Scaling laws in cognitive sciences

Neuronal long-range temporal correlations and avalanche dynamics are correlated with behavioral scaling laws

Scale-free fluctuations are ubiquitous in behavioral performance and neuronal activity. In time scales from seconds to hundreds of seconds, psychophysical dynamics and the amplitude fluctuations of neuronal oscillations are governed by power-law-form long-range temporal correlations (LRTCs). In millisecond time scales, neuronal activity comprises cascade-like neuronal avalanches that exhibit power-law size and lifetime distributions. However, it remains unknown whether these neuronal scaling laws are correlated with those characterizing behavioral performance or whether neuronal LRTCs and avalanches are related. Here, we show that the neuronal scaling laws are strongly correlated both with each other and with behavioral scaling laws. We used source reconstructed magneto- and electroencephalographic recordings to characterize the dynamics of ongoing cortical activity. We found robust power-law scaling in neuronal LRTCs and avalanches in resting-state data and during the performance of audiovisual threshold stimulus detection tasks. The LRTC scaling exponents of the behavioral performance fluctuations were correlated with those of concurrent neuronal avalanches and LRTCs in anatomically identified brain systems. The behavioral exponents also were correlated with neuronal scaling laws derived from a resting-state condition and with a similar anatomical topography. Finally, despite the difference in time scales, the scaling exponents of neuronal LRTCs and avalanches were strongly correlated during both rest and task performance. Thus, long and short time-scale neuronal dynamics are related and functionally significant at the behavioral level. These data suggest that the temporal structures of human cognitive fluctuations and behavioral variability stem from the scaling laws of individual and intrinsic brain dynamics.

Long-range temporal correlations in the subthalamic nucleus of patients with Parkinson's disease

Neuronal activity in the subthalamic nucleus (STN) of patients with Parkinson's disease (PD) is characterised by excessive neuronal synchronization, particularly in the beta frequency range. However, less is known about the temporal dynamics of neuronal oscillations in PD. In this respect long-range temporal correlations (LRTC) are of special interest as they quantify the neuronal dynamics on different timescales and have been shown to be relevant for optimal information processing in the brain. While the presence of LRTC has been demonstrated in cortical data, their existence in deep brain structures remains an open question. We investigated (i) whether LRTC are present in local field potentials (LFP) recorded bilaterally from the STN at wakeful rest in ten patients with PD after overnight withdrawal of levodopa (OFF) and (ii) whether LRTC can be modulated by levodopa treatment (ON). Detrended fluctuation analysis was utilised in order to quantify the temporal dynamics in the amplitude fluctuations of LFP oscillations. We demonstrated for the first time the presence of LRTC (extending up to 50 s) in the STN. Importantly, the ON state was characterised by significantly stronger LRTC than the OFF state, both in beta (13-35 Hz) and high-frequency (> 200 Hz) oscillations. The existence of LRTC in subcortical structures such as STN provides further evidence for their ubiquitous nature in the brain. The weaker LRTC in the OFF state might indicate limited information processing in the dopamine-depleted basal ganglia. The present results implicate LRTC as a potential biomarker of pathological neuronal processes in PD.

Interaction vs. observation: distinctive modes of social cognition in human brain and behavior? A combined fMRI and eye-tracking study

Human cognition has usually been approached on the level of individual minds and brains, but social interaction is a challenging case. Is it best thought of as a self-contained individual cognitive process aiming at an "understanding of the other," or should it rather be approached as an collective, inter-personal process where individual cognitive components interact on a moment-to-moment basis to form coupled dynamics? In a combined fMRI and eye-tracking study we directly contrasted these models of social cognition. We found that the perception of situations affording social contingent responsiveness (e.g., someone offering or showing you an object) elicited activations in regions of the right posterior temporal sulcus and yielded greater pupil dilation corresponding to a model of coupled dynamics (joint action). In contrast, the social-cognitive perception of someone "privately" manipulating an object elicited activation in medial prefrontal cortex, the right inferior frontal gyrus and right inferior parietal lobus, regions normally associated with Theory of Mind and with the mirror neuron system. Our findings support a distinction in social cognition between social observation and social interaction, and demonstrate that simple ostensive cues may shift participants' experience, behavior, and brain activity between these modes. The identification of a distinct, interactive mode has implications for research on social cognition, both in everyday life and in clinical conditions.

