Attractor States Research Articles

The EEG microstate topography is predominantly determined by intracortical sources in the alpha band

Human brain electric activity can be measured at high temporal and fairly good spatial resolution via electroencephalography (EEG). The EEG microstate analysis is an increasingly popular method used to investigate this activity at a millisecond resolution by segmenting it into quasi-stable states of approximately 100 ms duration. These so-called EEG microstates were postulated to represent atoms of thoughts and emotions and can be classified into four classes of topographies A through D, which explain up to 90% of the variance of continuous EEG. The present study investigated whether these topographies are primarily driven by alpha activity originating from the posterior cingulate cortex (all topographies), left and right posterior cortices, and the anterior cingulate cortex (topographies A, B, and C, respectively).We analyzed two 64-channel resting state EEG datasets (N = 61 and N = 78) of healthy participants. Sources of head-surface signals were determined via exact low resolution electromagnetic tomography (eLORETA). The Hilbert transformation was applied to identify instantaneous source strength of four EEG frequency bands (delta through beta). These source strength values were averaged for each participant across time periods belonging to a particular microstate. For each dataset, these averages of the different microstate classes were compared for each voxel. Consistent differences across datasets were identified via a conjunction analysis.The intracortical strength and spatial distribution of alpha band activity mainly determined whether a head-surface topography of EEG microstate class A, B, C, or D was induced. EEG microstate class C was characterized by stronger alpha activity compared to all other classes in large portions of the cortex. Class A was associated with stronger left posterior alpha activity than classes B and D, and class B was associated with stronger right posterior alpha activity than A and D.Previous results indicated that EEG microstate dynamics reflect a fundamental mechanism of the human brain that is altered in different mental states in health and disease. They are characterized by systematic transitions between four head-surface topographies, the EEG microstate classes. Our results show that intra-cortical alpha oscillations, which likely reflect decreased cortical excitability, primarily account for the emergence of these classes. We suggest that microstate class dynamics reflect transitions between four global attractor states that are characterized by selective inhibition of specific intra-cortical regions.

Geometric disequilibrium of river basins produces long-lived transient landscapes

Although equilibrium has long been considered the attractor state for landscapes, the time required to reach equilibrium or even the possibility of reaching equilibrium is still debated. Using 10Be-based catchment-averaged denudation rates, topographic analysis, and analysis of the basin topology and geometry, including its area-channel length scaling relationship, we show that an ancient postorogenic dome on the North American Craton, the Ozark dome, is not in a state of equilibrium. The persistent state of disequilibrium on the Ozark dome is characterized by nonuniform erosion rates that vary by a factor of three, asymmetric drainage divides, and evidence for drainage rearrangement via stream capture. We find that planform geometric disequilibrium of river basins and drainage area exchange between adjoining basins can hold river networks in a disequilibrium state for potentially hundreds of million years and that, when sustained over time, erosion rate differences associated with drainage area exchange can lead to transient events such as stream capture and production of relief in the form of elevated, low-relief surfaces. Our results suggest that landscapes with slowly moving drainage divides might not reach equilibrium, and that river basin dynamics may contribute to setting the large-scale morphology of old cratonic landscapes.

Socioeconomic complexity and the resilience of hunter-gatherer societies

Human societies have been challenged by internal and external disturbances throughout history. However, our knowledge of the dynamics and parameters of their resilience remains remarkably incomplete. This deficiency is particularly evident for the longest part of our past, when humans lived as hunter-gatherers.Following Holling's adaptive cycle model, we propose an approach to reconstruct socio-economic developments in hunter-gatherer populations as transitions between different attractor states of complex adaptive systems, with connectedness as a key concept. This allows a reinterpretation of the classical ‘simple’–‘complex’ hunter-gatherer dichotomy by shifting attention to the mechanisms of adaptation and dynamics holding socio-ecologic systems of hunter-gatherers in tension. Applied to the situation in Europe during the late Pleistocene, a model explaining the different long-term dynamics observable in the aftermath of the arrival of the first anatomically modern humans is discussed.

