Hierarchical nonlinear dynamics of human attention

Human learning of hierarchical graphs

Humans are exposed to sequences of events in the environment, and the interevent transition probabilities in these sequences can be modeled as a graph or network. Many real-world networks are organized hierarchically and while much is known about how humans learn basic transition graph topology, whether and to what degree humans can learn hierarchical structures in such graphs remains unknown. We probe the mental estimates of transition probabilities via the surprisal effect phenomenon: humans react more slowly to less expected transitions. Using mean-field predictions and numerical simulations, we show that surprisal effects are stronger for finer-level than coarser-level hierarchical transitions, and that surprisal effects at coarser levels are difficult to detect for limited learning times or in small samples. Using a serial response experiment with human participants (n=100), we replicate our predictions by detecting a surprisal effect at the finer level of the hierarchy but not at the coarser level of the hierarchy. We then evaluate the presence of a trade-off in learning, whereby humans who learned the finer level of the hierarchy better also tended to learn the coarser level worse, and vice versa. This study elucidates the processes by which humans learn sequential events in hierarchical contexts. More broadly, our work charts a road map for future investigation of the neural underpinnings and behavioral manifestations of graph learning.

Heteroclinic networks for brain dynamics

Heteroclinic networks are a mathematical concept in dynamic systems theory that is suited to describe metastable states and switching events in brain dynamics. The framework is sensitive to external input and, at the same time, reproducible and robust against perturbations. Solutions of the corresponding differential equations are spatiotemporal patterns that are supposed to encode information both in space and time coordinates. We focus on the concept of winnerless competition as realized in generalized Lotka-Volterra equations and report on results for binding and chunking dynamics, synchronization on spatial grids, and entrainment to heteroclinic motion. We summarize proposals of how to design heteroclinic networks as desired in view of reproducing experimental observations from neuronal networks and discuss the subtle role of noise. The review is on a phenomenological level with possible applications to brain dynamics, while we refer to the literature for a rigorous mathematical treatment. We conclude with promising perspectives for future research.

On relaxation times of heteroclinic dynamics

Heteroclinic dynamics provide a suitable framework for describing transient dynamics such as cognitive processes in the brain. It is appreciated for being well reproducible and at the same time highly sensitive to external input. It is supposed to capture features of switching statistics between metastable states in the brain. Beyond the high sensitivity, a further desirable feature of these dynamics is to enable a fast adaptation to new external input. In view of this, we analyze relaxation times of heteroclinic motion toward a new resting state, when oscillations in heteroclinic networks are arrested by a quench of a bifurcation parameter from a parameter regime of oscillations to a regime of equilibrium states. As it turns out, the relaxation is underdamped and depends on the nesting of the attractor space, the size of the attractor's basin of attraction, the depth of the quench, and the level of noise. In the case of coupled heteroclinic units, it depends on the coupling strength, the coupling type, and synchronization between different units. Depending on how these factors are combined, finite relaxation times may support or impede a fast switching to new external input. Our results also shed some light on the discussion of how the stability of a system changes with its complexity.

Children and adults rely on different heuristics for estimation of durations

Time is a uniquely human yet culturally ubiquitous concept acquired over childhood and provides an underlying dimension for episodic memory and estimating durations. Because time, unlike distance, lacks a sensory representation, we hypothesized that subjects at different ages attribute different meanings to it when comparing durations; pre-kindergarten children compare the density of events, while adults use the concept of observer-independent absolute time. We asked groups of pre-kindergarteners, school-age children, and adults to compare the durations of an "eventful" and "uneventful" video, both 1-minute long but durations unknown to subjects. In addition, participants were asked to express the durations of both videos non-verbally with simple hand gestures. Statistical analysis has revealed highly polarized temporal biases in each group, where pre-kindergarteners estimated the duration of the eventful video as "longer." In contrast, the school-age group of children and adults claimed the same about the uneventful video. The tendency to represent temporal durations with a horizontal hand gesture was evident among all three groups, with an increasing prevalence with age. These results support the hypothesis that pre-kindergarten-age children use heuristics to estimate time, and they convert from availability to sampling heuristics between pre-kindergarten and school age.

