Untangling Brain-Wide Dynamics in Consciousness by Cross-Embedding

Ensemble dynamics and information flow deduction from whole-brain imaging data

The recent advancements in large-scale activity imaging of neuronal ensembles offer valuable opportunities to comprehend the process involved in generating brain activity patterns and understanding how information is transmitted between neurons or neuronal ensembles. However, existing methodologies for extracting the underlying properties that generate overall dynamics are still limited. In this study, we applied previously unexplored methodologies to analyze time-lapse 3D imaging (4D imaging) data of head neurons of the nematode Caenorhabditis elegans. By combining time-delay embedding with the independent component analysis, we successfully decomposed whole-brain activities into a small number of component dynamics. Through the integration of results from multiple samples, we extracted common dynamics from neuronal activities that exhibit apparent divergence across different animals. Notably, while several components show common cooperativity across samples, some component pairs exhibited distinct relationships between individual samples. We further developed time series prediction models of synaptic communications. By combining dimension reduction using the general framework, gradient kernel dimension reduction, and probabilistic modeling, the overall relationships of neural activities were incorporated. By this approach, the stochastic but coordinated dynamics were reproduced in the simulated whole-brain neural network. We found that noise in the nervous system is crucial for generating realistic whole-brain dynamics. Furthermore, by evaluating synaptic interaction properties in the models, strong interactions within the core neural circuit, variable sensory transmission and importance of gap junctions were inferred. Virtual optogenetics can be also performed using the model. These analyses provide a solid foundation for understanding information flow in real neural networks.

Empirical dynamic modelling and enhanced causal analysis of short-length Culex abundance timeseries with vector correlation metrics

Employing Empirical Dynamic Modelling we investigate whether model free methods could be applied in the study of Culex mosquitoes in Northern Greece. Applying Simplex Projection and S-Map algorithms on yearly timeseries of maximum abundances from 2011 to 2020 we successfully predict the decreasing trend in the maximum number of mosquitoes which was observed in the rural area of Thessaloniki during 2021. Leveraging the use of vector correlation metrics we were able to deduce the main environmental factors driving mosquito abundance such as temperature, rain and wind during 2012 and study the causal interaction between neighbouring populations in the industrial area of Thessaloniki between 2019 and 2020. In all three cases a chaotic and non-linear behaviour of the underlying system was observed. Given the health risk associated with the presence of mosquitoes as vectors of viral diseases these results hint to the usefulness of EDM methods in entomological studies as guides for the construction of more accurate and realistic mechanistic models which are indispensable to public health authorities for the design of targeted control strategies and health prevention measures.

Establishing brain states in neuroimaging data

The definition of a brain state remains elusive, with varying interpretations across different sub-fields of neuroscience-from the level of wakefulness in anaesthesia, to activity of individual neurons, voltage in EEG, and blood flow in fMRI. This lack of consensus presents a significant challenge to the development of accurate models of neural dynamics. However, at the foundation of dynamical systems theory lies a definition of what constitutes the 'state' of a system-i.e., a specification of the system's future. Here, we propose to adopt this definition to establish brain states in neuroimaging timeseries by applying Dynamic Causal Modelling (DCM) to low-dimensional embedding of resting and task condition fMRI data. We find that ~90% of subjects in resting conditions are better described by first-order models, whereas ~55% of subjects in task conditions are better described by second-order models. Our work calls into question the status quo of using first-order equations almost exclusively within computational neuroscience and provides a new way of establishing brain states, as well as their associated phase space representations, in neuroimaging datasets.

Common population codes produce extremely nonlinear neural manifolds

Populations of neurons represent sensory, motor, and cognitive variables via patterns of activity distributed across the population. The size of the population used to encode a variable is typically much greater than the dimension of the variable itself, and thus, the corresponding neural population activity occupies lower-dimensional subsets of the full set of possible activity states. Given population activity data with such lower-dimensional structure, a fundamental question asks how close the low-dimensional data lie to a linear subspace. The linearity or nonlinearity of the low-dimensional structure reflects important computational features of the encoding, such as robustness and generalizability. Moreover, identifying such linear structure underlies common data analysis methods such as Principal Component Analysis (PCA). Here, we show that for data drawn from many common population codes the resulting point clouds and manifolds are exceedingly nonlinear, with the dimension of the best-fitting linear subspace growing at least exponentially with the true dimension of the data. Consequently, linear methods like PCA fail dramatically at identifying the true underlying structure, even in the limit of arbitrarily many data points and no noise.

