Non-stationary Dynamics Research Articles

Accounting for non-stationary stock–recruitment relationships in the development of MSY-based reference points

Asbtract Stock–recruitment relationships (SRRs) may vary over time due to ecological and anthropogenic impacts, challenging traditional approaches of calculating maximum sustainable yield (MSY)-based reference points that assume constant population traits. We compare seven methods to calculate MSY, FMSY and BMSY by modelling constant, stochastic (uncorrelated), and autocorrelated SRRs using simulations and two case studies [Atlantic cod (Gadus morhua) and American plaice (Hippoglossoides platessoides) on the Grand Bank off Newfoundland, Canada]. Results indicated that the method used to model SRRs strongly affected the temporal pattern of recruitment projection, and the variations generated by autocorrelated SRRs were more similar to observed patterns. When the population productivity had low-frequency and large-magnitude variations, stochastic SRRs generated greater MSY and FMSY estimates than constant or autocorrelated SRRs, while no consistent pattern of BMSY was detected. In the case studies, stochastic and autocorrelated SRRs produced asymmetric relationships between fishing mortality and yield, with higher risk of overfishing by going beyond FMSY. Overall, our results suggest that caution should be taken when calculating MSY-based reference points in highly dynamic ecosystems, and correctly accounting for non-stationary population dynamics could, therefore, lead to more sustainable fisheries.

Data-driven stock trading in financial markets: an adaptive control approach

In financial markets, stock trading techniques usually require to learn a model of the non-stationary dynamics of the underlying asset in order to make reliable predictions and take effective decisions. In the recently introduced feedback approach to trading, the stock price is instead treated as an exogenous disturbance to a feedback loop scheme and a controller is synthesised with the unique goal of minimising the impact of the return variations on the investment gain. Since such an approach is intrinsically model-free, the tuning of the controller represents a critical task. In this work, we propose a data-driven adaptive control strategy, exploiting the knowledge of the gain/loss as well as the measured returns over a moving window. The proposed approach is extensively back-tested on real-world financial series and the related performance is compared to that of classical feedback schemes and to benchmark investment strategies.

Seek and learn: Automated identification of microevents in animal behaviour using envelopes of acceleration data and machine learning

Abstract Animal‐borne accelerometers have been used across more than 120 species to infer biologically significant information such as energy expenditure and broad behavioural categories. While the accelerometer's high sensitivity to movement and fast response times present the unprecedented opportunity to resolve fine‐scale behaviour, leveraging this opportunity will require overcoming the challenge of developing general, automated methods to analyse the nonstationary signals generated by nonlinear processes governing erratic, impulsive movement characteristic of fine‐scale behaviour. We address this issue by conceptualising fine‐scale behaviour in terms of characteristic microevents: impulsive movements producing brief (<1 s) shock signals in accelerometer data. We propose a ‘seek‐and‐learn’ approach: a novel microevent detection step first locates where shock signals occur (‘seek’) by searching for peaks in envelopes of acceleration data. Robust machine learning (‘learn’) employing meaningful features then separates microevents. We showcase the application of our method on tri‐axial accelerometer data collected on 10 free‐living meerkats Suricata suricatta for four fine‐scale foraging behaviours – searching for digging sites, one‐armed digging, two‐armed digging and head jerks during prey ingestion. Annotated videos served as groundtruth, and performance was benchmarked against that of a variety of classical machine learning approaches. Microevent identification (μEvId) with eight features in a three‐node hierarchical classification scheme employing logistic regression at each node achieved a mean overall accuracy of >85% during leave‐one‐individual‐out cross‐validation, and exceeded that of the best classical machine learning approach by 8.6%. μEvId was found to be robust not only to inter‐individual variation but also to large changes in model parameters. Our results show that microevents can be modelled as impulse responses of the animal body‐and‐sensor system. The microevent detection step retains only informative regions of the signal, which results in the selection of discriminative features that reflect biomechanical differences between microevents. Moving‐window‐based classical machine learning approaches lack this prefiltering step, and were found to be suboptimal for capturing the nonstationary dynamics of the recorded signals. The general, automated technique of μEvId, together with existing models that can identify broad behavioural categories, provides future studies with a powerful toolkit to exploit the full potential of accelerometers for animal behaviour recognition.

