Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions

Data-driven and equation-free methods for neurological disorders: analysis and control of the striatum network

The striatum as part of the basal ganglia is central to both motor, and cognitive functions. Here, we propose a large-scale biophysical network for this part of the brain, using modified Hodgkin-Huxley dynamics to model neurons, and a connectivity informed by a detailed human atlas. The model shows different spatio-temporal activity patterns corresponding to lower (presumably normal) and increased cortico-striatal activation (as found in, e.g., obsessive-compulsive disorder), depending on the intensity of the cortical inputs. By applying equation-free methods, we are able to perform a macroscopic network analysis directly from microscale simulations. We identify the mean synaptic activity as the macroscopic variable of the system, which shows similarity with local field potentials. The equation-free approach results in a numerical bifurcation and stability analysis of the macroscopic dynamics of the striatal network. The different macroscopic states can be assigned to normal/healthy and pathological conditions, as known from neurological disorders. Finally, guided by the equation-free bifurcation analysis, we propose a therapeutic close loop control scheme for the striatal network.

Situational Understanding in the Human and the Machine

The Air Force research programs envision developing AI technologies that will ensure battlespace dominance, by radical increases in the speed of battlespace understanding and decision-making. In the last half century, advances in AI have been concentrated in the area of machine learning. Recent experimental findings and insights in systems neuroscience, the biophysics of cognition, and other disciplines provide converging results that set the stage for technologies of machine understanding and machine-augmented Situational Understanding. This paper will review some of the key ideas and results in the literature, and outline new suggestions. We define situational understanding and the distinctions between understanding and awareness, consider examples of how understanding-or lack of it-manifest in performance, and review hypotheses concerning the underlying neuronal mechanisms. Suggestions for further R&D are motivated by these hypotheses and are centered on the notions of Active Inference and Virtual Associative Networks.

Evolutionary Advantages of Stimulus-Driven EEG Phase Transitions in the Upper Cortical Layers

Spatio-temporal brain activity monitored by EEG recordings in humans and other mammals has identified beta/gamma oscillations (20-80 Hz), which are self-organized into spatio-temporal structures recurring at theta/alpha rates (4-12 Hz). These structures have statistically significant correlations with sensory stimuli and reinforcement contingencies perceived by the subject. The repeated collapse of self-organized structures at theta/alpha rates generates laterally propagating phase gradients (phase cones), ignited at some specific location of the cortical sheet. Phase cones have been interpreted as neural signatures of transient perceptual experiences according to the cinematic theory of brain dynamics. The rapid expansion of essentially isotropic phase cones is consistent with the propagation of perceptual broadcasts postulated by Global Workspace Theory (GWT). What is the evolutionary advantage of brains operating with repeatedly collapsing dynamics? This question is answered using thermodynamic concepts. According to neuropercolation theory, waking brains are described as non-equilibrium thermodynamic systems operating at the edge of criticality, undergoing repeated phase transitions. This work analyzes the role of long-range axonal connections and metabolic processes in the regulation of critical brain dynamics. Historically, the near 10 Hz domain has been associated with conscious sensory integration, cortical "ignitions" linked to conscious visual perception, and conscious experiences. We can therefore combine a very large body of experimental evidence and theory, including graph theory, neuropercolation, and GWT. This cortical operating style may optimize a tradeoff between rapid adaptation to novelty vs. stable and widespread self-organization, therefore resulting in significant Darwinian benefits.