How J M Keynes's Logical Theory of Probability Totally Refutes All Attacks on the Concept of Probability

J Derbyshire has recently repeated G L S Shackle’s original attack on the concept of probability in a number of recent articles. He adds nothing new to Shackle’s arguments of forty to eighty years ago that were completely refuted in 1959 by R. Weckstein, who based his refutation of Shackle on a relatively limited understanding of chapters 1-3 and 6 of Keynes’s A Treatise on Probability (1921). Shackle never replied to Weckstein’s repeated demonstrations in 1959 that Keynes’s approach refuted his arguments, which held only against the limiting frequency, relative frequency, propensity and subjective interpretations of probability. Shackle’s arguments failed completely when confronted with Keynes’s theory of logical probability. J M Keynes’s theory of probability is a logical, objective, epistemological approach that is based on partial ordering and not complete orderings. This results in non additive, non linear interval valued probabilities, specified and operationalized in terms of logical propositions about any kind of event. It can easily deal with unique events, single events, crucial events, infrequent events, frequent events, non repeatable events, irreversible events, path dependence, sensitivity to initial conditions, emergence, complex causation, attractor states, partial uncertainty, complete and total uncertainty, fundamental uncertainty, irreducible uncertainty, by means of Keynes’s weight of the evidence analysis, which, when combined with his interval valued probability, can demonstrate that Shackle’s theory is a very special theory that applies only to situations of complete and total uncertainty, which Keynes categorized as ignorance. There is not a single one of Derbyshire’s objections to the concept of probability left standing if Keynes’s logical approach to probability is used.

Seeing through the eyes of the perpetrator: A goal-directed function of introjection

This paper proposes that introjection experienced as a traumatic presence has a goal-directed function, subcortically mediated with essential cortical participation. Anticipation of further relational trauma activates this post-traumatic process in which the victim remains watchfully engaged, monitoring from the dominant other’s perspective. In consequence, the victim endures a persistent objectifying perspective, a seeing and experiencing from out-there and in consequence, a loss of seeing and experiencing from within. This objectifying perspective emerges from the ontogenetic origins of shame designed to shape compliance with the wishes and needs of more dominant others for the child’s protection, social learning, and guidance. However, this ontogenetic process becomes disintegrating and maladaptive in the context of sustained interpersonal trauma. With sufficient reinforcement, it evolves into an attractor state experienced as a traumatic presence. Emerging information on the role of the cingulate in directing attention and mentalizing is consistent with this conceptualization. A sequence of clinical vignettes is used, not as a case study, but rather as a means to access experiential phenomena that illustrate the origins and evolution of this introjective process.

Relating emotional arousal to work vigour: A dynamic systems perspective

We examined the emotional basis of work engagement by focusing on the relationship between arousal and work vigour. Drawing on the DynAff model of Kuppens, Oravecz, and Tuerlinckx (2010), we looked at three elements underlying the temporal dynamics of arousal: (1) the level of baseline arousal (i.e., the attractor state around which arousal fluctuates), (2) the amount of variability in arousal around this baseline, and (3) the swiftness with which people return to their arousal baseline once they deviated from it. We conducted a five-day experience sampling study, in which 88 employees reported on their momentary core affect (i.e., their momentary level of valence and arousal), while vigour was measured at the end of the study. Results showed that higher levels of baseline arousal were related to increased levels of vigour. Furthermore, we found that baseline arousal interacted with arousal variability in the sense that only people with low levels of baseline arousal and low levels of arousal variability experienced lower levels of vigour. Together, our findings suggest that, if we want to advance our understanding of the emotional basis of work engagement, we need to look into the temporal dynamics underlying it.

Boolean analysis reveals systematic interactions among low-abundance species in the human gut microbiome.

The analysis of microbiome compositions in the human gut has gained increasing interest due to the broader availability of data and functional databases and substantial progress in data analysis methods, but also due to the high relevance of the microbiome in human health and disease. While most analyses infer interactions among highly abundant species, the large number of low-abundance species has received less attention. Here we present a novel analysis method based on Boolean operations applied to microbial co-occurrence patterns. We calibrate our approach with simulated data based on a dynamical Boolean network model from which we interpret the statistics of attractor states as a theoretical proxy for microbiome composition. We show that for given fractions of synergistic and competitive interactions in the model our Boolean abundance analysis can reliably detect these interactions. Analyzing a novel data set of 822 microbiome compositions of the human gut, we find a large number of highly significant synergistic interactions among these low-abundance species, forming a connected network, and a few isolated competitive interactions.