Modelling the impact of structural directionality on connectome-based models of neural activity

AbstractUnderstanding structure--function relationships in the brain remains an important challenge in neuroscience. However, whilst structural brain networks are intrinsically directed, due to the prevalence of chemical synapses in the cortex, most studies in network neuroscience represent the brain as an undirected network. Here, we explore the role that directionality plays in shaping transition dynamics of functional brain states. Using a system of Hopfield neural elements with heterogeneous structural connectivity given by different species and parcellations (cat, Caenorhabditis elegans and two macaque networks), we investigate the effect of removing directionality of connections on brain capacity, which we quantify via its ability to store attractor states. In addition to determining large numbers of fixed-point attractor sets, we deploy the recently developed basin stability technique in order to assess the global stability of such brain states, which can be considered a proxy for network state robustness. Our study indicates that not only can directed network topology have a significant effect on the information capacity of connectome-based networks, but it can also impact significantly the domains of attraction of the aforementioned brain states. In particular, we find network modularity to be a key mechanism underlying the formation of neural activity patterns, and moreover, our results suggest that neglecting network directionality has the scope to eliminate states that correlate highly with the directed modular structure of the brain. A numerical analysis of the distribution of attractor states identified a small set of prototypical direction-dependent activity patterns that potentially constitute a `skeleton' of the non-stationary dynamics typically observed in the brain. This study thereby emphasizes the substantial role network directionality can have in shaping the brain's ability to both store and process information.

Vector features of pulsating soliton in an ultrafast fiber laser.

Pulsating soliton in ultrafast fiber lasers has interesting non-stationary dynamics, which is one of the hot topics in field of nonlinear soliton. So far, most researchers only focused on the spectral and temporal characteristics of pulsating soliton. However, the vector features of pulsating soliton were rarely studied. In this work, we experimentally studied the pulsating vector solitons in an ultrafast fiber laser. Three categories of vector solitons with different polarization evolution characteristics could be obtained by adjusting the pump power and polarization controller, such as pulsating polarization-locked vector soliton (PLVS), pulsating polarization-rotation vector soliton (PRVS) and progressive pulsating PRVS. Interestingly, besides the basic polarization rotation with a period of 2 roundtrips, the polarization angle also evolves with progressive mode in the progressive pulsating PRVS state. The abundant results of pulsating vector solitons demonstrate that investigating vector features of nonlinear soliton dynamics is necessary and significant and would greatly enrich the research of soliton dynamics.

A Holistic Probabilistic Framework for Monitoring Nonstationary Dynamic Industrial Processes

Multivariate statistical process monitoring (MSPM) methods provide sensitive indicators of process conditions by harnessing the value of massive process data. Large-scale industrial processes are subject to wide-range time-varying operating conditions such that some variables inevitably exhibit nonstationary behavior, which poses significant challenges for the design of MSPM schemes. In this brief, a novel nonstationary probabilistic slow feature analysis algorithm is developed to comprehensively describe both nonstationary and stationary variations that underlie process measurements during routine operations. For efficient parameter estimation, the expectation-maximization algorithm is employed. By modeling nonstationarity and stationarity as the random walk and stable autoregressive processes, interpretable monitoring statistics are constructed to detect abnormality in nonstationary dynamics, stationary dynamics, and stationary steady conditions. This forms a holistic and pragmatic monitoring framework for industrial processes, which is beneficial for reducing false alarms and providing meaningful operational information for industrial practitioners. The efficacy of the proposed monitoring framework is validated via two case studies.

