Dynamical Systems Approach Research Articles

Exacerbating patellofemoral pain alters trunk and lower limb coordination patterns and hip-knee mechanics

The exacerbation of patellofemoral pain (PFP) may lead to compensatory trunk and lower limb movement patterns in order to minimize patellofemoral joint loading. However, joint kinematics are often analysed in isolation, which limits the understanding of how the underlying segments were coordinated to produce limb postures and distribute load across the limb. In this study we used a dynamical systems approach to investigate how women with PFP coordinate trunk, hip, and knee motion and distribute hip-knee moment demands following symptom exacerbation. Coordination patterns and coordination variability of the trunk, hip, and knee from 61 women with PFP were obtained during stair descent, ascent, and step down tasks, before and after a pain exacerbation protocol. Hip-knee extensor moment impulse ratio was also calculated. Following the exacerbation of PFP, women utilized knee dominant coordination patterns less often (p = 0.039–0.027; d = 0.51–0.53), while coordination patterns with the trunk leaning forward were utilized more during stair negotiation (p = 0.043-<0.001; d = 0.52–0.96). Although no significant differences in hip-knee coordination patterns were found, there was an increase in the hip-knee impulse ratio during stair negotiation (p = 0.014-<0.001; d = 0.27–0.36). These findings seem to display a movement strategy utilized by women with PFP in order to distribute more load to the hip joint and less to the knee joint, possibly in an attempt to avoid/manage pain.

Large-scale structure power spectrum from scalar–tensor gravity

This work deals with the computation of the power spectrum of large-scale structure using the dynamical system approach for a multifluid universe in scalar–tensor theory of gravity. We use the 1 + 3 covariant approach to obtain evolution equations and study the behavior of the matter power spectrum of perturbation equations. The study is based on the equivalence between f(R) theory of gravity and scalar–tensor theory of gravity. We find that, for power-law [Formula: see text] models, with [Formula: see text], we have the power spectrum evolving above general relativistic scale-invariant line. For [Formula: see text], the power spectrum starts with constant amplitude then it experiences oscillations and eventually saturates at finite amplitude. Such behavior is consistent with other observations in the literature. The result supports the ongoing investigations of the equivalence between f(R) and scalar–tensor theory at linear order.

Discrete Dynamical System Approaches for Boolean Polynomial Optimization

In this article, we discuss the numerical solution of Boolean polynomial programs by algorithms borrowing from numerical methods for differential equations, namely the Houbolt scheme, the Lie scheme, and a Runge-Kutta scheme. We first introduce a quartic penalty functional (of Ginzburg-Landau type) to approximate the Boolean program by a continuous one and prove some convergence results as the penalty parameter $$\varepsilon $$ converges to 0. We prove also that, under reasonable assumptions, the distance between local minimizers of the penalized problem and the set $$\{\pm 1\}^n$$ is of order $$O(\sqrt{n}\varepsilon )$$ . Next, we introduce algorithms for the numerical solution of the penalized problem, these algorithms relying on the Houbolt, Lie and Runge-Kutta schemes, classical methods for the numerical solution of ordinary or partial differential equations. We performed numerical experiments to investigate the impact of various parameters on the convergence of the algorithms. We have tested our ODE approaches and compared with the classical nonlinear optimization solver IPOPT and a quadratic binary formulation approach (QB-G) as well as an exhaustive method using parallel computing techniques. The numerical results on various datasets (including small and large-scale randomly generated synthetic datasets of general Boolean polynomial optimization problems, and a large-scale heterogeneous MQLib benchmark dataset of Max-Cut and Quadratic Unconstrained Binary Optimization (QUBO) problems) show good performances for our ODE approaches. As a result, our ODE algorithms often converge faster than the other compared methods to better integer solutions of the Boolean program.

