Dynamical Systems Perspective Research Articles

Using State Space Grids to Quantify and Examine Dynamics of Dyadic Conversation

ABSTRACT This paper illustrates how to implement state space grid analysis for analyzing the back-and-forth multi-turn dynamics that manifest in dyadic conversations. In doing so, we contribute to a dynamic dyadic systems perspective that seeks to advance theories about individual and relational antecedents and outcomes of interpersonal communication through the articulation and study of dyadic interaction dynamics. We first review state space grid terminology, data requirements, visualizations, and quantifications, and how the use of state space grid analysis maps to conversation-related research questions. We then illustrate the application of state space grids to the examination of dyadic support conversations; specifically, we demonstrate how this method can be used to derive parameters that operationalize the use of or movement in the state space and to examine between-dyad differences in movement through the state space. Empirically, we found that conversation behavior flexibility was related to characteristics of the dyadic relationship but not to support receiver outcomes, and that our operationalizations of conversation attractors were related to neither relational characteristics nor support receiver outcomes. We conclude with a discussion of theoretical, methodological, and practical issues that researchers can consider when using state space grids in the analysis of conversation dynamics.

Statistical physics and dynamical systems perspectives on geophysical extreme events

Statistical physics and dynamical systems perspectives on geophysical extreme events

A generic shared attention mechanism for various backbone neural networks

The self-attention mechanism is crucial for enhancing various backbone neural networks’ performance. However, current methods add self-attention modules (SAMs) to each network layer without fully utilizing their potential, resulting in suboptimal performance and higher parameter consumption as network depth increases. In this paper, we reveal an inherent phenomenon: SAMs produce highly correlated attention maps across layers, with an average Pearson correlation coefficient of 0.85. Inspired by this inherent observation, we propose Dense-and-Implicit Attention (DIA), which shares SAMs across layers and uses a long short-term memory module to calibrate and connect these correlated attention maps, improving parameter efficiency. This approach aligns with the neural network’s dynamic system perspective. Extensive experiments show DIA consistently enhances various backbones like ResNet, Transformer, and UNet in tasks such as image classification, object detection, and image generation with diffusion models. Our analysis indicates that DIA’s effectiveness stems from its dense inter-layer information connections, absent in conventional mechanisms, stabilizing training and providing regularization effects. This paper’s insights advance our understanding of attention mechanisms, optimizing them and paving the way for future developments across diverse neural networks.

A dynamic bidirectional system of stress processes: Feedback loops between stressors, psychological distress, and physical symptoms.

Stress processes have long been of interest to researchers. A growing body of research explores the bidirectional relations between stressors, psychological and physical states. However, research on stress processes and their individual differences from a dynamic systems perspective is still lacking. This study examined dynamic feedback loops between stressors, psychological distress, and physical symptoms simultaneously using ecological momentary assessment. Three hundred and fifty-six participants completed five momentary assessments on stressors, psychological distress, and physical symptoms per day for 7 days in 2023. They also completed measures of their Big Five personality traits, depressive symptoms, and anxiety symptoms. Dynamic structural equation models showed positive cross-lagged and feedback effects of stressors with psychological distress and physical symptoms, suggesting their self-perpetuating loops. Agreeableness and conscientiousness were protective factors, and neuroticism was a risk factor for the stressor-psychological loop. Individuals with depressive and/or anxiety symptoms were characterized by (a) greater inertia of psychological distress and physical symptoms, (b) stronger reverse effects of psychological distress and physical symptoms on subsequent stressors, (c) significant reciprocal effects between psychological distress and physical symptoms, and (d) stronger self-perpetuating loops of stressors with psychological distress and physical symptoms. Our findings highlight the importance of analyzing feedback loops to understand bidirectional relations and individual differences in dynamic stress processes, providing insights for relevant personalized interventions. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A decentralized control approach in hypergraph distributed optimization decomposition cases

We study the main decomposition approaches (primal, dual and primal–dual) for a distributed optimization problem from a dynamical system perspective where the couplings among the variables of the optimization problem are described by an undirected, unweighted hypergraph. We conduct stability analysis for the respective dynamical systems of the decomposition cases by using non linear decentralized control theoretic techniques and spectral properties of the respective communication matrices, i.e., the incidence and the Laplacian matrices of the hypergraph. Finally, we provide numerical simulations under a specific coalitional setting that demonstrate the superiority of the hypergraph compared to its respective graph analogue, the clique expansion graph, for the given decomposition algorithms in terms of convergence rate and information transmission efficiency.

