Dynamical Systems Perspective Research Articles

An Ecological Perspective on Classroom‐Based Assessment

AbstractClassroom‐based assessment (CBA) takes place in learning environments influenced by myriad individual and contextual factors. Nevertheless, factors related to individual differences and learner psychology are seldom considered in creating instructional environments designed to facilitate learners' use of CBA. This article introduces the concept of language assessment ecology (LAE)—a dynamic classroom environment where learners' needs are addressed through deliberate and informed orchestration of a language learning environment so that learners can make effective use of assessment for their learning. Informed by Ecological Systems Theory, we postulate that LAE is a multi‐layered system, where learners' engagement with CBA is an outcome of alignment between learning contexts and learners' cognitive‐psychological needs. At the outset of this article, we provide a review of current CBA frameworks to underscore the merits of LAE. Contextual and learner variables that need to be considered in an LAE are then identified and discussed. From a complex dynamic systems perspective, the versatility and complexity of the interplay among these variables will be stressed. The article concludes with the implications of LAE for conducting CBA research.

Continuous-time modeling of financial returns based on Limit Order Book data

The Limit Order Book (LOB) of a financial security contains the list of buy and sell orders placed by traders on a single or across many exchanges for a given stock. As such, the amount of information contained in the LOB is much richer than that contained in the time history of the mean price, so it can potentially be exploited to model and predict more accurately the future returns. As far as we are aware, this work offers - for the first time - a dynamical systems perspective on the latter modeling problem, leading to a two-fold contribution: (i) we will define a new regressor, called Base Imbalance, and we will show that its predictive potential is more significant than the ones usually employed in the literature; (ii) we will discuss that the most suitable way to derive a model of the LOB dynamics is via continuous-time system identification, due to the event-based nature of the phenomenon at hand. The effectiveness of the proposed modeling strategy to be used in trading policies will be illustrated by means of a benchmark experimental data.

In Tune? Multimodal Mother-Child Interpersonal Coordination During Early Childhood’

ABSTRACT A complex dynamic systems perspective was applied to explore how mother and child mutually shape interpersonal coordination. Applying a microanalytic design, this study examined the moment-to-moment interaction behavior of 39 Dutch mothers and their three- and four-year-old children (53.8% girls, predominantly White) during a collaboration task. Fine-grained time-series data were extracted about the verbal, affective, and body movement modalities. Research Findings: Cross-recurrence quantification analysis showed that mothers and children were coupled within all three modalities. Recurrent behaviors were found with varying delays, spanning from the immediate to the entire length of the interaction. Many of the interactions were characterized by a certain degree of patternedness, whereby the amount of patternedness varied substantially between dyads. Measures of interpersonal coordination were not associated between modalities. Practice or Policy: Next to the content of interaction behavior (e.g., what a parent actually says), practitioners should also consider how behaviors of a mother and her child vary together. Thereby, an appraisal of the caregiver–child relationship should not merely focus on caregiving behavior, but acknowledge the active and autonomous involvement of the child. It remains to be investigated how different patterns of interpersonal coordination may serve as a diagnostic marker of (mal)adaptive child development.

A Nonlinear Dynamic Approach of the Notion of Interaction.

Although it is not so obvious reading many of the interactionist works, interactionist theories can be tightly linked with a nonlinear dynamic approach of the psychological and social processes. The mathematical theory of dynamic systems (DST) could offer a more systematic conceptual and methodological outlook over the notion of interaction. From a DST perspective, interaction may be conceived as an interdependent continuous evolution in time of two or more dynamic variables, which are paradoxically simultaneously separated (as independent sources of variation), and undistinguishable, being united in a new, emergent, source of variation. This conception differs from the popular conception of the interaction as a succession of action and reaction. The key notion that, from a dynamic systems perspective, is linked with interaction is that of coupling, which is rarely used in the interactionist works. Future studies should specify the link between the dynamic approach of interaction and action theories.

Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks

The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infected individuals to an endemic state. Here, we study this transition, from the perspective of dynamical systems, for a discrete-time compartmental epidemic model known as Microscopic Markov Chain Approach, whose applicability for forecasting future scenarios of epidemic spreading has been proved very useful during the COVID-19 pandemic. We show that there is an endemic state which is stable and a global attractor and that its existence is a consequence of a transcritical bifurcation. This mathematical analysis grounds the results of the model in practical applications.

Complexity of locomotion activities in an outside-of-the-lab wearable motion capture dataset.