From calcium imaging to graph topology

Systems neuroscience is facing an ever-growing mountain of data. Recent advances in protein engineering and microscopy have together led to a paradigm shift in neuroscience; using fluorescence, we can now image the activity of every neuron through the whole brain of behaving animals. Even in larger organisms, the number of neurons that we can record simultaneously is increasing exponentially with time. This increase in the dimensionality of the data is being met with an explosion of computational and mathematical methods, each using disparate terminology, distinct approaches, and diverse mathematical concepts. Here we collect, organize, and explain multiple data analysis techniques that have been, or could be, applied to whole-brain imaging, using larval zebrafish as an example model. We begin with methods such as linear regression that are designed to detect relations between two variables. Next, we progress through network science and applied topological methods, which focus on the patterns of relations among many variables. Finally, we highlight the potential of generative models that could provide testable hypotheses on wiring rules and network progression through time, or disease progression. While we use examples of imaging from larval zebrafish, these approaches are suitable for any population-scale neural network modeling, and indeed, to applications beyond systems neuroscience. Computational approaches from network science and applied topology are not limited to larval zebrafish, or even to systems neuroscience, and we therefore conclude with a discussion of how such methods can be applied to diverse problems across the biological sciences.

Causal Analysis of Activity in Social Brain Areas During Human-Agent Conversation

This article investigates the differences in cognitive and neural mechanisms between human-human and human-virtual agent interaction using a dataset recorded in an ecologically realistic environment. We use Convergent Cross Mapping (CCM) to investigate functional connectivity between pairs of regions involved in the framework of social cognitive neuroscience, namely the fusiform gyrus, superior temporal sulcus (STS), temporoparietal junction (TPJ), and the dorsolateral prefrontal cortex (DLPFC)-taken as prefrontal asymmetry. Our approach is a compromise between investigating local activation in specific regions and investigating connectivity networks that may form part of larger networks. In addition to concording with previous studies, our results suggest that the right TPJ is one of the most reliable areas for assessing processes occurring during human-virtual agent interactions, both in a static and dynamic sense.

Manifold-adaptive dimension estimation revisited

Data dimensionality informs us about data complexity and sets limit on the structure of successful signal processing pipelines. In this work we revisit and improve the manifold adaptive Farahmand-Szepesvári-Audibert (FSA) dimension estimator, making it one of the best nearest neighbor-based dimension estimators available. We compute the probability density function of local FSA estimates, if the local manifold density is uniform. Based on the probability density function, we propose to use the median of local estimates as a basic global measure of intrinsic dimensionality, and we demonstrate the advantages of this asymptotically unbiased estimator over the previously proposed statistics: the mode and the mean. Additionally, from the probability density function, we derive the maximum likelihood formula for global intrinsic dimensionality, if i.i.d. holds. We tackle edge and finite-sample effects with an exponential correction formula, calibrated on hypercube datasets. We compare the performance of the corrected median-FSA estimator with kNN estimators: maximum likelihood (Levina-Bickel), the 2NN and two implementations of DANCo (R and MATLAB). We show that corrected median-FSA estimator beats the maximum likelihood estimator and it is on equal footing with DANCo for standard synthetic benchmarks according to mean percentage error and error rate metrics. With the median-FSA algorithm, we reveal diverse changes in the neural dynamics while resting state and during epileptic seizures. We identify brain areas with lower-dimensional dynamics that are possible causal sources and candidates for being seizure onset zones.

Unsupervised Methods for Detection of Neural States: Case Study of Hippocampal-Amygdala Interactions

The hippocampus and amygdala are functionally coupled brain regions that play a crucial role in processes involving memory and learning. Because interareal communication has been reported both during specific sleep stages and in awake, behaving animals, these brain regions can serve as an archetype to establish that measuring functional interactions is important for comprehending neural systems. To this end, we analyze here a public dataset of local field potentials (LFPs) recorded in rats simultaneously from the hippocampus and amygdala during different behaviors. Employing a specific, time-lagged embedding technique, named topological causality (TC), we infer directed interactions between the LFP band powers of the two regions across six frequency bands in a time-resolved manner. The combined power and interaction signals are processed with our own unsupervised tools developed originally for the analysis of molecular dynamics simulations to effectively visualize and identify putative, neural states that are visited by the animals repeatedly. Our proposed methodology minimizes impositions onto the data, such as isolating specific epochs, or averaging across externally annotated behavioral stages, and succeeds in separating internal states by external labels such as sleep or stimulus events. We show that this works better for two of the three rats we analyzed, and highlight the need to acknowledge individuality in analyses of this type. Importantly, we demonstrate that the quantification of functional interactions is a significant factor in discriminating these external labels, and we suggest our methodology as a general tool for large, multisite recordings.

