Dynamical Systems Perspective Research Articles

Queues with Delayed Information: A Dynamical Systems Perspective

Queues with Delayed Information: A Dynamical Systems Perspective

SIGEST

The SIAM Journal on Mathematics of Data Science (SIMODS) launched in February 2019. The SIGEST article in this issue, “Dimensionality Reduction via Dynamical Systems: The Case of t-SNE,” by George C. Linderman and Stefan Steinerberger, is therefore our first SIMODS representative. Here the authors study t-SNE, a widely adopted clustering and visualization algorithm proposed by Laurens van der Maaten and Geoffrey Hinton in 2008---that publication has received over 24,000 Google Scholar citations to date. The SIMODS editorial board commented that ``[f]or anyone who tries to interact with people in bioinformatics, they will know that t-SNE is truly one of the most commonly used visualization algorithms, and in those visualizations the interpretation is always about the clusters that arise. Basically, t-SNE was something that was one principled way for dimensionality reduction that got co-opted for so much more. It's a rare theorist that takes what's actually already being used and working, and tries to explain it. This paper is certain to make a long term impact." In this work the authors use a dynamical systems perspective to explain why, and at what rate, the algorithm is guaranteed to converge successfully when applied to data that contains well-separated clusters. They also discuss fundamental connections to spectral clustering algorithms. Throughout, ideas are illustrated via colorful visualizations on both synthetic and real datasets. In preparing the article for SIGEST, the authors have appended the new section 7, which gives a big-picture, accessible overview of the topic. This new section also outlines recent developments in the area and lists a number of open problems.

On the Importance of Being Flexible: Dynamic Brain Networks and Their Potential Functional Significances.

In this theoretical review, we begin by discussing brains and minds from a dynamical systems perspective, and then go on to describe methods for characterizing the flexibility of dynamic networks. We discuss how varying degrees and kinds of flexibility may be adaptive (or maladaptive) in different contexts, specifically focusing on measures related to either more disjoint or cohesive dynamics. While disjointed flexibility may be useful for assessing neural entropy, cohesive flexibility may potentially serve as a proxy for self-organized criticality as a fundamental property enabling adaptive behavior in complex systems. Particular attention is given to recent studies in which flexibility methods have been used to investigate neurological and cognitive maturation, as well as the breakdown of conscious processing under varying levels of anesthesia. We further discuss how these findings and methods might be contextualized within the Free Energy Principle with respect to the fundamentals of brain organization and biological functioning more generally, and describe potential methodological advances from this paradigm. Finally, with relevance to computational psychiatry, we propose a research program for obtaining a better understanding of ways that dynamic networks may relate to different forms of psychological flexibility, which may be the single most important factor for ensuring human flourishing.

Modeling Tumor Disease and Sepsis by Networks of Adaptively Coupled Phase Oscillators.

In this study, we provide a dynamical systems perspective to the modelling of pathological states induced by tumors or infection. A unified disease model is established using the innate immune system as the reference point. We propose a two-layer network model for carcinogenesis and sepsis based upon the interaction of parenchymal cells and immune cells via cytokines, and the co-evolutionary dynamics of parenchymal, immune cells, and cytokines. Our aim is to show that the complex cellular cooperation between parenchyma and stroma (immune layer) in the physiological and pathological case can be qualitatively and functionally described by a simple paradigmatic model of phase oscillators. By this, we explain carcinogenesis, tumor progression, and sepsis by destabilization of the healthy homeostatic state (frequency synchronized), and emergence of a pathological state (desynchronized or multifrequency cluster). The coupled dynamics of parenchymal cells (metabolism) and nonspecific immune cells (reaction of innate immune system) are represented by nodes of a duplex layer. The cytokine interaction is modeled by adaptive coupling weights between the nodes representing the immune cells (with fast adaptation time scale) and the parenchymal cells (slow adaptation time scale) and between the pairs of parenchymal and immune cells in the duplex network (fixed bidirectional coupling). Thereby, carcinogenesis, organ dysfunction in sepsis, and recurrence risk can be described in a correct functional context.

Return of the math: Markov blankets, dynamical systems theory, and the bounds of mind

Bruineberg and colleagues highlight work using Markov blankets to demarcate the bounds of the mind. This echoes earlier attempts to demarcate the bounds of the mind from a dynamical systems perspective. Advocates of mechanistic explanation have challenged the dynamical approach to independently motivate the application of the formalism, a challenge that Markov blanket theorists must also meet.

