The fractal brain: scale-invariance in structure and dynamics.

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

Membrane resonance enables stable and robust gamma oscillations.

Neuronal mechanisms underlying beta/gamma oscillations (20-80 Hz) are not completely understood. Here, we show that in vivo beta/gamma oscillations in the cat visual cortex sometimes exhibit remarkably stable frequency even when inputs fluctuate dramatically. Enhanced frequency stability is associated with stronger oscillations measured in individual units and larger power in the local field potential. Simulations of neuronal circuitry demonstrate that membrane properties of inhibitory interneurons strongly determine the characteristics of emergent oscillations. Exploration of networks containing either integrator or resonator inhibitory interneurons revealed that: (i) Resonance, as opposed to integration, promotes robust oscillations with large power and stable frequency via a mechanism called RING (Resonance INduced Gamma); resonance favors synchronization by reducing phase delays between interneurons and imposes bounds on oscillation cycle duration; (ii) Stability of frequency and robustness of the oscillation also depend on the relative timing of excitatory and inhibitory volleys within the oscillation cycle; (iii) RING can reproduce characteristics of both Pyramidal INterneuron Gamma (PING) and INterneuron Gamma (ING), transcending such classifications; (iv) In RING, robust gamma oscillations are promoted by slow but are impaired by fast inputs. Results suggest that interneuronal membrane resonance can be an important ingredient for generation of robust gamma oscillations having stable frequency.

Randomness impacts the building of specific priors, visual exploration, and perception in object recognition.

Recognising objects is a vital skill on which humans heavily rely to respond quickly and adaptively to their environment. Yet, we lack a full understanding of the role visual information sampling plays in this process, and its relation to the individual's priors. To bridge this gap, the eye-movements of 18 adult participants were recorded during a free-viewing object-recognition task using Dots stimuli1. Participants viewed the stimuli in one of three orders: from most visible to least (Descending), least visible to most (Ascending), or in a randomised order (Random). This dictated the strength of their priors along the experiment. Visibility order influenced the participants' recognition performance and visual exploration. In addition, we found that while orders allowing for stronger priors generally led participants to visually sample more informative locations, this was not the case of Random participants. Indeed, they appeared to behave naïvely, and their use of specific object-related priors was fully impaired, while they maintained the ability to use general, task-related priors to guide their exploration. These findings have important implications for our understanding of perception, which appears to be influenced by complex cognitive processes, even at the basic level of visual sampling during object recognition.

Brain dynamics supported by a hierarchy of complex correlation patterns defining a robust functional architecture.

Functional magnetic resonance imaging (fMRI) provides insights into cognitive processes with significant clinical potential. However, delays in brain region communication and dynamic variations are often overlooked in functional network studies. We demonstrate that networks extracted from fMRI cross-correlation matrices, considering time lags between signals, show remarkable reliability when focusing on statistical distributions of network properties. This reveals a robust brain functional connectivity pattern, featuring a sparse backbone of strong 0-lag correlations and weaker links capturing coordination at various time delays. This dynamic yet stable network architecture is consistent across rats, marmosets, and humans, as well as in electroencephalogram (EEG) data, indicating potential universality in brain dynamics. Second-order properties of the dynamic functional network reveal a remarkably stable hierarchy of functional correlations in both group-level comparisons and test-retest analyses. Validation using alcohol use disorder fMRI data uncovers broader shifts in network properties than previously reported, demonstrating the potential of this method for identifying disease biomarkers.

Time-frequency super-resolution with superlets.

Due to the Heisenberg-Gabor uncertainty principle, finite oscillation transients are difficult to localize simultaneously in both time and frequency. Classical estimators, like the short-time Fourier transform or the continuous-wavelet transform optimize either temporal or frequency resolution, or find a suboptimal tradeoff. Here, we introduce a spectral estimator enabling time-frequency super-resolution, called superlet, that uses sets of wavelets with increasingly constrained bandwidth. These are combined geometrically in order to maintain the good temporal resolution of single wavelets and gain frequency resolution in upper bands. The normalization of wavelets in the set facilitates exploration of data with scale-free, fractal nature, containing oscillation packets that are self-similar across frequencies. Superlets perform well on synthetic data and brain signals recorded in humans and rodents, resolving high frequency bursts with excellent precision. Importantly, they can reveal fast transient oscillation events in single trials that may be hidden in the averaged time-frequency spectrum by other methods.