State Transitions During Discrimination Learning in the Gerbil Auditory Cortex Analyzed by Network Causality Metrics

This work studies the evolution of cortical networks during the transition from escape strategy to avoidance strategy in auditory discrimination learning in Mongolian gerbils trained by the well-established two-way active avoidance learning paradigm. The animals were implanted with electrode arrays centered on the surface of the primary auditory cortex and electrocorticogram (ECoG) recordings were made during performance of an auditory Go/NoGo discrimination task. Our experiments confirm previous results on a sudden behavioral change from the initial naïve state to an avoidance strategy as learning progresses. We employed two causality metrics using Granger Causality (GC) and New Causality (NC) to quantify changes in the causality flow between ECoG channels as the animals switched to avoidance strategy. We found that the number of channel pairs with inverse causal interaction significantly increased after the animal acquired successful discrimination, which indicates structural changes in the cortical networks as a result of learning. A suitable graph-theoretical model is developed to interpret the findings in terms of cortical networks evolving during cognitive state transitions. Structural changes lead to changes in the dynamics of neural populations, which are described as phase transitions in the network graph model with small-world connections. Overall, our findings underscore the importance of functional reorganization in sensory cortical areas as a possible neural contributor to behavioral changes.

Scaling in Colloidal and Biological Networks

Scaling and dimensional analysis is applied to networks that describe various physical systems. Some of these networks possess fractal, scale-free, and small-world properties. The amount of information contained in a network is found by calculating its Shannon entropy. First, we consider networks arising from granular and colloidal systems (small colloidal and droplet clusters) due to pairwise interaction between the particles. Many networks found in colloidal science possess self-organizing properties due to the effect of percolation and/or self-organized criticality. Then, we discuss the allometric laws in branching vascular networks, artificial neural networks, cortical neural networks, as well as immune networks, which serve as a source of inspiration for both surface engineering and information technology. Scaling relationships in complex networks of neurons, which are organized in the neocortex in a hierarchical manner, suggest that the characteristic time constant is independent of brain size when interspecies comparison is conducted. The information content, scaling, dimensional, and topological properties of these networks are discussed.

Applying a Dynamical Systems Model and Network Theory to Major Depressive Disorder

Mental disorders like major depressive disorder can be modeled as complex dynamical systems. In this study we investigate the dynamic behavior of individuals to see whether or not we can expect a transition to another mood state. We introduce a mean field model to a binomial process, where we reduce a dynamic multidimensional system (stochastic cellular automaton) to a one-dimensional system to analyse the dynamics. Using maximum likelihood estimation, we can estimate the parameter of interest which, in combination with a bifurcation diagram, reflects the expectancy that someone has to transition to another mood state. After numerically illustrating the proposed method with simulated data, we apply this method to two empirical examples, where we show its use in a clinical sample consisting of patients diagnosed with major depressive disorder, and a general population sample. Results showed that the majority of the clinical sample was categorized as having an expectancy for a transition, while the majority of the general population sample did not have this expectancy. We conclude that the mean field model has great potential in assessing the expectancy for a transition between mood states. With some extensions it could, in the future, aid clinical therapists in the treatment of depressed patients.

Influence Maximization for Fixed Heterogeneous Thresholds

Influence Maximization is a NP-hard problem of selecting the optimal set of influencers in a network. Here, we propose two new approaches to influence maximization based on two very different metrics. The first metric, termed Balanced Index (BI), is fast to compute and assigns top values to two kinds of nodes: those with high resistance to adoption, and those with large out-degree. This is done by linearly combining three properties of a node: its degree, susceptibility to new opinions, and the impact its activation will have on its neighborhood. Controlling the weights between those three terms has a huge impact on performance. The second metric, termed Group Performance Index (GPI), measures performance of each node as an initiator when it is a part of randomly selected initiator set. In each such selection, the score assigned to each teammate is inversely proportional to the number of initiators causing the desired spread. These two metrics are applicable to various cascade models; here we test them on the Linear Threshold Model with fixed and known thresholds. Furthermore, we study the impact of network degree assortativity and threshold distribution on the cascade size for metrics including ours. The results demonstrate our two metrics deliver strong performance for influence maximization.