A Primer on the Dynamical Systems Approach to Transport in Porous Media

Historically, the dominant conceptual paradigm of porous media flow, solute mixing and transport was based on steady two-dimensional flows in heterogeneous porous media. Although it is now well recognised that novel transport phenomena can arise in unsteady and/or three-dimensional flows at both the pore- or Darcy-scales, appropriate methods for analysis and understanding of these more complex flows have not been widely employed. In this primer we advocate for methods borrowed from dynamical systems (chaos) theory, which aim to uncover the \emph{Lagrangian kinematics} of these flows: namely how fluid particle trajectories (which form a dynamical system) are organized and interact and the associated impacts on solute transport and mixing. This dynamical systems approach to transport is inherently Lagrangian, and the Lagrangian kinematics form Lagrangian coherent structures (LCSs), special sets of trajectories that divide the Lagrangian frame into chaotic mixing regions, poorly mixing hold-up regions (and in some cases non-mixing ``islands'') and the transport barriers that organise these regions. Hence the dynamical systems approach provides insights into flows that may exhibit chaotic, regular (non-chaotic) or mixed Lagrangian kinematics, and also into how LCSs organize solute transport and mixing. Novel experimental methods are only recently permitting visualization of LCSs are in porous media flows. In this primer we review the dynamical systems approach to porous media flow and transport and connect the associated tools and techniques with the latest research findings from pore to Darcy scales. This primer provides an introduction to the methods and tools of dynamical systems theory. Once familiar with these approaches, porous media researchers will be better positioned to know when to expect complex Lagrangian kinematics, how to uncover and understand LCSs and their impacts ...

Government Policy Analysis to Develop the Krian-Manyar-Gresik Toll in order to Reduce Traffic Jam using A Dynamic System Approach

Infrastructure development in an area, including the construction of toll roads, is aimed at developing a region and increasing the economy of the region. The construction of the toll road which is connected from Krian-Manyar-Gresik is carried out to facilitate traffic connecting the two cities. Traffic jams often occur at the link between the two cities. Congestion that occurs is usually caused by an increase in the volume of vehicles. Therefore, the construction of a toll road connecting the two cities is the best alternative. This research aimed to know government policies effectiveness in the construction of this toll road. The method used in this research is to use a dynamic system approach. From the results of the traffic simulation model design, it is found that the construction of toll roads is considered very influential and can be a way out of congestion problems. This is due to a decrease in the degree of saturation of congestion and although there is an increase from year to year, it is only slightly and not too significant. So the researchers suggest to continue the planned toll road construction project.

Modern Koopman Theory for Dynamical Systems

The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches that formulate models in operator-theoretic or probabilistic frameworks. Koopman spectral theory has emerged as a dominant perspective over the past decade, in which nonlinear dynamics are represented in terms of an infinite-dimensional linear operator acting on the space of all possible measurement functions of the system. This linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. However, obtaining finite-dimensional coordinate systems and embeddings in which the dynamics appear approximately linear remains a central open challenge. The success of Koopman analysis is due primarily to three key factors: (1) there exists rigorous theory connecting it to classical geometric approaches for dynamical systems; (2) the approach is formulated in terms of measurements, making it ideal for leveraging big data and machine learning techniques; and (3) simple, yet powerful numerical algorithms, such as the dynamic mode decomposition (DMD), have been developed and extended to reduce Koopman theory to practice in real-world applications. In this review, we provide an overview of modern Koopman operator theory, describing recent theoretical and algorithmic developments and highlighting these methods with a diverse range of applications. We also discuss key advances and challenges in the rapidly growing field of machine learning that are likely to drive future developments and significantly transform the theoretical landscape of dynamical systems.

The Impact of Social Media Engagement on Market Share: A System Dynamics Model

Background: Some studies have shown that Return on Total Assets is a strategy to increase market share. Other studies have also shown that social media like WeChat can increase market share. However, no studies have considered Instagram engagement in increasing market share. Objective: This study aims to identify variable linkage that increases market share through a dynamic system approach in small and medium-sized enterprises (SMEs). Methods: Using a System Dynamics approach, this study presents a model simulation with a proposed increase in market share by considering Instagram features. This approach creates a Causal Loop Diagram converted into a simulated Stock Flow Diagram. The value generated from the simulation is validated with the mean comparison and % error variance formulas. Results: Instagram engagement increases market share from 0.009 to 0.018. Such engagement can be increased by posting regularly and doing more activities, such as increasing post frequency, holding contests, and maximizing all features. Conclusion: This study has successfully modeled information technology, i.e., a promotion module on social media. However, this work has not yet demonstrated how the features can gain more market share, so future research is needed. Keywords: Causal Loop Diagram, Engagement, Market Share, Stock Flow Diagram, System Dynamics

Dynamical systems approach for travel time prediction in intermediate section under mixed traffic conditions

An urban arterial can be considered a series of intersections, intermediate sections (defined as those that link intersections and mid-block areas), and mid-block sections. The intermediate section is characterized by varying speed characteristics at its entry and exit. A vehicle exiting the intersection and entering the intermediate section would accelerate and gradually attain uniform speed when it leaves the intermediate section (entry to the mid-block). Most of the reported travel time studies considered the delays at intersections and the travel times in mid-blocks to get the network level travel time without paying attention to the variability of speeds and travel time at intermediate sections. The present study concentrates on the travel time estimation of the intermediate section, which is not well-discussed in the literature. A speed estimation scheme was developed for the entry and exit of the intermediate section (characterized by varying speed ranges) using a dynamic model-based estimation scheme that captured the speed variations effectively. Intermediate link travel time was then estimated using a weighted average speed-based method. The effects of heterogeneity and limited lane discipline in the traffic stream of mixed traffic were considered using two model formulations, one that represented the traffic stream in Passenger Car Units (PCU) and the other in different vehicle classes for travel time estimation. The developed estimation schemes can be used as a possible application in Intelligent Transportation Systems (ITS) for real-time estimation of travel time at urban arterials under mixed traffic conditions.