Gait complexity is widely used to understand risk factors for injury, rehabilitation, the performance of assistive devices, and other matters of clinical interest. We analyze the complexity of out-of-the-lab locomotion activities via measures that have previously been used in gait analysis literature, as well as measures from other domains of data analysis. We categorize these broadly as quantifying either the intrinsic dimensionality, the variability, or the regularity, periodicity, or self-similarity of the data from a nonlinear dynamical systems perspective. We perform this analysis on a novel full-body motion capture dataset collected in out-of-the-lab conditions for a variety of indoor environments. This is a unique dataset with a large amount (over 24 h total) of data from participants behaving without low-level instructions in out-of-the-lab indoor environments. We show that reasonable complexity measures can yield surprising, and even profoundly contradictory, results. We suggest that future complexity analysis can use these guidelines to be more specific and intentional about what aspect of complexity a quantitative measure expresses. This will become more important as wearable motion capture technology increasingly allows for comparison of ecologically relevant behavior with lab-based measurements.

Language learners’ emotional dynamics: insights from a Q methodology intensive single-case study

ABSTRACT Learner emotions represent sudden, dynamic, and complex adaptations to the language classroom environment. Recent Second Language Acquisition research calls for a more holistic perspective in approaching classroom emotions, one that considers emotional variations between and across learners, and which foregrounds the interconnections among emotions and between emotions and the learning environment. This paper approaches emotions from a complex dynamic systems perspective and investigates the classroom emotions of five university students of Korean as a foreign language using a Q methodology intensive single-case study design. Overall results show that students have sometimes similar, sometimes different emotional reactions depending on classroom events, indicating different levels of interaction between a learner’s emotional system and other individual characteristics. Additionally, a more fine-grained analysis at the level of individual learners reveals clusters of emotions triggered by the same event and foregrounds the relevance of epistemic emotions for instructed foreign language learning. The results are discussed focusing on new hypotheses to inform future SLA emotion research and classroom practices.

Multifaceted characteristics of aridity changes and causal mechanisms in Chinese drylands

The water cycle is accelerating in the context of global warming. However, how the multifaceted characteristics of aridity, particularly atmospheric, hydrological, and ecological drying, change and interact with each other are largely unknown. A gap we bridged was discovering the causal relationships underlying the atmosphere-hydrosphere-biosphere nexus from the nonlinear dynamic system perspective based on convergent cross mapping (CCM). Dryland area in China has expanded since 1982, while the vegetation greenness indicated by leaf area index has been increasing during the same period. The results showed that the causality among atmospheric, hydrological, and ecological drying in different subtypes of drylands was different. In arid and semi-arid regions: vegetation changes were mainly driven by soil moisture (SM) and vapor pressure deficit (VPD), and VPD regulated SM. In hyper-arid and dry sub-humid areas: VPD dominated vegetation changes. VPD increases did not contribute to SM loss under the intense water stress in hyper-arid regions, as the soil water supply cannot meet the atmospheric water demand. In dry sub-humid areas, human disturbances have attenuated the dependence of vegetation changes on SM variability. This research pioneers complex nonlinear dynamic analyses on the multifaceted characteristics of ecosystems, which can deepen our understanding of atmosphere-vegetation-soil interactions in drylands and guide the sustainable management of dryland ecosystems in China and elsewhere.

Greater Climate Sensitivity and Variability on TRAPPIST-1e than Earth

The atmospheres of rocky exoplanets are close to being characterized by astronomical observations, in part due to the commissioning of the JWST. These observations compel us to understand exoplanetary atmospheres, in the voyage to find habitable planets. With this aim, we investigate the effect that CO2 partial pressure (pCO2) has on exoplanets’ climate variability, by analyzing results from ExoCAM model simulations of the tidally locked TRAPPIST-1e exoplanet, an Earth-like aqua-planet, and Earth itself. First, we relate the differences between the planets to their elementary parameters. Then, we compare the sensitivity of the Earth analog and TRAPPIST-1e’s surface temperature and precipitation to pCO2. Our simulations suggest that the climatology and extremes of TRAPPIST-1e’s temperature are ∼1.5 times more sensitive to pCO2 relative to Earth. The precipitation sensitivity strongly depends on the specific region analyzed. Indeed, the precipitation near mid-latitude and equatorial substellar regions of TRAPPIST-1e is more sensitive to pCO2, and the precipitation sensitivity is ∼2 times larger in TRAPPIST-1e. A dynamical systems perspective, which provides information about how the atmosphere evolves in phase space, provides additional insights. Notably, an increase in pCO2 results in an increase in atmospheric persistence on both planets, and the persistence of TRAPPIST-1e is more sensitive to pCO2 than Earth. We conclude that the climate of TRAPPIST-1e may be more sensitive to pCO2, particularly on its dayside. This study documents a new pathway for understanding the effect that varying planetary parameters have on the climate variability of potentially habitable exoplanets and on Earth.

