Critical-like Brain Dynamics in a Continuum from Second- to First-Order Phase Transition

The classic brain criticality hypothesis postulates that the brain benefits from operating near a continuous second-order phase transition. Slow feedback regulation of neuronal activity could, however, lead to a discontinuous first-order transition and thereby bistable activity. Observations of bistability in awake brain activity have nonetheless remained scarce and its functional significance unclear. Moreover, there is no empirical evidence to support the hypothesis that the human brain could flexibly operate near either a first- or second-order phase transition despite such a continuum being common in models. Here, using computational modeling, we found bistable synchronization dynamics to emerge through elevated positive feedback and occur exclusively in a regimen of critical-like dynamics. We then assessed bistability in vivo with resting-state MEG in healthy adults (7 females, 11 males) and stereo-electroencephalography in epilepsy patients (28 females, 36 males). This analysis revealed that a large fraction of the neocortices exhibited varying degrees of bistability in neuronal oscillations from 3 to 200 Hz. In line with our modeling results, the neuronal bistability was positively correlated with classic assessment of brain criticality across narrow-band frequencies. Excessive bistability was predictive of epileptic pathophysiology in the patients, whereas moderate bistability was positively correlated with task performance in the healthy subjects. These empirical findings thus reveal the human brain as a one-of-a-kind complex system that exhibits critical-like dynamics in a continuum between continuous and discontinuous phase transitions.SIGNIFICANCE STATEMENT In the model, while synchrony per se was controlled by connectivity, increasing positive local feedback led to gradually emerging bistable synchrony with scale-free dynamics, suggesting a continuum between second- and first-order phase transitions in synchrony dynamics inside a critical-like regimen. In resting-state MEG and SEEG, bistability of ongoing neuronal oscillations was pervasive across brain areas and frequency bands and was observed only with concurring critical-like dynamics as the modeling predicted. As evidence for functional relevance, moderate bistability was positively correlated with executive functioning in the healthy subjects, and excessive bistability was associated with epileptic pathophysiology. These findings show that critical-like neuronal dynamics in vivo involves both continuous and discontinuous phase transitions in a frequency-, neuroanatomy-, and state-dependent manner.

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto's law of wealth and the Gutenberg-Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov-Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

Scale-free behavioral dynamics directly linked with scale-free cortical dynamics

Naturally occurring body movements and collective neural activity both exhibit complex dynamics, often with scale-free, fractal spatiotemporal structure. Scale-free dynamics of both brain and behavior are important because each is associated with functional benefits to the organism. Despite their similarities, scale-free brain activity and scale-free behavior have been studied separately, without a unified explanation. Here, we show that scale-free dynamics of mouse behavior and neurons in the visual cortex are strongly related. Surprisingly, the scale-free neural activity is limited to specific subsets of neurons, and these scale-free subsets exhibit stochastic winner-take-all competition with other neural subsets. This observation is inconsistent with prevailing theories of scale-free dynamics in neural systems, which stem from the criticality hypothesis. We develop a computational model which incorporates known cell-type-specific circuit structure, explaining our findings with a new type of critical dynamics. Our results establish neural underpinnings of scale-free behavior and clear behavioral relevance of scale-free neural activity.

Identification of Relevant Protein Interactions with Partial Knowledge: A Complex Network and Deep Learning Approach

Protein-protein interactions (PPIs) are the basis for understanding most cellular events in biological systems. Several experimental methods, e.g., biochemical, molecular, and genetic methods, have been used to identify protein-protein associations. However, some of them, such as mass spectrometry, are time-consuming and expensive. Machine learning (ML) techniques have been widely used to characterize PPIs, increasing the number of proteins analyzed simultaneously and optimizing time and resources for identifying and predicting protein-protein functional linkages. Previous ML approaches have focused on well-known networks or specific targets but not on identifying relevant proteins with partial or null knowledge of the interaction networks. The proposed approach aims to generate a relevant protein sequence based on bidirectional Long-Short Term Memory (LSTM) with partial knowledge of interactions. The general framework comprises conducting a scale-free and fractal complex network analysis. The outcome of these analyses is then used to fine-tune the fractal method for the vital protein extraction of PPI networks. The results show that several PPI networks are self-similar or fractal, but that both features cannot coexist. The generated protein sequences (by the bidirectional LSTM) also contain an average of 39.5% of proteins in the original sequence. The average length of the generated sequences was 17% of the original one. Finally, 95% of the generated sequences were true.

How critical is brain criticality?

Criticality is the singular state of complex systems poised at the brink of a phase transition between order and randomness. Such systems display remarkable information-processing capabilities, evoking the compelling hypothesis that the brain may itself be critical. This foundational idea is now drawing renewed interest thanks to high-density data and converging cross-disciplinary knowledge. Together, these lines of inquiry have shed light on the intimate link between criticality, computation, and cognition. Here, we review these emerging trends in criticality neuroscience, highlighting new data pertaining to the edge of chaos and near-criticality, and making a case for the distance to criticality as a useful metric for probing cognitive states and mental illness. This unfolding progress in the field contributes to establishing criticality theory as a powerful mechanistic framework for studying emergent function and its efficiency in both biological and artificial neural networks.

