Aperiodic Fluctuations Research Articles

Aperiodic brain activity tracks temporal fluctuations during sleep: an (i)EEG study

Aperiodic brain activity tracks temporal fluctuations during sleep: an (i)EEG study

Early warnings of tipping in a non-autonomous turbulent reactive flow system: Efficacy, reliability, and warning times.

Real-world complex systems such as the earth's climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit aperiodic fluctuations, either chaotic or stochastic in nature. Often, the parameters describing a system vary with time, showing time dependency. Constrained by these effects, it becomes difficult to be warned of an impending critical transition, as such effects contaminate the precursory signals of the transition. Therefore, a need for efficient and reliable early-warning signals (EWSs) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWSs in the context of a non-autonomous turbulent thermoacoustic system. In particular, we investigate the efficacy of different EWS in forecasting the onset of thermoacoustic instability (TAI) and their reliability with respect to the rate of change of the control parameter. This is the first experimental study of tipping points in a non-autonomous turbulent thermoacoustic system. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWSs are derived from critical slowing down, spectral properties, and fractal characteristics of the system variables. The state of TAI is associated with large amplitude acoustic pressure oscillations that could lead thermoacoustic systems to break down. We consider acoustic pressure fluctuations as a potential system variable to perform the analysis. Our analysis shows that irrespective of the rate of variation of the control parameter, the Hurst exponent and variance of autocorrelation coefficients warn of an impending transition well in advance and are more reliable than other EWS measures. Additionally, we show the variation in the warning time to an impending TAI with rates of change of the control parameter. We also investigate the variation in amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws that could be significant in prediction and devising control actions to mitigate TAI.

Oscillatory vs. non-oscillatory subthalamic beta activity in Parkinson's disease.

Parkinson's disease is characterized by exaggerated beta activity (13-35Hz) in cortico-basal ganglia motor loops. Beta activity includes both periodic fluctuations (i.e. oscillatory activity) and aperiodic fluctuations reflecting spiking activity and excitation/inhibition balance (i.e. non-oscillatory activity). However, the relative contribution, dopamine dependency and clinical correlations of oscillatory vs. non-oscillatory beta activity remain unclear. We recorded, modelled and analysed subthalamic local field potentials in parkinsonian patients at rest while off or on medication. Autoregressive modelling with additive 1/f noise clarified the relationships between measures of beta activity in the time domain (i.e. amplitude and duration of beta bursts) or in the frequency domain (i.e. power and sharpness of the spectral peak) and oscillatory vs. non-oscillatory activity: burst duration and spectral sharpness are specifically sensitive to oscillatory activity, whereas burst amplitude and spectral power are ambiguously sensitive to both oscillatory and non-oscillatory activity. Our experimental data confirmed the model predictions and assumptions. We subsequently analysed the effect of levodopa, obtaining strong-to-extreme Bayesian evidence that oscillatory beta activity is reduced in patients on vs. off medication, with moderate evidence for absence of modulation of the non-oscillatory component. Finally, specifically the oscillatory component of beta activity correlated with the rate of motor progression of the disease. Methodologically, these results provide an integrative understanding of beta-based biomarkers relevant for adaptive deep brain stimulation. Biologically, they suggest that primarily the oscillatory component of subthalamic beta activity is dopamine dependent and may play a role not only in the pathophysiology but also in the progression of Parkinson's disease. KEY POINTS: Betaactivity in Parkinson's disease includes both true periodic fluctuations (i.e. oscillatory activity) and aperiodic fluctuationsreflecting spiking activity and synaptic balance (i.e. non-oscillatory activity). Therelative contribution, dopamine dependency and clinical correlations of oscillatory vs.non-oscillatory beta activity remain unclear. Burstduration and spectral sharpness are specifically sensitive to oscillatoryactivity, while burst amplitude and spectral power are ambiguously sensitive toboth oscillatory and non-oscillatory activity. Only theoscillatory component of subthalamic beta activity is dopamine-dependent. Stronger beta oscillatory activity correlates with faster motor progression of the disease.