Explicating the effects of big data analytics capabilities on supply chain resilience dimensions: dynamic capabilities approach and complex adaptive system perspective

In an uncertain business environment, industries need to be resilient in their supply chains to be able to face the possible changes, identify them, and react to the real ones. This study aims at presenting a general approach to evaluate big data analytics (BDA) potential regarding supply chain resilience. The effects of three enablers of BDA capabilities, namely BDA management ability, BDA infrastructure flexibility, and BDA personnel expertise ability on supply chain resilience dimensions, namely efficiency-based capabilities, adaptive capability, and collaborative capability were studied in a conceptual framework. Evaluation of the research measurement as well as structural model validity was performed via partial least squares structural equation modelling (PLS-SEM). The results show that BDA capabilities have a positive and meaningful effect on supply chain resiliency. Moreover, according to the findings, capabilities of BDA personnel along with BDA infrastructure flexibility had a greater impact on supply chain resilience.

Voluntary safety commitments provide an escape from over-regulation in AI development

With the introduction of Artificial Intelligence (AI) and related technologies in our daily lives, fear and anxiety about their misuse as well as their inherent biases, incorporated during their creation, have led to a demand for governance and associated regulation. Yet regulating an innovation process that is not well understood may stifle this process and reduce benefits that society may gain from the generated technology, even under the best intentions. Instruments to shed light on such processes are thus needed as they can ensure that imposed policies achieve the ambitions for which they were designed. Starting from a game-theoretical model that captures the fundamental dynamics of a race for domain supremacy using AI technology, we show how socially unwanted outcomes may be produced when sanctioning is applied unconditionally to risk-taking, i.e. potentially unsafe, behaviours. We demonstrate here the potential of a regulatory approach that combines a voluntary commitment approach reminiscent of soft law, wherein technologists have the freedom of choice between independently pursuing their course of actions or establishing binding agreements to act safely, with either a peer or governmental sanctioning system of those that do not abide by what they pledged. As commitments are binding and sanctioned, they go beyond the classic view of soft law, akin more closely to actual law-enforced regulation. Overall, this work reveals how voluntary but sanctionable commitments generate socially beneficial outcomes in all scenarios envisageable in a short-term race towards domain supremacy through AI technology. These results provide an original dynamic systems perspective of the governance potential of enforceable soft law techniques or co-regulatory mechanisms, showing how they may impact the ambitions of developers in the context of the AI-based applications.

Trajectories of Idea Emergence in Dialogic Collaborative Problem Solving: Toward a Complex Dynamic Systems Perspective.

According to the complex dynamic systems (CDS) perspective, learning emerges at various system levels. This study built a coherent theoretical framework based on CDS and Bakhtinian dialogic theory and further employed the concept of attractor (i.e., certain stable states that recur over time) in CDS theory to investigate the trajectories of idea emergence and how they diversified group outcomes in dialogic collaborative problem solving (D-CPS). Two contrasting groups were compared using visual and qualitative analysis approaches. The analysis based on idea tree diagrams showed that new ideas emergent in group discussion tended to attract local utterances and performed features of attractors in CDS in both high-performing and low-performing groups. The analysis based on idea hierarchy diagrams revealed how ideas emerged at various system levels. It was also found that status problems were likely to affect the functioning of regulative feedback loops, which might give rise to different structures of idea evolution. This study proposed CDS theory as an alternative perspective, augmented by the ethical considerations of Bakhtinian dialogism, for examining the dynamics of D-CPS.

Analytical results in transient brush tyre models: theory for large camber angles and classic solutions with limited friction

This paper establishes new analytical results in the mathematical theory of brush tyre models. In the first part, the exact problem which considers large camber angles is analysed from the perspective of linear dynamical systems. Under the assumption of vanishing sliding, the most salient properties of the model are discussed with some insights on concepts as existence and uniqueness of the solution. A comparison against the classic steady-state theory suggests that the latter represents a very good approximation even in case of large camber angles. Furthermore, in respect to the classic theory, the more general situation of limited friction is explored. It is demonstrated that, in transient conditions, exact sliding solutions can be determined for all the one-dimensional problems. For the case of pure lateral slip, the investigation is conducted under the assumption of a strictly concave pressure distribution in the rolling direction.

A Machine Learning Approach to Analyze Home Advantage during COVID-19 Pandemic Period with Regards to Margin of Victory and to Different Tournaments in Professional Rugby Union Competitions.

Home advantage (HA) is the tendency for sporting teams to perform better at their home ground than away from home, it is also influenced by the crowd support, and its existence has been well established in a wide range of team sports including rugby union. Among all the HA determinants, the positive contribute of the crowd support on the game outcome can be analyzed in the unique pandemic situation of COVID-19. Therefore, the aim of the present study was to analyze the HA of professional high-level rugby club competition from a complex dynamical system perspective before and during the COVID-19 pandemic. HA was analyzed in northern and southern hemisphere rugby tournaments with (2013–2019) and without (2020/21) crowd support by the means of the exhaustive chi-square automatic interaction detection (CHAID) decision trees (DT). HA was mitigated by the crowd absence especially in closed games, although differences between tournaments emerged. Both for northern and southern hemisphere, the effect of playing without the crowd support had a negative impact on the home team advantage. These findings evidenced that in ghost games, where differences in the final score were less than a converted try (7 points), HA has disappeared.