Prediction in Chaotic Environments Based on Weak Quadratic Classifiers

The problem of prediction in chaotic environments based on identifying analog situations in arrays of retrospective data are considered. Traditional recognition schemes are ineffective and form weak classifiers in cases where the system component of the observed process is represented by a non-periodic oscillatory time series (realization of chaotic dynamics). The objective is to develop a system of such classifiers, which allows for improvements in the quality of forecasts for non-stationary dynamics in flow processes. The introduced technique can be applied for the prediction of oscillatory non-periodic processes with non-stationary noise, i.e., dependence of different relay frequencies, external electric potential and microchannel width in an electrokinetic micromixer.

Limit cycles in models of circular gene networks regulated by negative feedback loops

BackgroundThe regulatory feedback loops that present in structural and functional organization of molecular-genetic systems and the phenomenon of the regulatory signal delay, a time period between the moment of signal reception and its implementation, provide natural conditions for complicated dynamic regimes in these systems. The delay phenomenon at the intracellular level is a consequence of the matrix principle of data transmission, implemented through the rather complex processes of transcription and translation.However, the rules of the influence of system structure on system dynamics are not clearly understood. Knowledge of these rules is particularly important for construction of synthetic gene networks with predetermined properties.ResultsWe study dynamical properties of models of simplest circular gene networks regulated by negative feedback mechanisms. We have shown existence and stability of oscillating trajectories (cycles) in these models. Two algorithms of construction and localization of these cycles have been proposed. For one of these models, we have solved an inverse problem of parameters identification.ConclusionsThe modeling results demonstrate that non-stationary dynamics in the models of circular gene networks with negative feedback loops is achieved by a high degree of non-linearity of the mechanism of the autorepressor influence on its own expression, by the presence of regulatory signal delay, the value of which must exceed a certain critical value, and transcription/translation should be initiated from a sufficiently strong promoter/Shine-Dalgarno site. We believe that the identified patterns are key elements of the oscillating construction design.

Intrinsic recurrence quantification analysis of nonlinear and nonstationary short-term time series.

Recurrence analysis is a powerful tool to appraise the nonlinear dynamics of complex systems and delineate the inherent laminar, divergent, or transient behaviors. Oftentimes, the effectiveness of recurrence quantification hinges upon the accurate reconstruction of the state space from a univariate time series with a uniform sampling rate. Few, if any, existing approaches quantify the recurrence properties from a short-term time series, particularly those sampled at a non-uniform rate, which are fairly ubiquitous in studies of rare or extreme events. This paper presents a novel intrinsic recurrence quantification analysis to portray the recurrence behaviors in complex dynamical systems with only short-term observations. As opposed to the traditional recurrence analysis, the proposed approach represents recurrence dynamics of a short-term time series in an intrinsic state space formed by proper rotations, attained from intrinsic time-scale decomposition (ITD) of the short time series. It is shown that intrinsic recurrence quantification analysis (iRQA), patterns harnessed from the corresponding recurrence plot, captures the underlying nonlinear and nonstationary dynamics of those short time series. In addition, as ITD does not require uniform sampling of the time series, iRQA is also applicable to unevenly spaced temporal data. Our findings are corroborated in two case studies: change detection in the Lorenz time series and early-stage identification of atrial fibrillation using short-term electrocardiogram signals.

Forced Oscillations of the Discrete Membrane Under Conditions of “Sonic Vacuum”

Abstract This study presents a new analytical model for nonlinear dynamics of a discrete rectangular membrane that is subjected to external harmonic force. It has recently been shown that the corresponding autonomous system admits a series of nonlinear normal modes. In this paper, we describe stationary and non-stationary dynamics on a single mode manifold. We suggest a simple formula for the amplitude-frequency response in both conservative and non-conservative cases and present an analytical expression (in parametric space) for thresholds for all possible bifurcations. Theoretical results obtained through asymptotic approach are confirmed by the experimental data. Experiments on the shaking table show that amplitude-frequency response to external force in a real system matches our theory. Substantial hysteresis is observed in the regimes with increasing and decreasing frequency of external force. The obtained results may be used in designing nonlinear energy sinks.