Intrinsic dynamics and topography of sensory input systems

The brain is continuously bombarded by external stimuli, which are processed in different input systems. The intrinsic features of these sensory input systems remain yet unclear. Investigating topography and dynamics of input systems is the goal of our study in order to better understand the intrinsic features that shape their neural processing. Using a functional magnetic resonance imaging dataset, we measured neural topography and dynamics of the input systems during rest and task states. Neural dynamics were probed by scale-free activity, measured with the power-law exponent (PLE), as well as by order/disorder as measured with sample entropy (SampEn). Our main findings during both rest and task states are: 1) differences in neural dynamics (PLE, SampEn) between regions within each of the three sensory input systems 2) differences in topography and dynamics among the three input systems; 3) PLE and SampEn correlate and, as demonstrated in simulation, show non-linear relationship in the critical range of PLE; 4) scale-free activity during rest mediates the transition of SampEn from rest to task as probed in a mediation model. We conclude that the sensory input systems are characterized by their intrinsic topographic and dynamic organization which, through scale-free activity, modulates their input processing.

Dynamical Mechanism Underlying Scale-Free Network Reorganization in Low Acetylcholine States Corresponding to Slow Wave Sleep

Sleep is indispensable for most animals' cognitive functions, and is hypothesized to be a major factor in memory consolidation. Although we do not fully understand the mechanisms of network reorganisation driving memory consolidation, available data suggests that sleep-associated neurochemical changes may be important for such processes. In particular, global acetylcholine levels change across the sleep/wake cycle, with high cholinergic tone during wake and REM sleep and low cholinergic tone during slow wave sleep. Furthermore, experimental perturbation of cholinergic tone has been shown to impact memory storage. Through in silico modeling of neuronal networks, we show how spiking dynamics change in highly heterogenous networks under varying levels of cholinergic tone, with neuronal networks under high cholinergic modulation firing asynchronously and at high frequencies, while those under low cholinergic modulation exhibit synchronous patterns of activity. We further examined the network's dynamics and its reorganization mediated via changing levels of acetylcholine within the context of different scale-free topologies, comparing network activity within the hub cells, a small group of neurons having high degree connectivity, and with the rest of the network. We show a dramatic, state-dependent change in information flow throughout the network, with highly active hub cells integrating information in a high-acetylcholine state, and transferring it to rest of the network in a low-acetylcholine state. This result is experimentally corroborated by frequency-dependent frequency changes observed in vivo experiments. Together, these findings provide insight into how new neurons are recruited into memory traces during sleep, a mechanism which may underlie system memory consolidation.

A Scale-Free, Fully Connected Global Transition Network Underlies Known Microbiome Diversity

Microbiomes are inherently linked by their structural similarity, yet the global features of such similarity are not clear. Here, we propose as a solution a search-based microbiome transition network. By traversing a composition-similarity-based network of 177,022 microbiomes, we show that although the compositions are distinct by habitat, each microbiome is on-average only seven neighbors from any other microbiome on Earth, indicating the inherent homology of microbiomes at the global scale. This network is scale-free, suggesting a high degree of stability and robustness in microbiome transition. By tracking the minimum spanning tree in this network, a global roadmap of microbiome dispersal was derived that tracks the potential paths of formulating and propagating microbiome diversity. Such search-based global microbiome networks, reconstructed within hours on just one computing node, provide a readily expanded reference for tracing the origin and evolution of existing or new microbiomes. IMPORTANCE It remains unclear whether and how compositional changes at the "community to community" level among microbiomes are linked to the origin and evolution of global microbiome diversity. Here we propose a microbiome transition model and a network-based analysis framework to describe and simulate the variation and dispersal of the global microbial beta-diversity across multiple habitats. The traversal of a transition network with 177,022 samples shows the inherent homology of microbiome at the global scale. Then a global roadmap of microbiome dispersal derived from the network tracks the potential paths of formulating and propagating microbiome diversity. Such search-based microbiome network provides a readily expanded reference for tracing the origin and evolution of existing or new microbiomes at the global scale.

Scale-Free Coupled Dynamics in Brain Networks Captured by Bivariate Focus-Based Multifractal Analysis

While most connectivity studies investigate functional connectivity (FC) in a scale-dependent manner, coupled neural processes may also exhibit broadband dynamics, manifesting as power-law scaling of their measures of interdependence. Here we introduce the bivariate focus-based multifractal (BFMF) analysis as a robust tool for capturing such scale-free relations and use resting-state electroencephalography (EEG) recordings of 12 subjects to demonstrate its performance in reconstructing physiological networks. BFMF was employed to characterize broadband FC between 62 cortical regions in a pairwise manner, with all investigated connections being tested for true bivariate multifractality. EEG channels were also grouped to represent the activity of six resting-state networks (RSNs) in the brain, thus allowing for the analysis of within- and between- RSNs connectivity, separately. Most connections featured true bivariate multifractality, which could be attributed to the genuine scale-free coupling of neural dynamics. Bivariate multifractality showed a characteristic topology over the cortex that was highly concordant among subjects. Long-term autocorrelation was higher in within-RSNs, while the degree of multifractality was generally found stronger in between-RSNs connections. These results offer statistical evidence of the bivariate multifractal nature of functional coupling in the brain and validate BFMF as a robust method to capture such scale-independent coupled dynamics.