Topological analysis of differential effects of ketamine and propofol anaesthesia on brain dynamics

Research has found that the vividness of conscious experience is related to brain dynamics. Despite both being anaesthetics, propofol and ketamine produce different subjective states: we explore the different effects of these two anaesthetics on the structure of dynamic attractors reconstructed from electrophysiological activity recorded from cerebral cortex of two macaques. We used two methods: the first embeds the recordings in a continuous high-dimensional manifold on which we use topological data analysis to infer the presence of higher-order dynamics. The second reconstruction, an ordinal partition network embedding, allows us to create a discrete state-transition network, which is amenable to information-theoretic analysis and contains rich information about state-transition dynamics. We find that the awake condition generally had the 'richest' structure, visiting the most states, the presence of pronounced higher-order structures, and the least deterministic dynamics. By contrast, the propofol condition had the most dissimilar dynamics, transitioning to a more impoverished, constrained, low-structure regime. The ketamine condition, interestingly, seemed to combine aspects of both: while it was generally less complex than the awake condition, it remained well above propofol in almost all measures. These results provide deeper and more comprehensive insights than what is typically gained by using point-measures of complexity.

Are networks of trophic interactions sufficient for understanding the dynamics of multi-trophic communities? Analysis of a tri-trophic insect food-web time-series

Resource-consumer interactions are considered a major driving force of population and community dynamics. However, species also interact in many non-trophic and indirect ways and it is currently not known to what extent the dynamic coupling of species corresponds to the distribution of trophic links. Here, using a 10-year data set of monthly observations of a 40-species tri-trophic insect community and nonlinear time series analysis, we compare the occurrence and strengths of both the trophic and dynamic interactions in the insect community. The matching between observed trophic and dynamic interactions provides evidence that population dynamic interactions reflect resource-consumer interactions in the many-species community. However, the presence of a trophic interaction does not always correspond to a detectable dynamic interaction especially for top-down effects. Moreover a considerable proportion of dynamic interactions are not attributable to direct trophic interactions, suggesting the unignorable role of non-trophic and indirect interactions as co-drivers of community dynamics.

Brain-scale cortico-cortical functional connectivity in the delta-theta band is a robust signature of conscious states: an intracranial and scalp EEG study

Long-range cortico-cortical functional connectivity has long been theorized to be necessary for conscious states. In the present work, we estimate long-range cortical connectivity in a series of intracranial and scalp EEG recordings experiments. In the two first experiments intracranial-EEG (iEEG) was recorded during four distinct states within the same individuals: conscious wakefulness (CW), rapid-eye-movement sleep (REM), stable periods of slow-wave sleep (SWS) and deep propofol anaesthesia (PA). We estimated functional connectivity using the following two methods: weighted Symbolic-Mutual-Information (wSMI) and phase-locked value (PLV). Our results showed that long-range functional connectivity in the delta-theta frequency band specifically discriminated CW and REM from SWS and PA. In the third experiment, we generalized this original finding on a large cohort of brain-injured patients. FC in the delta-theta band was significantly higher in patients being in a minimally conscious state (MCS) than in those being in a vegetative state (or unresponsive wakefulness syndrome). Taken together the present results suggest that FC of cortical activity in this slow frequency band is a new and robust signature of conscious states.

Scalable Implementation of Hippocampal Network on Digital Neuromorphic System towards Brain-Inspired Intelligence

In this paper, an expanded digital hippocampal spurt neural network (HSNN) is innovatively proposed to simulate the mammalian cognitive system and to perform the neuroregulatory dynamics that play a critical role in the cognitive processes of the brain, such as memory and learning. The real-time computation of a large-scale peak neural network can be realized by the scalable on-chip network and parallel topology. By exploring the latest research in the field of neurons and comparing with the results of this paper, it can be found that the implementation of the hippocampal neuron model using the coordinate rotation numerical calculation algorithm can significantly reduce the cost of hardware resources. In addition, the rational use of on-chip network technology can further improve the performance of the system, and even significantly improve the network scalability on a single field programmable gate array chip. The neuromodulation dynamics are considered in the proposed system, which can replicate more relevant biological dynamics. Based on the analysis of biological theory and the theory of hardware integration, it is shown that the innovative system proposed in this paper can reproduce the biological characteristics of the hippocampal network and may be applied to brain-inspired intelligent subjects. The study in this paper will have an unexpected effect on the future research of digital neuromorphic design of spike neural network and the dynamics of the hippocampal network.

Conscious Processing and the Global Neuronal Workspace Hypothesis

We review the central tenets and neuroanatomical basis of the global neuronal workspace (GNW) hypothesis, which attempts to account for the main scientific observations regarding the elementary mechanisms of conscious processing in the human brain. The GNW hypothesis proposes that, in the conscious state, a non-linear network ignition associated with recurrent processing amplifies and sustains a neural representation, allowing the corresponding information to be globally accessed by local processors. We examine this hypothesis in light of recent data that contrast brain activity evoked by either conscious or non-conscious contents, as well as during conscious or non-conscious states, particularly general anesthesia. We also discuss the relationship between the intertwined concepts of conscious processing, attention, and working memory.