A Dynamic Systems Approach for Detecting and Localizing of Infarct-Related Artery in Acute Myocardial Infarction Using Compressed Paper-Based Electrocardiogram (ECG).

Timely evaluation and reperfusion have improved the myocardial salvage and the subsequent recovery rate of the patients hospitalized with acute myocardial infarction (MI). Long waiting time and time-consuming procedures of in-hospital diagnostic testing severely affect the timeliness. We present a Poincare pattern ensemble-based method with the consideration of multi-correlated non-stationary stochastic system dynamics to localize the infarct-related artery (IRA) in acute MI by fully harnessing information from paper-based Electrocardiogram (ECG). The vectorcardiogram (VCG) diagnostic features extracted from only 2.5-s long paper ECG recordings were used to hierarchically localize the IRA—not mere localization of the infarcted cardiac tissues—in acute MI. Paper ECG records and angiograms of 106 acute MI patients collected at the Heart Artery and Vein Center at Fresno California and the 12-lead ECG signals from the Physionet PTB online database were employed to validate the proposed approach. We reported the overall accuracies of 97.41% for healthy control (HC) vs. MI, 89.41 ± 9.89 for left and right culprit arteries vs. others, 88.2 ± 11.6 for left main arteries vs. right-coronary-ascending (RCA) and 93.67 ± 4.89 for left-anterior-descending (LAD) vs. left-circumflex (LCX). The IRA localization from paper ECG can be used to timely triage the patients with acute coronary syndromes to the percutaneous coronary intervention facilities.

A Nonconvex Archetypal Analysis for One-Class Classification Based Anomaly Detection in Cyber-Physical Systems

Data-driven anomaly detection is one of the central issues for the implementation of predictive maintenance in cyber-physical systems (CPS). The increasing nonstationary dynamics in CPS lead to complex shapes of collected process data, e.g., convex and nonconvex. Algorithms with the ability of handling nonconvex data are desired for anomaly detection tasks in CPS. Archetypal analysis selects extreme points (archetypes) to represent a dataset-mainly to improve run times, e.g., for anomaly detection. The classic archetypal analysis uses convex combinations of archetypes to represent a set of observations (data points). This leads to the performance depression of the classic archetypal analysis methods for anomaly detection tasks on nonconvex datasets. Such nonconvex sets are typical for CPS. In this article, the anomaly detection tasks are considered as one-class classification problem due to the lack of abnormal samples. A novel nonconvex archetypal one-class classification algorithm is proposed to address the challenge of nonconvex data, which combines the random projection and the AdaBoost algorithm. The major advantages of this method are its high efficiency, flexibility, and its ability to handle both convex and nonconvex datasets, i.e., it can be applied to CPS analysis tasks. The usefulness of the presented approach is evaluated for fault diagnosis tasks in CPS.

Nonstationary Dynamics of Elliptic Isotropic Conical Shells Under Distributed Loads*

We considered a solution to the problem of the forced vibrations of a truncated elliptic conical shell under a distributed impulsive load. A linear version of the equations of the Timoshenko type theory of conical shells is obtained in a non-orthogonal curvilinear coordinate system. To solve the problem, we elaborated a numerical algorithm based on the finite-difference approximation of the initial equations in the spatial and time coordinates. An example of the dynamical behavior of the conical shell is studied numerically.

Atomic self-organization emerging from tunable quadrature coupling

The recent experimental observation of dissipation-induced structural instability provides new opportunities for exploring the competition mechanism between stationary and nonstationary dynamics [Science 366, 1496 (2019)]. In that study, two orthogonal quadratures of cavity field are coupled to two different Zeeman states of a spinor Bose-Einstein condensate (BEC). Here we propose a novel scheme to couple two density-wave degrees of freedom of a BEC to two quadratures of the cavity field. Being drastically different from previous studies, the light-matter quadratures coupling in our model is endowed with a tunable coupling angle. Apart from the uniform and self-organized phases, we unravel a dynamically unstable state induced by the cavity dissipation. Interestingly, the dissipation defines a particular coupling angle, across which the instabilities disappear. Moreover, at this critical coupling angle, one of the two atomic density waves can be independently excited without affecting one another. It is also found that our system can be mapped into a reduced three-level model under the commonly used low-excitation-mode approximation. However, the effectiveness of this approximation is shown to be broken by the dissipation nature for some special system parameters, hinting that the low-excitation-mode approximation is insufficient in capturing some dissipation-sensitive physics. Our work enriches the quantum simulation toolbox in the cavity-quantum-electrodynamics system and broadens the frontiers of light-matter interaction.