Properties of multivariate data investigated by fractal dimensionality.

Elaborated data-mining techniques are widely available today. Nevertheless, many non-linear relations among variables remain undiscovered in multi-dimensional datasets. To address this issue we propose a method based on the concept of fractal dimension that explores the structure of multivariate data and apply the method to simulated data, as well as to local field potentials recorded from cat visual cortex. We find that with changes in the analysis scale, the dimensionality of the data often changes, indicating first that the data are not simple fractals with one unique dimension and second, that, at a certain scale, important changes in the geometric structure of the data may occur. The method can be used as a data-mining tool but also as a method for testing a model's fit to the data. We achieve the latter by comparing the dimensionality of the original data to the dimensionality of the data reconstructed from a model's description of the data (here using the general linear model). The method provides indispensable help in estimating the complexity of non-linear relationships within multivariate datasets.

Visual exploration and object recognition by lattice deformation.

Mechanisms of explicit object recognition are often difficult to investigate and require stimuli with controlled features whose expression can be manipulated in a precise quantitative fashion. Here, we developed a novel method (called "Dots"), for generating visual stimuli, which is based on the progressive deformation of a regular lattice of dots, driven by local contour information from images of objects. By applying progressively larger deformation to the lattice, the latter conveys progressively more information about the target object. Stimuli generated with the presented method enable a precise control of object-related information content while preserving low-level image statistics, globally, and affecting them only little, locally. We show that such stimuli are useful for investigating object recognition under a naturalistic setting--free visual exploration--enabling a clear dissociation between object detection and explicit recognition. Using the introduced stimuli, we show that top-down modulation induced by previous exposure to target objects can greatly influence perceptual decisions, lowering perceptual thresholds not only for object recognition but also for object detection (visual hysteresis). Visual hysteresis is target-specific, its expression and magnitude depending on the identity of individual objects. Relying on the particular features of dot stimuli and on eye-tracking measurements, we further demonstrate that top-down processes guide visual exploration, controlling how visual information is integrated by successive fixations. Prior knowledge about objects can guide saccades/fixations to sample locations that are supposed to be highly informative, even when the actual information is missing from those locations in the stimulus. The duration of individual fixations is modulated by the novelty and difficulty of the stimulus, likely reflecting cognitive demand.

EEG under anesthesia--feature extraction with TESPAR.

We investigated the problem of automatic depth of anesthesia (DOA) estimation from electroencephalogram (EEG) recordings. We employed Time Encoded Signal Processing And Recognition (TESPAR), a time-domain signal processing technique, in combination with multi-layer perceptrons to identify DOA levels. The presented system learns to discriminate between five DOA classes assessed by human experts whose judgements were based on EEG mid-latency auditory evoked potentials (MLAEPs) and clinical observations. We found that our system closely mimicked the behavior of the human expert, thus proving the utility of the method. Further analyses on the features extracted by our technique indicated that information related to DOA is mostly distributed across frequency bands and that the presence of high frequencies (> 80 Hz), which reflect mostly muscle activity, is beneficial for DOA detection.

The oscillation score: an efficient method for estimating oscillation strength in neuronal activity.

We present a method that estimates the strength of neuronal oscillations at the cellular level, relying on autocorrelation histograms computed on spike trains. The method delivers a number, termed oscillation score, that estimates the degree to which a neuron is oscillating in a given frequency band. Moreover, it can also reliably identify the oscillation frequency and strength in the given band, independently of the oscillation in other frequency bands, and thus it can handle superimposed oscillations on multiple scales (theta, alpha, beta, gamma, etc.). The method is relatively simple and fast. It can cope with a low number of spikes, converging exponentially fast with the number of spikes, to a stable estimation of the oscillation strength. It thus lends itself to the analysis of spike-sorted single-unit activity from electrophysiological recordings. We show that the method performs well on experimental data recorded from cat visual cortex and also compares favorably to other methods. In addition, we provide a measure, termed confidence score, that determines the stability of the oscillation score estimate over trials.