The energy landscape underpinning module dynamics in the human brain connectome

Human brain dynamics can be viewed through the lens of statistical mechanics, where neurophysiological activity evolves around and between local attractors representing mental states. Many physically-inspired models of these dynamics define brain states based on instantaneous measurements of regional activity. Yet, recent work in network neuroscience has provided evidence that the brain might also be well-characterized by time-varying states composed of locally coherent activity or functional modules. We study this network-based notion of brain state to understand how functional modules dynamically interact with one another to perform cognitive functions. We estimate the functional relationships between regions of interest (ROIs) by fitting a pair-wise maximum entropy model to each ROI's pattern of allegiance to functional modules. This process uses an information theoretic notion of energy (as opposed to a metabolic one) to produce an energy landscape in which local minima represent attractor states characterized by specific patterns of modular structure. The clustering of local minima highlights three classes of ROIs with similar patterns of allegiance to community states. Visual, attention, sensorimotor, and subcortical ROIs are well-characterized by a single functional community. The remaining ROIs affiliate with a putative executive control community or a putative default mode and salience community. We simulate the brain's dynamic transitions between these community states using a random walk process. We observe that simulated transition probabilities between basins are statistically consistent with empirically observed transitions in resting state fMRI data. These results offer a view of the brain as a dynamical system that transitions between basins of attraction characterized by coherent activity in groups of brain regions, and that the strength of these attractors depends on the ongoing cognitive computations.

Working Memory Requires a Combination of Transient and Attractor-Dominated Dynamics to Process Unreliably Timed Inputs

Working memory stores and processes information received as a stream of continuously incoming stimuli. This requires accurate sequencing and it remains puzzling how this can be reliably achieved by the neuronal system as our perceptual inputs show a high degree of temporal variability. One hypothesis is that accurate timing is achieved by purely transient neuronal dynamics; by contrast a second hypothesis states that the underlying network dynamics are dominated by attractor states. In this study, we resolve this contradiction by theoretically investigating the performance of the system using stimuli with differently accurate timing. Interestingly, only the combination of attractor and transient dynamics enables the network to perform with a low error rate. Further analysis reveals that the transient dynamics of the system are used to process information, while the attractor states store it. The interaction between both types of dynamics yields experimentally testable predictions and we show that this way the system can reliably interact with a timing-unreliable Hebbian-network representing long-term memory. Thus, this study provides a potential solution to the long-standing problem of the basic neuronal dynamics underlying working memory.

Modeling the Social Dynamics of Moral Enhancement: Social Strategies Sold Over the Counter and the Stability of Society.

How individuals tend to evaluate the combination of their own and other's payoffs-social value orientations-is likely to be a potential target of future moral enhancers. However, the stability of cooperation in human societies has been buttressed by evolved mildly prosocial orientations. If they could be changed, would this destabilize the cooperative structure of society? We simulate a model of moral enhancement in which agents play games with each other and can enhance their orientations based on maximizing personal satisfaction. We find that given the assumption that very low payoffs lead agents to be removed from the population, there is a broadly stable prosocial attractor state. However, the balance between prosociality and individual payoff-maximization is affected by different factors. Agents maximizing their own satisfaction can produce emergent shifts in society that reduce everybody's satisfaction. Moral enhancement considerations should take the issues of social emergence into account.

Coupling dynamics in speech gestures: amplitude and rate influences

Speech is a complex oral motor function that involves multiple articulators that need to be coordinated in space and time at relatively high movement speeds. How this is accomplished remains an important and largely unresolved empirical question. From a coordination dynamics perspective, coordination involves the assembly of coordinative units that are characterized by inherently stable coupling patterns that act as attractor states for task-specific actions. In the motor control literature, one particular model formulated by Haken et al. (Biol Cybern 51(5):347-356, 1985) or HKB has received considerable attention in the way it can account for changes in the nature and stability of specific coordination patterns between limbs or between limbs and external stimuli. In this model (and related versions), movement amplitude is considered a critical factor in the formation of these patterns. Several studies have demonstrated its role for bimanual coordination and similar types of tasks, but for speech motor control such studies are lacking. The current study describes a systematic approach to evaluate the impact of movement amplitude and movement duration on coordination stability in the production of bilabial and tongue body gestures for specific vowel-consonant-vowel strings. The vowel combinations that were used induced a natural contrast in movement amplitude at three speaking rate conditions (slow, habitual, fast). Data were collected on ten young adults using electromagnetic articulography, recording movement data from lips and tongue with high temporal and spatial precision. The results showed that with small movement amplitudes there is a decrease in coordination stability, independent from movement duration. These findings were found to be robust across all individuals and are interpreted as further evidence that principles of coupling dynamics operate in the oral motor control system similar to other motor systems and can be explained in terms of coupling mechanisms between neural oscillators (organized in networks) and effector systems. The relevance of these findings for understanding motor control issues in people with speech disorders is discussed as well.