Detrended fluctuation analysis: a scale-free view on neuronal oscillations

Recent years of research have shown that the complex temporal structure of ongoing oscillations is scale-free and characterized by long-range temporal correlations. Detrended fluctuation analysis (DFA) has proven particularly useful, revealing that genetic variation, normal development, or disease can lead to differences in the scale-free amplitude modulation of oscillations. Furthermore, amplitude dynamics is remarkably independent of the time-averaged oscillation power, indicating that the DFA provides unique insights into the functional organization of neuronal systems. To facilitate understanding and encourage wider use of scaling analysis of neuronal oscillations, we provide a pedagogical explanation of the DFA algorithm and its underlying theory. Practical advice on applying DFA to oscillations is supported by MATLAB scripts from the Neurophysiological Biomarker Toolbox (NBT) and links to the NBT tutorial website http://www.nbtwiki.net/. Finally, we provide a brief overview of insights derived from the application of DFA to ongoing oscillations in health and disease, and discuss the putative relevance of criticality for understanding the mechanism underlying scale-free modulation of oscillations.

The self-organization of a spoken word

Pronunciation time probability density and hazard functions from large speeded word naming data sets were assessed for empirical patterns consistent with multiplicative and reciprocal feedback dynamics – interaction dominant dynamics. Lognormal and inverse power law distributions are associated with multiplicative and interdependent dynamics in many natural systems. Mixtures of lognormal and inverse power law distributions offered better descriptions of the participant’s distributions than the ex-Gaussian or ex-Wald – alternatives corresponding to additive, superposed, component processes. The evidence for interaction dominant dynamics suggests fundamental links between the observed coordinative synergies that support speech production and the shapes of pronunciation time distributions.

On the origin of long-range correlations in texts

The complexity of human interactions with social and natural phenomena is mirrored in the way we describe our experiences through natural language. In order to retain and convey such a high dimensional information, the statistical properties of our linguistic output has to be highly correlated in time. An example are the robust observations, still largely not understood, of correlations on arbitrary long scales in literary texts. In this paper we explain how long-range correlations flow from highly structured linguistic levels down to the building blocks of a text (words, letters, etc..). By combining calculations and data analysis we show that correlations take form of a bursty sequence of events once we approach the semantically relevant topics of the text. The mechanisms we identify are fairly general and can be equally applied to other hierarchical settings.

The interactive brain hypothesis

Enactive approaches foreground the role of interpersonal interaction in explanations of social understanding. This motivates, in combination with a recent interest in neuroscientific studies involving actual interactions, the question of how interactive processes relate to neural mechanisms involved in social understanding. We introduce the Interactive Brain Hypothesis (IBH) in order to help map the spectrum of possible relations between social interaction and neural processes. The hypothesis states that interactive experience and skills play enabling roles in both the development and current function of social brain mechanisms, even in cases where social understanding happens in the absence of immediate interaction. We examine the plausibility of this hypothesis against developmental and neurobiological evidence and contrast it with the widespread assumption that mindreading is crucial to all social cognition. We describe the elements of social interaction that bear most directly on this hypothesis and discuss the empirical possibilities open to social neuroscience. We propose that the link between coordination dynamics and social understanding can be best grasped by studying transitions between states of coordination. These transitions form part of the self-organization of interaction processes that characterize the dynamics of social engagement. The patterns and synergies of this self-organization help explain how individuals understand each other. Various possibilities for role-taking emerge during interaction, determining a spectrum of participation. This view contrasts sharply with the observational stance that has guided research in social neuroscience until recently. We also introduce the concept of readiness to interact to describe the practices and dispositions that are summoned in situations of social significance (even if not interactive). This latter idea links interactive factors to more classical observational scenarios.

