Attractor States Research Articles

Critical alterations in the brain and psyche

Critical alterations in the brain and psyche are often triggered by critical points and feedback effects in closely networked systems. Such crises can occur in the form of neurological disorders, such as epilepsy or mental disorders, such as bipolar disorder and depression. A central mechanism is the excitation-inhibition (EI) balance in the brain, which is responsible for an optimal processing of information. Disruptions in this balance can lead to pathological conditions. The concept of attractors, which represent the stable conditions in neuronal networks, helps to explain the consolidation of memories, behavioral patterns and mental states. These attractor states can be triggered by external stimuli and may become anchored in pathological contexts. Advances in measurement technologies and methods of artificial intelligence enable a deeper analysis of neuronal dynamics and open up new pathways for targeted therapeutic interventions for the treatment of mental disorders.

Changes in Language Learners’ Affect: A Complex Dynamic Systems Theory Perspective

AbstractThis study investigated changes in motivation, self‐efficacy beliefs, and a range of emotions, including enjoyment, hope, pride, curiosity, anxiety, boredom, apathy, confusion, and shame, from a complex dynamic systems theory (CDST) perspective over a 2‐year period in the Hungarian English as a Foreign Language (EFL) context. Using the same questionnaire, we collected data four times throughout 4 semesters from 101 participants studying English in two Hungarian high schools. For data analysis, we used latent growth curve modeling (LGCM) to detect the group‐level changes in learners’ motivation, self‐efficacy, and emotions. We also employed dynamic cluster analysis to identify trends in learners’ trajectories regarding these variables. In our panel data, linear models described the data well concerning the ought‐to second language (L2) self, language learning experience, boredom, apathy, and confusion, and for enjoyment, curiosity, anxiety, and shame, nonlinear models had the best fit. We could also identify trajectories depicting attractor states and learner paths that featured influences of perturbations.

Barcode activity in a recurrent network model of the hippocampus enables efficient memory binding.

Forming an episodic memory requires binding together disparate elements that co-occur in a single experience. One model of this process is that neurons representing different components of a memory bind to an "index" - a subset of neurons unique to that memory. Evidence for this model has recently been found in chickadees, which use hippocampal memory to store and recall locations of cached food. Chickadee hippocampus produces sparse, high-dimensional patterns ("barcodes") that uniquely specify each caching event. Unexpectedly, the same neurons that participate in barcodes also exhibit conventional place tuning. It is unknown how barcode activity is generated, and what role it plays in memory formation and retrieval. It is also unclear how a memory index (e.g. barcodes) could function in the same neural population that represents memory content (e.g. place). Here, we design a biologically plausible model that generates barcodes and uses them to bind experiential content. Our model generates barcodes from place inputs through the chaotic dynamics of a recurrent neural network and uses Hebbian plasticity to store barcodes as attractor states. The model matches experimental observations that memory indices (barcodes) and content signals (place tuning) are randomly intermixed in the activity of single neurons. We demonstrate that barcodes reduce memory interference between correlated experiences. We also show that place tuning plays a complementary role to barcodes, enabling flexible, contextually-appropriate memory retrieval. Finally, our model is compatible with previous models of the hippocampus as generating a predictive map. Distinct predictive and indexing functions of the network are achieved via an adjustment of global recurrent gain. Our results suggest how the hippocampus may use barcodes to resolve fundamental tensions between memory specificity (pattern separation) and flexible recall (pattern completion) in general memory systems.

