Minimal motifs for habituating systems.

Habituation-a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld-is universally observed in living systems from animals to unicellular organisms. Despite its prevalence, generic mechanisms for this fundamental form of learning remain poorly defined. Drawing inspiration from prior work on systems that respond adaptively to step inputs, we study habituation from a nonlinear dynamics perspective. This approach enables us to formalize classical hallmarks of habituation that have been experimentally identified in diverse organisms and stimulus scenarios. We use this framework to investigate distinct dynamical circuits capable of habituation. In particular, we show that driven linear dynamics of a memory variable with static nonlinearities acting at the input and output can implement numerous hallmarks in a mathematically interpretable manner. This work establishes a foundation for understanding the dynamical substrates of this primitive learning behavior and offers a blueprint for the identification of habituating circuits in biological systems.

Challenges and Approaches in the Study of Neural Entrainment.

When exposed to rhythmic stimulation, the human brain displays rhythmic activity across sensory modalities and regions. Given the ubiquity of this phenomenon, how sensory rhythms are transformed into neural rhythms remains surprisingly inconclusive. An influential model posits that endogenous oscillations entrain to external rhythms, thereby encoding environmental dynamics and shaping perception. However, research on neural entrainment faces multiple challenges, from ambiguous definitions to methodological difficulties when endogenous oscillations need to be identified and disentangled from other stimulus-related mechanisms that can lead to similar phase-locked responses. Yet, recent years have seen novel approaches to overcome these challenges, including computational modeling, insights from dynamical systems theory, sophisticated stimulus designs, and study of neuropsychological impairments. This review outlines key challenges in neural entrainment research, delineates state-of-the-art approaches, and integrates findings from human and animal neurophysiology to provide a broad perspective on the usefulness, validity, and constraints of oscillatory models in brain-environment interaction.

Global stability of coexistence equilibria for n-species models of facultative mutualism.

We further pursue an investigation on an abstract model characterizing the dynamics of a general class of n-species facultative mutualisms that was initiated in Georgescu et al. (2017),establishing biologically relevant sufficient conditions for the global asymptotic stability of the coexistence equilibria. These conditions are given in terms of per-species limits of growth-to-loss ratios computed at higher population densities, complemented by either monotonicity or sublinearity inequalities, and are observed to hold for n-species versions of mutualistic models in current use. The specific modelling details that require either of these conditions being satisfied are outlined and discussed. As mutualisms can enhance species diversification and facilitate stable coexistence via a plethora of mechanisms, it is then important to understand the stability of speciose mutualisms, our results being of potential interest to theoretical ecologists studying the coexistence of many interacting species and to conservationists aiming for rare species preservation.

EnhancerNet: a predictive model of cell identity dynamics through enhancer selection.

Understanding how cell identity is encoded by the genome and acquired during differentiation is a central challenge in cell biology. I have developed a theoretical framework called EnhancerNet, which models the regulation of cell identity through the lens of transcription factor-enhancer interactions. I demonstrate that autoregulation in these interactions imposes a constraint on the model, resulting in simplified dynamics that can be parameterized from observed cell identities. Despite its simplicity, EnhancerNet recapitulates a broad range of experimental observations on cell identity dynamics, including enhancer selection, cell fate induction, hierarchical differentiation through multipotent progenitor states and direct reprogramming by transcription factor overexpression. The model makes specific quantitative predictions, reproducing known reprogramming recipes and the complex haematopoietic differentiation hierarchy without fitting unobserved parameters. EnhancerNet provides insights into how new cell types could evolve and highlights the functional importance of distal regulatory elements with dynamic chromatin in multicellular evolution.

Investigation of a Camera-Based Contactless Pulse Oximeter with Time-Division Multiplex Illumination Applied on Piglets for Neonatological Applications.