Revisiting Functional Connectivity for Infraslow Scale-Free Brain Dynamics Using Complex Wavelets

The analysis of human brain functional networks is achieved by computing functional connectivity indices reflecting phase coupling and interactions between remote brain regions. In magneto- and electroencephalography, the most frequently used functional connectivity indices are constructed based on Fourier-based cross-spectral estimation applied to specific fast and band-limited oscillatory regimes. Recently, infraslow arrhythmic fluctuations (below the 1 Hz) were recognized as playing a leading role in spontaneous brain activity. The present work aims to propose to assess functional connectivity from fractal dynamics, thus extending the assessment of functional connectivity to the infraslow arrhythmic or scale-free temporal dynamics of M/EEG-quantified brain activity. Instead of being based on Fourier analysis, new Imaginary Coherence and weighted Phase Lag indices are constructed from complex-wavelet representations. Their performances are first assessed on synthetic data by means of Monte-Carlo simulations, and they are then compared favorably against the classical Fourier-based indices. These new assessments of functional connectivity indices are also applied to MEG data collected on 36 individuals both at rest and during the learning of a visual motion discrimination task. They demonstrate a higher statistical sensitivity, compared to their Fourier counterparts, in capturing significant and relevant functional interactions in the infraslow regime and modulations from rest to task. Notably, the consistent overall increase in functional connectivity assessed from fractal dynamics from rest to task correlated with a change in temporal dynamics as well as with improved performance in task completion, which suggests that the complex-wavelet weighted Phase Lag index is the sole index is able to capture brain plasticity in the infraslow scale-free regime.

Scale-Free Dynamics in Animal Groups and Brain Networks

Collective phenomena fascinate by the emergence of order in systems composed of a myriad of small entities. They are ubiquitous in nature and can be found over a vast range of scales in physical and biological systems. Their key feature is the seemingly effortless emergence of adaptive collective behavior that cannot be trivially explained by the properties of the system's individual components. This perspective focuses on recent insights into the similarities of correlations for two apparently disparate phenomena: flocking in animal groups and neuronal ensemble activity in the brain. We first will summarize findings on the spontaneous organization in bird flocks and macro-scale human brain activity utilizing correlation functions and insights from critical dynamics. We then will discuss recent experimental findings that apply these approaches to the collective response of neurons to visual and motor processing, i.e., to local perturbations of neuronal networks at the meso- and microscale. We show how scale-free correlation functions capture the collective organization of neuronal avalanches in evoked neuronal populations in nonhuman primates and between neurons during visual processing in rodents. These experimental findings suggest that the coherent collective neural activity observed at scales much larger than the length of the direct neuronal interactions is demonstrative of a phase transition and we discuss the experimental support for either discontinuous or continuous phase transitions. We conclude that at or near a phase-transition neuronal information can propagate in the brain with similar efficiency as proposed to occur in the collective adaptive response observed in some animal groups.

FW-PSO Algorithm to Enhance the Invulnerability of Industrial Wireless Sensor Networks Topology

When an industrial wireless sensor network (WSN) is seriously disturbed and intentionally attacked, sometimes it fails easily, even leading to the paralysis of the entire industrial wireless network. In order to improve the invulnerability of networks, in this paper, the scale-free network in complex networks is taken as the research object, and the industrial WSN with scale-free characteristics is modeled. Based on the advantages of the fireworks algorithm, such as strong searching ability and diversity of population, a so-called fireworks and particle swarm optimization (FW-PSO) algorithm is proposed, which can improve the global search ability and convergence speed effectively. The proposed FW-PSO algorithm is used to optimize the network topology and form a network with the largest natural connectivity, which can effectively promote the ability of network to resist the cascade failure problem. The dynamic invulnerability of the optimized network under highest-degree (HD) attack and lowest-degree (LD) attack strategies, as well as the static invulnerability under random attack, were evaluated respectively. Simulation experiments show that the industrial WSN optimized by FW-PSO can significantly improve the performance of the dynamic and static invulnerabilities compared with the initial network and the networks optimized by the other two existing algorithms.

Single-Cell Membrane Potential Fluctuations Evince Network Scale-Freeness and Quasicriticality