Complex Dynamical Behavior of Locally Active Discrete Memristor-Coupled Neural Networks with Synaptic Crosstalk: Attractor Coexistence and Reentrant Feigenbaum Trees

In continuous neural modeling, memristor coupling has been investigated widely. Yet, there is little research on discrete neural networks in the field. Discrete models with synaptic crosstalk are even less common. In this paper, two locally active discrete memristors are used to couple two discrete Aihara neurons to form a map called DMCAN. Then, the synapse is modeled using a discrete memristor and the DMCAN map with crosstalk is constructed. The DMCAN map is investigated using phase diagram, chaotic sequence, Lyapunov exponent spectrum (LEs) and bifurcation diagrams (BD). Its rich and complex dynamical behavior, which includes attractor coexistence, state transfer, Feigenbaum trees, and complexity, is systematically analyzed. In addition, the DMCAN map is implemented in hardware on a DSP platform. Numerical simulations are further validated for correctness. Numerical and experimental findings show that the synaptic connections of neurons can be modeled by discrete memristor coupling which leads to the construction of more complicated discrete neural networks.

Developmental dynamics in oral fluency and learner motivation: A dual‐focus approach

AbstractAdopting a comprehensive dual‐focus approach to oral fluency development, the present study examined the developmental trajectories of oral fluency in tertiary‐level Chinese EFL learners and identified the motivational attractor states helpful for shaping their oral production. Quantitative and qualitative data were collected over two semesters with monologue tasks and semi‐structured interviews, respectively. Oral fluency development was examined using moving min–max graphs, change point analysis, and Monte Carlo simulations, while the retrodiction approach was utilized to identify influential motivational attractor states. Results showed that, over the course of the study, the two learners experienced distinct variability and phase shifts in their development of oral fluency, largely attributable to their unique motivational attractor states. By employing such a dual‐focus approach, the present study provided a nuanced picture of Chinese EFL learners’ developmental dynamics in terms of both oral fluency and learning motivation and the adaptive interactions between them, thus enriching our understanding of how oral fluency development relates to learner motivation.

Unveiling serotonergic dysfunction of obsessive-compulsive disorder on prefrontal network dynamics: a computational perspective.

Serotonin (5-HT) regulates working memory within the prefrontal cortex network, which is crucial for understanding obsessive-compulsive disorder. However, the mechanisms how network dynamics and serotonin interact in obsessive-compulsive disorder remain elusive. Here, we incorporate 5-HT receptors (5-HT1A, 5-HT2A) and dopamine receptors into a multistable prefrontal cortex network model, replicating the experimentally observed inverted U-curve phenomenon. We show how the two 5-HT receptors antagonize neuronal activity and modulate network multistability. Reduced binding of 5-HT1A receptors increases global firing, while reduced binding of 5-HT2A receptors deepens attractors. The obtained results suggest reward-dependent synaptic plasticity mechanisms may attenuate 5-HT related network impairments. Integrating serotonin-mediated dopamine release into circuit, we observe that decreased serotonin concentration triggers the network into a deep attractor state, expanding the domain of attraction of stable nodes with high firing rate, potentially causing aberrant reverse learning. This suggests a hypothesis wherein elevated dopamine concentrations in obsessive-compulsive disorder might result from primary deficits in serotonin levels. Findings of this work underscore the pivotal role of serotonergic dysregulation in modulating synaptic plasticity through dopamine pathways, potentially contributing to learned obsessions. Interestingly, serotonin reuptake inhibitors and antidopaminergic potentiators can counteract the over-stable state of high-firing stable points, providing new insights into obsessive-compulsive disorder treatment.

Analysis of a new three-dimensional jerk chaotic system with transient chaos and its adaptive backstepping synchronous control

A new three-dimensional Jerk chaotic system with line equilibrium points is proposed. The system is researched in detail by the Lyapunov exponent graph, bifurcation diagram, phase diagram, and time domain waveform diagram, which show that the system has rich dynamical behaviors, such as eight types of coexisting attractors, extreme multistability of four different attractor states, and offset boosting in two directions. In addition, the system also has six types of transient chaos, which greatly increase the complexity of the system. We study the variation of the spectral entropy (SE) and C0 complexity when the system takes different initial values. Also, in this paper, the initial conditions under which the system is in a synchronized state are determined by initial values with higher complexity. The correctness of the theoretical analysis and numerical simulation is verified by circuit simulation and hardware experiments. Finally, the new system achieves synchronization control utilizing a designed adaptive backstepping controller, laying the foundation for its subsequent use in secure communications.