(1) Objective: This study aims to lay a foundation for noncontact intensive care monitoring of premature babies. (2) Methods: Arterial oxygen saturation and heart rate were measured using a monochrome camera and time-division multiplex controlled lighting at three different wavelengths (660 nm, 810 nm and 940 nm) on a piglet model. (3) Results: Using this camera system and our newly designed algorithm for further analysis, the detection of a heartbeat and the calculation of oxygen saturation were evaluated. In motionless individuals, heartbeat and respiration were separated clearly during light breathing and with only minor intervention. In this case, the mean difference between noncontact and contact saturation measurements was 0.7% (RMSE = 3.8%, MAE = 2.93%). (4) Conclusions: The new sensor was proven effective under ideal animal experimental conditions. The results allow a systematic improvement for the further development of contactless vital sign monitoring systems. The results presented here are a major step towards the development of an incubator with noncontact sensor systems for use in the neonatal intensive care unit.

Exploring Limit Cycles of Differential Equations through Information Geometry Unveils the Solution to Hilbert's 16th Problem.

The detection of limit cycles of differential equations poses a challenge due to the type of the nonlinear system, the regime of interest, and the broader context of applicable models. Consequently, attempts to solve Hilbert's sixteenth problem on the maximum number of limit cycles of polynomial differential equations have been uniformly unsuccessful due to failing results and their lack of consistency. Here, the answer to this problem is finally obtained through information geometry, in which the Riemannian metrical structure of the parameter space of differential equations is investigated with the aid of the Fisher information metric and its scalar curvature R. We find that the total number of divergences of |R| to infinity provides the maximum number of limit cycles of differential equations. Additionally, we demonstrate that real polynomial systems of degree n≥2 have the maximum number of 2(n-1)(4(n-1)-2) limit cycles. The research findings highlight the effectiveness of geometric methods in analyzing complex systems and offer valuable insights across information theory, applied mathematics, and nonlinear dynamics. These insights may pave the way for advancements in differential equations, presenting exciting opportunities for future developments.

Dynamical systems theory applied to short walking trials.

Human walking is an extremely complex neuromuscular activity whose simplicity disappears when an attempt is made to provide a quantitative description of the process. The dynamical systems theory provides a framework for analyzing the stability and chaotic nature of dynamical systems, employing Floquet multipliers (FM) and long and short-term Lyapunov exponents (LE), respectively. This report compares FM and LE from three methods: method A (false nearest neighbors and numerical approximation), method B (false nearest neighbors and semi-analytical technique) and method C (singular value decomposition and semi-analytical technique). Data from 33 healthy older adults with no history of falls were used to explain the dynamic system. A surrogate center of mass trajectory was calculated for the analysis of sway in the transverse plane. Results revealed methodological differences in LE and FM calculations with semi-analytical solutions providing closer approximations to observed gait behavior. The long-term LE from Methods A and B were similar, but other LE pairings differed. Method A's short-term LE indicated chaotic gaits for all subjects, while long-term LE from Methods A and B indicated chaos for half the subjects. Method C showed non-chaotic gait for most subjects. Method B's FM indicated over 30% of subjects had unstable gait. Method C yielded values of LE and FM that most closely matched the subjects' gait patterns. This study offers a methodological foundation for gait analysis using short time-series data, facilitating deeper insights into both stability and chaos within gait dynamics.

An approximate solution of the SLIP model under the regime of linear angular dynamics during stance and the stability of symmetric periodic running gaits.

Terrestrial locomotion is a complex phenomenon that is often linked to the survival of an individual and of an animal species. Mathematical models seek to express in quantitative terms how animals move, but this is challenging because the ways in which the nervous and musculoskeletal systems interact to produce body movement is not completely understood. Models with many variables tend to lack biological interpretability and describe the motion of an animal with too many independent degrees of freedom. Instead, reductionist models aim to describe the essential features of a gait with the smallest number of variables, often concentrating on the center of mass dynamics. In particular, spring-mass models have been successful in extracting and describing important characteristics of running. In this paper, we consider the spring loaded inverted pendulum model under the regime of constant angular velocity, small compression, and small angle swept during stance. We provide conditions for the asymptotic stability of periodic trajectories for the full range of parameters. The hypothesis of linear angular dynamics during stance is successfully tested on publicly available human data of individuals running on a treadmill at different velocities. Our analysis highlights a novel bifurcation phenomenon for varying Froude number: there are periodic trajectories of the spring loaded inverted pendulum model that are stable only in a restricted range of Froude numbers, while they become unstable for smaller or larger Froude numbers.