Consciousness & Brain Functional Complexity in Propofol Anaesthesia

The brain is possibly the most complex system known to mankind, and its complexity has been called upon to explain the emergence of consciousness. However, complexity has been defined in many ways by multiple different fields: here, we investigate measures of algorithmic and process complexity in both the temporal and topological domains, testing them on functional MRI BOLD signal data obtained from individuals undergoing various levels of sedation with the anaesthetic agent propofol, replicating our results in two separate datasets. We demonstrate that the various measures are differently able to discriminate between levels of sedation, with temporal measures showing higher sensitivity. Further, we show that all measures are strongly related to a single underlying construct explaining most of the variance, as assessed by Principal Component Analysis, which we interpret as a measure of “overall complexity” of our data. This overall complexity was also able to discriminate between levels of sedation and serum concentrations of propofol, supporting the hypothesis that consciousness is related to complexity - independent of how the latter is measured.

Constructing a Consciousness Meter Based on the Combination of Non-Linear Measurements and Genetic Algorithm-Based Support Vector Machine

OBJECTIVE

Constructing a framework to evaluate consciousness is an important issue in neuroscience research and clinical practice. However, there is still no systematic framework for quantifying altered consciousness along the dimensions of both level and content. This study builds a framework to differentiate the following states: coma, general anesthesia, minimally conscious state (MCS), and normal wakefulness.

METHODS

This study analyzed electroencephalography (EEG) recorded from frontal channels in patients with disorders of consciousness (either coma or MCS), patients under general anesthesia, and healthy participants in normal waking consciousness (NWC). Four non-linear methods-permutation entropy (PE), sample entropy (SampEn), permutation Lempel-Ziv complexity (PLZC), and detrended fluctuation analysis (DFA)-as well as relative power (RP), extracted features from the EEG recordings. A genetic algorithm-based support vector machine (GA-SVM) classified the states of consciousness based on the extracted features. A multivariable linear regression model then built EEG indices for level and content of consciousness.

RESULTS

The PE differentiated all four states of consciousness (p<0.001). Altered contents of consciousness for NWC, MCS, coma, and general anesthesia were best differentiated by the SampEn, and PLZC. In contrast, the levels of consciousness for these four states were best differentiated by RP of Gamma and PE. A multi-dimensional index, combined with the GA-SVM, showed that the integration of PE, PLZC, SampEn, and DFA had the highest classification accuracy (92.3%). The GA-SVM was better than random forest and neural networks at differentiating these four states. The 'coordinate value' in the dimensions of level and content were constructed by the multivariable linear regression model and the non-linear measures PE, PLZC, SampEn, and DFA.

CONCLUSIONS

Multi-dimensional measurements, especially the PE, SampEn, PLZC, and DFA, when combined with GA-SVM, are promising methods for constructing a framework to quantify consciousness.

Can Community Structure Causally Determine Dynamics of Constituent Species? A Test Using a Host-Parasite Community

Structures of communities have been widely studied with the assumption that they not only are a useful bookkeeping tool but also can causally influence dynamics of the populations from which they emerge. However, convincing tests of this assumption have remained elusive because generally the only way to alter a community property is by manipulating its constituent populations, thereby preventing independent measurements of effects on those populations. There is a growing body of evidence that methods like convergent cross-mapping (CCM) can be used to make inferences about causal interactions using state space reconstructions of coupled time series, a method that relies on only observational data. Here we show that CCM can be used to test the causal effects of community properties using a well-studied Slovakian rodent-ectoparasite community. CCM identified causal drivers across the organizational scales of this community, including evidence that host dynamics were influenced by the degree to which the community at large was connected and clustered. Our findings add to the growing literature on the importance of community structures in disease dynamics and argue for a broader use of causal inference in the analysis of community dynamics.

Climate drivers of malaria at its southern fringe in the Americas

In this work we analyze potential environmental drivers of malaria cases in Northwestern Argentina. We inspect causal links between malaria and climatic variables by means of the convergent cross mapping technique, which provides a causality criterion from the theory of dynamic systems. Analysis is based on 12 years of weekly malaria P. vivax cases in Tartagal, Salta, Argentina-at the southern fringe of malaria incidence in the Americas-together with humidity and temperature time-series spanning the same period. Our results show that there are causal links between malaria cases and both maximum temperature, with a delay of five weeks, and minimum temperature, with delays of zero and twenty two weeks. Humidity is also a driver of malaria cases, with thirteen weeks delay between cause and effect. Furthermore we also determined the sign and strength of the effects. Temperature has always a positive non-linear effect on cases, with maximum temperature effects more pronounced above 25°C and minimum above 17°C, while effects of humidity are more intricate: maximum humidity above 85% has a negative effect, whereas minimum humidity has a positive effect on cases. These results might be signaling processes operating at short (below 5 weeks) and long (over 12 weeks) time delays, corresponding to effects related to parasite cycle and mosquito population dynamics respectively. The non-linearities found for the strength of the effect of temperature on malaria cases make warmer areas more prone to higher increases in the disease incidence. Moreover, our results indicate that an increase of extreme weather events could enhance the risks of malaria spreading and re-emergence beyond the current distribution. Both situations, warmer climate and increase of extreme events, will be remarkably increased by the end of the century in this hot spot of climate change.