Interacting information streams on the nephron arterial network

Blood flow and glomerular filtration in the kidney are regulated by two mechanisms acting on the afferent arteriole of each nephron. The two mechanisms operate as limit cycle oscillators, each responding to a different signal. The myogenic mechanism is sensitive to a transmural pressure difference across the wall of the arteriole, and tubuloglomerular feedback (TGF) responds to the NaCl concentration in tubular fluid flowing into the nephron’s distal tubule,. The two mechanisms interact with each other, synchronize, cause oscillations in tubular flow and pressure, and form a bimodal electrical signal that propagates into the arterial network. The electrical signal enables nephrons adjacent to each other in the arterial network to synchronize, but non-adjacent nephrons do not synchronize. The arteries supplying the nephrons have the morphologic characteristics of a rooted tree network, with 3 motifs characterizing nephron distribution. We developed a model of 10 nephrons and their afferent arterioles in an arterial network that reproduced these structural characteristics, with half of its components on the renal surface, where experimental data suitable for model validation is available, and the other half below the surface, from which no experimental data has been reported. The model simulated several interactions: TGF-myogenic in each nephron with TGF modulating amplitude and frequency of the myogenic oscillation; adjacent nephron-nephron with strong coupling; non-adjacent nephron-nephron, with weak coupling because of electrical signal transmission through electrically conductive arterial walls; and coupling involving arterial nodal pressure at the ends of each arterial segment, and between arterial nodes and the afferent arterioles originating at the nodes. The model predicted full synchronization between adjacent nephrons pairs and partial synchronization among weakly coupled nephrons, reproducing experimental findings. The model also predicted aperiodic fluctuations of tubular and arterial pressures lasting longer than TGF oscillations in nephrons, again confirming experimental observations. The model did not predict complete synchronization of all nephrons.

Experimental Investigation of Combustion Dynamics in a High-Pressure Liquid-Fueled Swirl Combustor

Abstract In this paper, we present combustor acoustics in a high-pressure liquid-fueled rich burn—quick quench—lean burn (RQL) styled swirl combustor with two separate fuel circuits. The fuel circuits are the primary (which has a pressure atomizer nozzle) and secondary (which has an air blast type nozzle) circuits. The data were acquired during two dynamical regimes—combustion noise, where there is an absence of large amplitude oscillations during the unsteady combustion process, and intermittency, where there are intermittent bursts of high amplitude oscillations that appear in a near-random fashion amidst regions of aperiodic low amplitude fluctuations. This dynamic transition from combustion noise to combustion intermittency is investigated experimentally by systematically varying the fuel equivalence ratio and primary-secondary fuel splits. Typical measures such as the amplitude of oscillations cannot serve as a measure of change in the dynamics from combustion noise to intermittency due to the highly turbulent nature. Hence, recurrence plots and complex networks are used to understand the differences in the combustor acoustics and velocity data during the two different regimes. We observe that the combustor transitions from stable operation to intermittency when the equivalence ratio is increased for a given primary fuel flowrate and conversely when the percentage of secondary fuel flowrate is increased for a given equivalence ratio. The contribution of this work is to demonstrate methodologies to detect combustion instability boundaries when approaching them from the stable side in highly turbulent, noisy combustors.

Can online particle counters and electrochemical sensors distinguish normal periodic and aperiodic drinking water quality fluctuations from contamination?

Early warning systems monitoring the quality of drinking water need to distinguish between normal quality fluctuations and those caused by contaminants. Thus, to decrease the number of false positive events, normal water quality fluctuations, whether periodic or aperiodic, need to be characterized. For this, we used a novel flow-imaging particle counter, a light-scattering particle counter, and electrochemical sensors to monitor the drinking water quality of a pressure zone in a building complex for 109 days. Data were analyzed to determine the feasibility of the sensors and particle counters to distinguish periodic and aperiodic fluctuations from real-life contaminants. The concentrations of particles smaller than 10 μm and N, Small, Large, and B particles showed sudden changes recurring daily, likely due to the flow rate changes in the building complex. Conversely, the concentrations of larger than 10 μm particles and C particles, in addition to the responses of electrochemical sensors, remained in their low typical values despite flow rate changes. The aperiodic events, likely resulting from an abnormally high flow rate in the water mains due to maintenance, were detected using particle counters and electrochemical sensors. This study provides insights into choosing water quality sensors by showing that machine learning-based particle classes, such as B, C, F, and particles larger than 10 μm are promising in distinguishing contamination from aperiodic and periodic fluctuations while the use of other particle classes and electrochemical sensors may require dynamic baseline to decrease false positive events in an early warning system.