Size‐dependent asymmetry of barchans indicates dune growth controlled by basal area or bulk volume

AbstractWe introduce a novel analytical model of the growth of barchan dunes in terms of their two flanks, from which we derive expressions for the size‐dependence of the bilateral asymmetry of these bedforms in three cases where different mechanisms dominate the growth process. Analysis of the morphology of barchans on Mars and Earth suggest that there may exist two distinct attractor states for the asymmetry distribution. By comparing our analytical results with the observations, we show that the growth of barchan dunes appears to be dominated by processes, which are proportional to the basal area or volume of the bedforms, rather than being linear to their width as is typically assumed. We propose hypotheses explaining area‐dominated growth as a result of variable wind regimes and volume‐dominated growth from collisions. These predictions appear to be in line with the available data for the terrestrial swarms and barchan‐like submarine bedforms and offer the potential of predicting patterns in inaccessible wind regimes from data on the morphology of the dunes.

Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph.

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using $10$ reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's $Z$-parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states.

A neural network-based model framework for cell-fate decisions and development

Gene regulatory networks (GRNs) fulfill the essential function of maintaining the stability of cellular differentiation states by sustaining lineage-specific gene expression, while driving the progression of development. However, accounting for the relative stability of intermediate differentiation stages and their divergent trajectories remains a major challenge for models of developmental biology. Here, we develop an empirical data-based associative GRN model (AGRN) in which regulatory networks store multilineage stage-specific gene expression profiles as associative memory patterns. These networks are capable of responding to multiple instructive signals and, depending on signal timing and identity, can dynamically drive the differentiation of multipotent cells toward different cell state attractors. The AGRN dynamics can thus generate diverse lineage-committed cell populations in a robust yet flexible manner, providing an attractor-based explanation for signal-driven cell fate decisions during differentiation and offering a readily generalizable modelling tool that can be applied to a wide variety of cell specification systems.

Coevolving edge rounding and shape of glacial erratics: the case of Shap granite, UK

Abstract. The size distributions and the shapes of detrital rock clasts can shed light on the environmental history of the clast assemblages and the processes responsible for clast comminution. For example, mechanical fracture due to the stresses imposed on a basal rock surface by a body of flowing glacial ice releases initial “parent” shapes of large blocks of rock from an outcrop, which then are modified by the mechanics of abrasion and fracture during subglacial transport. The latter processes produce subsequent generations of shapes, possibly distinct in form from the parent blocks. A complete understanding of both the processes responsible for block shape changes and the trends in shape adjustment with time and distance away from the source outcrop is lacking. Field data on edge rounding and shape changes of Shap granite blocks (dispersed by Devensian ice eastwards from the outcrop) are used herein to explore the systematic changes in block form with distance from the outcrop. The degree of edge rounding for individual blocks increases in a punctuated fashion with the distance from the outcrop as blocks fracture repeatedly to introduce new fresh unrounded edges. In contrast, block shape is conservative, with parent blocks fracturing to produce self-similar “child” shapes with distance. Measured block shapes evolve in accord with two well-known models for block fracture mechanics – (1) stochastic and (2) silver ratio models – towards one or the other of these two attractor states. Progressive reduction in block size, in accord with fracture mechanics, reflects the fact that most blocks were transported at the sole of the ice mass and were subject to the compressive and tensile forces of the ice acting on the stoss surfaces of blocks lying against a bedrock or till surface. The interpretations might apply to a range of homogeneous hard rock lithologies.

Stability/Flexibility: the tightly coupled homeostasis generator is at the same time the driver of change.

