyond the "death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating nonergodic renewal processes, by taking as stimulus a similar nonergodic process. The ideal condition of 1/f noise corresponds to a singularity that is expected to be relevant in several experimental conditions.

Fractals in the nervous system: conceptual implications for theoretical neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power-law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review.

The Living Matter Way to exchange information

It is hypothesized that the special way information is exchanged between living networks, the Living Matter Way (LMW), is determined by the Principle of Complexity Matching, which asserts that the relative complexity of two complex networks determines the transfer of information between them. The LMW explains the neurophysiology of habituation and why classical music persists in your head long after the music stops.

Spontaneous brain activity as a source of ideal 1/f noise

We study the electroencephalogram (EEG) of 30 closed-eye awake subjects with a technique of analysis recently proposed to detect punctual events signaling rapid transitions between different metastable states. After single-EEG-channel event detection, we study global properties of events simultaneously occurring among two or more electrodes termed coincidences. We convert the coincidences into a diffusion process with three distinct rules that can yield the same mu only in the case where the coincidences are driven by a renewal process. We establish that the time interval between two consecutive renewal events driving the coincidences has a waiting-time distribution with inverse power-law index mu approximately 2 corresponding to ideal 1/f noise. We argue that this discovery, shared by all subjects of our study, supports the conviction that 1/f noise is an optimal communication channel for complex networks as in art or language and may therefore be the channel through which the brain influences complex processes and is influenced by them.

Scale-free music of the brain

Background

There is growing interest in the relation between the brain and music. The appealing similarity between brainwaves and the rhythms of music has motivated many scientists to seek a connection between them. A variety of transferring rules has been utilized to convert the brainwaves into music; and most of them are mainly based on spectra feature of EEG.

Methodology/Principal Findings

In this study, audibly recognizable scale-free music was deduced from individual Electroencephalogram (EEG) waveforms. The translation rules include the direct mapping from the period of an EEG waveform to the duration of a note, the logarithmic mapping of the change of average power of EEG to music intensity according to the Fechner's law, and a scale-free based mapping from the amplitude of EEG to music pitch according to the power law. To show the actual effect, we applied the deduced sonification rules to EEG segments recorded during rapid-eye movement sleep (REM) and slow-wave sleep (SWS). The resulting music is vivid and different between the two mental states; the melody during REM sleep sounds fast and lively, whereas that in SWS sleep is slow and tranquil. 60 volunteers evaluated 25 music pieces, 10 from REM, 10 from SWS and 5 from white noise (WN), 74.3% experienced a happy emotion from REM and felt boring and drowsy when listening to SWS, and the average accuracy for all the music pieces identification is 86.8%(κ = 0.800, P<0.001). We also applied the method to the EEG data from eyes closed, eyes open and epileptic EEG, and the results showed these mental states can be identified by listeners.

Conclusions/Significance

The sonification rules may identify the mental states of the brain, which provide a real-time strategy for monitoring brain activities and are potentially useful to neurofeedback therapy.

1/falpha noise in reaction times: a proposed model based on Piéron's law and information processing

Piéron's law relates human reaction times to the intensity of a sensory stimulus by a power function. The neural processes responsible for this nonlinear behavior are not understood. A simple neural model based on the Brownian motion of spikes and information theory is presented. The model shows that Piéron's law is a transformation function in time. The shape of Piéron's law is invariant and scales into the intensity-response function of single neurons in a fractal-like process. The model also shows that Piéron's law gives rise to 1/falpha noise together with a high-frequency thermal noise limit. It is proposed that the biophysical origin of reaction time variability is related to a form of noise-induced synchronization in weakly coupled neurons. The implications in visual-motor transduction are discussed.

Visual coding in locust photoreceptors

Information capture by photoreceptors ultimately limits the quality of visual processing in the brain. Using conventional sharp microelectrodes, we studied how locust photoreceptors encode random (white-noise, WN) and naturalistic (1/f stimuli, NS) light patterns in vivo and how this coding changes with mean illumination and ambient temperature. We also examined the role of their plasma membrane in shaping voltage responses. We found that brightening or warming increase and accelerate voltage responses, but reduce noise, enabling photoreceptors to encode more information. For WN stimuli, this was accompanied by broadening of the linear frequency range. On the contrary, with NS the signaling took place within a constant bandwidth, possibly revealing a ‘preference’ for inputs with 1/f statistics. The faster signaling was caused by acceleration of the elementary phototransduction current - leading to bumps - and their distribution. The membrane linearly translated phototransduction currents into voltage responses without limiting the throughput of these messages. As the bumps reflected fast changes in membrane resistance, the data suggest that their shape is predominantly driven by fast changes in the light-gated conductance. On the other hand, the slower bump latency distribution is likely to represent slower enzymatic intracellular reactions. Furthermore, the Q₁₀s of bump duration and latency distribution depended on light intensity. Altogether, this study suggests that biochemical constraints imposed upon signaling change continuously as locust photoreceptors adapt to environmental light and temperature conditions.

An information theoretic characterisation of auditory encoding

The entropy metric derived from information theory provides a means to quantify the amount of information transmitted in acoustic streams like speech or music. By systematically varying the entropy of pitch sequences, we sought brain areas where neural activity and energetic demands increase as a function of entropy. Such a relationship is predicted to occur in an efficient encoding mechanism that uses less computational resource when less information is present in the signal: we specifically tested the hypothesis that such a relationship is present in the planum temporale (PT). In two convergent functional MRI studies, we demonstrated this relationship in PT for encoding, while furthermore showing that a distributed fronto-parietal network for retrieval of acoustic information is independent of entropy. The results establish PT as an efficient neural engine that demands less computational resource to encode redundant signals than those with high information content.

Understanding how the brain makes sense of our acoustic environment remains a major challenge. One way to describe the complexity of our acoustic environment is in terms of information entropy: acoustic signals with high entropy convey large amounts of information, whereas low entropy signifies redundancy. To investigate how the brain processes this information, we controlled the amount of entropy in the signal by using pitch sequences. Participants listened to pitch sequences with varying amounts of entropy while we measured their brain activity using functional magnetic resonance imaging (fMRI). We show that the planum temporale (PT), a region of auditory association cortex, is sensitive to the entropy in pitch sequences. In two convergent fMRI studies, activity in PT increases as the entropy in the pitch sequence increases. The results establish PT as an important “computational hub” that requires less resource to encode redundant signals than it does to encode signals with high information content.

A part of the auditory cortex (planum temporale) encodes the information content of pitch sequences.