Enhanced ADRC With Quasi-Resonant Control for PMSM Speed Regulation Considering Aperiodic and Periodic Disturbances

Smooth speed regulation is important for permanent magnet synchronous motor (PMSM) drives. However, there exist aperiodic and periodic disturbances in the speed loop, causing speed fluctuations. To address the problem, an active disturbance rejection control (ADRC) is combined with quasi-resonant controllers (QRCs) for the PMSM speed loop. The QRCs are embedded in the control law of the ADRC and operate in parallel with the extended state observer (ESO). The QRCs are designed to compensate for the periodic disturbance, while the ESO is designed to estimate and compensate for the aperiodic disturbance. The stability and antidisturbance capability of the studied scheme are analyzed systematically, which can guide the tuning of control parameters. Compared with the existing ADRC-based schemes, the proposed approach is designed to attenuate aperiodic and periodic speed fluctuations simultaneously. Finally, the effectiveness of the studied approach is validated on a 2.2-kW PMSM drive platform.

Numerical study of the vortex breakdown and vortex reconnection in the flow path of high-pressure water turbine

The paper presents a study of the instability of the precessing vortex core in the model of the draft tube of a hydraulic turbine. The study was carried out using numerical modeling using various approaches: URANS, RSM, LES. The best agreement with the experimental data was shown by the RSM and LES methods with the modelling of the runner rotation by the sliding mesh method. In the regime under consideration, the precessing vortex rope is subject to instability, which leads to reconnection of its turns and the formation of an isolated vortex ring. Reconnection of the vortex core leads to aperiodic and intense pressure fluctuations recorded on the diffuser wall.

Interpretation of Intermittent Combustion Oscillations by a New Linearization Procedure

The transition from the low-amplitude, aperiodic fluctuation to thermoacoustic instability is usually treated as a Hopf bifurcation, but the transition incorporates complex dynamical behaviors. Intermittent oscillations commonly occur in the transition process wherein chaotic states alternate with limit cycle oscillations and both the chaotic state and the limit cycle oscillation last with no fixed period. Intermittent oscillations that occur in the thermoacoustic system are demonstrated to be deterministic. A Koopman linearization procedure is implemented to model the intermittent combustion oscillations in the backward-facing step combustor. The nonlinear dynamics of intermittent combustion oscillations are approximated as a forced linear system in an orthogonal space, which is constructed by singular value decomposition of a delay coordinates matrix. The phase space of an intermittent combustion oscillation can be divided into linear and nonlinear regions by the magnitude of the nonlinear term in the forced linear system. As a result, intermittent combustion oscillations can be described as the transition between chaotic states and limit cycle oscillations, and the transition occurs when the nonlinear term is large.

Inferring kinetic parameters of oscillatory gene regulation from single cell time-series data.

Gene expression dynamics, such as stochastic oscillations and aperiodic fluctuations, have been associated with cell fate changes in multiple contexts, including development and cancer. Single cell live imaging of protein expression with endogenous reporters is widely used to observe such gene expression dynamics. However, the experimental investigation of regulatory mechanisms underlying the observed dynamics is challenging, since these mechanisms include complex interactions of multiple processes, including transcription, translation and protein degradation. Here, we present a Bayesian method to infer kinetic parameters of oscillatory gene expression regulation using an auto-negative feedback motif with delay. Specifically, we use a delay-adapted nonlinear Kalman filter within a Metropolis-adjusted Langevin algorithm to identify posterior probability distributions. Our method can be applied to time-series data on gene expression from single cells and is able to infer multiple parameters simultaneously. We apply it to published data on murine neural progenitor cells and show that it outperforms alternative methods. We further analyse how parameter uncertainty depends on the duration and time resolution of an imaging experiment, to make experimental design recommendations. This work demonstrates the utility of parameter inference on time course data from single cells and enables new studies on cell fate changes and population heterogeneity.