Cinematic Operation of the Cerebral Cortex Interpreted via Critical Transitions in Self-Organized Dynamic Systems

Measurements of local field potentials over the cortical surface and the scalp of animals and human subjects reveal intermittent bursts of beta and gamma oscillations. During the bursts, narrow-band metastable amplitude modulation (AM) patters emerge for a fraction of a second and ultimately dissolve to the broad-band random background activity. The burst process depends on previously learnt conditioned stimuli (CS), thus different AM patterns may emerge in response to different CS. This observation leads to our cinematic theory of cognition when perception happens in discrete steps manifested in the sequence of AM patterns. Our article summarizes findings in the past decades on experimental evidence of cinematic theory of cognition and relevant mathematical models. We treat cortices as dissipative systems that self-organize themselves near a critical level of activity that is a non-equilibrium metastable state. Criticality is arguably a key aspect of brains in their rapid adaptation, reconfiguration, high storage capacity, and sensitive response to external stimuli. Self-organized criticality (SOC) became an important concept to describe neural systems. We argue that transitions from one AM pattern to the other require the concept of phase transitions, extending beyond the dynamics described by SOC. We employ random graph theory (RGT) and percolation dynamics as fundamental mathematical approaches to model fluctuations in the cortical tissue. Our results indicate that perceptions are formed through a phase transition from a disorganized (high entropy) to a well-organized (low entropy) state, which explains the swiftness of the emergence of the perceptual experience in response to learned stimuli.

Life and Understanding: The Origins of "Understanding" in Self-Organizing Nervous Systems

This article is motivated by a formulation of biotic self-organization in Friston (2013), where the emergence of "life" in coupled material entities (e.g., macromolecules) was predicated on bounded subsets that maintain a degree of statistical independence from the rest of the network. Boundary elements in such systems constitute a Markov blanket; separating the internal states of a system from its surrounding states. In this article, we ask whether Markov blankets operate in the nervous system and underlie the development of intelligence, enabling a progression from the ability to sense the environment to the ability to understand it. Markov blankets have been previously hypothesized to form in neuronal networks as a result of phase transitions that cause network subsets to fold into bounded assemblies, or packets (Yufik and Sheridan, 1997; Yufik, 1998a). The ensuing neuronal packets hypothesis builds on the notion of neuronal assemblies (Hebb, 1949, 1980), treating such assemblies as flexible but stable biophysical structures capable of withstanding entropic erosion. In other words, structures that maintain their integrity under changing conditions. In this treatment, neuronal packets give rise to perception of "objects"; i.e., quasi-stable (stimulus bound) feature groupings that are conserved over multiple presentations (e.g., the experience of perceiving "apple" can be interrupted and resumed many times). Monitoring the variations in such groups enables the apprehension of behavior; i.e., attributing to objects the ability to undergo changes without loss of self-identity. Ultimately, "understanding" involves self-directed composition and manipulation of the ensuing "mental models" that are constituted by neuronal packets, whose dynamics capture relationships among objects: that is, dependencies in the behavior of objects under varying conditions. For example, movement is known to involve rotation of population vectors in the motor cortex (Georgopoulos et al., 1988, 1993). The neuronal packet hypothesis associates "understanding" with the ability to detect and generate coordinated rotation of population vectors-in neuronal packets-in associative cortex and other regions in the brain. The ability to coordinate vector representations in this way is assumed to have developed in conjunction with the ability to postpone overt motor expression of implicit movement, thus creating a mechanism for prediction and behavioral optimization via mental modeling that is unique to higher species. This article advances the notion that Markov blankets-necessary for the emergence of life-have been subsequently exploited by evolution and thus ground the ways that living organisms adapt to their environment, culminating in their ability to understand it.