Expectation and attention increase the integration of top-down and bottom-up signals in perception through different pathways

Perception likely results from the interplay between sensory information and top-down signals. In this electroencephalography (EEG) study, we utilised the hierarchical frequency tagging (HFT) method to examine how such integration is modulated by expectation and attention. Using intermodulation (IM) components as a measure of nonlinear signal integration, we show in three different experiments that both expectation and attention enhance integration between top-down and bottom-up signals. Based on a multispectral phase coherence (MSPC) measure, we present two direct physiological measures to demonstrate the distinct yet related mechanisms of expectation and attention, which would not have been possible using other amplitude-based measures. Our results link expectation to the modulation of descending signals and to the integration of top-down and bottom-up information at lower levels of the visual hierarchy. Meanwhile, the results link attention to the modulation of ascending signals and to the integration of information at higher levels of the visual hierarchy. These results are consistent with the predictive coding account of perception.

Adaptive, locally linear models of complex dynamics

The dynamics of complex systems generally include high-dimensional, nonstationary, and nonlinear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties, we detail an approach based on local linear models within windows determined adaptively from data. While the dynamics within each window are simple, consisting of exponential decay, growth, and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a likelihood-based hierarchical clustering, and we examine the eigenvalues of the linear dynamics. We demonstrate our analysis with the Lorenz system undergoing stable spiral dynamics and in the standard chaotic regime. Applied to the posture dynamics of the nematode Caenorhabditis elegans, our approach identifies fine-grained behavioral states and model dynamics which fluctuate about an instability boundary, and we detail a bifurcation in a transition from forward to backward crawling. We analyze whole-brain imaging in C. elegans and show that global brain dynamics is damped away from the instability boundary by a decrease in oxygen concentration. We provide additional evidence for such near-critical dynamics from the analysis of electrocorticography in monkey and the imaging of a neural population from mouse visual cortex at single-cell resolution.

Informativeness of Auditory Stimuli Does Not Affect EEG Signal Diversity

Brain signal diversity constitutes a robust neuronal marker of the global states of consciousness. It has been demonstrated that, in comparison to the resting wakefulness, signal diversity is lower during unconscious states, and higher during psychedelic states. A plausible interpretation of these findings is that the neuronal diversity corresponds to the diversity of subjective conscious experiences. Therefore, in the present study we varied an information rate processed by the subjects and hypothesized that greater information rate will be related to richer and more differentiated phenomenology and, consequently, to greater signal diversity. To test this hypothesis speech recordings (excerpts from an audio-book) were presented to subjects at five different speeds (65, 83, 100, 117, and 135% of the original speed). By increasing or decreasing speed of the recordings we were able to, respectively, increase or decrease the presented information rate. We also included a backward (unintelligible) speech presentation and a resting-state condition (no auditory stimulation). We tested 19 healthy subjects and analyzed the recorded EEG signal (64 channels) in terms of Lempel-Ziv diversity (LZs). We report the following findings. First, our main hypothesis was not confirmed, as Bayes Factor indicates evidence for no effect when comparing LZs among five presentation speeds. Second, we found that LZs during the resting-state was greater than during processing of both meaningful and unintelligible speech. Third, an additional analysis uncovered a gradual decrease of diversity over the time-course of the experiment, which might reflect a decrease in vigilance. We thus speculate that higher signal diversity during the unconstrained resting-state might be due to a greater variety of experiences, involving spontaneous attention switching and mind wandering.

Geometric classification of brain network dynamics via conic derivative discriminants

BACKGROUND

Over the past decade, pattern decoding techniques have granted neuroscientists improved anatomical specificity in mapping neural representations associated with function and cognition. Dynamical patterns are of particular interest, as evidenced by the proliferation and success of frequency domain methods that reveal structured spatiotemporal rhythmic brain activity. One drawback of such approaches, however, is the need to estimate spectral power, which limits the temporal resolution of classification.

NEW METHOD

We propose an alternative method that enables classification of dynamical patterns with high temporal fidelity. The key feature of the method is a conversion of time-series data into temporal derivatives. By doing so, dynamically-coded information may be revealed in terms of geometric patterns in the phase space of the derivative signal.

RESULTS

We derive a geometric classifier for this problem which simplifies into a straightforward calculation in terms of covariances. We demonstrate the relative advantages and disadvantages of the technique with simulated data and benchmark its performance with an EEG dataset of covert spatial attention. We reveal the timecourse of covert spatial attention and, by mapping the classifier weights anatomically, its retinotopic organization.

COMPARISON WITH EXISTING METHOD

We especially highlight the ability of the method to provide strong group-level classification performance compared to existing benchmarks, while providing information that is complementary with classical spectral-based techniques. The robustness and sensitivity of the method to noise is also examined relative to spectral-based techniques.