What information single neurons receive about general neural circuit activity is a fundamental question for neuroscience. Somatic membrane potential (V _m) fluctuations are driven by the convergence of synaptic inputs from a diverse cross-section of upstream neurons. Furthermore, neural activity is often scale-free, implying that some measurements should be the same, whether taken at large or small scales. Together, convergence and scale-freeness support the hypothesis that single V _m recordings carry useful information about high-dimensional cortical activity. Conveniently, the theory of "critical branching networks" (one purported explanation for scale-freeness) provides testable predictions about scale-free measurements that are readily applied to V _m fluctuations. To investigate, we obtained whole-cell current-clamp recordings of pyramidal neurons in visual cortex of turtles with unknown genders. We isolated fluctuations in V _m below the firing threshold and analyzed them by adapting the definition of "neuronal avalanches" (i.e., spurts of population spiking). The V _m fluctuations which we analyzed were scale-free and consistent with critical branching. These findings recapitulated results from large-scale cortical population data obtained separately in complementary experiments using microelectrode arrays described previously (Shew et al., 2015). Simultaneously recorded single-unit local field potential did not provide a good match, demonstrating the specific utility of V _m Modeling shows that estimation of dynamical network properties from neuronal inputs is most accurate when networks are structured as critical branching networks. In conclusion, these findings extend evidence of critical phenomena while also establishing subthreshold pyramidal neuron V _m fluctuations as an informative gauge of high-dimensional cortical population activity.SIGNIFICANCE STATEMENT The relationship between membrane potential (V _m) dynamics of single neurons and population dynamics is indispensable to understanding cortical circuits. Just as important to the biophysics of computation are emergent properties such as scale-freeness, where critical branching networks offer insight. This report makes progress on both fronts by comparing statistics from single-neuron whole-cell recordings with population statistics obtained with microelectrode arrays. Not only are fluctuations of somatic V _m scale-free, they match fluctuations of population activity. Thus, our results demonstrate appropriation of the brain's own subsampling method (convergence of synaptic inputs) while extending the range of fundamental evidence for critical phenomena in neural systems from the previously observed mesoscale (fMRI, LFP, population spiking) to the microscale, namely, V _m fluctuations.

Rigidity percolation and geometric information in floppy origami

Origami structures with a large number of excess folds are capable of storing distinguishable geometric states that are energetically equivalent. As the number of excess folds is reduced, the system has fewer equivalent states and can eventually become rigid. We quantify this transition from a floppy to a rigid state as a function of the presence of folding constraints in a classic origami tessellation, Miura-ori. We show that in a fully triangulated Miura-ori that is maximally floppy, adding constraints via the elimination of diagonal folds in the quads decreases the number of degrees of freedom in the system, first linearly and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via a redundancy in the assignment of constraints, and the degrees of freedom depend on constraint density in a scale-invariant manner. A percolation transition in the redundancy in the constraints as a function of constraint density suggests how excess folds in an origami structure can be used to store geometric information in a scale-invariant way.

The temporal signature of self: Temporal measures of resting-state EEG predict self-consciousness

The self is the core of our mental life. Previous investigations have demonstrated a strong neural overlap between self-related activity and resting state activity. This suggests that information about self-relatedness is encoded in our brain's spontaneous activity. The exact neuronal mechanisms of such "rest-self containment," however, remain unclear. The present EEG study investigated temporal measures of resting state EEG to relate them to self-consciousness. This was obtained with the self-consciousness scale (SCS) which measures Private, Public, and Social dimensions of self. We demonstrate positive correlations between Private self-consciousness and three temporal measures of resting state activity: scale-free activity as indexed by the power-law exponent (PLE), the auto-correlation window (ACW), and modulation index (MI). Specifically, higher PLE, longer ACW, and stronger MI were related to higher degrees of Private self-consciousness. Finally, conducting eLORETA for spatial tomography, we found significant correlation of Private self-consciousness with activity in cortical midline structures such as the perigenual anterior cingulate cortex and posterior cingulate cortex. These results were reinforced with a data-driven analysis; a machine learning algorithm accurately predicted an individual as having a "high" or "low" Private self-consciousness score based on these measures of the brain's spatiotemporal structure. In conclusion, our results demonstrate that Private self-consciousness is related to the temporal structure of resting state activity as featured by temporal nestedness (PLE), temporal continuity (ACW), and temporal integration (MI). Our results support the hypothesis that self-related information is temporally contained in the brain's resting state. "Rest-self containment" can thus be featured by a temporal signature.

Hearing the Sound in the Brain: Influences of Different EEG References

If the scalp potential signals, the electroencephalogram (EEG), are due to neural "singers" in the brain, how could we listen to them with less distortion? One crucial point is that the data recording on the scalp should be faithful and accurate, thus the choice of reference electrode is a vital factor determining the faithfulness of the data. In this study, music on the scalp derived from data in the brain using three different reference electrodes were compared, including approximate zero reference-reference electrode standardization technique (REST), average reference (AR), and linked mastoids reference (LM). The classic music pieces in waveform format were used as simulated sources inside a head model, and they were forward calculated to scalp as standard potential recordings, i.e., waveform format music from the brain with true zero reference. Then these scalp music was re-referenced into REST, AR, and LM based data, and compared with the original forward data (true zero reference). For real data, the EEG recorded in an orthodontic pain control experiment were utilized for music generation with the three references, and the scale free index (SFI) of these music pieces were compared. The results showed that in the simulation for only one source, different references do not change the music/waveform; for two sources or more, REST provide the most faithful music/waveform to the original ones inside the brain, and the distortions caused by AR and LM were spatial locations of both source and scalp electrode dependent. The brainwave music from the real EEG data showed that REST and AR make the differences of SFI between two states more recognized and found the frontal is the main region that producing the music. In conclusion, REST can reconstruct the true signals approximately, and it can be used to help to listen to the true voice of the neural singers in the brain.