Case Report: Aperiodic Fluctuations of Neural Activity in the Ictal MEG of a Child With Drug-Resistant Fronto-Temporal Epilepsy.

Successful surgical treatment of patients with focal drug-resistant epilepsy remains challenging, especially in cases for which it is difficult to define the area of cortex from which seizures originate, the seizure onset zone (SOZ). Various diagnostic methods are needed to select surgical candidates and determine the extent of resection. Interictal magnetoencephalography (MEG) with source imaging has proven to be useful for presurgical evaluation, but the use of ictal MEG data remains limited. The purpose of the present study was to determine whether pre-ictal variations of spectral properties of neural activity from ictal MEG recordings are predictive of SOZ location.We performed a 4 h overnight MEG recording in an 8-year-old child with drug-resistant focal epilepsy of suspected right fronto-temporal origin and captured one ~45-s seizure. The patient underwent a right temporal resection from the anterior temporal neocortex and amygdala to the mid-posterior temporal neocortex, sparing the hippocampus proper. She remains seizure-free 21 months postoperatively. The histopathological assessment confirmed frank focal cortical dysplasia (FCD) type IIa in the MEG-defined SOZ, which was based on source imaging of averaged ictal spikes at seizure onset. We investigated temporal changes (inter-ictal, pre-ictal, and ictal periods) together with spatial differences (SOZ vs. control regions) in spectral parameters of background brain activity, namely the aperiodic broadband offset and slope, and assessed how they confounded the interpretation of apparent variations of signal power in typical electrophysiological bands. Our data show that the SOZ was associated with a higher aperiodic offset and exponent during the seizure compared to control regions. Both parameters increased in all regions from 2 min before the seizure onwards. Regions anatomically closer to the SOZ also expressed higher values compared to contralateral regions, potentially indicating ictal spread. We also show that narrow-band power changes were caused by these fluctuations in the aperiodic component of ongoing brain activity. Our results indicate that the broadband aperiodic component of ongoing brain activity cannot be reduced to background noise of no physiological interest, and rather may be indicative of the neuropathophysiology of the SOZ. We believe these findings will inspire future studies of ictal MEG cases and confirm their significance.

Capturing multifractality of pressure fluctuations in thermoacoustic systems using fractional-order derivatives.

The stable operation of a turbulent combustor is not completely silent; instead, there is a background of small amplitude aperiodic acoustic fluctuations known as combustion noise. Pressure fluctuations during this state of combustion noise are multifractal due to the presence of multiple temporal scales that contribute to its dynamics. However, existing models are unable to capture the multifractality in the pressure fluctuations. We conjecture an underlying fractional dynamics for the thermoacoustic system and obtain a fractional-order model for pressure fluctuations. The data from this model has remarkable visual similarity to the experimental data and also has a wide multifractal spectrum during the state of combustion noise. Quantitative similarity with the experimental data in terms of the Hurst exponent and the multifractal spectrum is observed during the state of combustion noise. This model is also able to produce pressure fluctuations that are qualitatively similar to the experimental data acquired during intermittency and thermoacoustic instability. Furthermore, we argue that the fractional dynamics vanish as we approach the state of thermoacoustic instability.

Observation of quantum interference conductance fluctuations in metal rings with strong spin–orbit coupling

We investigated the magnetotransport properties of mesoscopic platinum nanostructures (wires and rings) with sub-100 nm lateral dimensions at very low temperatures. Despite the strong spin–orbit interaction in platinum, oscillation of the conductance as a function of the external magnetic field due to quantum interference effects was found to appear. The oscillation was decomposed into Aharonov–Bohm periodic oscillations and aperiodic fluctuations of the conductance due to a magnetic flux piercing the loop of the ring and the metal wires forming the nanostructures, respectively. We also investigated the magnetotransport under different bias currents to explore the interplay between electron phase coherence and spin accumulation effects in strong spin–orbit conductors.