Reimagining the Introductory Math Curriculum for Life Sciences Students.

Calculus is typically one of the first college courses encountered by science, technology, engineering, and mathematics (STEM) majors. Calculus often presents major challenges affecting STEM student persistence, particularly for students from groups historically underrepresented in STEM. For life sciences majors, calculus courses may not offer content that is relevant to biological systems or connect with students’ interests in biology. We developed a transformative approach to teaching college-level math, using a dynamical systems perspective that focuses first on demonstrating why students need math to understand living systems, followed by providing quantitative and computational skills, including concepts from calculus, that students need to build and analyze mathematical models representing these systems. We found that students who complete these new math courses perform better in subsequent science courses than their counterparts who take traditional calculus courses. We also provide evidence that the new math curriculum positively impacts students’ academic performance, with data that show narrowing of the achievement gap, based on students’ math grades, between student subgroups in the new math courses. Moreover, our results indicate that students’ interest in the concepts and skills critical to the quantitative preparation of 21st-century life sciences majors increases after completing the new contextualized math curriculum.

Bifurcations and Exact Solitary Wave, Compacton and Pseudo-Peakon Solutions in a Modified Generalized KdV Equation

A modified generalized KdV equation is considered in this paper. Under the given parameter conditions, the corresponding traveling wave system is a singular planar dynamical system with three singular straight lines. The bifurcations and traveling wave solutions of the system are investigated in the parameter space from the perspective of dynamical systems. The existence of solitary wave solutions, periodic peakon solutions, pseudo-peakon solutions, kink and anti-kink wave solutions and compactons is proved. Furthermore, possible exact explicit parametric representations of various solutions are given. Particularly, the model has uncountably infinite many solitary wave and pseudo-peakon solutions.

Multiscale co-simulation of deep brain stimulation with The Virtual Brain

Abstract Deep brain stimulation (DBS) has been successfully applied in various neurodegenerative diseases as an effective symptomatic treatment. However, its mechanisms of action within the brain network are still poorly understood. Many virtual DBS models analyze a subnetwork around the basal ganglia and its dynamics as a spiking network with their details validated by experimental data. However, connectomic evidence shows widespread effects of DBS affecting many different cortical and subcortical areas. From a clinical perspective, various effects of DBS besides the motoric impact have been demonstrated. The neuroinformatics platform The Virtual Brain (TVB) offers a modeling framework allowing us to virtually perform stimulation, including DBS, and forecast the outcome from a dynamic systems perspective prior to invasive surgery with DBS lead placement. For an accurate prediction of the effects of DBS, we implement a detailed spiking model of the basal ganglia, which we combine with TVB via our previously developed co-simulation environment. This multiscale co-simulation approach builds on the extensive previous literature of spiking models of the basal ganglia while simultaneously offering a whole-brain perspective on widespread effects of the stimulation going beyond the motor circuit. In the first demonstration of our model, we show that virtual DBS can move the firing rates of a Parkinson’s disease patient’s thalamus - basal ganglia network towards the healthy regime while, at the same time, altering the activity in distributed cortical regions with a pronounced effect in frontal regions. Thus, we provide proof of concept for virtual DBS in a co-simulation environment with TVB. The developed modeling approach has the potential to optimize DBS lead placement and configuration and forecast the success of DBS treatment for individual patients. Keywords: basal ganglia, The Virtual Brain, multiscale model, Parkinson's disease

Dynamical system analysis of a data-driven model constructed by reservoir computing.

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical characteristics can be reconstructed much more precisely by a data-driven model than by computing directly from training data. With this idea, we predict the laminar lasting time distribution of a particular macroscopic variable of chaotic fluid flow, which cannot be calculated from a direct numerical simulation of the Navier-Stokes equation because of its high computational cost.

Regularity and randomness in ageing: Differences in resting-state EEG complexity measured by largest Lyapunov exponent

The loss of complexity in ageing hypothesis (LOCH) has found support from EEG studies, most of which adopted signal-domain complexity measures. The present study adopted the largest Lyapunov exponent (LLE) to measure complexity from a nonlinear dynamical systems perspective. A total of 144 participants were included and divided into young, young-old and old-old groups. Both sensor-space and source-space results showed significantly lower LLE for older than younger adults. The age-related differences were region-dependent, being most prominent in the frontal region, followed by bilateral temporal regions. The occipital region showed non-significant differences. Significant reduction of LLE in the posterior cingulate was also observed by virtue of the source-space analysis. We also evaluated the relationships between LLE and other complexity measures. The most intriguing result was the negative correlation between LLE and Lempel-Ziv complexity (LZC). The age-related decrease in LLE indicated a higher regularity in dynamics, while the higher LZC indicated a higher randomness in the signal domain. The new findings support the LOCH by demonstrating the simultaneous increase in regularity and randomness.