Reflections on a giant of brain science: How lucky we are having Walter J. Freeman as our beacon in cognitive neurodynamics research

Walter J. Freeman was a giant of the field of neuroscience whose visionary work contributed various experimental and theoretical breakthroughs to brain research in the past 60 years. He has pioneered a number of Electroencephalogram and Electrocorticogram tools and approaches that shaped the field, while "Freeman Neurodynamics" is a theoretical concept that is widely known, used, and respected among neuroscientists all over the world. His recent death is a profound loss to neuroscience and biomedical engineering. Many of his revolutionary ideas on brain dynamics have been ahead of their time by decades. We summarize his following groundbreaking achievements: (1) Mass Action in the Nervous System, from microscopic (single cell) recordings, through mesoscopic populations, to large-scale collective brain patterns underlying cognition; (2) Freeman-Kachalsky model of multi-scale, modular brain dynamics; (3) cinematic theory of cognitive dynamics; (4) phase transitions in cortical dynamics modeled with random graphs and quantum field theory; (5) philosophical aspects of intentionality, consciousness, and the unity of brain-mind-body. His work has been admired by many of his neuroscientist colleagues and followers. At the same time, his multidisciplinary approach combining advanced concepts of control theory and the mathematics of nonlinear systems and chaos, poses significant challenges to those who wish to thoroughly understand his message. The goal of this commemorative paper is to review key aspects of Freeman's neurodynamics and to provide some handles to gain better understanding about Freeman's extraordinary intellectual achievement.

Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website.

Multiscale Enaction Model (MEM): the case of complexity and "context-sensitivity" in vision

I review the data on human visual perception that reveal the critical role played by non-visual contextual factors influencing visual activity. The global perspective that progressively emerges reveals that vision is sensitive to multiple couplings with other systems whose nature and levels of abstraction in science are highly variable. Contrary to some views where vision is immersed in modular hard-wired modules, rather independent from higher-level or other non-cognitive processes, converging data gathered in this article suggest that visual perception can be theorized in the larger context of biological, physical, and social systems with which it is coupled, and through which it is enacted. Therefore, any attempt to model complexity and multiscale couplings, or to develop a complex synthesis in the fields of mind, brain, and behavior, shall involve a systematic empirical study of both connectedness between systems or subsystems, and the embodied, multiscale and flexible teleology of subsystems. The conceptual model (Multiscale Enaction Model [MEM]) that is introduced in this paper finally relates empirical evidence gathered from psychology to biocomputational data concerning the human brain. Both psychological and biocomputational descriptions of MEM are proposed in order to help fill in the gap between scales of scientific analysis and to provide an account for both the autopoiesis-driven search for information, and emerging perception.

Role of cortical neurodynamics for understanding the neural basis of motivated behavior - lessons from auditory category learning

Rhythmic activity appears in the auditory cortex in both microscopic and macroscopic observables and is modulated by both bottom-up and top-down processes. How this activity serves both types of processes is largely unknown. Here we review studies that have recently improved our understanding of potential functional roles of large-scale global dynamic activity patterns in auditory cortex. The experimental paradigm of auditory category learning allowed critical testing of the hypothesis that global auditory cortical activity states are associated with endogenous cognitive states mediating the meaning associated with an acoustic stimulus rather than with activity states that merely represent the stimulus for further processing.

Structural phase transitions in neural networks

A model is considered for a neural network that is a stochastic process on a random graph. The neurons are represented by "integrate-and-fire" processes. The structure of the graph is determined by the probabilities of the connections, and it depends on the activity in the network. The dependence between the initial level of sparseness of the connections and the dynamics of activation in the network was investigated. A balanced regime was found between activity, i.e., the level of excitation in the network, and inhibition, that allows formation of synfire chains.

The metastable brain

Neural ensembles oscillate across a broad range of frequencies and are transiently coupled or "bound" together when people attend to a stimulus, perceive, think, and act. This is a dynamic, self-assembling process, with parts of the brain engaging and disengaging in time. But how is it done? The theory of Coordination Dynamics proposes a mechanism called metastability, a subtle blend of integration and segregation. Tendencies for brain regions to express their individual autonomy and specialized functions (segregation, modularity) coexist with tendencies to couple and coordinate globally for multiple functions (integration). Although metastability has garnered increasing attention, it has yet to be demonstrated and treated within a fully spatiotemporal perspective. Here, we illustrate metastability in continuous neural and behavioral recordings, and we discuss theory and experiments at multiple scales, suggesting that metastable dynamics underlie the real-time coordination necessary for the brain's dynamic cognitive, behavioral, and social functions.