Information and the Origin of Qualia.

This article argues that qualia are a likely outcome of the processing of information in local cortical networks. It uses an information-based approach and makes a distinction between information structures (the physical embodiment of information in the brain, primarily patterns of action potentials), and information messages (the meaning of those structures to the brain, and the basis of qualia). It develops formal relationships between these two kinds of information, showing how information structures can represent messages, and how information messages can be identified from structures. The article applies this perspective to basic processing in cortical networks or ensembles, showing how networks can transform between the two kinds of information. The article argues that an input pattern of firing is identified by a network as an information message, and that the output pattern of firing generated is a representation of that message. If a network is encouraged to develop an attractor state through attention or other re-entrant processes, then the message identified each time physical information is cycled through the network becomes “representation of the previous message”. Using an example of olfactory perception, it is shown how this piggy-backing of messages on top of previous messages could lead to olfactory qualia. The message identified on each pass of information could evolve from inner identity, to inner form, to inner likeness or image. The outcome is an olfactory quale. It is shown that the same outcome could result from information cycled through a hierarchy of networks in a resonant state. The argument for qualia generation is applied to other sensory modalities, showing how, through a process of brain-wide constraint satisfaction, a particular state of consciousness could develop at any given moment. Evidence for some of the key predictions of the theory is presented, using ECoG data and studies of gamma oscillations and attractors, together with an outline of what further evidence is needed to provide support for the theory.

Feedforward Approximations to Dynamic Recurrent Network Architectures.

Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solving systems of differential equations, and the number of evaluations required to determine their response to a given input can vary with the input or can be indeterminate altogether in the case of oscillations or instability. In feedforward networks, by contrast, only a single pass through the network is needed to determine the response to a given input. Modern machine learning systems are designed to operate efficiently on feedforward architectures. We hypothesized that two-layer feedforward architectures with simple, deterministic dynamics could approximate the responses of single-layer recurrent network architectures. By identifying the fixed-point responses of a given recurrent network, we trained two-layer networks to directly approximate the fixed-point response to a given input. These feedforward networks then embodied useful computations, including competitive interactions, information transformations, and noise rejection. Our approach was able to find useful approximations to recurrent networks, which can then be evaluated in linear and deterministic time complexity.

Nonlinear behavior of a novel chaotic jerk system: antimonotonicity, crises, and multiple coexisting attractors

In this contribution, a novel Jerk system with a smooth piecewise quadratic nonlinearity is introduced. The new nonlinearity provides a similar smoothness as the cubic polynomial function, but a faster response and a simpler circuitry. The basic dynamical properties of the model are discussed in terms of its parameters by using standard nonlinear analysis tools including phase space trajectory plots, frequency spectra, bifurcation diagrams and Lyapunov exponent plots. The bifurcation analysis yields very rich and interesting scenarios such as period-doubling bifurcations, antimonotonicity (i.e. the concurrent creation and annihilation of periodic orbits), periodic windows, and symmetry recovering crises. One of the main findings of this work is the presence of a window in the parameter space in which the novel jerk system experiences the unusual and striking feature of multiple coexisting attractors (i.e. coexistence of four or six disconnected periodic and chaotic attractors) for the same parameters’ setting. Correspondingly, basins of attraction of various competing attractors display extremely complex basin boundaries. Compared to some lower dimensional systems (e.g. Leipnik–Newton system, modified Sprott B system) capable of displaying such type of behavior reported to date, the jerk system introduced in this work represents the simplest and the most ‘elegant’ paradigm. An electronic circuit for allowing an illustration of the theoretical model is proposed and implemented in PSpice. The results obtained in this work let us conjecture that there exist some regions in its parameter space (that need to be uncovered) in which the universal Chua’s circuit experiences six disconnected non static attractors similar to those presented in this work.