Symmetry and symmetry breaking in cancer: a foundational approach to the cancer problem

Symmetry and symmetry breaking concepts from physics and biology are applied to the problem of cancer. Three categories of symmetry breaking in cancer are examined: combinatorial, geometric, and functional. Within these categories, symmetry breaking is examined for relevant cancer features, including epithelial-mesenchymal transition (EMT); tumor heterogeneity; tensegrity; fractal geometric and information structure; functional interaction networks; and network stabilizability and attack tolerance. The new cancer symmetry concepts are relevant to homeostasis loss in cancer and to its origin, spread, treatment and resistance. Symmetry and symmetry breaking could provide a new way of thinking and a pathway to a solution of the cancer problem.

Remodeling Pearson's Correlation for Functional Brain Network Estimation and Autism Spectrum Disorder Identification

Functional brain network (FBN) has been becoming an increasingly important way to model the statistical dependence among neural time courses of brain, and provides effective imaging biomarkers for diagnosis of some neurological or psychological disorders. Currently, Pearson's Correlation (PC) is the simplest and most widely-used method in constructing FBNs. Despite its advantages in statistical meaning and calculated performance, the PC tends to result in a FBN with dense connections. Therefore, in practice, the PC-based FBN needs to be sparsified by removing weak (potential noisy) connections. However, such a scheme depends on a hard-threshold without enough flexibility. Different from this traditional strategy, in this paper, we propose a new approach for estimating FBNs by remodeling PC as an optimization problem, which provides a way to incorporate biological/physical priors into the FBNs. In particular, we introduce an L₁-norm regularizer into the optimization model for obtaining a sparse solution. Compared with the hard-threshold scheme, the proposed framework gives an elegant mathematical formulation for sparsifying PC-based networks. More importantly, it provides a platform to encode other biological/physical priors into the PC-based FBNs. To further illustrate the flexibility of the proposed method, we extend the model to a weighted counterpart for learning both sparse and scale-free networks, and then conduct experiments to identify autism spectrum disorders (ASD) from normal controls (NC) based on the constructed FBNs. Consequently, we achieved an 81.52% classification accuracy which outperforms the baseline and state-of-the-art methods.

Network rewiring dynamics with convergence towards a star network

Network rewiring as a method for producing a range of structures was first introduced in 1998 by Watts & Strogatz (Nature393, 440-442. (doi:10.1038/30918)). This approach allowed a transition from regular through small-world to a random network. The subsequent interest in scale-free networks motivated a number of methods for developing rewiring approaches that converged to scale-free networks. This paper presents a rewiring algorithm (RtoS) for undirected, non-degenerate, fixed size networks that transitions from regular, through small-world and scale-free to star-like networks. Applications of the approach to models for the spread of infectious disease and fixation time for a simple genetics model are used to demonstrate the efficacy and application of the approach.

Homeostasis as the Mechanism of Evolution

Homeostasis is conventionally thought of merely as a synchronic (same time) servo-mechanism that maintains the status quo for organismal physiology. However, when seen from the perspective of developmental physiology, homeostasis is a robust, dynamic, intergenerational, diachronic (across-time) mechanism for the maintenance, perpetuation and modification of physiologic structure and function. The integral relationships generated by cell-cell signaling for the mechanisms of embryogenesis, physiology and repair provide the needed insight to the scale-free universality of the homeostatic principle, offering a novel opportunity for a Systems approach to Biology. Starting with the inception of life itself, with the advent of reproduction during meiosis and mitosis, moving forward both ontogenetically and phylogenetically through the evolutionary steps involved in adaptation to an ever-changing environment, Biology and Evolution Theory need no longer default to teleology.

Cortical burst dynamics predict clinical outcome early in extremely preterm infants

Intermittent bursts of electrical activity are a ubiquitous signature of very early brain activity. Previous studies have largely focused on assessing the amplitudes of these transient cortical bursts or the intervals between them. Recent advances in basic neuroscience have identified the presence of scale-free 'avalanche' processes in bursting patterns of cortical activity in other clinical contexts. Here, we hypothesize that cortical bursts in human preterm infants also exhibit scale-free properties, providing new insights into the nature, temporal evolution, and prognostic value of spontaneous brain activity in the days immediately following preterm birth. We examined electroencephalographic recordings from 43 extremely preterm infants (gestational age 22-28 weeks) and demonstrated that their cortical bursts exhibit scale-free properties as early as 12 h after birth. The scaling relationships of cortical bursts correlate significantly with later mental development-particularly within the first 12 h of life. These findings show that early preterm brain activity is characterized by scale-free dynamics which carry developmental significance, hence offering novel means for rapid and early clinical prediction of neurodevelopmental outcomes.