A theoretical and experimental study of neuromorphic atomic switch networks for reservoir computing

Atomic switch networks (ASNs) have been shown to generate network level dynamics that resemble those observed in biological neural networks. To facilitate understanding and control of these behaviors, we developed a numerical model based on the synapse-like properties of individual atomic switches and the random nature of the network wiring. We validated the model against various experimental results highlighting the possibility to functionalize the network plasticity and the differences between an atomic switch in isolation and its behaviors in a network. The effects of changing connectivity density on the nonlinear dynamics were examined as characterized by higher harmonic generation in response to AC inputs. To demonstrate their utility for computation, we subjected the simulated network to training within the framework of reservoir computing and showed initial evidence of the ASN acting as a reservoir which may be optimized for specific tasks by adjusting the input gain. The work presented represents steps in a unified approach to experimentation and theory of complex systems to make ASNs a uniquely scalable platform for neuromorphic computing.

Hierarchical random cellular neural networks for system-level brain-like signal processing

Sensory information processing and cognition in brains are modeled using dynamic systems theory. The brain's dynamic state is described by a trajectory evolving in a high-dimensional state space. We introduce a hierarchy of random cellular automata as the mathematical tools to describe the spatio-temporal dynamics of the cortex. The corresponding brain model is called neuropercolation which has distinct advantages compared to traditional models using differential equations, especially in describing spatio-temporal discontinuities in the form of phase transitions. Phase transitions demarcate singularities in brain operations at critical conditions, which are viewed as hallmarks of higher cognition and awareness experience. The introduced Monte-Carlo simulations obtained by parallel computing point to the importance of computer implementations using very large-scale integration (VLSI) and analog platforms.

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.

Solving the "human problem": the frontal feedback model

This paper argues that humans possess unique cognitive abilities due to the presence of a functional system that exists in the human brain that is absent in the non-human brain. This system, the frontal feedback system, was born in the hominin brain when the great phylogenetic expansion of the prefrontal cortex relative to posterior sensory regions surpassed a critical threshold. Surpassing that threshold effectively reversed the preferred direction of information flow in the highest association regions of the neocortex, producing the frontal feedback system. This reversal was from the caudo-rostral bias characteristic of non-human, or pre-human, brain dynamics to a rostro-caudal bias characteristic of modern human brain dynamics. The frontal feedback system works through frontal motor routines, or action schemes, manipulating the release and reconstruction of stored sensory memories in posterior sensory areas. As an obligatory feature of frontal feedback, a central character, or self, emerges within this cortical network that manifests itself as agent in these reconstructions as well as in the experience of sensory perceptions. Dynamical-systems modeling of cortical interactions is combined in the paper with recent neuroimaging studies of "resting-state" brain activity to bridge the gap between microscopic and macroscopic levels of cortical behavior. This synthesis is used to support the proposal of an information flow reversal occurring in the hominin brain and also to explain how such a reversal generates the wide variety of cognitive and experiential phenomena that many consider to be uniquely human.

MODELING GOAL-ORIENTED DECISION MAKING THROUGH COGNITIVE PHASE TRANSITIONS

Cognitive experiments indicate the presence of discontinuities in brain dynamics during high-level cognitive processing. Non-linear dynamic theory of brains pioneered by Freeman explains the experimental findings through the theory of metastability and edge-of-criticality in cognitive systems, which are key properties associated with robust operation and fast and reliable decision making. Recently, neuropercolation has been proposed to model such critical behavior. Neuropercolation is a family of probabilistic models based on the mathematical theory of bootstrap percolations on lattices and random graphs and motivated by structural and dynamical properties of neural populations in the cortex. Neuropercolation exhibits phase transitions and it provides a novel mathematical tool for studying spatio-temporal dynamics of multi-stable systems. The present work reviews the theory of cognitive phase transitions based on neuropercolation models and outlines the implications to decision making in brains and in artificial designs.