CONCLUSION

The proposed classification technique enables decoding of dynamic patterns with high temporal resolution, performs favorably to benchmark methods, and facilitates anatomical inference.

Estimating the impact of structural directionality: How reliable are undirected connectomes?

Directionality is a fundamental feature of network connections. Most structural brain networks are intrinsically directed because of the nature of chemical synapses, which comprise most neuronal connections. Because of the limitations of noninvasive imaging techniques, the directionality of connections between structurally connected regions of the human brain cannot be confirmed. Hence, connections are represented as undirected, and it is still unknown how this lack of directionality affects brain network topology. Using six directed brain networks from different species and parcellations (cat, mouse, C. elegans, and three macaque networks), we estimate the inaccuracies in network measures (degree, betweenness, clustering coefficient, path length, global efficiency, participation index, and small-worldness) associated with the removal of the directionality of connections. We employ three different methods to render directed brain networks undirected: (a) remove unidirectional connections, (b) add reciprocal connections, and (c) combine equal numbers of removed and added unidirectional connections. We quantify the extent of inaccuracy in network measures introduced through neglecting connection directionality for individual nodes and across the network. We find that the coarse division between core and peripheral nodes remains accurate for undirected networks. However, hub nodes differ considerably when directionality is neglected. Comparing the different methods to generate undirected networks from directed ones, we generally find that the addition of reciprocal connections (false positives) causes larger errors in graph-theoretic measures than the removal of the same number of directed connections (false negatives). These findings suggest that directionality plays an essential role in shaping brain networks and highlight some limitations of undirected connectomes.

Mutual connectivity analysis of resting-state functional MRI data with local models

Functional connectivity analysis of functional MRI (fMRI) can represent brain networks and reveal insights into interactions amongst different brain regions. However, most connectivity analysis approaches adopted in practice are linear and non-directional. In this paper, we demonstrate the advantage of a data-driven, directed connectivity analysis approach called Mutual Connectivity Analysis using Local Models (MCA-LM) that approximates connectivity by modeling nonlinear dependencies of signal interaction, over more conventionally used approaches, such as Pearson's and partial correlation, Patel's conditional dependence measures, etcetera. We demonstrate on realistic simulations of fMRI data that, at long sampling intervals, i.e. high repetition time (TR) of fMRI signals, MCA-LM performs better than or comparable to correlation-based methods and Patel's measures. However, at fast image acquisition rates corresponding to low TR, MCA-LM significantly outperforms these methods. This insight is particularly useful in the light of recent advances in fast fMRI acquisition techniques. Methods that can capture the complex dynamics of brain activity, such as MCA-LM, should be adopted to extract as much information as possible from the improved representation. Furthermore, MCA-LM works very well for simulations generated at weak neuronal interaction strengths, and simulations modeling inhibitory and excitatory connections as it disentangles the two opposing effects between pairs of regions/voxels. Additionally, we demonstrate that MCA-LM is capable of capturing meaningful directed connectivity on experimental fMRI data. Such results suggest that it introduces sufficient complexity into modeling fMRI time-series interactions that simple, linear approaches cannot, while being data-driven, computationally practical and easy to use. In conclusion, MCA-LM can provide valuable insights towards better understanding brain activity.

Efficient communication dynamics on macro-connectome, and the propagation speed

Global communication dynamics in the brain can be captured using fMRI, MEG, or electrocorticography (ECoG), and the global slow dynamics often represent anatomical constraints. Complementary single-/multi-unit recordings have described local fast temporal dynamics. However, global fast temporal dynamics remain incompletely understood with considering of anatomical constraints. Therefore, we compared temporal aspects of cross-area propagations of single-unit recordings and ECoG, and investigated their anatomical bases. First, we demonstrated how both evoked and spontaneous ECoGs can accurately predict latencies of single-unit recordings. Next, we estimated the propagation velocity (1.0–1.5 m/s) from brain-wide data and found that it was fairly stable among different conscious levels. We also found that the shortest paths in anatomical topology strongly predicted the latencies. Finally, we demonstrated that Communicability, a novel graph-theoretic measure, is able to quantify that more than 90% of paths should use shortest paths and the remaining are non-shortest walks. These results revealed that macro-connectome is efficiently wired for detailed communication dynamics in the brain.

