Framework Of Dynamical Systems Research Articles

Accounting for Individual Trajectories in L2 Learning: A One‑Year Pilot Case Study with Adult Professionals

This paper seeks to explore the links between individual trajectories followed over time by adult professionals and the way these trajectories shape their L2 learning routes. Embracing the theoretical framework of Individual Differences and complex dynamic systems, we sought to study these links via an appraisal of the contribution of non‑classroom integrated telecollaboration as an opportunity for L2 learning which embraces the inherent variability of individual learning pathways. A case study approach was adopted given the size of our sample (10 adult learners from Cnam Paris; 10 students from Cardiff University), the qualitative nature of the collected data, and the reliability of individual longitudinal case studies in determining factors structuring L2 learning. A three-phase protocol (introductory tutorial, telecollaboration sessions, final feedback) was designed for this one‑year project. Data gathered from the semi-structured interviews of the two most successful French participants were analyzed and cross-checked with data from reflective logbooks and feedback reports focusing on factors shaping L2 development over time and perceptions of learning benefits. Our findings further confirm the intrinsic relationship between individual trajectories and language learning, thus calling for the necessity of learner-centeredness in the design process of (time‑limited) institutional L2 courses particularly for adult professionals.

Active extremum Kriging-based multi-level linkage reliability analysis and its application in aeroengine mechanism systems

To improve the computational efficiency and accuracy of dynamic multi-component system reliability analysis involving complex characteristics like dynamic traits, high-nonlinearity, and failure correlation, an active extremum Kriging-based multi-level linkage method (AEK-MLL) is proposed by incorporating the benefits of extremum selection technique, active learning Kriging model, and the multi-level linkage strategy. In AEK-MLL modeling, the extremum selection technique first converts the dynamic candidate sample domain into a steady-state candidate sample domain, and the active learning technique searches for the best training samples, to build the active extremum Kriging model of component-level limit state functions (LSFs); moreover, the multi-level linkage strategy is adopted to take failure correlation into account, to establish a reliability framework for complex dynamic multi-component systems. The proposed method is first validated by a dynamic numerical case and three system numerical cases, and then applied to the dynamic multi-component reliability analysis of a typical aero-engine mechanism system. The numerical cases and engineering case show that the AEK-MLL holds the high-accuracy and high-efficiency in dealing with the complex dynamic multi-component system reliability analysis.

Reactive and Risk-Aware Control for Signal Temporal Logic

The deployment of autonomous systems in uncertain and dynamic environments has raised fundamental questions. Addressing these is pivotal to build fully autonomous systems and requires a systematic integration of planning and control. We first propose reactive risk signal interval temporal logic (ReRiSITL) as an extension of signal temporal logic (STL) to formulate complex spatiotemporal specifications. Unlike STL, ReRiSITL allows to consider uncontrollable propositions that may model humans as well as random environmental events such as sensor failures. Additionally, ReRiSITL allows to incorporate risk measures, such as (but not limited to) the conditional value-at-risk, to measure the risk of violating certain spatial specifications. Second, we propose an algorithm to check if an ReRiSITL specification is satisfiable. For this purpose, we abstract the ReRiSITL specification into a timed signal transducer and devise a game-based approach. Third, we propose a reactive planning and control framework for dynamical control systems under ReRiSITL specifications.

Bistable traveling waves for time periodic reaction-diffusion equations in strip with Dirichlet boundary condition

We study the existence of bistable traveling wave solutions for time periodic reaction-diffusion equations in straight strips subject to the Dirichlet boundary condition. We first employ a monotone dynamical system framework to establish the existence of such a wave by assuming a bistability structure in terms of multiplicity and stability of periodic solutions in the section of the strip, which is then realized under a set of sufficient explicit conditions; in particular, the bistability structure appears if the reaction term is a time periodic smooth perturbation of the nonlinearity λu(1−u)(u−a) when a∈(0,1/2) and λ>λ⁎ for some λ⁎>0.