Adaptive time-varying detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a technique commonly used to assess and quantify the presence of long-range temporal correlations (LRTCs) in neurophysiological time series. Convergence of the method is asymptotic only and therefore its application assumes a constant scaling exponent. However, most neurophysiological data are likely to involve either spontaneous or experimentally induced scaling exponent changes. We present a novel extension of the DFA method that permits the characterisation of time-varying scaling exponents. The effectiveness of the methodology in recovering known changes in scaling exponents is demonstrated through its application to synthetic data. The dependence of the method on its free parameters is systematically explored. Finally, application of the methodology to neurophysiological data demonstrates that it provides experimenters with a way to identify previously un-recognised changes in the scaling exponent in the data. We suggest that this methodology will make it possible to go beyond a simple demonstration of the presence of scaling to an appreciation of how it may vary in response to either intrinsic changes or experimental perturbations.

The Functional Benefits of Criticality in the Cortex

Rapidly growing empirical evidence supports the hypothesis that the cortex operates near criticality. Although the confirmation of this hypothesis would mark a significant advance in fundamental understanding of cortical physiology, a natural question arises: What functional benefits are endowed to cortical circuits that operate at criticality? In this review, we first describe an introductory-level thought experiment to provide the reader with an intuitive understanding of criticality. Second, we discuss some practical approaches for investigating criticality. Finally, we review quantitative evidence that three functional properties of the cortex are optimized at criticality: 1) dynamic range, 2) information transmission, and 3) information capacity. We focus on recently reported experimental evidence and briefly discuss the theory and history of these ideas.

Studying language change using price equation and Pólya-urn dynamics

Language change takes place primarily via diffusion of linguistic variants in a population of individuals. Identifying selective pressures on this process is important not only to construe and predict changes, but also to inform theories of evolutionary dynamics of socio-cultural factors. In this paper, we advocate the Price equation from evolutionary biology and the Pólya-urn dynamics from contagion studies as efficient ways to discover selective pressures. Using the Price equation to process the simulation results of a computer model that follows the Pólya-urn dynamics, we analyze theoretically a variety of factors that could affect language change, including variant prestige, transmission error, individual influence and preference, and social structure. Among these factors, variant prestige is identified as the sole selective pressure, whereas others help modulate the degree of diffusion only if variant prestige is involved. This multidisciplinary study discerns the primary and complementary roles of linguistic, individual learning, and socio-cultural factors in language change, and offers insight into empirical studies of language change.

Interactive rhythmic auditory stimulation reinstates natural 1/f timing in gait of Parkinson's patients

Parkinson's disease (PD) and basal ganglia dysfunction impair movement timing, which leads to gait instability and falls. Parkinsonian gait consists of random, disconnected stride times—rather than the 1/f structure observed in healthy gait—and this randomness of stride times (low fractal scaling) predicts falling. Walking with fixed-tempo Rhythmic Auditory Stimulation (RAS) can improve many aspects of gait timing; however, it lowers fractal scaling (away from healthy 1/f structure) and requires attention. Here we show that interactive rhythmic auditory stimulation reestablishes healthy gait dynamics in PD patients. In the experiment, PD patients and healthy participants walked with a) no auditory stimulation, b) fixed-tempo RAS, and c) interactive rhythmic auditory stimulation. The interactive system used foot sensors and nonlinear oscillators to track and mutually entrain with the human's step timing. Patients consistently synchronized with the interactive system, their fractal scaling returned to levels of healthy participants, and their gait felt more stable to them. Patients and healthy participants rarely synchronized with fixed-tempo RAS, and when they did synchronize their fractal scaling declined from healthy 1/f levels. Five minutes after removing the interactive rhythmic stimulation, the PD patients' gait retained high fractal scaling, suggesting that the interaction stabilized the internal rhythm generating system and reintegrated timing networks. The experiment demonstrates that complex interaction is important in the (re)emergence of 1/f structure in human behavior and that interactive rhythmic auditory stimulation is a promising therapeutic tool for improving gait of PD patients.