There is "no Flexibility without Stability and no Stability without Flexibility": this is a crucial feature common to any system interacting with its environment. This tight link between two apparently opposite features is at the basis of the time-honoured concept of homeostasis (the tendency of any adaptive system to go back to its "comfort zone" contrasting the incoming perturbations) and is widely recognized since long time. On the contrary, the fact that the escape from a stable attractor state is a consequence of the same homeostasis mechanisms is often overlooked. In this brief note, we will try to give a proof-of-concept of the relation existing between stability/flexibility based homeostasis and the state changes at all the levels of biological organization. The ubiquity of the same principles across very different systems is a signature of a new attitude to look at scientific enterprise from a network-based viewpoint.

DEEP REINFORCEMENT LEARNING FOR SCALABLE CONTROL OF BOOLEAN MODELS IN THE CONTEXT OF CELLULAR REPROGRAMMING

Cellular reprogramming, understood as the artificial changing of one cell type into another, could potentially be used for the prevention or cure of complex diseases, such as cancer or neurodegenerative disorders. However, the identification of efficient reprogramming targets and strategies with classical wet-lab experiments is hindered by lengthy time commitments and high costs. To address these issues, in-silico methods are considered. In this study, we formulate a novel control problem in the context of cellular reprogramming for the Boolean network (BN) and Probabilistic Boolean Network (PBN) computational models of gene regulatory networks [1]. To solve this problem, we develop pbn-STAC - a novel computational framework based on deep reinforcement learning (DRL) [2] that facilitates the identification of reprogramming strategies for large BN/PBN models. To address the issue of the computational complexity of finding stable states, i.e., configurations which correspond to cell types or cellular phenotypic states, we introduce the notion of a pseudo-attractor and we devise a procedure for the identification of pseudo-attractor states during DRL training. Given source and target (pseudo-)attractor states, pbn-STAC finds proper control targets and strategies that drive the network from the source to the target by intervening only in intermediate attractor states that correspond to phenotypic cellular states observable in wet-lab practice. We evaluate the performance of pbn-STAC on a number of models of various sizes and a biological case study, i.e., a published BN model of immune response against B. bronchiseptica infection. We compare the results obtained with our approach with the exact, optimal solutions wherever possible and we show the effectiveness of PBN-STAC in identifying control targets and strategies. We consider our framework as a contribution towards the ultimate aim of developing scalable control methods for large models of gene regulatory networks.

Mechanisms of Action of TMS in the Treatment of Depression.

Transcranial magnetic stimulation (TMS) is entering increasingly widespread use in treating depression. The most common stimulation target, in the dorsolateral prefrontal cortex (DLPFC), emerged from early neuroimaging studies in depression. Recently, more rigorous casual methods have revealed whole-brain target networks and anti-networks based on the effects of focal brain lesions and focal brain stimulation on depression symptoms. Symptom improvement during therapeutic DLPFC-TMS appears to involve directional changes in signaling between the DLPFC, subgenual and dorsal anterior cingulate cortex, and salience-network regions. However, different networks may be involved in the therapeutic mechanisms for other TMS targets in depression, such as dorsomedial prefrontal cortex or orbitofrontal cortex. The durability of therapeutic effects for TMS involves synaptic neuroplasticity, and specifically may depend upon dopamine acting at the D1 receptor family, as well as NMDA-receptor-dependent synaptic plasticity mechanisms. Although TMS protocols are classically considered 'excitatory' or 'inhibitory', the actual effects in individuals appear quite variable, and might be better understood at the level of populations of synapses rather than individual synapses. Synaptic meta-plasticity may provide a built-in protective mechanism to avoid runaway facilitation or inhibition during treatment, and may account for the relatively small number of patients who worsen rather than improve with TMS. From an ethological perspective, the antidepressant effects of TMS may involve promoting a whole-brain attractor state associated with foraging/hunting behaviors, centered on the rostrolateral periaqueductal gray and salience network, and suppressing an attractor state associated with passive threat defense, centered on the ventrolateral periaqueductal gray and default-mode network.