The emergence of connectivity in neuronal networks: from bootstrap percolation to auto-associative memory

We consider a random synaptic pruning in an initially highly interconnected network. It is proved that a random network can maintain a self-sustained activity level for some parameters. For such a set of parameters a pruning is constructed so that in the resulting network each neuron/node has almost equal numbers of in- and out-connections. It is also shown that the set of parameters which admits a self-sustained activity level is rather small within the whole space of possible parameters. It is pointed out here that the threshold of connectivity for an auto-associative memory in a Hopfield model on a random graph coincides with the threshold for the bootstrap percolation on the same random graph. It is argued that this coincidence reflects the relations between the auto-associative memory mechanism and the properties of the underlying random network structure. This article is part of a Special Issue entitled "Neural Coding".

Fractals in the nervous system: conceptual implications for theoretical neuroscience

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

Vortices in brain activity: their mechanism and significance for perception

Brains interface with the world through perception. The process extracts information from microscopic sensory inputs and incorporates it into the mesoscopic memory store for retrieval in recognition. The process requires creation of spatiotemporal patterns of neural activity. The construction is done through phase transitions in cortical populations that condense the background activity through spontaneous symmetry breaking. Large-scale interactions create fields of synaptically driven activity that is observed by measuring brain waves (electrocorticogram, ECoG) and evaluated by constructing a mesoscopic vectorial order parameter as follows. The negative feedback among excitatory and inhibitory neurons creates spatially and spectrally distributed gamma oscillations (20-80 Hz) in the background activity. Band pass filtering reveals beats in ECoG log analytic power. In some beats that recur at theta rates (3-7 Hz), the order parameter transiently approaches zero, giving a null spike in which the microscopic activity is uniformly disordered (symmetric). A phase transition that is manifested in an analytic phase discontinuity breaks the symmetry. As the null spike terminates, the resurgent order parameter imposes mesoscopic order seen in spatial patterns of ECoG amplitude modulation (AM) that actualize and update the memory of a stimulus. Read-out is through a divergent/convergent projection that performs on cortical output an irreversible spatiotemporal integral transformation. The ECoG reveals a conic phase gradient that accompanies an AM pattern. The phase cone manifests a vortex, which is initiated by the null spike, and which is inferred to help stabilize and prolong its accompanying AM pattern that might otherwise be rapidly degraded by the turbulent neural noise from which it emerges.

Percolation transition at growing spatiotemporal fractal patterns in models of mesoscopic neural networks

Spike packet propagation is modeled in mesoscopic-scale networks, composed of locally and recurrently coupled neural pools, and embedded in a two-dimensional lattice. Site dynamics is governed by three key parameters--pool connectedness probability, synaptic strength (following the steady-state distribution of some realizations of spike-timing-dependent plasticity learning rule), and the neuron refractoriness. Formation of spatiotemporal patterns in our model, synfire chains, exhibits critical behavior, with the emerging percolation phase transition controlled by the probability for nonzero synaptic strength value. Applying the finite-size scaling method, we infer the critical probability dependence on synaptic strength and refractoriness and determine the effects of connection topology on the pertaining percolation clusters fractal dimensions. We find that the directed percolation and the pair contact process with diffusion constitute the relevant universality classes of phase transitions observed in a class of mesoscopic-scale network models, which may be related to recently reported data on in vitro cultures.