A convergent cross‐mapping approach for unveiling congestion spatial causality in urban traffic networks

AbstractSpatial causality in urban traffic networks explores how events or conditions in one location affect those in another. Unveiling congestion spatial causality is crucial for identifying congestion‐inducing bottlenecks in traffic networks and offering valuable insights for traffic network management and control. This study introduces the traffic‐convergent‐cross‐mapping (T‐CCM) method, a state‐space‐reconstruction approach from the dynamic system perspective, to identify causality among roads within urban traffic networks using time series data. Simultaneously, it effectively addresses the intricate challenges of uncertainty and interdependency among sensors caused by traffic flow dynamics. Empirical findings from real‐world (PeMS‐Bay area) traffic speed data validate the effectiveness of the T‐CCM method in detecting causality. This study reveals bidirectional causal effects between downstream and upstream roads in short‐term congestion generation and dissipation periods, which can pinpoint congestion origins and inform quick traffic management response. Furthermore, it elucidates the long‐term causality impacts between distant roads, particularly with regard to traveler choices and road land use attributes, guiding infrastructure investment and public transit improvements.

Motivational Change in EFL Students before and after Entering College: A Complex Dynamic Systems Perspective

Motivational Change in EFL Students before and after Entering College: A Complex Dynamic Systems Perspective

Sensor-Based Multifaceted Feature Extraction and Ensemble Elastic Net Approach for Assessing Fall Risk in Community-Dwelling Older Adults.

Accurate identification of community-dwelling older adults at high fall risk can facilitate timely intervention and significantly reduce fall incidents. Analyzing gait and balance capabilities via feature extraction and modeling through sensor-based motion data has emerged as a viable approach for fall risk assessment. However, the existing approaches for extracting key features related to fall risk lack inclusiveness, with limited consideration of the non-linear characteristics of sensor signals, such as signal complexity, self-similarity, and local stability. In this study, we developed a multifaceted feature extraction scheme employing diverse feature types, including demographic, descriptive statistical, non-linear, spatiotemporal and spectral features, derived from three-axis accelerometers and gyroscope data. This study is the first attempt to investigate non-linear features related to fall risk in multi-task scenarios from a dynamic system perspective. Based on the extracted multifaceted features, we propose an ensemble elastic net (E-E-N) approach for handling imbalanced data and offering high model interpretability. The E-E-N utilizes bootstrap sampling to construct base classifiers and employs a weighting mechanism to aggregate the base classifiers. We conducted a set of validation experiments using real-world data for comprehensive comparative analysis. The results demonstrate that the E-E-N approach exhibits superior predictive performance on fall risk classification. Our proposed approach offers a cost-effective tool for accurately assessing fall risk and alleviating the burden of continuous health monitoring in the long term.

The Evolution of Maritime Technology Development: A Dynamic Positioning System Perspective of Maritime Autonomous Surface Ship

The Evolution of Maritime Technology Development: A Dynamic Positioning System Perspective of Maritime Autonomous Surface Ship

Students’ and teachers’ emotions in the classroom: an ecological dynamic systems perspective

Students’ and teachers’ emotions in the classroom: an ecological dynamic systems perspective

FDE-Net: A memory-efficiency densely connected network inspired from fractional-order differential equations for single image super-resolution

Dense connection has proved an effective way to take full advantage of hierarchical features extracted from low-resolution images using deep neural networks (DNNs) for single image super-resolution (SISR). However, existing densely connected networks are often manually designed and overly depended on practical experience, thus leading to suboptimal performance. Moreover, due to their complicated connections, they are memory-consuming and lack of interpretability. To address all these problems with one stone, we propose to construct a new densely connected network for SISR from a dynamic system perspective. Following this idea, we cast the hierarchical transformation of DNNs into the state evolution of a fractional-order dynamic system, which empowers us to automatically construct two interdependent densely connected modules based on the system solution rather manual design. They are a prediction module that controls the system to iteratively predict the next state, and a correction module that iteratively refines the predicted state to improve the prediction accuracy. With these two modules as backbone, we establish a Fractional-order Differential Equations-based network (FDE-Net) for SISR. Since the iterative computational manner requires both densely connected modules to be of the recurrent structure, FDE-Net is memory-efficiency and good interpretability. In addition, we analyze the existence and uniqueness of the solution for FDE to theoretically guarantee the feasibility of FDE-Net. Experiments on four SISR benchmark datasets demonstrate the superiority of FDE-Net over existing densely connected networks and other baselines in terms of generalization capacity, especially with limited memory.

A Dynamic Entropy Approach Reveals Reduced Functional Network Connectivity Trajectory Complexity in Schizophrenia.