Explosion induced rogue waves and chaotic multi-pulsing in a passively mode-locked all-normal dispersion fiber laser

In this work, an experimental study of non-stationary pulse dynamics consisting of explosion events and chaotic multi-pulsing from an all-normal dispersion Yb-fiber laser operating in noise-like pulse (NLP) state have been reported. During explosion in NLP state, which resembled soliton explosion, dispersive Fourier transform measurements revealed large, intermittent amplitude fluctuations in the real-time spectrum indicative of rogue waves. The fluctuations either appeared randomly at the lasing wavelength within the Yb-gain spectra or at the frequency downshifted Raman Stokes wavelength. It was also observed that such fluctuation at the Raman wavelength could even exceed the amplitude of the spectral components at the main lasing wavelength. With suitable adjustments to polarization controllers, the laser operation could be switched to chaotic multi-pulsing state where the acquisition of a large number of consecutive roundtrips revealed inter-pulse motion with unique trajectories occurring over millisecond time scales.

0439 Nonlinear Dynamics Forecasting for Personalize Prognosis of Obstructive Sleep Apnea Onsets

Abstract Introduction The emphasis on disease prevention, early detection, and preventive treatments will revolutionize the way sleep clinicians evaluate their patients. Obstructive Sleep Apnea (OSA) is one of the most prevalent sleep disorders with approximately 100 millions patients been diagnosed worldwide. The effectiveness of sleep disorder therapies can be enhanced by providing personalized and real-time prediction of OSA episode onsets. Previous attempts at OSA prediction are limited to capturing the nonlinear, nonstationary dynamics of the underlying physiological processes. Methods This paper reports an investigation into heart rate dynamics aiming to predict in real time the onsets of OSA episode before the clinical symptoms appear. The method includes (a) a representation of a transition state space network to characterize dynamic transition of apneic states (b) a Dirichlet-Process Mixture-Gaussian-Process prognostic method for estimating the distribution of the time estimate the remaining time until the onset of an impending OSA episode by considering the stochastic evolution of the normal states to an anomalous (apnea) Results The approach was tested using three datasets including (1) 20 records from 14 OSA subjects in benchmark ECG apnea databases (Physionet.org), (2) records of eight subjects from previous work. The average prediction accuracy (R2) is reported as 0.75%, with 87% of observations within the 95% confidence interval. Estimated risk indicators at 1 to 3 min till apnea onset are reported as 85.8 %, 80.2 %, and 75.5 %, respectively. Conclusion The present prognosis approach can be integrated with wearable devices to facilitate individualized treatments and timely prevention therapies. Support N/A

Non-stationary nonlinear analysis of a composite rotating shaft passing through critical speed

In this paper, nonlinear non-stationary dynamics of a nonlinear composite shaft passing through critical speed is studied. The nonlinearity is due to the large amplitude of shaft vibration. The equations of motion are obtained by three-dimensional constitutive relationships of composite materials. The gyroscopic effect, rotary inertia and coupling caused by material anisotropy are considered but shear deformation is neglected. Without any simplification, axial-flexural-flexural-torsional equations of motion (EOM) for the elastic composite shaft with variable rotational speed are obtained. The approximate analytical method namely asymptotic method is applied to analyze the nonstationary behavior of the composite shaft with constant acceleration. First, the EOMs are discretized using one and two-term Galerkin method. Then, the resulted equations are transformed to normal coordinates. Finally, the asymptotic method is applied to equations described in normal coordinates. Analytical expressions governing the amplitude and phase of motion during passage through critical speeds are obtained. By comparing the results obtained from analytical solutions, it is shown that discretization by one mode is not enough due to the existence of coupling in the equations and at least two modes are necessary for this purpose. Effects of damping, eccentricity, initial angular velocity and fiber angle on response amplitude are investigated. For verification, the results of perturbation theory are compared with numerical simulations and it is shown that there is good agreement between both methods.