Techniques for blocking the propagation of two simultaneous contagions over networks using a graph dynamical systems framework

AbstractWe consider the simultaneous propagation of two contagions over a social network. We assume a threshold model for the propagation of the two contagions and use the formal framework of discrete dynamical systems. In particular, we study an optimization problem where the goal is to minimize the total number of new infections subject to a budget constraint on the total number of available vaccinations for the contagions. While this problem has been considered in the literature for a single contagion, our work considers the simultaneous propagation of two contagions. This optimization problem is NP-hard. We present two main solution approaches for the problem, namely an integer linear programming (ILP) formulation to obtain optimal solutions and a heuristic based on a generalization of the set cover problem. We carry out a comprehensive experimental evaluation of our solution approaches using many real-world networks. The experimental results show that our heuristic algorithm produces solutions that are close to the optimal solution and runs several orders of magnitude faster than the ILP-based approach for obtaining optimal solutions. We also carry out sensitivity studies of our heuristic algorithm.

Detecting criticality in complex univariate time-series: A case study of the U.S. housing market crisis and other markets

The indices of asset markets are a key measure of an asset’s value and how this varies over time. However, these indices are known to switch abruptly between qualitatively different behavioural epochs underscoring the complexity of collective decision-making in large, interacting populations of economic agents. A central question in the study of index dynamics is how to represent these transitions in a way that allows for both equilibrium and non-equilibrium behaviour in a dynamical systems framework. With this in mind, we sought to detect non-equilibrium transitions between stable equilibria in housing market data across thirteen OECD countries from 1975 through to 2019. We are able to precisely locate transitions using the quadrant scan method that has been used in earlier studies to detect critical points in other dynamical systems. We then use stochastic Catastrophe Theory to reconstruct the multi-modal distributions near the U.S. housing crisis point and show mode-switching behaviour of markets transitioning from one equilibrium to another. Our results are in contrast to other recent findings for the U.S. market that were unable to find a critical point near the 2007 crisis.

Gesture-speech synchrony in schizophrenia: A pilot study using a kinematic-acoustic analysis

Severe impairment of social functioning is the core feature of schizophrenia that persists despite treatment, and contributes to chronic functional disability. Abnormal non-verbal behaviors have been reported during interpersonal interactions but the temporal coordination of co-speech gestures with language abilities have been poorly studied to date in this pathology. Using the dynamical systems framework, the goal of the current study was to investigate whether gestures and speech synchrony is impaired in schizophrenia, exploring a new approach to report communicational skill disorders. Performing the first continuous kinematic-acoustic analysis in individuals with schizophrenia, we examined gesture-speech synchrony in solo spontaneous speech and in sensorimotor synchronization task. The experimental group consisted of twenty-eight participants with a diagnosis of schizophrenia and the control group consisted of twenty-four healthy participants age-gender-education matched. The results showed that spontaneous gesture-speech synchrony was preserved while intentional finger tapping-speech synchrony was impaired. In sensorimotor synchronization task, the schizophrenia group displayed greater asynchronies between finger tapping and syllable uttering and lower stability of coordination patterns. These findings suggest a specific deficit in time delay of information circulation and processing, especially in explicit functions. Thus, investigating intrapersonal coordination in schizophrenia may constitute a promising window into brain/behavior dynamic relationship.

A tool or a social being? A dynamic longitudinal investigation of functional use and relational use of AI voice assistants

This study integrates two lines of research: technologies as tools and technologies as social beings, under the theoretical framework of dynamic systems, to investigate the reciprocal dynamics between functional use and relational use of artificial intelligence (AI) voice assistants, and the mediating roles of self-disclosure and privacy concerns. A two-wave longitudinal survey was conducted among 354 AI voice assistant users across 2 months. Factor analysis results supported the conceptualization and operationalization of functional use and relational use of voice assistants. Results from the cross-lagged panel model confirmed that functional use and relational use reinforced themselves over time, respectively. Relational use increased subsequent functional use, and relational use reinforced itself through self-disclosure. Surprisingly, functional use did not increase subsequent relational use; instead, longitudinal mediation analysis showed that functional use reduced subsequent relational use due to the lack of self-disclosure. Furthermore, while self-disclosure increased subsequent privacy concerns, privacy concerns did not reduce subsequent self-disclosure.