Loss of consciousness is related to hyper-correlated gamma-band activity in anesthetized macaques and sleeping humans

Loss of consciousness can result from a wide range of causes, including natural sleep and pharmacologically induced anesthesia. Important insights might thus come from identifying neuronal mechanisms of loss and re-emergence of consciousness independent of a specific manipulation. Therefore, to seek neuronal signatures of loss of consciousness common to sleep and anesthesia we analyzed spontaneous electrophysiological activity recorded in two experiments. First, electrocorticography (ECoG) acquired from 4 macaque monkeys anesthetized with different anesthetic agents (ketamine, medetomidine, propofol) and, second, stereo-electroencephalography (sEEG) from 10 epilepsy patients in different wake-sleep stages (wakefulness, NREM, REM). Specifically, we investigated co-activation patterns among brain areas, defined as correlations between local amplitudes of gamma-band activity. We found that resting wakefulness was associated with intermediate levels of gamma-band coupling, indicating neither complete dependence, nor full independence among brain regions. In contrast, loss of consciousness during NREM sleep and propofol anesthesia was associated with excessively correlated brain activity, as indicated by a robust increase of number and strength of positive correlations. However, such excessively correlated brain signals were not observed during REM sleep, and were present only to a limited extent during ketamine anesthesia. This might be related to the fact that, despite suppression of behavioral responsiveness, REM sleep and ketamine anesthesia often involve presence of dream-like conscious experiences. We conclude that hyper-correlated gamma-band activity might be a signature of loss of consciousness common across various manipulations and independent of behavioral responsiveness.

Locally embedded presages of global network bursts

Spontaneous, synchronous bursting of neural population is a widely observed phenomenon in nervous networks, which is considered important for functions and dysfunctions of the brain. However, how the global synchrony across a large number of neurons emerges from an initially nonbursting network state is not fully understood. In this study, we develop a state-space reconstruction method combined with high-resolution recordings of cultured neurons. This method extracts deterministic signatures of upcoming global bursts in "local" dynamics of individual neurons during nonbursting periods. We find that local information within a single-cell time series can compare with or even outperform the global mean-field activity for predicting future global bursts. Moreover, the intercell variability in the burst predictability is found to reflect the network structure realized in the nonbursting periods. These findings suggest that deterministic local dynamics can predict seemingly stochastic global events in self-organized networks, implying the potential applications of the present methodology to detecting locally concentrated early warnings of spontaneous seizure occurrence in the brain.

Intracranial markers of conscious face perception in humans

Investigations of the neural basis of consciousness have greatly benefited from protocols that involve the presentation of stimuli at perceptual threshold, enabling the assessment of the patterns of brain activity that correlate with conscious perception, independently of any changes in sensory input. However, the comparison between perceived and unperceived trials would be expected to reveal not only the core neural substrate of a particular conscious perception, but also aspects of brain activity that facilitate, hinder or tend to follow conscious perception. We take a step towards the resolution of these confounds by combining an analysis of neural responses observed during the presentation of faces partially masked by Continuous Flash Suppression, and those responses observed during the unmasked presentation of faces and other images in the same subjects. We employed multidimensional classifiers to decode physical properties of stimuli or perceptual states from spectrotemporal representations of electrocorticographic signals (1071 channels in 5 subjects). Neural activity in certain face responsive areas located in both the fusiform gyrus and in the lateral-temporal/inferior-parietal cortex discriminated seen vs. unseen faces in the masked paradigm and upright faces vs. other categories in the unmasked paradigm. However, only the former discriminated upright vs. inverted faces in the unmasked paradigm. Our results suggest a prominent role for the fusiform gyrus in the configural perception of faces, and possibly other objects that are holistically processed. More generally, we advocate comparative analysis of neural recordings obtained during different, but related, experimental protocols as a promising direction towards elucidating the functional specificities of the patterns of neural activation that accompany our conscious experiences.

Topological Causality in Dynamical Systems

Determination of causal relations among observables is of fundamental interest in many fields dealing with complex systems. Since nonlinear systems generically behave as wholes, classical notions of causality assuming separability of subsystems often turn out inadequate. Still lacking is a mathematically transparent measure of the magnitude of effective causal influences in cyclic systems. For deterministic systems we found that the expansions of mappings among time-delay state space reconstructions from different observables not only reflect the directed coupling strengths, but also the dependency of effective influences on the system's temporally varying state. Estimation of the expansions from pairs of time series is straightforward and used to define novel causality indices. Mathematical and numerical analysis demonstrate that they reveal the asymmetry of causal influences including their time dependence, as well as provide measures for the effective strengths of causal links in complex systems.

An Investigation of the Dynamical Transitions in Harmonically Driven Random Networks of Firing-Rate Neurons

Continuous-time recurrent neural networks are widely used as models of neural dynamics and also have applications in machine learning. But their dynamics are not yet well understood, especially when they are driven by external stimuli. In this article, we study the response of stable and unstable networks to different harmonically oscillating stimuli by varying a parameter ρ, the ratio between the timescale of the network and the stimulus, and use the dimensionality of the network’s attractor as an estimate of the complexity of this response. Additionally, we propose a novel technique for exploring the stationary points and locally linear dynamics of these networks in order to understand the origin of input-dependent dynamical transitions. Attractors in both stable and unstable networks show a peak in dimensionality for intermediate values of ρ, with the latter consistently showing a higher dimensionality than the former, which exhibit a resonance-like phenomenon. We explain changes in the dimensionality of a network’s dynamics in terms of changes in the underlying structure of its vector field by analysing stationary points. Furthermore, we uncover the coexistence of underlying attractors with various geometric forms in unstable networks. As ρ is increased, our visualisation technique shows the network passing through a series of phase transitions with its trajectory taking on a sequence of qualitatively distinct figure-of-eight, cylinder, and spiral shapes. These findings bring us one step closer to a comprehensive theory of this important class of neural networks by revealing the subtle structure of their dynamics under different conditions.