Versifying adversity: Using dramaturgically framed poetic inquiry to explore complexity in the second language learning experience

Over the past 15 years, research in the field of second language learning motivation has been dominated by the second language (L2) motivational self system, conceptualizing motivation as a combination of the ideal L2 self, ought-to L2 self, and L2 learning experience. Despite the analytical strength demonstrated by the self components of the L2 motivational self system, the influential role of the L2 learning experience component is still in need of greater elucidation. Using a hybridized research approach combining a complex dynamic systems (CDS) perspective with dramaturgical coding and poetic inquiry, we unpack a Japanese undergraduate student's L2 learning experience. Taking the learner as both a complex system and a situated actor, key themes are identified and explored as attractor states. Humanizing what can often be an impersonal perspective, dramaturgically framed poetic inquiry is seen to add analytical power to the CDS perspective and afford its artistic and evocative representation.

It's about time: Linking dynamical systems with human neuroimaging to understand the brain.

Most human neuroscience research to date has focused on statistical approaches that describe stationary patterns of localized neural activity or blood flow. While these patterns are often interpreted in light of dynamic, information-processing concepts, the static, local, and inferential nature of the statistical approach makes it challenging to directly link neuroimaging results to plausible underlying neural mechanisms. Here, we argue that dynamical systems theory provides the crucial mechanistic framework for characterizing both the brain's time-varying quality and its partial stability in the face of perturbations, and hence, that this perspective can have a profound impact on the interpretation of human neuroimaging results and their relationship with behavior. After briefly reviewing some key terminology, we identify three key ways in which neuroimaging analyses can embrace a dynamical systems perspective: by shifting from a local to a more global perspective, by focusing on dynamics instead of static snapshots of neural activity, and by embracing modeling approaches that map neural dynamics using "forward" models. Through this approach, we envisage ample opportunities for neuroimaging researchers to enrich their understanding of the dynamic neural mechanisms that support a wide array of brain functions, both in health and in the setting of psychopathology.

A new hybrid optimizer for stochastic optimization acceleration of deep neural networks: Dynamical system perspective

Stochastic optimization acceleration is extremely significant and challenging for deep neural networks (DNNs). In recent years, several novel proportional-integral–differential-based (PID-based) optimizers have been proposed to speed up the optimization by alleviating the oscillation behavior of stochastic gradient descent with momentum (SGD-M), yet lacked theoretical analysis. Along this line of research, this paper adopts dynamical system theory to design a new hybrid optimizer and present theoretical analysis. Firstly, it is found that DNN optimization is equivalent to a discrete time dynamical system. Building upon the equivalence, high order augmented dynamical system viewpoint is utilized to design a PI-like optimizer for ensuring high accuracy, which is more stable than SGD-M. Then, hybrid dynamical system viewpoint is employed to improve the PI-like optimizer as a new hybrid form for suppressing oscillation and accelerating optimization. Lyapunov method, Taylor series, matrix theory and equilibrium are combined to theoretically investigate the convergence and the oscillation of loss function, showing that the proposed hybrid optimizer can alleviate oscillation, boost optimization speed, and maintain high accuracy. In theoretical analyses, explicit conditions of hyper-parameters that guarantee training stability are calculated and presented, practically guiding the adjustment of hyper-parameters and promoting the application of hybrid optimizer. Experiments are presented on three commonly used benchmark datasets, i.e., MNIST, CIFAR10 and CIFAR100, demonstrating that the hybrid optimizer obtains up to 42% acceleration with competitive accuracy relative to state-of-the-art optimizers. In short, this paper not only presents a new hybrid optimizer for accelerating optimization, but also provides a novel, theoretical and systematic perspective to find and analyze new optimizer for DNNs.

Dynamic analysis of aeroacoustic hysteresis of a low-Reynolds-number airfoil

This work reports that the frequency spectra can exhibit different behavior at the same flow condition, which constitutes the hysteresis phenomenon. Results are analyzed from the perspective of modern dynamical systems. The boundary layer is viewed as the forced oscillator, with the acoustic waves being the forcing mechanism. Both the bifurcation theory and the Poincar\'e section are introduced to investigate the dynamic process when freestream velocity changes.