Oscillation-Based Connectivity Architecture Is Dominated by an Intrinsic Spatial Organization, Not Cognitive State or Frequency.

Functional connectivity of neural oscillations (oscillation-based FC) is thought to afford dynamic information exchange across task-relevant neural ensembles. Although oscillation-based FC is classically defined relative to a prestimulus baseline, giving rise to rapid, context-dependent changes in individual connections, studies of distributed spatial patterns show that oscillation-based FC is omnipresent, occurring even in the absence of explicit cognitive demands. Thus, the issue of whether oscillation-based FC is primarily shaped by cognitive state or is intrinsic in nature remains open. Accordingly, we sought to reconcile these observations by interrogating the ECoG recordings of 18 presurgical human patients (8 females) for state dependence of oscillation-based FC in five canonical frequency bands across an array of six task states. FC analysis of phase and amplitude coupling revealed a highly similar, largely state-invariant (i.e., intrinsic) spatial component across cognitive states. This spatial organization was shared across all frequency bands. Crucially, however, each band also exhibited temporally independent FC dynamics capable of supporting frequency-specific information exchange. In conclusion, the spatial organization of oscillation-based FC is largely stable over cognitive states (i.e., primarily intrinsic in nature) and shared across frequency bands. Together, our findings converge with previous observations of spatially invariant patterns of FC derived from extremely slow and aperiodic fluctuations in fMRI signals. Our observations indicate that "background" FC should be accounted for in conceptual frameworks of oscillation-based FC targeting task-related changes.SIGNIFICANCE STATEMENT A fundamental property of neural activity is that it is periodic, enabling functional connectivity (FC) between distant regions through coupling of their oscillations. According to task-based studies, such oscillation-based FC is rapid and malleable to meet cognitive task demands. Studying distributed FC patterns instead of FC in a few individual connections, we found that oscillation-based FC is largely stable across various cognitive states and shares a common layout across oscillation frequencies. This stable spatial organization of FC in fast oscillatory brain signals parallels the known stability of fMRI-based intrinsic FC architecture. Despite the observed spatial state and frequency invariance, FC of individual connections was temporally independent between frequency bands, suggesting a putative mechanism for malleable frequency-specific FC to support cognitive tasks.

Bursting during intermittency route to thermoacoustic instability: Effects of slow-fast dynamics.

Intermittency observed prior to thermoacoustic instability is characterized by the occurrence of bursts of high-amplitude periodic oscillations (active state) amidst epochs of low-amplitude aperiodic fluctuations (rest state). Several model-based studies conjectured that bursting arises due to the underlying turbulence in the system. However, such intermittent bursts occur even in laminar and low-turbulence combustors, which cannot be explained by models based on turbulence. We assert that bursting in such combustors may arise due to the existence of subsystems with varying timescales of oscillations, thus forming slow-fast systems. Experiments were performed on a horizontal Rijke tube and the effect of slow-fast oscillations was studied by externally introducing low-frequency sinusoidal modulations in the control parameter. The induced bursts display an abrupt transition between the rest and the active states. The growth and decay patterns of such bursts show asymmetry due to delayed bifurcation caused by slow oscillations of the control parameter about the Hopf bifurcation point. Further, we develop a phenomenological model for the interaction between different subsystems of a thermoacoustic system by either coupling the slow and fast subsystems or by introducing noise in the absence of slow oscillations of the control parameter. We show that interaction between subsystems with different timescales leads to regular amplitude modulated bursting, while the presence of noise induces irregular amplitude modulations in the bursts. Thus, we speculate that bursting in laminar and low-turbulence systems occurs predominantly due to the interdependence between slow and fast oscillations, while bursting in high-turbulence systems is predominantly influenced by the underlying turbulence.