Integrated information and dimensionality in continuous attractor dynamics

There has been increasing interest in the integrated information theory (IIT) of consciousness, which hypothesizes that consciousness is integrated information within neuronal dynamics. However, the current formulation of IIT poses both practical and theoretical problems when empirically testing the theory by computing integrated information from neuronal signals. For example, measuring integrated information requires observing all the elements in a considered system at the same time, but this is practically very difficult. Here, we propose that some aspects of these problems are resolved by considering the topological dimensionality of shared attractor dynamics as an indicator of integrated information in continuous attractor dynamics. In this formulation, the effects of unobserved nodes on the attractor dynamics can be reconstructed using a technique called delay embedding, which allows us to identify the dimensionality of an embedded attractor from partial observations. We propose that the topological dimensionality represents a critical property of integrated information, as it is invariant to general coordinate transformations. We illustrate this new framework with simple examples and discuss how it fits with recent findings based on neural recordings from awake and anesthetized animals. This topological approach extends the existing notions of IIT to continuous dynamical systems and offers a much-needed framework for testing the theory with experimental data by substantially relaxing the conditions required for evaluating integrated information in real neural systems.

20 Years of ASSC: are we ready for its coming of age?

This is a subjective summary of the recent meeting of the Association for the Scientific Study of Consciousness (ASSC) in Buenos Aires (2016), with some highlights, as well as reflections on the state of the field in general. I argue that we are likely at a critical point where the field is in the process of transforming itself, and the ASSC meeting is accordingly becoming the premier venue to update each other on the latest exciting findings, rigorous methods, and novel ideas. I also discuss the rapidly changing roles of authoritative opinion and theoretical ideas based largely on speculation, whether we still need them, and where may be the best venues for disseminating them.

Revealing physical interaction networks from statistics of collective dynamics

Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of detail often not available. We exploit changes in invariant measures, in particular distributions of sampled states of the system in response to driving signals, and use compressed sensing to reveal physical interaction networks. Dynamical observations following driving suffice to infer physical connectivity even if they are temporally disordered, are acquired at large sampling intervals, and stem from different experiments. Testing various nonlinear dynamic processes emerging on artificial and real network topologies indicates high reconstruction quality for existence as well as type of interactions. These results advance our ability to reveal physical interaction networks in complex synthetic and natural systems.

Limits to Causal Inference with State-Space Reconstruction for Infectious Disease

Infectious diseases are notorious for their complex dynamics, which make it difficult to fit models to test hypotheses. Methods based on state-space reconstruction have been proposed to infer causal interactions in noisy, nonlinear dynamical systems. These “model-free” methods are collectively known as convergent cross-mapping (CCM). Although CCM has theoretical support, natural systems routinely violate its assumptions. To identify the practical limits of causal inference under CCM, we simulated the dynamics of two pathogen strains with varying interaction strengths. The original method of CCM is extremely sensitive to periodic fluctuations, inferring interactions between independent strains that oscillate with similar frequencies. This sensitivity vanishes with alternative criteria for inferring causality. However, CCM remains sensitive to high levels of process noise and changes to the deterministic attractor. This sensitivity is problematic because it remains challenging to gauge noise and dynamical changes in natural systems, including the quality of reconstructed attractors that underlie cross-mapping. We illustrate these challenges by analyzing time series of reportable childhood infections in New York City and Chicago during the pre-vaccine era. We comment on the statistical and conceptual challenges that currently limit the use of state-space reconstruction in causal inference.

How does the brain solve muscle redundancy? Filling the gap between optimization and muscle synergy hypotheses

The question of how the central nervous system coordinates redundant muscles has been a long-standing problem in motor neuroscience. The optimization hypothesis posits that the brain can select the muscle activation pattern that minimizes the motor effort cost from among many solutions that satisfy the requirements of the task. On the other hand, the muscle-synergy hypothesis proposes that neurally established functional groupings of muscles alleviate the computational burden associated with motor control and learning. Although the two hypotheses are not mutually exclusive, the relationship between them has not been well analyzed. This is probably because both hypotheses are formulated mathematically without a clear concept of their neural implementation. Here, we introduce a biologically plausible hypothesis ("the forgetting hypothesis") for how optimization is realized by a population of neurons. We further demonstrate that low-dimensional structure can be detected in an optimal network even if no muscle-synergies are explicitly assumed. Finally, we briefly discuss an inherent difficulty in testing the muscle-synergy hypothesis, which arises when population level optimization is assumed.