Infra-slow fluctuations in electrophysiological recordings, blood-oxygenation-level-dependent signals, and psychophysical time series

Converging electrophysiological and neuroimaging data show that mammalian brain dynamics are governed by spontaneous modulations of neuronal activity levels in cortical and subcortical structures. The time scales of these fluctuations form a continuum from seconds to tens and hundreds of seconds corresponding to slow (0.1-1Hz), infra-slow (0.01-0.1Hz), and "ultradian" (<0.01Hz) frequency bands, respectively. We focus here on the spontaneous neuronal dynamics in the infra-slow frequency band, infra-slow fluctuations (ISFs), and explore their electrophysiological substrates and behavioral correlates. Although electrophysiological ISFs and the associated infra-slow modulations of fast (here, >1Hz) neuronal activities have been recognized on numerous occasions since late 50's, a resurgence in interest towards this frequency band has been driven by a discovery that ISFs in blood-oxygenation-level dependent (BOLD) signals are correlated among specific constellations of brain regions, which constitute intrinsic connectivity networks and define the dynamic architecture of spontaneous brain activity at large. Importantly, electrophysiological and BOLD signal ISFs are directly correlated both with ISFs in amplitudes of fast neuronal activities and with ISFs in behavioral performance. Moreover, both electrophysiological and neuroimaging data suggest that the apparently scale-free ISFs may arise from more local quasi-periodic infra-slow oscillations with a contribution of time-scale-specific cellular-level mechanisms. We conclude that ISFs in electrophysiological recordings, BOLD signals, neuronal activity levels, and behavioral time series are likely to reflect the same underlying phenomenon; a superstructure of interacting and transiently oscillatory ISFs that regulate both the integration within and decoupling between concurrently active neuronal communities.

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.

Eye movement dynamics and cognitive self-organization in typical and atypical development

This study analyzed distributions of Euclidean displacements in gaze (i.e. "gaze steps") to evaluate the degree of componential cognitive constraints on audio-visual speech perception tasks. Children performing these tasks exhibited distributions of gaze steps that were closest to power-law or lognormal distributions, suggesting a multiplicatively interactive, flexible, self-organizing cognitive system rather than a component-dominant stipulated cognitive structure. Younger children and children diagnosed with an autism spectrum disorder (ASD) exhibited distributions that were closer to power-law than lognormal, indicating a reduced degree of self-organized structure. The relative goodness of lognormal fit was also a significant predictor of ASD, suggesting that this type of analysis may point towards a promising diagnostic tool. These results lend further support to an interaction-dominant framework that casts cognitive processing and development in terms of self-organization instead of fixed components and show that these analytical methods are sensitive to important developmental and neuropsychological differences.

Scale-free modulation of resting-state neuronal oscillations reflects prolonged brain maturation in humans

Human neuronal circuits undergo life-long functional reorganization with profound effects on cognition and behavior. Well documented prolonged development of anatomical brain structures includes white and gray matter changes that continue into the third decade of life. We investigated resting-state EEG oscillations in 1433 subjects from 5 to 71 years. Neuronal oscillations exhibit scale-free amplitude modulation as reflected in power-law decay of autocorrelations--also known as long-range temporal correlations (LRTC)--which was assessed by detrended fluctuation analysis. We observed pronounced increases in LRTC from childhood to adolescence, during adolescence, and even into early adulthood (∼25 years of age) after which the temporal structure stabilized. A principal component analysis of the spatial distribution of LRTC revealed increasingly uniform scores across the scalp. Together, these findings indicate that the scale-free modulation of resting-state oscillations reflects brain maturation, and suggests that scaling analysis may prove useful as a biomarker of pathophysiology in neurodevelopmental disorders such as attention deficit hyperactivity disorder and schizophrenia.