Instabilities in quasiperiodic motion lead to intermittent large-intensity events in Zeeman laser.

We report intermittent large-intensity pulses that originate in Zeeman laser due to instabilities in quasiperiodic motion, one route follows torus-doubling to chaos and another goes via quasiperiodic intermittency in response to variation in system parameters. The quasiperiodic breakdown route to chaos via torus-doubling is well known; however, the laser model shows intermittent large-intensity pulses for parameter variation beyond the chaotic regime. During quasiperiodic intermittency, the temporal evolution of the laser shows intermittent chaotic bursting episodes intermediate to the quasiperiodic motion instead of periodic motion as usually seen during the Pomeau-Manneville intermittency. The intermittent bursting appears as occasional large-intensity events. In particular, this quasiperiodic intermittency has not been given much attention so far from the dynamical system perspective, in general. In both cases, the infrequent and recurrent large events show non-Gaussian probability distribution of event height extended beyond a significant threshold with a decaying probability confirming rare occurrence of large-intensity pulses.

Effect of the Coriolis force on bounded traveling waves of the rotation-two-component Camassa–Holm system

In this paper, we qualitatively study the effect of the Coriolis force on traveling waves of the rotation-two-component Camassa–Holm system in the rotating fluid, which is a model in the equatorial water waves, from the perspective of dynamical systems. We obtain the explicit critical rotational speed (A is a parameter of the system characterizing a linear underlying shear flow and c is the wave speed), which reflects the Coriolis force. Based on this critical vorticity, we obtain phase portraits of the system under exact explicit parameters conditions. Then we not only show the existence of various bounded traveling waves including smooth solitary waves, peakons and kink waves, under corresponding exact explicit parameters conditions, but also obtain their exact expressions. Of particular interest is that we find that kink waves (which were not found previouly) exist only when , that is, the rotational speed Ω should be greater than .

On the Search for Brain Bifurcation Parameters: Lessons From FMRI Studies on Visual Illusions

Data from three functional magnetic resonance imaging (fMRI) studies that involved in total about 100 participants and showed that the strength of several visual illusions such as the Ebbinghaus, Ponzo, and Muller-Lyer illusions depends on neuroanatomical subject measures such as visual cortex surface area and parahippocampal cortex gray matter volume were evaluated using a dynamical systems perspective to determine brain bifurcation parameters. Bifurcation parameters that involved power laws and captured relational dependencies were fitted separately to the three fMRI studies. The bifurcation parameter hypothesis that states that such parameters show unique quantities and are no longer correlated to structural systems properties was tested. The power law exponents and mean bifurcation parameter values were determined. For all three studies and three illusion types, the bifurcation parameter hypothesis was supported. Accordingly, the constructed parameters characterized the reactions of the participants under the Ebbinghaus, Ponzo, and Muller-Lyer illusions in terms of unique threshold values that no longer depended on neuroanatomical subject measures. Power law exponents in the range from 1 to 7 were found. The fMRI data describing gray matter volume of certain active regions in the parahippocampal cortex showed some interesting relationship between the mean bifurcation parameter values.

Modeling Identities in Context: A Dynamical Systems Approach to Leader-Follower Identities

Although leadership and followership processes are flexible and fluid, our theoretical and empirical knowledge of the short-term dynamics in individuals’ leadership and followership identities are limited. Building on a Dynamical Systems Perspective we argue that leadership and followership identities are complex systems, that are composed of multiple interacting elements that exhibit emergent and nonlinear intra-personal identity dynamics. With the goal to explore these patterns of leader-follower identity variability across different contexts we address two questions: (1) How are individuals’ leadership and followership identity dynamics characterized in different contexts associated with uncertainty? (2) How are these leadership and followership identity dynamics interrelated within different contexts? We collected daily data from a total of 69 Undergraduate students (1,159 data points) in the United Kingdom across seven-day periods in three different contexts during the academic year. Findings from dynamical systems modeling reveal the entangled nature of leadership and followership identities, different attractor states as well as consequences of COVID-19 on leadership and followership identity dynamics.

On the dynamics and adaptivity of mental processes: Relating adaptive dynamical systems and self-modeling network models by mathematical analysis

In this paper, it is addressed by mathematical analysis how network-oriented modeling relates to the dynamical systems perspective on mental processes. It has been mathematically proven that any dynamical system can be modeled as a temporal-causal network model and that any adaptive dynamical system (of any order) can be modeled by a self-modeling network (of the same order).