A Dynamic Autocatalytic Network Model of Therapeutic Change.

Psychotherapy involves the modification of a client’s worldview to reduce distress and enhance well-being. We take a human dynamical systems approach to modeling this process, using Reflexively Autocatalytic foodset-derived (RAF) networks. RAFs have been used to model the self-organization of adaptive networks associated with the origin and early evolution of both biological life, as well as the evolution and development of the kind of cognitive structure necessary for cultural evolution. The RAF approach is applicable in these seemingly disparate cases because it provides a theoretical framework for formally describing under what conditions systems composed of elements that interact and ‘catalyze’ the formation of new elements collectively become integrated wholes. In our application, the elements are mental representations, and the whole is a conceptual network. The initial components—referred to as foodset items—are mental representations that are innate, or were acquired through social learning or individual learning (of pre-existing information). The new elements—referred to as foodset-derived items—are mental representations that result from creative thought (resulting in new information). In clinical psychology, a client’s distress may be due to, or exacerbated by, one or more beliefs that diminish self-esteem. Such beliefs may be formed and sustained through distorted thinking, and the tendency to interpret ambiguous events as confirmation of these beliefs. We view psychotherapy as a creative collaborative process between therapist and client, in which the output is not an artwork or invention but a more well-adapted worldview and approach to life on the part of the client. In this paper, we model a hypothetical albeit representative example of the formation and dissolution of such beliefs over the course of a therapist–client interaction using RAF networks. We show how the therapist is able to elicit this worldview from the client and create a conceptualization of the client’s concerns. We then formally demonstrate four distinct ways in which the therapist is able to facilitate change in the client’s worldview: (1) challenging the client’s negative interpretations of events, (2) providing direct evidence that runs contrary to and counteracts the client’s distressing beliefs, (3) using self-disclosure to provide examples of strategies one can use to diffuse a negative conclusion, and (4) reinforcing the client’s attempts to assimilate such strategies into their own ways of thinking. We then discuss the implications of such an approach to expanding our knowledge of the development of mental health concerns and the trajectory of the therapeutic change.

Deep learning via dynamical systems: An approximation perspective

We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for universal approximation using continuous-time deep residual networks, which can also be understood as approximation theories in L^p using flow maps of dynamical systems. In specific cases, rates of approximation in terms of the time horizon are also established. Overall, these results reveal that composition function approximation through flow maps presents a new paradigm in approximation theory and contributes to building a useful mathematical framework to investigate deep learning.

Challenges and responses: A Complex Dynamic Systems approach to exploring language teacher agency in a blended classroom

Challenges and responses: A Complex Dynamic Systems approach to exploring language teacher agency in a blended classroom

Learning Accurate and Stable Point-to-Point Motions: A Dynamic System Approach

This letter proposes a dynamic system approach to learn point-to-point motions while keeping the stability of the dynamic system. The proposed approach is grounded on a Learning from Demonstration (LfD) method based on a neural network, which gets a better reproduction performance while guaranteeing the generalization ability. The proposed approach has been experimentally validated on the LASA dataset and by the &#x201C;pick-and-place&#x201D; task of Franka Emika robot, and experimental results demonstrate that: (1) compared with the state-of-the-art results, the trajectory generated by the proposed approach achieves higher accuracy (approximately 24.79&#x0025;) in terms of the similarity with respect to the demonstration; (2) the proposed approach can handle high dimensional data and learn from one or more demonstrations; (3) the proposed approach can guarantee the performance regardless of the variation of starting points even in the case of high dimensional complex motions.

A Commentary on Whitall and Colleagues’ 2020 Article “Motor Development Research: II. The First Two Decades of the 21st Century Shaping Our Future”

This commentary reflects on the discussions of Whitall et al.’s paper “Motor Development Research: II. The First Two Decades of the 21st Century Shaping Our Future.” Comments focus on (a) the emergence and importance of the Developmental Systems approach to motor development, (b) the perceived ambiguity between Dynamic and Developmental Systems approaches, and (c) a case for the evolution of Developmental Motor Neuroscience from the field of Developmental Cognitive Neuroscience.