(Invited) Design of Hydrogel Material and 3D-Printed Molding for Imitating the Tactile Textured Properties of Moon Jellyfish

The current research on jellyfish robots designs a mechanical body that can assemble a waterproof and flexible drive system consisting of cables, motors and actuators to reproduce a swimming mechanism of jellyfish. On the other hand, research on jellyfish robots as visual art focuses on soft materials and demonstrates a technique to produce jellyfish swimming by the drag force received from the running water of the pump without using a special control mechanism. Most jellyfish robots that have been developed as toys imitate only their appearance, and they are being developed as commercial products with a low economic burden by using inexpensive materials such as vinyl and fishing line. The swimming of such jellyfish robots is far from the actual jellyfish. From this, it can be seen that the mechanism or material factor is largely due to the imitation of jellyfish. This study proposes a hydrogel jellyfish robot that approximates shape, water content, color and texture to a jellyfish. The body composition of moon jellyfish is gelatinous with a water content of 95% or more. The texture mimicry of jellyfish-inspired robots can be realized by using an equivalent hydrogel as a constituent material. Therefore, we develop a DMAAm gel that can artificially reproduce the tactile characteristics depending on the constituent materials. The chemical composition of the gel contains dimethylacrylamide (DMAAm) as the monomer, N, N'-Methylenebisacrylamide (MBAA) as the cross-linking agent, diphenyl (2,4,6-trimethylbenzoyl) phosphine oxide (TPO) as the photopolymerization initiator, polyethylene glycol and water as the solvent. The gel of this formulation produces a white translucent color due to the solvent PEG and has a swelling ratio of about 2.5 times. Additionally, this study shows a three-dimensional modeling technology that molds this gel into the appearance of a jellyfish. Our hydrogel modeling adopts silicone resin using 3D printer. This mold consists of both an umbrella-shaped silicone and a silicone with the geometric pattern of a jellyfish stomach.The two molds are combined and the gel solution is poured from the solution inlet provided in the upper mold and cured by UV irradiation for molding. In addition, a gel film is created by sandwiching the pre-gel solution in a PET plate and UV curing. By irradiating the gel film and the gel jellyfish umbrella with UV again, we can develop a jellyfish robot with tentacles. Our jellyfish robot has a thickness accuracy on the order of a few millimeters and a hardness that can be crushed by its own weight outside water, and circulates in a liquid at a flow rate of about 40 L / min. Moreover, the tentacles have a thickness accuracy of the order of a few micrometers, and they are gel body structures with different thicknesses. We show that hydrogel jellyfish can imitate swimming by approximating the constituent material and shape to the actual moon jellyfish. Then, using our DMAAm gel and Wizard gel, we will compare and verify the visual effect caused by the difference in the texture of the blended gel from the time series change of the projected area by binary image processing. The results show that the wizard gel jellyfish does not deform under the conditions of circulating water flow in a water tank used for breeding commercial jellyfish, and it is difficult to exhibit jellyfish-like behavior. However, the millimeter-scale DMMAm gel reproduces the periodic contraction due to the elastic change, and the micrometer-order DMMAm gel has an aperiodic fluctuation behavior. Therefore, our gel jellyfish robot can simultaneously observe jellyfish contraction and tentacle fluctuation behavior. Finally, this study discusses a method for quantitatively evaluating from swimming by the gel jellyfish robot developed by soft body simulation based on Position Based Dynamics in virtual space. Figure 1

Forecasting unprecedented ecological fluctuations.

Forecasting 'Black Swan' events in ecosystems is an important but challenging task. Many ecosystems display aperiodic fluctuations in species abundance spanning orders of magnitude in scale, which have vast environmental and economic impact. Empirical evidence and theoretical analyses suggest that these dynamics are in a regime where system nonlinearities limit accurate forecasting of unprecedented events due to poor extrapolation of historical data to unsampled states. Leveraging increasingly available long-term high-frequency ecological tracking data, we analyze multiple natural and experimental ecosystems (marine plankton, intertidal mollusks, and deciduous forest), and recover hidden linearity embedded in universal 'scaling laws' of species dynamics. We then develop a method using these scaling laws to reduce data dependence in ecological forecasting and accurately predict extreme events beyond the span of historical observations in diverse ecosystems.