Learning of spatio-temporal codes in a coupled oscillator system

In this paper, we consider a learning strategy that allows one to transmit information between two coupled phase oscillator systems (called teaching and learning systems) via frequency adaptation. The dynamics of these systems can be modeled with reference to a number of partially synchronized cluster states and transitions between them. Forcing the teaching system by steady but spatially nonhomogeneous inputs produces cyclic sequences of transitions between the cluster states, that is, information about inputs is encoded via a "winnerless competition" process into spatio-temporal codes. The large variety of codes can be learned by the learning system that adapts its frequencies to those of the teaching system. We visualize the dynamics using "weighted order parameters (WOPs)" that are analogous to "local field potentials" in neural systems. Since spatio-temporal coding is a mechanism that appears in olfactory systems, the developed learning rules may help to extract information from these neural ensembles.

Evolutionary radiation and the spectrum of consciousness

Evolution is littered with polyphyletic parallelism: many roads lead to functional Romes. We propose consciousness embodies one such example, and represent it here with an equivalence class structure that factors the broad realm of necessary conditions information theoretic realizations of Baars' global workspace model. The construction suggests many different physiological systems can support rapidly shifting, highly tunable, and even simultaneous temporary assemblages of interacting unconscious cognitive modules. The discovery implies various animal taxa exhibiting behaviors we broadly recognize as conscious are, in fact, expressing different forms of the same underlying phenomenon. The variety of possibilities suggests minds today may be only a small surviving fraction of ancient evolutionary radiations--bush phylogenies of consciousness pruned by selection and chance extinction. Although few traces of the radiations may be found in the fossil record, exaptations and vestiges are scattered across the living mind.

Viewing brain processes as Critical State Transitions across levels of organization: Neural events in Cognition and Consciousness, and general principles

In this theoretical and speculative essay, I propose that insights into certain aspects of neural system functions can be gained from viewing brain function in terms of the branch of Statistical Mechanics currently referred to as "Modern Critical Theory" [Stanley, H.E., 1987. Introduction to Phase Transitions and Critical Phenomena. Oxford University Press; Marro, J., Dickman, R., 1999. Nonequilibrium Phase Transitions in Lattice Models. Cambridge University Press, Cambridge, UK]. The application of this framework is here explored in two stages: in the first place, its principles are applied to state transitions in global brain dynamics, with benchmarks of Cognitive Neuroscience providing the relevant empirical reference points. The second stage generalizes to suggest in more detail how the same principles could also apply to the relation between other levels of the structural-functional hierarchy of the nervous system and between neural assemblies. In this view, state transitions resulting from the processing at one level are the input to the next, in the image of a 'bucket brigade', with the content of each bucket being passed on along the chain, after having undergone a state transition. The unique features of a process of this kind will be discussed and illustrated.

Intermittent spatio-temporal desynchronization and sequenced synchrony in ECoG signals

Electrocorticographic (ECoG) signals from the brain surface typically exhibit high synchrony across large cortical areas, interrupted by brief periods of desynchronization exhibiting propagating phase discontinuities, across which spatial patterns of phase emerge in selected frequency bands. Experiments with rabbits trained using classical conditioning paradigms indicated that such desynchronization periods demarcate cognitive processing in the subjects; the ECoG in the frames between such periods revealed spatial patterns of amplitude modulation that were classified with respect to sensory stimuli that the rabbits had been trained to recognize. The present work describes intermittent synchrony and desynchronization of ECoG signals measured over the visual cortex. We analyze the analytic amplitude (AA) and analytic phase (AP) of the signals bandpassed over the beta band (12.5-25 Hz) and theta band (3-7 Hz) using the Hilbert transform. The AP of analytic signals evaluated using a Shannon-based synchronization index in theta band exhibits phase synchronization for varying time periods averaging about 1 s, interrupted by desynchronization periods of duration about 0.1 s. Synchronization periods in the beta-band last <100 ms, with interruptions by desynchronization lasting one-tenth that, in which the analytic amplitude drops drastically. During these "null spikes," the analytic phase is undefined, and the spatial and temporal phase differences show high dispersion. Detailed examination of the bandpass filtered ECoG confirms the presence of a shared mean frequency in a frame of synchronized oscillation, at which frequency the spatial pattern of the AP has the form of a cone. Between frames the AA approaches zero. The form of the null spike resembles a tornado (a vortex), as shown in sequential frames by a rotating spatial pattern of amplitude in the filtered ECoG.