On finite time singularities in scalar field dark energy models based in the RS-II Braneworld

The quest of deciphering the true nature of dark energy has proven to be one of the most exciting in recent times in cosmology. Various ideas have been put forward in this regard besides the usual cosmological constant approach, ranging from scalar field based models like Quintessence and Phantom dark energy to various modified gravity approaches as well. A very interesting idea then is to consider scalar field dark energy models in quantum gravitationally corrected cosmologies with the RS-II Braneworld being one of the most well known in this regard. So in this work, we consider RS-II Braneworld based scalar field dark energy models and try to look out for the existence of finite time singularities in these regimes both through a dynamical system perspective, for which we employ the Goriely–Hyde singularity analysis method, and a physical perspective. Our approach is general in the sense that it is not limited to any particular class of potentials or for any constrained parameter region for the brane tension and is valid for both Quintessence and phantom dark energy regimes. We firstly show through Goriely–Hyde procedure that finite time singularities can exist in these models for a limited set of initial conditions and that this result would hold irrespective of any consideration given to the swampland dS conjecture. We then discuss the physical nature of the singularities that can occur in this regime, where we use a well motivated ansatz for the Hubble parameter and show that these models of dark energy can allow for weak singularities like those of Type III and Type IV and can also allow for strong singularities like the Big Rip (Type I).

From the Ravine Method to the Nesterov Method and Vice Versa: A Dynamical System Perspective

We revisit the Ravine method of Gelfand and Tsetlin from a dynamical system perspective, study its convergence properties, and highlight its similarities and differences with the Nesterov accelerated gradient method. The two methods are closely related. They can be deduced from each other by reversing the order of the extrapolation and gradient operations in their definitions. They benefit from similar fast convergence of values and convergence of iterates for general convex objective functions. We will also establish the high resolution ODE of the Ravine and Nesterov methods and reveal an additional geometric damping term driven by the Hessian for both methods. This will allow us to prove fast convergence toward zero of the gradients not only for the Ravine method but also for the Nesterov method for the first time. In the strongly convex case, we show linear convergence for the Ravine method at an optimal rate. We also highlight connections to other algorithms resulting from more subtle discretization schemes and finally describe a Ravine version of the proximal-gradient algorithms for general structured smooth + nonsmooth convex optimization problems.

A Per-second Investigation of the Interconnectedness between Linguistic and Cognitive Factors Underlying L2 Willingness to Communicate

Willingness to communicate (WTC) research has recently witnessed a paradigm shift with the more recent studies looking at the shifting and dynamic nature of the variable. A growing body of literature has interpreted such dynamicity from a complex dynamic systems (CDS) perspective. The theory of CDS has four basic properties, one of which, and the focus of this study, is the interconnectedness among subsystems. This property mainly involves the interplay amongst parts of a system, which interact and influence one another, determining the subsequent dynamics in the system. This qualitative, exploratory study employed an idiodynamic method to investigate the interconnectedness of the cognitive and linguistic factors underlying second language (L2) WTC. To this end, 20 participants completed four three-minute monologic speaking tasks while being video-recorded. Immediately after, they viewed their recordings, rated their WTC moment by moment, and explained the WTC changes in stimulated recall interviews. The interviews were coded, and instances where WTC was affected by cognitive and linguistic factors were identified and analysed. Three patterns of interconnectedness emerged: (1) WTC and linguistic factors; (2) WTC and cognitive factors; and (3) WTC, and linguistic and cognitive factors. Findings provide a clearer account of the interconnectedness property in the WTC system, lending support to viewing WTC as a CDS. The article highlights the importance of self-perception and availability of content message, in addition to the above factors, and concludes with a brief discussion of the pedagogical implications for L2 classroom.

Traveling pulses with oscillatory tails, figure-eight-like stack of isolas, and dynamics in heterogeneous media