A comprehensive study on spectral analysis and anomaly detection of river water quality dynamics with high time resolution measurements

Systemic analysis of hydrology and water quality fluctuations using a data-intensive approach is an emerging research area and is significant for understanding hydrological processes. However, there is very limited understanding of the high-frequency characteristics of water quality fluctuations in the frequency domain. This study proposes a generic systemic framework to comprehensively analyse river water quality dynamics using a combination of Fourier and wavelet spectral analyses with high temporal resolution measurements. This framework identifies long-term, short-term, periodic, aperiodic, normal baseline and abnormal fluctuations, with particularly focus on detecting transient anomaly events due to their importance for watershed management. This study was conducted on the Potomac River, USA, where seven parameters, water temperature (Temp), pH, dissolved oxygen (DO), conductance (Cond), turbidity (Turb), nitrate plus nitrite (NOx-N) and discharge (Disc), were monitored every 15 min for two years at five sites/sub-catchments. Fast Fourier transform (FFT) revealed that Temp, pH and DO exhibited typical low-frequency periodic fluctuations, such as seasonal and bi-annual fluctuations, as well as interesting high-frequency periodic fluctuations, such as 12-hour and 8-hour fluctuations, which were identified as periodic anomalies. Cond, Turb and NOx-N presented universal temporal scaling phenomena, i.e., 1/f fluctuation, at all sites, as shown by the power spectral density. The scaling exponent β ranged between 1 and 3 and presented the order of βCond > βNOx-N > βTurb. The continuous wavelet transform (CWT) associated with contour-based scalograms successfully identified the time, location, duration and magnitude of transient anomaly events and classified two anomaly patterns: abrupt changes and large swings. The two patterns exhibited clearly different spectral energy distributions, i.e., pseudo-frequencies, on the CWT scales. A preliminary causality analysis found that the frequency of occurrence of turbidity anomaly events (FOATurb) was proportional to the product of the developed land area percentage and FOATemp, and FOANOx-N was proportional to the product of forest land area percentage and FOAdisc. Wavelet coherence analysis showed different hysteresis characteristics of different water quality parameters. In particular, Turb and NOx-N presented significantly different coherent fluctuation behaviours between high-frequency and low-frequency regions. Some findings of this study are still difficult to explain at this stage. High-frequency monitoring combined with spectral analysis provides new insights into the details of water quality dynamics, which can help to develop a new index and framework for the reliability, resilience, and management of watershed water quality vulnerability. These results can also be used to design new algorithms for online anomaly detection.

Two-dimensional correlation analysis of periodicity in active galactic nuclei time series

Abstract The active galactic nuclei (AGN) are among the most powerful sources with an inherent, pronounced and random variation of brightness. The randomness of their time series is so subtle as to blur the border between aperiodic fluctuations and noisy oscillations. This poses challenges to analysing of such time series because neither visual inspection nor pre-exisitng methods can identify well oscillatory signals in them. Thus, there is a need for an objective method for periodicity detection. Here we review our a new data analysis method that combines a two-dimensional correlation (2D) of time series with the powerful methods of Gaussian processes. To demonstrate the utility of this technique, we apply it to two example problems which were not exploited enough: damped rednoised artificial time series mimicking AGN time series and newly published observed time series of changing look AGN (CL AGN) NGC 3516. The method successfully detected periodicities in both types of time series. Identified periodicity of ~4 yr in NGC 3516 allows us to speculate that if the thermal instability formed in its accretion disc (AD) on a time scale resembling detected periodicity then AD radius could be ~0.0024 pc.

Early detection of thermoacoustic combustion oscillations using a methodology combining statistical complexity and machine learning.

We conduct an experimental study on early detection of thermoacoustic combustion oscillations using a method combining statistical complexity and machine learning, including the characterization of intermittent combustion oscillations. Abrupt switching from aperiodic small-amplitude oscillations to periodic large-amplitude oscillations and vice versa appears in pressure fluctuations. The dynamic behavior of aperiodic small-amplitude pressure fluctuations represents chaos. The complexity-entropy causality plane effectively captures the subtle changes in the combustion state during a transition to well-developed combustion oscillations. The feature space of the complexity-entropy causality plane, which is obtained by a support vector machine, has potential use for detecting a precursor of combustion oscillations.