Narrow-band oscillations in probabilistic cellular automata

Dynamical properties of neural populations are studied using probabilistic cellular automata. Previous work demonstrated the emergence of critical behavior as the function of system noise and density of long-range axonal connections. Finite-size scaling theory identified critical properties, which were consistent with properties of a weak Ising universality class. The present work extends the studies to neural populations with excitatory and inhibitory interactions. It is shown that the populations can exhibit narrow-band oscillations when confined to a range of inhibition levels, with clear boundaries marking the parameter region of prominent oscillations. Phase diagrams have been constructed to characterize unimodal, bimodal, and quadromodal oscillatory states. The significance of these findings is discussed in the context of large-scale narrow-band oscillations in neural tissues, as observed in electroencephalographic and magnetoencephalographic measurements.

Endogenous multifractal brain dynamics are modulated by age, cholinergic blockade and cognitive performance

The intuitive notion that a healthy organism is characterised by regular, homeostatic function has been challenged by observations that a loss of complexity is, in fact, indicative of ill-health. Monofractals succinctly describe complex processes and are controlled by a single time-invariant scaling exponent, H, simply related to the fractal dimension. Previous analyses of resting fMRI time-series demonstrated that ageing and scopolamine administration were both associated with increases in H and that faster response in a prior encoding task was also associated with increased H. We revisit this experiment with a novel, multifractal approach in which fractal dynamics are assumed to be non-stationary and defined by a spectrum of local singularity exponents. Parameterisation of this spectrum was capable of refracting the effects of age, scopolamine and task performance as well as a refining a description of the associated signal changes. Using the same imaging data, we also explored turbulence as a possible mechanism underlying multifractal dynamics. Evidence is provided that Carstaing's model of turbulent information flow from high to low scales has only limited validity, and that scale invariance of energy dissipation is better explained by critical-phase phenomena, supporting the proposition that the brain maintains a state of self-organised criticality.

Consciousness related neural events viewed as brain state space transitions

This theoretical and speculative essay addresses a categorical distinction between neural events of sensory-motor cognition and those presumably associated with consciousness. It proposes to view this distinction in the framework of the branch of Statistical Physics currently referred to as Modern Critical Theory (Stanley, Introduction to phase transitions and critical phenomena, 1987; Marro and Dickman, Nonequilibrium phase transitions in lattice, 1999). Based on established landmarks of brain dynamics, network configurations and their role for conveying oscillatory activity of certain frequencies bands, the question is examined: what kind of state space transitions can systems with these properties undergo, and could the relation between neural processes of sensory-motor cognition and those of events in consciousness be of the same category as is characterized by state transitions in non-equilibrium physical systems? Approaches for empirical validation of this view by suitably designed brain imaging studies, and for computational simulations of the proposed principle are discussed.

Brain dynamics across levels of organization

After initially presenting evidence that the electrical activity recorded from the brain surface can reflect metastable state transitions of neuronal configurations at the mesoscopic level, I will suggest that their patterns may correspond to the distinctive spatio-temporal activity in the dynamic core (DC) and the global neuronal workspace (GNW), respectively, in the models of the Edelman group on the one hand, and of Dehaene-Changeux, on the other. In both cases, the recursively reentrant activity flow in intra-cortical and cortical-subcortical neuron loops plays an essential and distinct role. Reasons will be given for viewing the temporal characteristics of this activity flow as signature of self-organized criticality (SOC), notably in reference to the dynamics of neuronal avalanches. This point of view enables the use of statistical physics approaches for exploring phase transitions, scaling and universality properties of DC and GNW, with relevance to the macroscopic electrical activity in EEG and EMG.