Grid codes vs. multi-scale, multi-field place codes for space.

Recent work on bats flying over long distances has revealed that single hippocampal cells have multiple place fields of different sizes. At the network level, a multi-scale, multi-field place cell code outperforms classical single-scale, single-field place codes, yet the performance boundaries of such a code remain an open question. In particular, it is unknown how general multi-field codes compare to a highly regular grid code, in which cells form distinct modules with different scales. In this work, we address the coding properties of theoretical spatial coding models with rigorous analyses of comprehensive simulations. Starting from a multi-scale, multi-field network, we performed evolutionary optimization. The resulting multi-field networks sometimes retained the multi-scale property at the single-cell level but most often converged to a single scale, with all place fields in a given cell having the same size. We compared the results against a single-scale single-field code and a one-dimensional grid code, focusing on two main characteristics: the performance of the code itself and the dynamics of the network generating it. Our simulation experiments revealed that, under normal conditions, a regular grid code outperforms all other codes with respect to decoding accuracy, achieving a given precision with fewer neurons and fields. In contrast, multi-field codes are more robust against noise and lesions, such as random drop-out of neurons, given that the significantly higher number of fields provides redundancy. Contrary to our expectations, the network dynamics of all models, from the original multi-scale models before optimization to the multi-field models that resulted from optimization, did not maintain activity bumps at their original locations when a position-specific external input was removed. Optimized multi-field codes appear to strike a compromise between a place code and a grid code that reflects a trade-off between accurate positional encoding and robustness. Surprisingly, the recurrent neural network models we implemented and optimized for either multi- or single-scale, multi-field codes did not intrinsically produce a persistent "memory" of attractor states. These models, therefore, were not continuous attractor networks.

How the dynamics of engagement explain the momentum of achievement and the inertia of disengagement: A complex systems theory approach

Engagement can be understood as a complex dynamic system that unfolds over time and interacts within the student, school, and environment. Most of the research on the dynamics of engagement comes from classroom settings and it is so far inconclusive how and why engagement and disengagement evolve over time. Using person-centered methods, sequence, transition, and covariate analysis, we examined a large dataset of 18 consecutive courses of 245 students over a full program. We identified three engagement states (active, average, and disengaged), as well as three distinct longitudinal engagement trajectories (engaged, fluctuating, and mostly disengaged). Taken together, our results showed that engagement trajectories are rather stable over time conforming to the universal dynamics of complex systems. Engaged students were driven by course materials, their achievement, and their previous engaged states (momentum). Most importantly, our results offer a novel theoretical grounding for the understanding of disengagement which has so far remained unexplained. According to our results, disengagement follows the dynamics of a complex system where stability does not require a hard-wired causal mechanism but rather, it is an attractor state that pulls the system to settle in (inertia). Thus, disengagement becomes a hard to change equilibrium state for those students t (or a stuck state).

Dendritic excitability controls overdispersion.

The brain is an intricate assembly of intercommunicating neurons whose input-output function is only partially understood. The role of active dendrites in shaping spiking responses, in particular, is unclear. Although existing models account for active dendrites and spiking responses, they are too complex to analyze analytically and demand long stochastic simulations. Here we combine cable and renewal theory to describe how input fluctuations shape the response of neuronal ensembles with active dendrites. We found that dendritic input readily and potently controls interspike interval dispersion. This phenomenon can be understood by considering that neurons display three fundamental operating regimes: one mean-driven regime and two fluctuation-driven regimes. We show that these results are expected to appear for a wide range of dendritic properties and verify predictions of the model in experimental data. These findings have implications for the role of interspike interval dispersion in learning and for theories of attractor states.

Multistability in neural systems with random cross-connections.