Exploring chaos and ergodic behavior of an inductorless circuit driven by stochastic parameters.

There exist extensive studies on periodic and random perturbations of various smooth maps investigating their dynamics. Unlike smooth maps, non-smooth maps are yet to be studied extensively under a stochastic regime. This paper presents a stochastic piecewise-smooth map derived from a simple inductorless switching circuit. The stochasticity is introduced in parameter values. The distribution of the parameter values is bounded and randomly selected from uniform and triangular distributions and ranges between high and low bifurcation parameter values of the deterministic map. Due to this inherent stochasticity in parameter values, the time evolution of the state variable cannot be predicted at a specific time instant. We observe that the state variable exhibits completely ergodic behavior when the minimum value of the parameter is the same as the minimum bifurcation parameter of the deterministic system. However, the ensemble average of the state variable converges to a fixed value. The system demonstrates nonchaotic behavior for a particular range of parameter values but the deterministic map in that bifurcation range shows interplay between chaos and periodic orbits. The values of Lyapunov exponents decrease monotonically with increased asymmetry of the distribution from which the bifurcation parameter values are chosen. We determine the probability density function of the stochastic map and verify its invariance under initial conditions. The most noteworthy result is the disappearance of chaotic behavior when the lower range of the distribution is varied while maintaining a fixed upper threshold for a particular distribution, even though the deterministic map exhibits an array of periodic and chaotic behaviors within the range. As the period-incrementing cascade with chaotic inclusion only occurs in nonsmooth maps, this paper numerically shows the stochasticity of a piecewise-smooth map obtained from a practical system for the first time where randomness is introduced in the parameter space.

Neural Dynamic Principles for an Intentional Embodied Agent.

How situated embodied agents may achieve goals using knowledge is the classical question of natural and artificial intelligence. How organisms achieve this with their nervous systems is a central challenge for a neural theory of embodied cognition. To structure this challenge, we borrow terms from Searle's analysis of intentionality in its two directions of fit and six psychological modes (perception, memory, belief, intention-in-action, prior intention, desire). We postulate that intentional states are instantiated by neural activation patterns that are stabilized by neural interaction. Dynamic instabilities provide the neural mechanism for initiating and terminating intentional states and are critical to organizing sequences of intentional states. Beliefs represented by networks of concept nodes are autonomously learned and activated in response to desired outcomes. The neural dynamic principles of an intentional agent are demonstrated in a toy scenario in which a robotic agent explores an environment and paints objects in desired colors based on learned color transformation rules.

Modeling engagement with a digital behavior change intervention (HeartSteps II): An exploratory system identification approach.

OBJECTIVE: Digital behavior change interventions (DBCIs) are feasibly effective tools for addressing physical activity. However, in-depth understanding of participants' long-term engagement with DBCIs remains sparse. Since the effectiveness of DBCIs to impact behavior change depends, in part, upon participant engagement, there is a need to better understand engagement as a dynamic process in response to an individual's ever-changing biological, psychological, social, and environmental context. METHODS: The year-long micro-randomized trial (MRT) HeartSteps II provides an unprecedented opportunity to investigate DBCI engagement among ethnically diverse participants. We combined data streams from wearable sensors (Fitbit Versa, i.e., walking behavior), the HeartSteps II app (i.e. page views), and ecological momentary assessments (EMAs, i.e. perceived intrinsic and extrinsic motivation) to build the idiographic models. A system identification approach and a fluid analogy model were used to conduct autoregressive with exogenous input (ARX) analyses that tested hypothesized relationships between these variables inspired by Self-Determination Theory (SDT) with DBCI engagement through time. RESULTS: Data from 11 HeartSteps II participants was used to test aspects of the hypothesized SDT dynamic model. The average age was 46.33 (SD=7.4) years, and the average steps per day at baseline was 5,507 steps (SD=6,239). The hypothesized 5-input SDT-inspired ARX model for app engagement resulted in a 31.75 % weighted RMSEA (31.50 % on validation and 31.91 % on estimation), indicating that the model predicted app page views almost 32 % better relative to the mean of the data. Among Hispanic/Latino participants, the average overall model fit across inventories of the SDT fluid analogy was 34.22 % (SD=10.53) compared to 22.39 % (SD=6.36) among non-Hispanic/Latino Whites, a difference of 11.83 %. Across individuals, the number of daily notification prompts received by the participant was positively associated with increased app page views. The weekend/weekday indicator and perceived daily busyness were also found to be key predictors of the number of daily application page views. CONCLUSIONS: This novel approach has significant implications for both personalized and adaptive DBCIs by identifying factors that foster or undermine engagement in an individual's respective context. Once identified, these factors can be tailored to promote engagement and support sustained behavior change over time.