A Dynamic System Approach to Spiking Second Order Memristor Networks

Second order memristors are two terminal devices that present a conductance depending on two orders of variables, namely the geometric parameters and the internal temperature. They have shown to be able to mimic some specific features of neuron synapses, specifically Spike-Timing-Dependent-Plasticity (STDP), and consequently to be good candidates for neuromorphic computing. In particular, memristor crossbar structures appear to be suitable for implementing locally competitive algorithms and for tackling classification problems by exploiting temporal learning techniques. On the other hand, neuromorphic studies and experiments have revealed the existence of different kinds of plasticity and have shown the effect of calcium concentration on synaptic changes. Computational studies have investigated the behavior of spiking networks in the context of supervised, unsupervised, and reinforcement learning. In this paper, we first derive a simplified, almost analytical, model of a second-order memristor, only involving two variables, the mem-conductance, and the temperature, directly attributable to the synaptic efficacy and to the calcium concentration. Then we study in detail the response of a single memristive synapse to the most relevant plasticity models, including cycles of spike pairs, triplets, and quadruplets at different frequencies. Finally, we accurately characterize memristor spiking networks as discrete nonlinear dynamic systems, with mem-conductances as state variables and pre and postsynaptic spikes as inputs and outputs, respectively. The result shows that the model developed in this manuscript can explain and accurately reproduce a significant portion of observed synaptic behaviors, including those not captured by classical spike pair-based STDP models. Furthermore, under such an approach, the global dynamic behavior of memristor networks and the related learning mechanisms can be deeply analyzed by employing advanced nonlinear dynamic techniques.

Dynamic optimization of 1,3-propanediol fermentation process: A switched dynamical system approach

This paper considers a dynamic optimization problem (DOP) of 1,3-propanediol fermentation process (1,3-PFP). Our main contributions are as follows. Firstly, the DOP of 1,3-PFP is modeled as an optimal control problem of switched dynamical systems. Unlike the existing switched dynamical system optimal control problem, the state-dependent switching method is applied to design the switching rule. Then, in order to obtain the numerical solution, by introducing a discrete-valued function and using a relaxation technique, this problem is transformed into a nonlinear parameter optimization problem (NPOP). Although the gradient-based algorithm is very efficient for solving NPOPs, the existing algorithm is always trapped in a local minimum for such problems with multiple local minima. Next, in order to overcome this challenge, a gradient-based random search algorithm (GRSA) is proposed based on an improved gradient-based algorithm (IGA) and a novel random search algorithm (NRSA), which cannot usually be trapped in a local minimum. The convergence results are also established, and show that the GRSA is globally convergent. Finally, a DOP of 1,3-PFP is provided to illustrate the effectiveness of the GRSA proposed by this paper.

Close TIES in relationships: A dynamic systems approach for modeling physiological linkage

We explore complex dynamic patterns of autonomic physiological linkage (i.e., statistical interdependence of partner’s physiology; PL), within the sympathetic and parasympathetic nervous systems (SNS and PNS), as potential correlates of emotional and regulatory dynamics in close relationships. We include electrodermal activity (EDA) as an indicator of SNS activation and respiratory sinus arrhythmia (RSA) as an indicator of regulatory and/or homeostatic processes within the PNS. Measures of EDA and RSA were collected in 10-second increments from 53 heterosexual couples during a mixed-emotion conversation in the laboratory. We used the R statistical package, rties (Butler &amp; Barnard, 2019), to model the dynamics of EDA and RSA with a coupled oscillator model and then categorized couples into qualitatively distinct profiles based on the set of parameters that emerged. We identified two patterns for EDA and three patterns for RSA. We then investigated associations between the PL patterns and self-report measures of relationship and conversation quality and emotional valence using Bayesian multilevel and logistic regression models. Overall, we found robust results indicating that PL profiles were credibly predicted by valence and relationship quality reported prior to the conversations. In contrast, we found very little evidence suggesting that PL patterns predict self-reported conversation quality or valence following the conversation. Together, these results suggest that PL across autonomic subsystems may reflect different processes and therefore have different implications when considering interpersonal dynamics.