A multi-fidelity ensemble Kalman filter with hyperreduced reduced-order models

We present an efficient data assimilation framework for nonlinear dynamical systems that uses multi-fidelity statistical estimates based on a full-order model and a projection-based hyperreduced order model (ROM) that is trained on-the-fly. This framework is particularly applicable to conservation laws in aerodynamics that yield expensive forward models. The formulation comprises the following technical components: (i) an ensemble Kalman filter to tractably handle high-dimensional, strongly nonlinear dynamical models; (ii) multi-fidelity forecast models, where ROM-based coarse fidelities are constructed on-the-fly; and (iii) hyperreduction for the ROM, based on proper orthogonal decomposition and the empirical quadrature procedure, constructed using the ensemble of full order model trajectories. We show that the multi-fidelity statistical estimates based on efficient, on-the-fly construction of the ROM enables rapid and reliable state estimation for practical nonlinear dynamical systems. We demonstrate the effectiveness of our framework to estimate the state of a separated flow around an airfoil by (i) showing that the ROM-based multi-fidelity method is more accurate than the single-fidelity method for comparable computational cost and (ii) showing that multi-fidelity statistics enable the use of a less accurate surrogate when compared against ROM-only filters, at negligible cost.

Linear-Time Verification of Data-Aware Dynamic Systems with Arithmetic

Combined modeling and verification of dynamic systems and the data they operate on has gained momentum in AI and in several application domains. We investigate the expressive yet concise framework of data-aware dynamic systems (DDS), extending it with linear arithmetic, and providing the following contributions. First, we introduce a new, semantic property of “finite summary”, which guarantees the existence of a faithful finite-state abstraction. We rely on this to show that checking whether a witness exists for a linear-time, finite-trace property is decidable for DDSs with finite summary. Second, we demonstrate that several decidability conditions studied in formal methods and database theory can be seen as concrete, checkable instances of this property. This also gives rise to new decidability results. Third, we show how the abstract, uniform property of finite summary leads to modularity results: a system enjoys finite summary if it can be partitioned appropriately into smaller systems that possess the property. Our results allow us to analyze systems that were out of reach in earlier approaches. Finally, we demonstrate the feasibility of our approach in a prototype implementation.

Modelling the lexical complexity of homogenous texts: a time series approach.

Lexical complexity of homogeneous texts, especially when produced by an institutional author over time, exhibits a generally observed increasing trend with local random fluctuations. Such an irreversible entropic process fits very cogently into the dynamical complexity system theory, where the social, economic, and cultural missions such texts set to serve constitute the underlying driving momentum for the texts to adapt themselves from low to high complexity. Structural equations have been shown effective in modeling such macroscopic behavior of the entropic process of the homogeneous texts. The current work formulates the problem from a time series modeling approach applied to a large sociolinguistic corpus in written Chinese. The findings show that such an alternative approach not only produces as valid models with strong goodness of fit as the structural equation approach, but also exhibits, by design, additional benefits in explaining the entropic process of homogeneous texts in the dynamical complexity system framework. Some technical challenges, such as phase change in model calibration, are also solved with less cost using the newly proposed approach. Further directions are pointed out to more fully compare these approaches in the setup of the current study and corpus linguistics in general.

Self-sustained oscillations of active viscoelastic matter

Models of active nematics in biological systems normally require complexity arising from the hydrodynamics involved at the microscopic level as well as the viscoelastic nature of the system. Here we show that a minimal, space-independent, model based on the temporal alignment of active and polymeric particles provides an avenue to predict and study their coupled dynamics within the framework of dynamical systems. In particular, we examine, using analytical and numerical methods, how such a simple model can display self-sustained oscillations in an activity-driven viscoelastic shear flow.