Scale-free brain dynamics under physical and psychological distress: pre-treatment effects in women diagnosed with breast cancer

Stressful life events are related to negative outcomes, including physical and psychological manifestations of distress, and behavioral deficits. Patients diagnosed with breast cancer report impaired attention and working memory prior to adjuvant therapy, which may be induced by distress. In this article, we examine whether brain dynamics show systematic changes due to the distress associated with cancer diagnosis. We hypothesized that impaired working memory is associated with suppression of "long-memory" neuronal dynamics; we tested this by measuring scale-free ("fractal") brain dynamics, quantified by the Hurst exponent (H). Fractal scaling refers to signals that do not occur at a specific time-scale, possessing a spectral power curve P(f)∝ f(-β); they are "long-memory" processes, with significant autocorrelations. In a BOLD functional magnetic resonance imaging study, we scanned three groups during a working memory task: women scheduled to receive chemotherapy or radiotherapy and aged-matched controls. Surprisingly, patients' BOLD signal exhibited greater H with increasing intensity of anticipated treatment. However, an analysis of H and functional connectivity against self-reported measures of psychological distress (Worry, Anxiety, Depression) and physical distress (Fatigue, Sleep problems) revealed significant interactions. The modulation of (Worry, Anxiety) versus (Fatigue, Sleep Problems, Depression) showed the strongest effect, where higher worry and lower fatigue was related to reduced H in regions involved in visuospatial search, attention, and memory processing. This is also linked to decreased functional connectivity in these brain regions. Our results indicate that the distress associated with cancer diagnosis alters BOLD scaling, and H is a sensitive measure of the interaction between psychological versus physical distress.

Network analysis of time-lapse microscopy recordings

Multicellular organisms rely on intercellular communication to regulate important cellular processes critical to life. To further our understanding of those processes there is a need to scrutinize dynamical signaling events and their functions in both cells and organisms. Here, we report a method and provide MATLAB code that analyzes time-lapse microscopy recordings to identify and characterize network structures within large cell populations, such as interconnected neurons. The approach is demonstrated using intracellular calcium (Ca²⁺) recordings in neural progenitors and cardiac myocytes, but could be applied to a wide variety of biosensors employed in diverse cell types and organisms. In this method, network structures are analyzed by applying cross-correlation signal processing and graph theory to single-cell recordings. The goal of the analysis is to determine if the single cell activity constitutes a network of interconnected cells and to decipher the properties of this network. The method can be applied in many fields of biology in which biosensors are used to monitor signaling events in living cells. Analyzing intercellular communication in cell ensembles can reveal essential network structures that provide important biological insights.

Scale-free bursting in human cortex following hypoxia at birth

The human brain is fragile in the face of oxygen deprivation. Even a brief interruption of metabolic supply at birth challenges an otherwise healthy neonatal cortex, leading to a cascade of homeostatic responses. During recovery from hypoxia, cortical activity exhibits a period of highly irregular electrical fluctuations known as burst suppression. Here we show that these bursts have fractal properties, with power-law scaling of burst sizes across a remarkable 5 orders of magnitude and a scale-free relationship between burst sizes and durations. Although burst waveforms vary greatly, their average shape converges to a simple form that is asymmetric at long time scales. Using a simple computational model, we argue that this asymmetry reflects activity-dependent changes in the excitatory-inhibitory balance of cortical neurons. Bursts become more symmetric following the resumption of normal activity, with a corresponding reorganization of burst scaling relationships. These findings place burst suppression in the broad class of scale-free physical processes termed crackling noise and suggest that the resumption of healthy activity reflects a fundamental reorganization in the relationship between neuronal activity and its underlying metabolic constraints.

Network epidemiology and plant trade networks

Models of epidemics in complex networks are improving our predictive understanding of infectious disease outbreaks. Nonetheless, applying network theory to plant pathology is still a challenge. This overview summarizes some key developments in network epidemiology that are likely to facilitate its application in the study and management of plant diseases. Recent surveys have provided much-needed datasets on contact patterns and human mobility in social networks, but plant trade networks are still understudied. Human (and plant) mobility levels across the planet are unprecedented-there is thus much potential in the use of network theory by plant health authorities and researchers. Given the directed and hierarchical nature of plant trade networks, there is a need for plant epidemiologists to further develop models based on undirected and homogeneous networks. More realistic plant health scenarios would also be obtained by developing epidemic models in dynamic, rather than static, networks. For plant diseases spread by the horticultural and ornamental trade, there is the challenge of developing spatio-temporal epidemic simulations integrating network data. The use of network theory in plant epidemiology is a promising avenue and could contribute to anticipating and preventing plant health emergencies such as European ash dieback.

Inference of neuronal network spike dynamics and topology from calcium imaging data

Two-photon calcium imaging enables functional analysis of neuronal circuits by inferring action potential (AP) occurrence ("spike trains") from cellular fluorescence signals. It remains unclear how experimental parameters such as signal-to-noise ratio (SNR) and acquisition rate affect spike inference and whether additional information about network structure can be extracted. Here we present a simulation framework for quantitatively assessing how well spike dynamics and network topology can be inferred from noisy calcium imaging data. For simulated AP-evoked calcium transients in neocortical pyramidal cells, we analyzed the quality of spike inference as a function of SNR and data acquisition rate using a recently introduced peeling algorithm. Given experimentally attainable values of SNR and acquisition rate, neural spike trains could be reconstructed accurately and with up to millisecond precision. We then applied statistical neuronal network models to explore how remaining uncertainties in spike inference affect estimates of network connectivity and topological features of network organization. We define the experimental conditions suitable for inferring whether the network has a scale-free structure and determine how well hub neurons can be identified. Our findings provide a benchmark for future calcium imaging studies that aim to reliably infer neuronal network properties.