Groundwater Flow System-Based Dynamic System Approach for Geofluids and Their Resources

The ‘Dynamic System Approach for Geofluids and their Resources’ was developed to harmonize research and the sustainable exploration of geofluids (e.g., groundwater, geothermal and hydrothermal fluids) and the related geo-resources (groundwater, geothermal energy and hydrothermal minerals). The conception is based on the basin-scale groundwater flow systems, which behave as a geologic agent, mobilize, transport and deposit matter and heat, whilst it can be evaluated quantitatively and in a distributed manner. Evaluation of these systems combined, for instance, with numerical, stochastic and isotope methods can jointly manage all types of geofluids, the related resources and the environmental consequences of their exploration and utilization. This paper describes the fundamental concepts of the approach and displays the proposed workflow and guidelines for practical applications such as groundwater vulnerability assessment, managed aquifer recharge, geothermal energy utilization, and the evaluation of hydrothermal mineral potential.

The mechanics of dynamic behaviors for SMEs’ growth by using fractional-order dynamic system approach

The goal of this paper is to establish a general framework for the development of small- or medium-sized enterprises’ (SMEs) growth path by using star-coupled stochastic dynamic system approach. The dynamic behaviors are related to the stochastic resonance (SR) phenomenon subject to multiplicative fluctuation and periodic force which could be interpreted as uncertain environments faced by SMEs (enterprises) during their growth process. The multiplicative noise is modeled as dichotomous noise (uncertainty under the innovation and capital paradigm) and the memory of risk environments is characterized by using fractional kernel function. By using the mathematical derivation, the analytical expressions for the first moment of the steady state response, the stability in the long-time limit in terms of (enterprises) systems’ asymptotic stability is obtained. Theoretic and simulation results show the nonmonotonic dependence between the output gain and the input signal frequency, noise parameters for SMEs dynamic behaviors. Furthermore, the fluctuation noise, the number of related parties (partners) for SMEs, and the fractional-order work together, producing more complex dynamic phenomena compared with the traditional integral-order systems (for enterprises). Finally, theoretical analyses with corresponding numerical simulations results established in this paper would provide a possible fundamental mathematical framework for the study of Schumpeter’s theory on the development for SMEs’ growth under the “innovation and capital paradigm” and related disciplines. In particular, the framework allows us, for the first time, to logically conclude that “in general, the ratio for SMEs’ growth successfully is around less than one-third”, this is actually consistent with what the market has been observing commonly in general.

Variation and variability in L2 learning trajectories: Learning the Finnish existential construction

Taking an onomasiological approach and a dynamic usage-based perspective, this study explores how four beginning L2 learners of Finnish develop in expressing existentiality (‘there is something somewhere’) before and after instruction. Data were collected weekly over a period of nine months and examined for conventionalized and non-conventionalized constructions that express existentiality. As expected from a dynamic usage-based perspective, both inter-individual variation and intra-individual variability were identified. The initial repertoires of two of the learners were quite variable, as they used several different non-conventionalized constructions before settling on more conventionalized ones. In contrast, the two other learners did not independently try out different ways of expressing the targeted meaning but started to use the conventionalized Finnish existential construction only after pedagogical intervention. As one would expect from a usage-based perspective, some learners’ initial repertoires included some item-based constructions that were similar to each other. As far as instruction is concerned, for all learners there was an increase in the use of the conventionalized construction after an explicit intervention, but the use was not morphologically accurate. The findings confirm two commonly held hypotheses in dynamic systems approaches: Learners own their own learning trajectories and initial trajectories are sometimes characterized by high degrees of variability because learners need to try out different strategies before they can adapt to the requirements of the new situation.

"A New Hope" for Positive Psychology: A Dynamic Systems Reconceptualization of Hope Theory.

In this review of the central tenets of hope theory, we examine the meta-theoretical, theoretical, and methodological foundations of the literature base. Our analysis moves from a broad examination of the research landscape in hope theory across disciplines, to a deeper investigation of the empirical literature in university students. This review highlights the significant impact of this body of research in advancing our understanding of aspects of thriving characterized by hope. However, we also evidence several limitations that may impede the advancement of the next wave of growth in this field. To address these limitations, we argue for an interdisciplinary approach to expanding the meta-theoretical, theoretical, and methodological horizons, enabling a more dynamic systems approach to the study of hope. Drawing on the intersection of positive psychology with systems thinking, we describe a methodological approach that enables a deeper examination of the processes and interactions through which hope emerges, using an analysis of the lived experience of young people. It is proposed that this research agenda will bring to life an alternate story about the resourcefulness of our youth through their own voice, enabling us to leverage this in the design of more effective strategies to facilitate hope in the future. This research agenda provides a roadmap that will provide alternative methodologies that address the current limitations in the field of hope research and, importantly, can provide fuel to spur on the acceleration of the next wave of research and practice in the field of positive psychology more broadly.