Over the past decade and a half, dynamic functional imaging has revealed low-dimensional brain connectivity measures, identified potential common human spatial connectivity states, tracked the transition patterns of these states, and demonstrated meaningful transition alterations in disorders and over the course of development. Recently, researchers have begun to analyze these data from the perspective of dynamic systems and information theory in the hopes of understanding how these dynamics support less easily quantified processes, such as information processing, cortical hierarchy, and consciousness. Little attention has been paid to the effects of psychiatric disease on these measures, however. We begin to rectify this by examining the complexity of subject trajectories in state space through the lens of information theory. Specifically, we identify a basis for the dynamic functional connectivity state space and track subject trajectories through this space over the course of the scan. The dynamic complexity of these trajectories is assessed along each dimension of the proposed basis space. Using these estimates, we demonstrate that schizophrenia patients display substantially simpler trajectories than demographically matched healthy controls and that this drop in complexity concentrates along specific dimensions. We also demonstrate that entropy generation in at least one of these dimensions is linked to cognitive performance. Overall, the results suggest great value in applying dynamic systems theory to problems of neuroimaging and reveal a substantial drop in the complexity of schizophrenia patients' brain function.

Emergence of locomotor behaviors: Associations with infant characteristics, developmental status, parental beliefs, and practices in typically developing Brazilian infants aged 5 to 15 months

Independent locomotion provides autonomy for infants, drastically changing their relationship with their surroundings. From a dynamic systems perspective, the interaction between environment, tasks, and organismic constraints leads to the emergence of new behaviors over time. This 6-month longitudinal study aimed to verify associations between the emergence of locomotor behaviors and infants' characteristics, developmental status, parental beliefs, and practices. This observational study remotely assessed 37 full-term Brazilian infants aged 5 to 15 months, divided into two groups (G1: 5 to 11 months, n = 19; and G2: 9 to 15 months, n = 18). The motor developmental status of infants was closely associated with the emergence of behaviors (p < 0.05). Infants in G2 whose parents agreed with the statement "In typically developing infants, motor development occurs naturally and there is no need to actively stimulate it" started to walk later than those whose parents disagreed. Infants whose parents expected them to walk around 10–11 months walked earlier compared to those expected to walk after 11 months (G2, p = 0.011). Infants in G2 with a high frequency of staying in the supine position started to walk, both with and without support, later than those with a low frequency (p < 0.05). For infants in G1 with a high frequency of playing on the floor, locomotion (p = 0.041) and crawling on hands-and-knees (p = 0.007) started sooner compared to those with a low frequency. Staying in the cradle more frequently was related to a later emergence of supported walk (p = 0.046) among infants in G2. The emergence of locomotor behaviors is associated with motor developmental status, the surfaces where the infant plays, and body position. Parental beliefs and expectations influence how infants are stimulated and, consequently, the emergence of independent walking.

Pulsing in the Ahu‘ail‘au pond–spillway system during the 2018 Klauea eruption: a dynamical systems perspective

During the 2018 K $\unicode{x012B}$ lauea lower East Rift Zone eruption, lava from 24 fissures inundated more than 8000 acres of land, destroying more than 700 structures over three months. Eruptive activity eventually focused at a single vent characterized by a continuously fed lava pond that was drained by a narrow spillway into a much wider, slower channelized flow. The spillway exhibited intervals of ‘pulsing’ behaviour in which the lava depth and velocity were observed to oscillate on time scales of several minutes. At the time, this was attributed to variations in vesiculation originating at depth. Here, we construct a toy fluid dynamical model of the pond–spillway system, and present an alternative hypothesis in which pulsing is generated at the surface, within this system. We posit that the appearance of pulsing is due to a supercritical Hopf bifurcation driven by an increase in the Reynolds number. Asymptotics for the limit cycle near the bifurcation point are derived with averaging methods and compare favourably with the cycle periodicity. Because oscillations in the pond were not observable directly due to the elevation of the cone rim and an obscuring volcanic plume, we model the observations using a spatially averaged Saint-Venant model of the spillway forced by the pond oscillator. The predicted spillway cycle periodicity and waveforms compare favourably with observations made during the eruption. The unusually well-documented nature of this eruption enables estimation of the viscosity of the erupting lava.

Reifying actions into artifacts: process–object duality from an embodied perspective on mathematics learning

Grasping mathematical objects as related to processes is often considered critical for mathematics understanding. Yet, the ontology of mathematical objects remains under debate. In this paper, we theoretically oppose internalist approaches that claim mental entities as the endpoints of process–object transitions and externalist approaches that stress mathematical artifacts—such as physical manipulatives and formulas—as constituting mathematical objects. We search for a view on process–object duality that overcomes the dualism of mind and body. One such approach is commognition that describes mathematical objects as discursive entities. This paper expands the nature of mathematical objects beyond discourse and highlights the role of learners’ interaction with the environment by adopting ecological onto-epistemology. We develop a functional dynamic systems perspective on process–object duality in mathematics learning emphasizing embodied actions and the re-invention of artifacts’ affordances. As a main result, we reconsider process–object duality as a reification of repetitive actions into a cultural artifact that consists of two steps: (1) forming a new sensory-motor coordination that brings new perception to the fore and (2) crystallizing a new artifact in a mathematical environment that captures this new perception. An empirical example from research on embodied action-based design for trigonometry illustrates our theoretical ideas.Graphical abstract

Qualitative and asymptotic analysis of repulsion systems with diverse applications

Repulsion systems under the discrete dynamical systems perspective are considered. The goal is to study the nonlinear dynamics of an arrangement of individual or cells under various types of repulsion laws. Repulsion is a natural mechanism, so we consider the following laws: global, open, cyclic and bounded repulsion. A first scenario under consideration is when particles are freely located on an Euclidean space and the second scenario where they are restricted to remain in a bounded set. We consider those two scenarios under the previous types of repulsion. The analysis culminates in a unification of two mechanisms: attraction and repulsion via a specific social behaviour problem.