Efficacy of the Sterile Insect Technique in the presence of inaccessible areas: A study using two-patch models.

The Sterile Insect Technique (SIT) is one of the sustainable strategies for the control of disease vectors, which consists of releasing sterilized males that will mate with the wild females, resulting in a reduction and, eventually a local elimination, of the wild population. The implementation of the SIT in the field can become problematic when there are inaccessible areas where the release of sterile insects cannot be carried out directly, and the migration of wild insects from these areas to the treated zone may influence the efficacy of this technique. However, we can also take advantage of the movement of sterile individuals to control the wild population in these unreachable places. In this paper, we derive a two-patch model for Aedes mosquitoes where we consider the discrete diffusion between the treated area and the inaccessible zone. We investigate two different release strategies (constant and impulsive periodic releases), and by using the monotonicity of the model, we show that if the number of released sterile males exceeds some threshold, the technique succeeds in driving the whole population in both areas to extinction. This threshold depends on not only the biological parameters of the population but also the diffusion between the two patches.

The iterative development and refinement of health psychology theories through formal, dynamical systems modelling: a scoping review and initial expert-derived 'best practice' recommendations.

This scoping review aimed to synthesise methodological steps taken by researchers in the development of formal, dynamical systems models of health psychology theories. We searched MEDLINE, PsycINFO, the ACM Digital Library and IEEE Xplore in July 2023. We included studies of any design providing that they reported on the development or refinement of a formal, dynamical systems model unfolding at the within-person level, with no restrictions on population or setting. A narrative synthesis with frequency analyses was conducted. A total of 17 modelling projects reported across 29 studies were included. Formal modelling efforts have largely been concentrated to a small number of interdisciplinary teams in the United States (79.3%). The models aimed to better understand dynamic processes (69.0%) or inform the development of adaptive interventions (31.0%). Models typically aimed to formalise the Social Cognitive Theory (31.0%) or the Self-Regulation Theory (17.2%) and varied in complexity (range: 3-30 model components). Only 3.4% of studies reported involving stakeholders in the modelling process and 10.3% drew on Open Science practices. We conclude by proposing an initial set of expert-derived 'best practice' recommendations. Formal, dynamical systems modelling is poised to help health psychologists develop and refine theories, ultimately leading to more potent interventions.

Perceptuomotor skill acquisition in a solo manual ball-and-beam task with varying accuracy requirements.

In the manual ball-and-beam task, participants have to control a ball that is rolling continuously on a long and hand-held beam. Since the task can be performed individually, in a solo action setting, as well as collaboratively, in a (dyadic) joint action setting, it allows us to investigate how joint performances arise from individual performances, which we investigate in a series of interrelated studies. Here we focused on individual skill acquisition on the ball-and-beam task in the solo action setting, with the goal to characterize the behavioral dynamics that arise from learning to couple (ball motion) perception and (beam motion) action. By moving a beam extremity up and down to manipulate the beam's inclination angle, the task's objective was to roll the ball as fast as and accurately as possible between two indicated targets on the beam. Based on research into reciprocal aiming tasks, we hypothesized that the emergent dynamics of the beam's inclination angle would be constrained by the size of the targets, such that large targets would evoke a continuous beam movement strategy, while small targets would lead to a discrete beam movement strategy. 16 participants individually practiced the task in two separate six-block sessions. Each block consisted of one trial per target-size condition (small, medium and large). Overall, the number of target hits increased over trials, due to a larger range of motion of the beam's inclination angle, a stronger correlation between the ball and beam motion and a smaller variability of the beam motion. Contrary to our expectations, target size did not appreciably affect the shape of the beam movement patterns. Instead, we found stable inter-individual differences in the movement strategies adopted that were uncorrelated with the number of target hits on a trial. We concluded that multiple movement strategies may lead to success on the task, while individual skill acquisition was characterized by the refinement of behavioral dynamics that emerged in an early stage of learning. We speculate that such differences in individual strategies on the task may affect the interpersonal coordination that arises in joint-action performances on the task.