Coexistence of Hopf-born rotation and heteroclinic cycling in a time-delayed three-gene auto-regulated and mutually-repressed core genetic regulation network

In this work, we study the behavior of a time-delayed mutually repressive auto-activating three-gene system. Delays are introduced to account for the location difference between DNA transcription that leads to production of messenger RNA and its translation that result in protein synthesis. We study the dynamics of the system using numerical simulations, computational bifurcation analysis and mathematical analysis. We find Hopf bifurcations leading to stable and unstable rotation in the system, and we study the rotational behavior as a function of cyclic mutual repression parameter asymmetry between each gene pair in the network. We focus on how rotation co-exists with a stable heteroclinic flow linking the three saddles in the system. We find that this coexistence allows for a transition between two markedly different types of rotation leading to strikingly different phenotypes. One type of rotation belongs to Hopf-induced rotation while the other type, belongs to heteroclinic cycling between three saddle nodes in the system. We discuss the evolutionary and biological implications of our findings.

Dynamic Computation in Visual Thalamocortical Networks

Contemporary neurodynamical frameworks, such as coordination dynamics and winnerless competition, posit that the brain approximates symbolic computation by transitioning between metastable attractive states. This article integrates these accounts with electrophysiological data suggesting that coherent, nested oscillations facilitate information representation and transmission in thalamocortical networks. We review the relationship between criticality, metastability, and representational capacity, outline existing methods for detecting metastable oscillatory patterns in neural time series data, and evaluate plausible spatiotemporal coding schemes based on phase alignment. We then survey the circuitry and the mechanisms underlying the generation of coordinated alpha and gamma rhythms in the primate visual system, with particular emphasis on the pulvinar and its role in biasing visual attention and awareness. To conclude the review, we begin to integrate this perspective with longstanding theories of consciousness and cognition.

Hierarchical dynamics of informational patterns and decision-making

Traditional studies on the interaction of cognitive functions in healthy and disordered brains have used the analyses of the connectivity of several specialized brain networks-the functional connectome. However, emerging evidence suggests that both brain networks and functional spontaneous brain-wide network communication are intrinsically dynamic. In the light of studies investigating the cooperation between different cognitive functions, we consider here the dynamics of hierarchical networks in cognitive space. We show, using an example of behavioural decision-making based on sequential episodic memory, how the description of metastable pattern dynamics underlying basic cognitive processes helps to understand and predict complex processes like sequential episodic memory recall and competition among decision strategies. The mathematical images of the discussed phenomena in the phase space of the corresponding cognitive model are hierarchical heteroclinic networks. One of the most important features of such networks is the robustness of their dynamics. Different kinds of instabilities of these dynamics can be related to 'dynamical signatures' of creativity and different psychiatric disorders. The suggested approach can also be useful for the understanding of the dynamical processes that are the basis of consciousness.

Metastable Pain-Attention Dynamics during Incremental Exhaustive Exercise

Background: Pain attracts attention on the bodily regions. Attentional allocation toward pain results from the neural communication across the brain-wide network "connectome" which consists of pain-attention related circuits. Connectome is intrinsically dynamic and spontaneously fluctuating on multiple time-scales. The present study delineates the pain-attention dynamics during incremental cycling performed until volitional exhaustion and investigates the potential presence of nested metastable dynamics. Method: Fifteen young and physically active adults completed a progressive incremental cycling test and reported their discomfort and pain on a body map every 15 s. Results: The analyses revealed that the number of body locations with perceived pain and discomfort increased throughout five temporal windows reaching an average of 4.26 ± 0.59 locations per participant. A total of 37 different locations were reported and marked as painful for all participants throughout the cycling task. Significant differences in entropy were observed between all temporal windows except the fourth and fifth windows. Transient dynamics of bodily locations with perceived discomfort and pain were spanned by three principal components. The metastable dynamics of the body pain locations groupings over time were discerned by three time scales: (1) the time scale of shifts (15 s); (2) the time scale of metastable configurations (100 s), and (3) the observational time scale (1000 s). Conclusion: The results of this study indicate that body locations perceived as painful increase throughout the incremental cycling task following a switching metastable and nested dynamics. These findings support the view that human brain is intrinsically organized into active, mutually interacting complex and nested functional networks, and that subjective experiences inherent in pain perception depict identical dynamical principles to the neural tissue in the brain.