Computer Simulation and Optimization of Second Language Writing Strategies from the Perspective of Dynamic Systems Theory

In response to the growing demand for effective second language (L2) writing strategies, this study aims to explore and optimize L2 writing strategies from a dynamic systems perspective. Utilizing computer simulation, the research investigates the interaction and adaptation of writing strategies in L2 learners. The research method involves the development of a computational model that simulates the writing process of L2 learners. This model captures various writing strategies, such as planning, drafting, revising, and self-monitoring, and analyzes how these strategies evolve over time in response to different linguistic and cognitive challenges. Data from L2 learners’ writing samples and writing process logs are used to calibrate and validate the simulation model. The results of the computer simulation demonstrate that L2 writing strategies are not static but rather adapt dynamically to the writer’s proficiency level, task demands, and cognitive resources. The simulation reveals that certain strategies, such as frequent self-monitoring and adaptive planning, are more effective in improving writing quality and efficiency. Additionally, the study identifies individual differences in strategy use, with some learners benefiting more from specific strategies than others. The findings underscore the complexity of L2 writing and suggest that personalized feedback and strategy training based on the simulation outcomes can significantly enhance L2 writing performance. The findings reveal significant insights into the dynamic nature of writing strategies, highlighting the importance of individual differences and context. The study concludes that computer simulation offers a promising approach for understanding and enhancing L2 writing strategies, potentially leading to more personalized and efficient writing instruction.

Optimizing with Attractor: A Tutorial

This tutorial presents a novel search system—the Attractor-Based Search System (ABSS)—that can solve the Traveling Salesman Problem very efficiently with optimality guarantee. From the perspective of dynamical systems, a heuristic local search algorithm for an NP-complete combinatorial problem is a discrete dynamical system. In a local search system, an attractor drives the search trajectories into the vicinity of a globally optimal point in the solution space, and the convergence of local search trajectories makes the search system become a global and deterministic system. The attractor contains a small set of the most promising solutions to the problem. The attractor can reduce the problem size exponentially, and thus make the exhaustive search feasible. Therefore, this new search paradigm is called optimizing with attractor. The ABSS consists of two search phases: local search phase and exhaustive search phase. The local search process is used to quickly construct the attractor in the solution space, and the exhaustive search process is used to completely search the attractor to identify the optimal solution. Therefore, the exact optimal solution can be found quickly by combining local search and exhaustive search. This tutorial introduces the concept of an attractor in a local search system, and describes the process of optimizing with the attractor, using the Traveling Salesman Problem as the study platform.

Transport and Scale Interactions in Geophysical Flows

This interdisciplinary workshop brought together researchers working on different aspects of transport and scale interactions across the spectrum of geophysical fluid dynamics: geometry and computation of transport and exchange processes in geophysical flows, Lagrangian coherent structures, (geo-strophic) turbulence, nonlinear waves and coherent structures in the Eulerian description of fluids, and stochastic methods in multiscale systems. Each of these topics have their own vibrant communities as well as well-established and emerging connections. This meeting aimed to bridge across the entire span of topics from a dynamical systems perspective, and to connect classical approaches with new developments in data-driven modeling and stochastic modeling.

Lyra cosmologies with the dynamical system perspective

In this study, we revisit the homogeneous and isotropic, spatially curved model in the Lyra geometry framework. We apply the dynamical system approach to study the Universe evolution in model. The present cosmic dynamical system formulation is independent of the model parameter which yields the Universe expansion phases dominated by the stiff fluid, radiation, dark matter and dark energy. These expansion phases in the Lyra model are consistent with the General relativity model. In addition, the displacement vector field of the Lyra geometry model will give rise to the stiff matter dominated phase during early times of the Universe evolution. The cosmographic parameters, EoS parameter and statefinder diagnostic have been utilized in the dynamical system to illustrate the cosmic evolution of the Universe. The numerical solution technique is used to illustrate graphical behaviors of the cosmological parameters. On the basis of dynamical system and numerical analysis, we exhibit that the model explains accelerating universe expansion with transition from the decelerating phase and it will lead to the Λ cold dark matter (ΛCDM) model in the near future.