Layer-by-layer unsupervised clustering of statistically relevant fluctuations in noisy time-series data of complex dynamical systems.

Complex systems are typically characterized by intricate internal dynamics that are often hard to elucidate. Ideally, this requires methods that allow to detect and classify in an unsupervised way the microscopic dynamical events occurring in the system. However, decoupling statistically relevant fluctuations from the internal noise remains most often nontrivial. Here, we describe "Onion Clustering": a simple, iterative unsupervised clustering method that efficiently detects and classifies statistically relevant fluctuations in noisy time-series data. We demonstrate its efficiency by analyzing simulation and experimental trajectories of various systems with complex internal dynamics, ranging from the atomic- to the microscopic-scale, in- and out-of-equilibrium. The method is based on an iterative detect-classify-archive approach. In a similar way as peeling the external (evident) layer of an onion reveals the internal hidden ones, the method performs a first detection/classification of the most populated dynamical environment in the system and of its characteristic noise. The signal of such dynamical cluster is then removed from the time-series data and the remaining part, cleared-out from its noise, is analyzed again. At every iteration, the detection of hidden dynamical subdomains is facilitated by an increasing (and adaptive) relevance-to-noise ratio. The process iterates until no new dynamical domains can be uncovered, revealing, as an output, the number of clusters that can be effectively distinguished/classified in a statistically robust way as a function of the time-resolution of the analysis. Onion Clustering is general and benefits from clear-cut physical interpretability. We expect that it will help analyzing a variety of complex dynamical systems and time-series data.

Behaviour settings, situated action and complexity theory.

In spite of the fact that Roger Barker's groundbreaking research was acclaimed sixty years ago by his contemporaries, it has all been but forgotten among recent generations of psychologists. However, in the wake of developments in dynamical systems and complexity theory, its value for understanding psychological processes in everyday life should be recognized anew. Barker's naturalistic studies of children's daily behaviours in their community revealed that their actions which initially seemed only marginally predictable at the level of individual interaction were, in fact, reliably context-dependent. These results led to the discovery that there are nested structures operating in human habitats as there are throughout the natural world. Barker's discovery of emergent eco-psychological structures, behaviour settings, that are generated from interdependent actions among individuals in the course of everyday life has yet to be fully appreciated because of the continuing dominance of linear, mechanistic models. His recognition of nested systems operating in human habitats is finally coming into its own with the current metatheoretical shift in psychology embracing dynamical models. Additionally, new understanding arises from the consideration of convergent individual developmental histories of situated action and their role in maintaining the historical dimensions of behaviour settings. This article is part of the theme issue 'People, places, things and communities: expanding behaviour settings theory in the twenty-first century'.

Local carbon reserves are insufficient for phloem terpene induction during drought in Pinus edulis in response to bark beetle-associated fungi.