The interplay between 1D traveling pulses with oscillatory tails (TPOs) and heterogeneities of the bump type is studied to formulate a generalized three-component FitzHugh–Nagumo system of equations. We present that stationary pulses with oscillatory tails (SPOs) form a “snaky” structure in homogeneous spaces and then TPO branches form a “figure-eight-like stack of isolas” located adjacent to the snaky structure of the SPO. Here, we adopt input resources such as the voltage-difference as a bifurcation parameter. A drift bifurcation from the SPO to TPO is observed by introducing another parameter at which these two solution sheets merge. In contrast to the monotone tail case, in the heterogeneous problem, a nonlocal interaction appears between the TPO and the heterogeneity, creating infinitely many saddle solutions and finitely many stable stationary solutions distributed across the line. The response of the TPO shows various dynamics including pinning and depinning processes along with penetration (PEN) and rebound (REB). The stable/unstable manifolds of these saddles interact with the TPO in a complex manner, creating a subtle dependence on the initial condition, and a difficulty to predict the behavior after collision even in 1D space. For the 1D case, a systematic global exploration of solution branches induced by heterogeneities (heterogeneity-induced-ordered patterns; HIOPs) reveals that HIOPs contain all the asymptotic states after collision to facilitate the prediction of the solution results without solving the PDEs. The reduction method of finite-dimensional system enables the clarification of the detailed mechanism of the transitions from PEN to pinning and pinning to REB based on a dynamical system perspective. Consequently, the basin boundary between two distinct outputs against the heterogeneities yields infinitely many successive reconnections of heteroclinic orbits among those saddles when the strength of heterogeneity increases. This causes the aforementioned subtle dependence of initial condition.

Inferring structural and dynamical properties of gene networks from data with deep learning.

The reconstruction of gene regulatory networks (GRNs) from data is vital in systems biology. Although different approaches have been proposed to infer causality from data, some challenges remain, such as how to accurately infer the direction and type of interactions, how to deal with complex network involving multiple feedbacks, as well as how to infer causality between variables from real-world data, especially single cell data. Here, we tackle these problems by deep neural networks (DNNs). The underlying regulatory network for different systems (gene regulations, ecology, diseases, development) can be successfully reconstructed from trained DNN models. We show that DNN is superior to existing approaches including Boolean network, Random Forest and partial cross mapping for network inference. Further, by interrogating the ensemble DNN model trained from single cell data from dynamical system perspective, we are able to unravel complex cell fate dynamics during preimplantation development. We also propose a data-driven approach to quantify the energy landscape for gene regulatory systems, by combining DNN with the partial self-consistent mean field approximation (PSCA) approach. We anticipate the proposed method can be applied to other fields to decipher the underlying dynamical mechanisms of systems from data.

Complexity in Advising for Language Learning: From Theory to Practice

Research on advising for language learning has benefited from various theoretical frameworks, such as sociocultural theory, ecological theory and, in recent years, the theory of complex dynamic systems. With its holistic perspective on second language acquisition, the theory of complex dynamic systems helps integrate the manifold aspects involved in language development. It recognizes the interrelation of individual and social aspects, of internal and contextual factors, and places the focus on the various, interconnected/ inseparable dimensions of the language learning process. In this paper I will first illustrate some principles of complex dynamic systems theory and their impact on research on second language acquisition and language learner autonomy. Then, I will focus on advising for language learning, as a means of supporting learners as they become more autonomous and they implement change in their unique learning trajectories. Drawing on research on advising from the perspective of complex dynamic systems, I will show how this metatheory helps expand our understanding of advising beyond its conceptualization as a one-to-one interaction between a learner (advisee) and an advisor, by integrating the reflective dialogue between advisor and advisee into additional processes in which both advisor and advisee are involved. Finally, I will reflect on some implications for my own advising practice.

A Dynamical Systems Perspective to Characterize the El Niño Diversity in Spatiotemporal Patterns

El Niño is the long-lasting anomalous warming of sea surface temperature (SST) and surface air temperature (SAT) over the tropical Pacific. Each El Niño event has its unique impact on the overlaying atmosphere, where the warming exhibits diversity in spatiotemporal patterns. It still remains an open question for discriminating the El Niño diversity, since the single area-averaging SST index often fails to distinguish the impact of the event diversity, which is partially due to the nonlinear and non-uniform variations of the warming patterns. Here, we introduced the Dynamical Systems metrics (DSMs) to measure instantaneous dimensions and persistence of the SAT warming patterns over the tropical Pacific. Our results show that different SAT warming patterns can be discriminated by their corresponding values of dimension and persistence, then the central Pacific and eastern Pacific El Niño events can be discriminated by DSM. Particularly, through the analyses of El Niño events, we can interpret the physical meaning of DSM parameters applied to the space-time SAT field: an instantaneous dimension reflects whether the sub-regions of the SAT field are consistently varying and to what degree the spatial pattern of anomalies is homogeneous, while the instantaneous persistence indicates how long an anomalous SAT pattern can be maintained. This work analyzes the spatiotemporal variability of El Niño from a dynamical system perspective, and DSM may also serve as a useful tool to study extreme events related to SST anomalies.