Attractor States in Teaching and Learning Processes: A Study of Out-of-School Science Education.

In order for out-of-school science activities that take place during school hours but outside the school context to be successful, instructors must have sufficient pedagogical content knowledge (PCK) to guarantee high-quality teaching and learning. We argue that PCK is a quality of the instructor-pupil system that is constructed in real-time interaction. When PCK is evident in real-time interaction, we define it as Expressed Pedagogical Content Knowledge (EPCK). The aim of this study is to empirically explore whether EPCK shows a systematic pattern of variation, and if so whether the pattern occurs in recurrent and temporary stable attractor states as predicted in the complex dynamic systems theory. This study concerned nine out-of-school activities in which pupils of upper primary school classes participated. A multivariate coding scheme was used to capture EPCK in real time. A principal component analysis of the time series of all the variables reduced the number of components. A cluster revealed general descriptions of the components across all cases. Cluster analyses of individual cases divided the time series into sequences, revealing High-, Low-, and Non-EPCK states. High-EPCK attractor states emerged at particular moments during activities, rather than being present all the time. Such High-EPCK attractor states were only found in a few cases, namely those where the pupils were prepared for the visit and the instructors were trained.

Predicting epileptic seizures from scalp EEG based on attractor state analysis

Background and ObjectiveEpilepsy is the second most common disease of the brain. Epilepsy makes it difficult for patients to live a normal life because it is difficult to predict when seizures will occur. In this regard, if seizures could be predicted a reasonable period of time before their occurrence, epilepsy patients could take precautions against them and improve their safety and quality of life. In this paper, we investigate a novel seizure precursor based on attractor state analysis for seizure prediction. MethodsWe analyze the transition process from normal to seizure attractor state and investigate a precursor phenomenon seen before reaching the seizure attractor state. From the result of an analysis, we define a quantified spectral measure in scalp EEG for seizure prediction. From scalp EEG recordings, the Fourier coefficients of six EEG frequency bands are extracted, and the defined spectral measure is computed based on the coefficients for each half-overlapped 20-second-long window. The computed spectral measure is applied to seizure prediction using a low-complexity methodology. ResultsWithin scalp EEG, we identified an early-warning indicator before an epileptic seizure occurs. Getting closer to the bifurcation point that triggers the transition from normal to seizure state, the power spectral density of low frequency bands of the perturbation of an attractor in the EEG, showed a relative increase. A low-complexity seizure prediction algorithm using this feature was evaluated, using ∼583h of scalp EEG in which 143 seizures in 16 patients were recorded. With the test dataset, the proposed method showed high sensitivity (86.67%) with a false prediction rate of 0.367h−1 and average prediction time of 45.3min. ConclusionsA novel seizure prediction method using scalp EEG, based on attractor state analysis, shows potential for application with real epilepsy patients. This is the first study in which the seizure-precursor phenomenon of an epileptic seizure is investigated based on attractor-based analysis of the macroscopic dynamics of the brain. With the scalp EEG, we first propose use of a spectral feature identified for seizure prediction, in which the dynamics of an attractor are excluded, and only the perturbation dynamics from the attractor are considered.

Novel Hybrid Phenotype Revealed in Small Cell Lung Cancer by a Transcription Factor Network Model That Can Explain Tumor Heterogeneity.

Small cell lung cancer (SCLC) is a devastating disease due to its propensity for early invasion and refractory relapse after initial treatment response. Although these aggressive traits have been associated with phenotypic heterogeneity, our understanding of this association remains incomplete. To fill this knowledge gap, we inferred a set of 33 transcription factors (TF) associated with gene signatures of the known neuroendocrine/epithelial (NE) and non-neuroendocrine/mesenchymal-like (ML) SCLC phenotypes. The topology of this SCLC TF network was derived from prior knowledge and was simulated using Boolean modeling. These simulations predicted that the network settles into attractors, or TF expression patterns, that correlate with NE or ML phenotypes, suggesting that TF network dynamics underlie the emergence of heterogeneous SCLC phenotypes. However, several cell lines and patient tumor specimens failed to correlate with either the NE or ML attractors. By flow cytometry, single cells within these cell lines simultaneously expressed surface markers of both NE and ML differentiation, confirming the existence of a "hybrid" phenotype. Upon exposure to standard-of-care cytotoxic drugs or epigenetic modifiers, NE and ML cell populations converged toward the hybrid state, suggesting possible escape from treatment. Our findings indicate that SCLC phenotypic heterogeneity can be specified dynamically by attractor states of a master regulatory TF network. Thus, SCLC heterogeneity may be best understood as states within an epigenetic landscape. Understanding phenotypic transitions within this landscape may provide insights to clinical applications. Cancer Res; 77(5); 1063-74. ©2016 AACR.