Stomatal closure during drought inhibits carbon uptake and may reduce a tree's defensive capacity. Limited carbon availability during drought may increase a tree's mortality risk, particularly if drought constrains trees' capacity to rapidly produce defenses during biotic attack. We parameterized a new model of conifer defense using physiological data on carbon reserves and chemical defenses before and after a simulated bark beetle attack in mature Pinus edulis under experimental drought. Attack was simulated using inoculations with a consistent bluestain fungus (Ophiostoma sp.) of Ips confusus, the main bark beetle colonizing this tree, to induce a defensive response. Trees with more carbon reserves produced more defenses but measured phloem carbon reserves only accounted for c. 23% of the induced defensive response. Our model predicted universal mortality if local reserves alone supported defense production, suggesting substantial remobilization and transport of stored resin or carbon reserves to the inoculation site. Our results show that de novo terpene synthesis represents only a fraction of the total measured phloem terpenes in P. edulis following fungal inoculation. Without direct attribution of phloem terpene concentrations to available carbon, many studies may be overestimating the scale and importance of de novo terpene synthesis in a tree's induced defense response.

Dynamics and bifurcations in genetic circuits with fibration symmetries.

Circuit building blocks of gene regulatory networks (GRN) have been identified through the fibration symmetries of the underlying biological graph. Here, we analyse analytically six of these circuits that occur as functional and synchronous building blocks in these networks. Of these, the lock-on, toggle switch, Smolen oscillator, feed-forward fibre and Fibonacci fibre circuits occur in living organisms, notably Escherichia coli; the sixth, the repressilator, is a synthetic GRN. We consider synchronous steady states determined by a fibration symmetry (or balanced colouring) and determine analytic conditions for local bifurcation from such states, which can in principle be either steady-state or Hopf bifurcations. We identify conditions that characterize the first bifurcation, the only one that can be stable near the bifurcation point. We model the state of each gene in terms of two variables: mRNA and protein concentration. We consider all possible 'admissible' models-those compatible with the network structure-and then specialize these general results to simple models based on Hill functions and linear degradation. The results systematically classify using graph symmetries the complexity and dynamics of these circuits, which are relevant to understand the functionality of natural and synthetic cells.

Neurodynamical Computing at the Information Boundaries of Intelligent Systems.

Artificial intelligence has not achieved defining features of biological intelligence despite models boasting more parameters than neurons in the human brain. In this perspective article, we synthesize historical approaches to understanding intelligent systems and argue that methodological and epistemic biases in these fields can be resolved by shifting away from cognitivist brain-as-computer theories and recognizing that brains exist within large, interdependent living systems. Integrating the dynamical systems view of cognition with the massive distributed feedback of perceptual control theory highlights a theoretical gap in our understanding of nonreductive neural mechanisms. Cell assemblies-properly conceived as reentrant dynamical flows and not merely as identified groups of neurons-may fill that gap by providing a minimal supraneuronal level of organization that establishes a neurodynamical base layer for computation. By considering information streams from physical embodiment and situational embedding, we discuss this computational base layer in terms of conserved oscillatory and structural properties of cortical-hippocampal networks. Our synthesis of embodied cognition, based in dynamical systems and perceptual control, aims to bypass the neurosymbolic stalemates that have arisen in artificial intelligence, cognitive science, and computational neuroscience.

Lower-limb coordination changes following a 6-week training intervention that elicited enhancements to maximum velocity sprint performance.

Alterations to intra- and inter-limb coordination with improved maximal velocity performance remain largely unexplored. This study quantified within-day variability in lower-limb segmental coordination profiles during maximal velocity sprinting and investigated the modifications to coordination strategies in 15 recreationally active males following a 6-week period comprised of a multimodal training programme [intervention group (INT); n=7] or continued participation in sports (control group; n=8). The INT demonstrated a large decrease (effect size=-1.54) in within-day coordination profile variability, suggesting potential skill development. Thigh-thigh coordination modifications for the INT were characterised by an earlier onset of trail thigh reversal in early swing (26 versus 28% stride) and lead thigh reversal in late swing (76 versus 79% stride), rather than increases in overall time spent in anti-phase. Moreover, an increase in backward rotation of thigh relative to shank (effect size, 95% CIs: 0.75, 0.17 to 1.33) and shank relative to foot (0.76, -0.17 to 1.68) during late swing likely facilitated more aggressive acceleration of the limb, contributing to reduced touchdown distance and more favourable lower-limb configuration at initial ground contact. These novel findings provide empirical support for the role of longitudinal coordination modifications in improving maximal velocity performance.