Exploring network theory for mass drug administration

Network theory is a well-established discipline that uses mathematical graphs to describe biological, physical, and social systems. The topologies across empirical networks display strikingly similar organizational properties. In particular, the characteristics of these networks allow computational analysis to contribute data unattainable from examining individual components in isolation. However, the interdisciplinary and quantitative nature of network analysis has yet to be exploited by public health initiatives to distribute preventive chemotherapies. One notable application is the 2012 World Health Organization (WHO) Roadmap for Neglected Tropical Diseases (NTDs) where there is a need to upscale distribution capacity and to target systematic noncompliers. An understanding of local networks for analysing the distributional properties of community-directed treatment may facilitate sustainable expansion of mass drug-administration (MDA) programs.

Characterization of scale-free properties of human electrocorticography in awake and slow wave sleep States

Like many complex dynamic systems, the brain exhibits scale-free dynamics that follow power-law scaling. Broadband power spectral density (PSD) of brain electrical activity exhibits state-dependent power-law scaling with a log frequency exponent that varies across frequency ranges. Widely divergent naturally occurring neural states, awake and slow wave sleep (SWS), were used to evaluate the nature of changes in scale-free indices of brain electrical activity. We demonstrate two analytic approaches to characterizing electrocorticographic (ECoG) data obtained during awake and SWS states. A data-driven approach was used, characterizing all available frequency ranges. Using an equal error state discriminator (EESD), a single frequency range did not best characterize state across data from all six subjects, though the ability to distinguish awake and SWS ECoG data in individual subjects was excellent. Multi-segment piecewise linear fits were used to characterize scale-free slopes across the entire frequency range (0.2–200 Hz). These scale-free slopes differed between awake and SWS states across subjects, particularly at frequencies below 10 Hz and showed little difference at frequencies above 70 Hz. A multivariate maximum likelihood analysis (MMLA) method using the multi-segment slope indices successfully categorized ECoG data in most subjects, though individual variation was seen. In exploring the differences between awake and SWS ECoG data, these analytic techniques show that no change in a single frequency range best characterizes differences between these two divergent biological states. With increasing computational tractability, the use of scale-free slope values to characterize ECoG and EEG data will have practical value in clinical and research studies.

Being critical of criticality in the brain

Relatively recent work has reported that networks of neurons can produce avalanches of activity whose sizes follow a power law distribution. This suggests that these networks may be operating near a critical point, poised between a phase where activity rapidly dies out and a phase where activity is amplified over time. The hypothesis that the electrical activity of neural networks in the brain is critical is potentially important, as many simulations suggest that information processing functions would be optimized at the critical point. This hypothesis, however, is still controversial. Here we will explain the concept of criticality and review the substantial objections to the criticality hypothesis raised by skeptics. Points and counter points are presented in dialog form.

Genome-Wide Scale-Free Network Inference for Candida albicans

Discovery of essential genes in pathogenic organisms is an important step in the development of new medication. Despite a growing number of genome data available, little is known about C. albicans, a major fungal pathogen. Most of the human population carries C. albicans as commensal, but it can cause systemic infection that may lead to the death of the host if the immune system has deteriorated. In many organisms central nodes in the interaction network (hubs) play a crucial role for information and energy transport. Knock-outs of such hubs often lead to lethal phenotypes making them interesting drug targets. To identify these central genes via topological analysis, we inferred gene regulatory networks that are sparse and scale-free. We collected information from various sources to complement the limited expression data available. We utilized a linear regression algorithm to infer genome-wide gene regulatory interaction networks. To evaluate the predictive power of our approach, we used an automated text-mining system that scanned full-text research papers for known interactions. With the help of the compendium of known interactions, we also optimize the influence of the prior knowledge and the sparseness of the model to achieve the best results. We compare the results of our approach with those of other state-of-the-art network inference methods and show that we outperform those methods. Finally we identify a number of hubs in the genome of the fungus and investigate their biological relevance.

Tinnitus: network pathophysiology-network pharmacology

Tinnitus, the phantom perception of sound, is a prevalent disorder. One in 10 adults has clinically significant subjective tinnitus, and for one in 100, tinnitus severely affects their quality of life. Despite the significant unmet clinical need for a safe and effective drug targeting tinnitus relief, there is currently not a single Food and Drug Administration (FDA)-approved drug on the market. The search for drugs that target tinnitus is hampered by the lack of a deep knowledge of the underlying neural substrates of this pathology. Recent studies are increasingly demonstrating that, as described for other central nervous system (CNS) disorders, tinnitus is a pathology of brain networks. The application of graph theoretical analysis to brain networks has recently provided new information concerning their topology, their robustness and their vulnerability to attacks. Moreover, the philosophy behind drug design and pharmacotherapy in CNS pathologies is changing from that of "magic bullets" that target individual chemoreceptors or "disease-causing genes" into that of "magic shotguns," "promiscuous" or "dirty drugs" that target "disease-causing networks," also known as network pharmacology. In the present work we provide some insight into how this knowledge could be applied to tinnitus pathophysiology and pharmacotherapy.