P201 Modulating cortical dynamics of binocular rivalry with tRNS over primary visual cortex

Question We have recently shown that adding random electrical noise transcranially to the cortex can enhance the detectability of weak visual signals, a phenomenon known as stochastic resonance (SR). However, the concept of stochastic resonance is not only valid for stable systems but can also be used to influence transitions of dynamical systems that consist of multiple attractor states. Here we use binocular rivalry as a model to investigate whether peripherally or centrally added noise influences transitions between different perceptual states. Binocular rivalry is characterized by three naturally occurring attractor states with different stabilities (i.e. seeing the left eye stimulus, the right eye stimulus, or both) and by a spontaneous stochastic switching between these states. This switching is believed to be driven by a combination of neuronal adaptation and noise. Methods In a series of experiments we presented visual gratings to each eye separately using a mirror stereoscope. Subjects continuously reported whether they perceived the left eye stimulus, the right eye stimulus or a mixed percept. We tested whether switching dynamics were influenced when noise was either added peripherally on the screen or centrally by applying tRNS (100–640 Hz, 1 mA amplitude) to the visual cortex. Results and conclusions For low contrast stimuli, we found a significantly faster transition from the mixed to the single precepts when noise was added directly to the visual stimulus ( p = 0.03) or to visual cortex using tRNS ( p = 0.02). Our results show that tRNS can be used to modulate the dynamics of cortical processing.

Self-Repairing Digital System Based on State Attractor Convergence Inspired by the Recovery Process of a Living Cell

Increasing attention is being paid to soft errors due to their high incidence. Although various approaches have been developed to mitigate such soft errors in digital storage components such as latches and flip-flops, most of them can detect only a single soft error and correct it only in limited cases, with a high overhead of hardware resources. In this paper, we propose a new self-repairing digital system based on the state attractor-converging mechanism, inspired by the recovery process of a living cell. To implement the state attractor-converging mechanism, the proposed system introduces additional states other than a working state, such that any abnormal transition to an additional state caused by a soft error can be recovered immediately. Moreover, the proposed system employs a reconfiguration method that enables a system with an erroneous state to be recovered regardless of any working state of the system while having a similar hardware overhead compared with the existing systems. From simulation analysis and experimental verification, we show that the proposed system can detect and correct not only a single soft error without any restriction but also two simultaneous soft errors under a few conditions. Furthermore, the proposed system can recover a soft error occurring in the control hardware used for error detection and correction, which is not possible with any other existing approaches.

Domain control of nonlinear networked systems and applications to complex disease networks

The control of complex nonlinear dynamical networks is an ongoing challenge in diverse contexts ranging from biology to social sciences. To explore a practical framework for controlling nonlinear dynamical networks based on meaningful physical and experimental considerations, we propose a new concept of the domain control for nonlinear dynamical networks, i.e., the control of a nonlinear network in transition from the domain of attraction of an undesired state (attractor) to the domain of attraction of a desired state. We theoretically prove the existence of a domain control. In particular, we offer an approach for identifying the driver nodes that need to be controlled and design a general form of control functions for realizing domain controllability. In addition, we demonstrate the effectiveness of our theory and approaches in three realistic disease-related networks: the epithelial-mesenchymal transition (EMT) core network, the T helper (Th) differentiation cellular network and the cancer network. Moreover, we reveal certain genes that are critical to phenotype transitions of these systems. Therefore, the approach described here not only offers a practical control scheme for nonlinear dynamical networks but also helps the development of new strategies for the prevention and treatment of complex diseases.