Autodifferentiable Ensemble Kalman Filters

Data assimilation is concerned with sequentially estimating a temporally evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and the state-space dynamics are unknown. This paper introduces a machine learning framework for learning dynamical systems in data assimilation. Our auto-differentiable ensemble Kalman filters (AD-EnKFs) blend ensemble Kalman filters for state recovery with machine learning tools for learning the dynamics. In doing so, AD-EnKFs leverage the ability of ensemble Kalman filters to scale to high-dimensional states and the power of automatic differentiation to train high-dimensional surrogate models for the dynamics. Numerical results using the Lorenz-96 model show that AD-EnKFs outperform existing methods that use expectation-maximization or particle filters to merge data assimilation and machine learning. In addition, AD-EnKFs are easy to implement and require minimal tuning.

Generative formalism of causality quantifiers for processes.

The concept of dynamical causal effect (DCE) is generalized and equipped with a formalism which allows one to formulate in a unified manner and interrelate a variety of causality quantifiers used in time series analysis. An elementary DCE from a subsystem Y to a subsystem X is defined within the stochastic dynamical systems framework as a response of a future X state to an appropriate variation of an initial (X,Y)-state distribution or a certain parameter of Y or of the coupling element Y→X; this response is quantified in a probabilistic sense via a certain distinction functional; elementary DCEs are assembled over a set of initial variations via an assemblage functional. To include all those aspects, a "triple brackets formula" for the general DCE is suggested and serves as a first principle to produce specific causality quantifiers as realizations of the general DCE. As an application, transfer entropy and Liang-Kleeman information flow are related surprisingly as opposite limit cases in a family of DCEs; it is shown that their "nats per time unit" may differ drastically. The suggested DCE viewpoint links any formal causality quantifier to "intervention-effect" experiments, i.e., future responses to initial variations, and so provides its dynamical interpretation, opening a way to its further physical interpretations in studies of physical systems.

Bohr/Levitan almost periodic and almost automorphic solutions of monotone difference equations with a strict monotone first integral

The paper is dedicated to the study of problem of Poisson stability (in particular, periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, Levitan almost periodicity, pseudo-periodicity, almost recurrence in the sense of Bebutov, recurrence in the sense of Birkhoff, pseudo recurrence and Poisson stability) and asymptotically Poisson stability of motions of monotone non-autonomous difference equations which have a strong monotone first integral. We solve this problem in the framework of general non-autonomous dynamical systems with discrete time.

On Incremental Structure from Motion Using Lines

Humans tend to build environments with structure, which consists of mainly planar surfaces. From the intersection of planar surfaces arise straight lines. Lines have more degrees of freedom than points. Thus, line-based structure-from-motion (SfM) provides more information about the environment. In this article, we present solutions for SfM using lines, namely, incremental SfM. These approaches consist of designing state observers for a camera’s dynamical visual system looking at a 3-D line. We start by presenting a model that uses spherical coordinates for representing the line’s moment vector. We show that this parameterization has singularities, and, therefore, we introduce a more suitable model that considers the line’s moment and shortest viewing ray. Concerning the observers, we present two different methodologies. The first uses a memory-less state-of-the-art framework for dynamic visual systems. Since the previous states of the robotic agent are accessible—while performing the 3-D mapping of the environment—the second approach aims at exploiting the use of memory to improve the estimation accuracy and convergence speed. The two models and the two observers are evaluated in simulation and real data, where mobile and manipulator robots are used.