Neural circuits with multiple discrete attractor states could support a variety of cognitive tasks according to both empirical data and model simulations. We assess the conditions for such multistability in neural systems using a firing rate model framework, in which clusters of similarly responsive neurons are represented as single units, which interact with each other through independent random connections. We explore the range of conditions in which multistability arises via recurrent input from other units while individual units, typically with some degree of self-excitation, lack sufficient self-excitation to become bistable on their own. We find many cases of multistability-defined as the system possessing more than one stable fixed point-in which stable states arise via a network effect, allowing subsets of units to maintain each others' activity because their net input to each other when active is sufficiently positive. In terms of the strength of within-unit self-excitation and standard deviation of random cross-connections, the region of multistability depends on the response function of units. Indeed, multistability can arise with zero self-excitation, purely through zero-mean random cross-connections, if the response function rises supralinearly at low inputs from a value near zero at zero input. We simulate and analyze finite systems, showing that the probability of multistability can peak at intermediate system size, and connect with other literature analyzing similar systems in the infinite-size limit. We find regions of multistability with a bimodal distribution for the number of active units in a stable state. Finally, we find evidence for a log-normal distribution of sizes of attractor basins, which produces Zipf's Law when enumerating the proportion of trials within which random initial conditions lead to a particular stable state of the system.

Quantifying the underlying landscape, entropy production and biological path of the cell fate decision between apoptosis and pyroptosis

Pyroptosis, a recently identified type of cell death, and apoptosis are fundamental and complex biological processes that underlie a multitude of diseases. However, the crosstalk between pyroptosis and apoptosis, as well as their molecular regulatory mechanisms governing decision-making, remain to be fully elucidated. In particular, comprehending how internal driving forces, including vital components of life such as proteins and reactions, collaborate with the environment to dictate cell fate remains an ongoing challenge. To address these issues, a cell death decision module model of the crosstalk between pyroptosis and apoptosis was developed. Stability analysis revealed the presence of three steady-state attractors within the death decision system: the apoptosis state attractor, the pyroptosis state attractor, and the concurrence state attractor. Landscape theory was employed to study the stochastic dynamic and global stability of the death decision system, allowing us to quantitatively describe the uncertainty of cell death decisions by measuring the production of Shannon entropy. In addition, we identified the dominant kinetic paths among different death mode attractors. We found that the dominant kinetic paths between different cell death modes usually do not pass through the minimum potential point. Through quantifying the underlying driving force of the system's dynamics, we determined that this phenomenon is attributed to the dependence of the driving force in non-equilibrium systems on both the gradient force and the curl force. In summary, this study offers a natural and physical groundwork for understanding the crosstalk network between pyroptosis and apoptosis, providing valuable insights and therapeutic strategies for the regulation of cell death modes in mammals.

Drive-specific selection in multistable mechanical networks.

Systems with many stable configurations abound in nature, both in living and inanimate matter, encoding a rich variety of behaviors. In equilibrium, a multistable system is more likely to be found in configurations with lower energy, but the presence of an external drive can alter the relative stability of different configurations in unexpected ways. Living systems are examples par excellence of metastable nonequilibrium attractors whose structure and stability are highly dependent on the specific form and pattern of the energy flow sustaining them. Taking this distinctively lifelike behavior as inspiration, we sought to investigate the more general physical phenomenon of drive-specific selection in nonequilibrium dynamics. To do so, we numerically studied driven disordered mechanical networks of bistable springs possessing a vast number of stable configurations arising from the two stable rest lengths of each spring, thereby capturing the essential physical properties of a broad class of multistable systems. We found that there exists a range of forcing amplitudes for which the attractor states of driven disordered multistable mechanical networks are fine-tuned with respect to the pattern of external forcing to have low energy absorption from it. Additionally, we found that these drive-specific attractor states are further stabilized by precise matching between the multidimensional shape of their orbit and that of the potential energy well they inhabit. Lastly, we showed evidence of drive-specific selection in an experimental system and proposed a general method to estimate the range of drive amplitudes for drive-specific selection.