Real Exchange Rates, Oil Price Spillover Effects, and Tripolarity

ABSTRACT The real exchange rates of the currencies of non-Eurozone countries are determined to a large extent by the behavior of the euro, because intra-EU trade accounts for a large proportion of the countries’ balances of payments. Given that their currencies and the euro are also influenced by the EUR/USD exchange rate and oil price changes, the tripolar model appears to provide an appropriate analytical framework. The empirical results of this study support the hypothesis that in the long run the euro-dollar and Polish zloty-euro exchange rates are driven by crude oil prices, and that the parities of the real risk-free interest rates determine the euro-dollar exchange rate in the short-run and the zloty-euro exchange rate in the long-run. They also show that in recent years the euro-dollar exchange rate was long influenced by the ECB’s asset purchase program. The impulse response analysis clearly indicates that in addition to shocks from credit default risk premiums and interest rates innovations oil price shocks too are a significant and pervasive source of the nonstationary dynamics of the exchange rates.

A Numerical Method Used for the Simulation of Self-Excited Vibrations that Arise in the Aircraft Engine Fan Blade Ring

Aeroelastic effects that are caused by blade vibrations under the action of perturbation forces are characterized by the energy exchange between the gas flow and the vibrating blades and form the basis of the physical mechanism of self-excited vibrations that can either decay (aerodamping) or be in unstable flutter mode that can result in the structure failure in a short period of time. Based on the developed mathematical model and the numerical method of aeroelastic behavior of the blade ring in the transonic gas flow (the coupled problem of nonstationary dynamics and elastic blade vibrations) the numerical analysis of aeroelasic behavior shown by the fan blade ring in the three-dimensional ideal gas flow was performed. The three-dimensional transonic ideal gas flow is described by the complete system of Euler equations represented in the integral form of the laws of conservation of mass, pulse and energy in the relative system of Cartesian coordinates. Using a modal approach, the dynamic model of a vibrating blade was reduced to the system of ordinary differential equations in terms of the modal coefficients of eigenmodes. The values of blade displacements and its speed were derived from the solution of a dynamic problem and these values are used as boundary conditions for aerodynamic problem during each of the iteration. This method of the solution of the coupled aeroelastic problem enables the prediction of the amplitude and frequency spectra for blade vibrations in the three-dimensional ideal gas flow, including forced and self-excided vibrations in order to increase the reliability of the blade systems of turbine machines. The investigations carried out provided the data on the nonstationary loads (peripheral and axial loads and the aerodynamic moment) that have an effect on the blades and also the amplitude and frequency spectra of blade vibrations.

On‐site surrogates for large‐scale calibration

AbstractMotivated by a computer model calibration problem from the oil and gas industry, involving the design of a honeycomb seal, we develop a new Bayesian methodology to cope with limitations in the canonical apparatus stemming from several factors. We propose a new strategy of on‐site design and surrogate modeling for a computer simulator acting on a high‐dimensional input space that, although relatively speedy, is prone to numerical instabilities, missing data, and nonstationary dynamics. Our aim is to strike a balance between data‐faithful modeling and computational tractability in a calibration framework—tailoring the computer model to a limited field experiment. Situating our on‐site surrogates within the canonical calibration apparatus requires updates to that framework. We describe a novel yet intuitive Bayesian setup that carefully decomposes otherwise prohibitively large matrices by exploiting the sparse blockwise structure. Empirical illustrations demonstrate that this approach performs well on toy data and our motivating honeycomb example.