Effects of accuracy feedback on fractal characteristics of time estimation

The current experiment investigated the effect of visual accuracy feedback on the structure of variability of time interval estimates in the continuation tapping paradigm. Participants were asked to repeatedly estimate a 1-s interval for a prolonged period of time by tapping their index finger. In some conditions, participants received accuracy feedback after every estimate, whereas in other conditions, no feedback was given. Also, the likelihood of receiving visual feedback was manipulated by adjusting the tolerance band around the 1-s target interval so that feedback was displayed only if the temporal estimate deviated from the target interval by more than 50, 100, or 200 ms respectively. We analyzed the structure of variability of the inter-tap intervals with fractal and multifractal methods that allow for a quantification of complex long-range correlation patterns in the timing performance. Our results indicate that feedback changes the long-range correlation structure of time estimates: Increased amounts of feedback lead to a decrease in fractal long-range correlations, as well to a decrease in the magnitude of local fluctuations in the performance. The multifractal characteristics of the time estimates were not impacted by the presence of accuracy feedback. Nevertheless, most of the data sets show significant multifractal signatures. We interpret these findings as showing that feedback acts to constrain and possibly reorganize timing performance. Implications for mechanistic and complex systems-based theories of timing behavior are discussed.

Global and local features of semantic networks: evidence from the Hebrew mental lexicon

BACKGROUND

Semantic memory has generated much research. As such, the majority of investigations have focused on the English language, and much less on other languages, such as Hebrew. Furthermore, little research has been done on search processes within the semantic network, even though they are abundant within cognitive semantic phenomena.

METHODOLOGY/PRINCIPAL FINDINGS

We examine a unique dataset of free association norms to a set of target words and make use of correlation and network theory methodologies to investigate the global and local features of the Hebrew lexicon. The global features of the lexicon are investigated through the use of association correlations--correlations between target words, based on their association responses similarity; the local features of the lexicon are investigated through the use of association dependencies--the influence words have in the network on other words.

CONCLUSIONS/SIGNIFICANCE

Our investigation uncovered Small-World Network features of the Hebrew lexicon, specifically a high clustering coefficient and a scale-free distribution, and provides means to examine how words group together into semantically related 'free categories'. Our novel approach enables us to identify how words facilitate or inhibit the spread of activation within the network, and how these words influence each other. We discuss how these properties relate to classical research on spreading activation and suggest that these properties influence cognitive semantic search processes. A semantic search task, the Remote Association Test is discussed in light of our findings.

Effects of multiplicative power law neural noise in visual information processing

The human visual system is intrinsically noisy. The benefits of internal noise as part of visual code are controversial. Here the information-theoretic properties of multiplicative (i.e. signal-dependent) neural noise are investigated. A quasi-linear communication channel model is presented. The model shows that multiplicative power law neural noise promotes the minimum information transfer after efficient coding. It is demonstrated that Weber's law and the human contrast sensitivity function arise on the basis of minimum transfer of information and power law neural noise. The implications of minimum information transfer in self-organized neural networks and weakly coupled neurons are discussed.

Roles of multiscale brain activity fluctuations in shaping the variability and dynamics of psychophysical performance

Spontaneous brain activity across many time scales influences sensory perception and human cognitive performance. Empirical insight into the underlying systems-level mechanisms has, however, remained fragmented. We review here recent studies on how wideband scale-free and scale-specific neuronal activity fluctuations together bias sensory processing and perceptual performance. We posit that these fluctuations constitute the neurophysiological foundation for both the trial-to-trial behavioral variability and the scaling laws governing psychophysical performance.

Complex times for earthquakes, stocks, and the brain's activity

A new study by He et al. in this issue of Neuron shows that large-scale arrhythmic (1/f) brain activity contains nested temporal structure in the form of crossfrequency coupling. This suggests temporal organization in neural mass activity beyond oscillations and draws attention to ubiquitous but often ignored arrhythmic patterns in neural activity.