Differentially expressed genes in major depression reside on the periphery of resilient gene coexpression networks

The structure of gene coexpression networks reflects the activation and interaction of multiple cellular systems. Since the pathology of neuropsychiatric disorders is influenced by diverse cellular systems and pathways, we investigated gene coexpression networks in major depression, and searched for putative unifying themes in network connectivity across neuropsychiatric disorders. Specifically, based on the prevalence of the lethality–centrality relationship in disease-related networks, we hypothesized that network changes between control and major depression-related networks would be centered around coexpression hubs, and secondly, that differentially expressed (DE) genes would have a characteristic position and connectivity level in those networks. Mathematically, the first hypothesis tests the relationship of differential coexpression to network connectivity, while the second “hybrid” expression-and-network hypothesis tests the relationship of differential expression to network connectivity. To answer these questions about the potential interaction of coexpression network structure with differential expression, we utilized all available human post-mortem depression-related datasets appropriate for coexpression analysis, which spanned different microarray platforms, cohorts, and brain regions. Similar studies were also performed in an animal model of depression and in schizophrenia and bipolar disorder microarray datasets. We now provide results which consistently support (1) that genes assemble into small-world and scale-free networks in control subjects, (2) that this efficient network topology is largely resilient to changes in depressed subjects, and (3) that DE genes are positioned on the periphery of coexpression networks. Similar results were observed in a mouse model of depression, and in selected bipolar- and schizophrenia-related networks. Finally, we show that baseline expression variability contributes to the propensity of genes to be network hubs and/or to be DE in disease. In summary, our results suggest that the small-world and scale-free properties of gene networks are resilient to pathological changes in major depression, and that the network structure may constrain the extent to which a gene may be DE in the illness, hence informing further gene-network-based mechanistic studies of neuropsychiatric disorders.

The interaction of intrinsic dynamics and network topology in determining network burst synchrony

The pre-Bötzinger complex (pre-BötC), within the mammalian respiratory brainstem, represents an ideal system for investigating the synchronization properties of complex neuronal circuits via the interaction of cell-type heterogeneity and network connectivity. In isolation, individual respiratory neurons from the pre-BötC may be tonically active, rhythmically bursting, or quiescent. Despite this intrinsic heterogeneity, coupled networks of pre-BötC neurons en bloc engage in synchronized bursting that can drive inspiratory motor neuron activation. The region's connection topology has been recently characterized and features dense clusters of cells with occasional connections between clusters. We investigate how the dynamics of individual neurons (quiescent/bursting/tonic) and the betweenness centrality of neurons' positions within the network connectivity graph interact to govern network burst synchrony, by simulating heterogeneous networks of computational model pre-BötC neurons. Furthermore, we compare the prevalence and synchrony of bursting across networks constructed with a variety of connection topologies, analyzing the same collection of heterogeneous neurons in small-world, scale-free, random, and regularly structured networks. We find that several measures of network burst synchronization are determined by interactions of network topology with the intrinsic dynamics of neurons at central network positions and by the strengths of synaptic connections between neurons. Surprisingly, despite the functional role of synchronized bursting within the pre-BötC, we find that synchronized network bursting is generally weakest when we use its specific connection topology, which leads to synchrony within clusters but poor coordination across clusters. Overall, our results highlight the relevance of interactions between topology and intrinsic dynamics in shaping the activity of networks and the concerted effects of connectivity patterns and dynamic heterogeneities.

A scale-free systems theory of motivation and addiction

Scale-free organizations, characterized by uneven distributions of linkages between nodal elements, describe the structure and function of many life-based complex systems developing under evolutionary pressures. We explore motivated behavior as a scale-free map toward a comprehensive translational theory of addiction. Motivational and behavioral repertoires are reframed as link and nodal element sets, respectively, comprising a scale-free structure. These sets are generated by semi-independent information-processing streams within cortical-striatal circuits that cooperatively provide decision-making and sequential processing functions necessary for traversing maps of motivational links connecting behavioral nodes. Dopamine modulation of cortical-striatal plasticity serves a central-hierarchical mechanism for survival-adaptive sculpting and development of motivational-behavioral repertoires by guiding a scale-free design. Drug-induced dopamine activity promotes drug taking as a highly connected behavioral hub at the expense of natural-adaptive motivational links and behavioral nodes. Conceptualizing addiction as pathological alteration of scale-free motivational-behavioral repertoires unifies neurobiological, neurocomputational and behavioral research while addressing addiction vulnerability in adolescence and psychiatric illness. This model may inform integrative research in defining more effective prevention and treatment strategies for addiction.

Graph topology plays a determinant role in the evolution of cooperation

We study the evolution of cooperation in communities described in terms of graphs, such that individuals occupy the vertices and engage in single rounds of the Prisoner's Dilemma with those individuals with whom they are connected through the edges of those graphs. We find an overwhelming dominance of cooperation whenever graphs are dynamically generated through the mechanisms of growth and preferential attachment. These mechanisms lead to the appearance of direct links between hubs, which constitute sufficient conditions to sustain cooperation. We show that cooperation dominates from large population sizes down to communities with nearly 100 individuals, even when extrinsic factors set a limit on the number of interactions that each individual may engage in.