Online optimization of LTI systems under persistent attacks: Stability, tracking, and robustness

We study the stability properties of a closed-loop system composed of a dynamical plant and a feedback controller, the latter generating control signals that can be compromised by a malicious attacker. We consider two classes of feedback controllers: a static output-feedback controller, and a dynamical gradient-flow controller that seeks to steer the output of the plant towards the solution of a convex optimization problem. In both cases, we analyze the stability properties of the closed-loop system under a class of switching attacks that persistently modify the control inputs generated by the controllers. Our stability analysis leverages the framework of hybrid dynamical systems, Lyapunov-based arguments for switching systems with unstable modes, and singular perturbation theory. Our results reveal that, under a suitable time-scale separation between plant and controllers, the stability of the interconnected system can be preserved when the attack occurs with “sufficiently low frequency” in any bounded time interval. We present simulation results in a power-grid example that corroborate the technical findings.

Random attractors for dissipative systems with rough noises

<p style='text-indent:20px;'>We provide an analytic approach to study the asymptotic dynamics of rough differential equations, with the driving noises of Hölder continuity. Such systems can be solved with Lyons' theory of rough paths, in particular the rough integrals are understood in the Gubinelli sense for controlled rough paths. Using the framework of random dynamical systems and random attractors, we prove the existence and upper semi-continuity of the global pullback attractor for dissipative systems perturbed by bounded noises. Moreover, if the unperturbed system is strictly dissipative then the random attractor is a singleton for sufficiently small noise intensity.</p>

АКСІОЛОГІЧНІ ОСНОВИ НАУКОВО-МЕТОДИЧНОГО АПАРАТУ ДЛЯ ІНФОРМАЦІЙНОКЕРУЮЧИХ ЗАСОБІВ ІНТЕЛЕКТУАЛЬНИХ ТРАНСПОРТНИХ СИСТЕМ

Ukraine, together with the world's leading countries, is actively promoting the development of intelligent transport systems (ITS). Target cycles are aimed at future forecast states, which are provided by the relevant strategic plans and programs for 2030-2050. Targeted resource-efficient satisfaction of society's needs in the form of expected services, products, goods according to new complex regulations, products, standards, safety criteria, functional stability, survivability, ecological economy is impossible without significant updating of technical and technological solutions (TTP). The interaction of sets of objects of complex dynamic systems (SDS) with heterogeneous contacts of the Air Force determines the desired paradigm of duality of direct and inverse, causal relations. Within the framework of complex dynamic systems (SDS) in advance, qualitatively complete, locally accurate modeling rules assess in advance their own actions and influences of factors of the interacting natural environment (APS). It is the predicative form of theoretical results and evidence on the facts of practice that determines the axiological basis of science. Known logical descriptions are immutable and decisive <if there is a specific fixed form of pair interaction of the Air Force → VTS, as a cause, then, as a consequence in these specific conditions, we have an accurate conclusion>. Similar facts of existence of the corresponding limited procedural result, effect of TTR, a condition of VDS and VPS are possible. For every constant, stationary, similar situation, a double, inverse statement is also valid. It is accurate based on multiple confirmations of the practice of scientific observations and comparisons in various fields of human activity. The article is devoted to the development of technologies for modeling integration processes that synergistically affect the level of road safety of vehicles under conditions of risk and uncertainty of nonstationary environmental factors. The mathematical description of the problem area and information space of interaction of the Air Force participants → VTS is formalized. The essence, peculiarity and specificity of situational modes of dynamic, continuous interaction in space-time discrete cells of the electronic map of the critical zone are substantiated on the basis of the frequency of previous accidents that are possible in the future.

Asymptotic Dynamics of Young Differential Equations

We provide a unified analytic approach to study the asymptotic dynamics of Young differential equations, using the framework of random dynamical systems and random attractors. Our method helps to generalize recent results (Duc et al. in J Differ Equ 264:1119–1145, 2018, SIAM J Control Optim 57(4):3046–3071, 2019; Garrido-Atienza et al. in Int J Bifurc Chaos 20(9):2761–2782, 2010) on the existence of the global pullback attractors for the generated random dynamical systems. We also prove sufficient conditions for the attractor to be a singleton, thus the pathwise convergence is in both pullback and forward senses.