Red Noise Research Articles

How Long Will the Quasar UV/Optical Flickering Be Damped? II. The Observational Test

The characteristic timescale at which the variability of active galactic nuclei (AGNs) turns from red noise to white noise can probe the accretion physics around supermassive black holes (SMBHs). A number of works have studied the characteristic timescale of quasars and obtained quite different scaling relations between the timescale and quasar physical properties. One possible reason for the discrepancies is that the characteristic timescale can be easily underestimated if the light curves are not long enough. In this work, we construct well-defined AGN samples to observationally test the relationships between the characteristic timescale and AGN properties obtained by previous works. Our samples eliminate the effects of insufficient light-curve lengths. We confirm that the timescale predictions of the Corona Heated Accretion disk Reprocessing model are consistent with our timescale measurements. The timescale predictions by empirical relations are systematically smaller than our measured ones. Our results provide further evidence that AGN variability is driven by thermal fluctuations in SMBH accretion disks. Future flagship time-domain surveys can critically test our conclusions and reveal the physical nature of AGN variability.

Solving Max-Cut Problem Using Spiking Boltzmann Machine Based on Neuromorphic Hardware with Phase Change Memory.

Efficiently solving combinatorial optimization problems (COPs) such as Max-Cut is challenging because the resources required increase exponentially with the problem size. This study proposes a hardware-friendly method for solving the Max-Cut problem by implementing a spiking neural network (SNN)-based Boltzmann machine (BM) in neuromorphic hardware systems. To implement the hardware-oriented version of the spiking Boltzmann machine (sBM), the stochastic dynamics of leaky integrate-and-fire (LIF) neurons with random walk noise are analyzed, and an innovative algorithm based on overlapping time windows is proposed. The simulation results demonstrate the effective convergence and high accuracy of the proposed method for large-scale Max-Cut problems. The proposed method is validated through successful hardware implementation on a 6-transistor/2-resistor (6T2R) neuromorphic chip with phase change memory (PCM) synapses. In addition, as an expansion of the algorithm, several annealing techniques and bias split methods are proposed to improve convergence, along with circuit design ideas for efficient evaluation of sampling convergence using cell arrays and spiking systems. Overall, the results of the proposed methods demonstrate the potential of energy-efficient and hardware-implementable approaches using SNNs to solve COPs. To the best of the author's knowledge, this is the first study to solve the Max-Cut problem using an SNN neuromorphic hardware chip.

Long-range cross-correlations between center of pressure velocity and colored noises provided during quiet standing

Unperceivable electrical noise stimulation has been applied to improve postural control through the enhancement of somatosensory feedback. It has been observed that stimulation with a pink noise (1/f) structure is more effective than stimulation with other noise structures. In addition, the 1/f structure embedded in the postural control system may have a superior effect on postural control stabilization. However, the direct relationship between the long-range correlations of the pink-noise signal applied to somatosensory receptors and those of the postural control system has not been elucidated. Thus, we aimed to explore a common long-range correlation factor shared in the time series of the provided noise and foot center of pressure (CoP) during quiet standing. Sixteen young adults stood quietly on the force platform for 65 s. Four noise conditions (no stimulation and stimulation of knee joints with white-, pink-, and red-noise-like signals) were employed during the standing trials. The detrending moving-average cross-correlation analysis revealed that in each of the anteroposterior and mediolateral directions, the CoP velocity time series displayed significant long-range cross-correlations with the white and pink noise signals provided at that time, whereas such an effect was not observed in the red noise signal. This result indicates that pink and white noise signals would alter the temporal behavior of the CoP during quiet standing, although the mechanism remains to be elucidated.

Searching for the mHz variability in the TESS observations of nova-like cataclysmic variables

We investigated the fast optical variability of selected nova-like cataclysmic variables observed by the satellite. We searched for break frequencies b $) in the corresponding power density spectra (PDS). The goal is to study whether these systems in an almost permanent high optical state exhibit preferred $f_ b $ around 1\,mHz. We selected non-interrupted light curve portions with durations of 5 and 10 days. We divided these portions into ten equally long light curve subsamples and calculated mean PDS. We searched for $f_ b $ in the frequency interval from log($f$/Hz) = -3.5 to -2.4. We defined as a positive detection when the $f_ b $ was present in at least 50<!PCT!> of the light curve portions with a predefined minimum number of detections. We have measured $f_ b $ in 15 nova-like systems and confirmed that the value of this frequency is clustered around 1\,mHz with a maximum of the distribution between log($f$/Hz) = -2.95 and -2.84. The confidence that this maximum is not a random feature of a uniform distribution is at least 96<!PCT!>. This is a considerable improvement on the previous value of 69<!PCT!>. We discuss the origin of these b $ in the context of the sandwich model in which a central hot X-ray corona surrounds a central optically thick disc. This scenario could be supported by a correlation between the white dwarf mass and $f_ b $; the larger the mass, the lower the frequency. We see such a tendency in the measured data; however, the data are too scattered and based on a low number of measurements. Finally, it appears that systems with detected $f_ b $ have a lower inclination than 60-75$^ circ $. In higher-inclination binaries, the central disc is not seen and the PDS is dominated by red noise. This also supports the inner disc regions as being the source of the observed $f_ b

Reducing Instrumental Errors in Parkes Pulsar Timing Array Data

This paper demonstrates the impact of state-of-the-art instrumental calibration techniques on the precision of arrival times obtained from 9.6 yr of observations of millisecond pulsars using the Murriyang 64 m CSIRO Parkes Radio Telescope. Our study focuses on 21 cm observations of 25 high-priority pulsars that are regularly observed as part of the Parkes Pulsar Timing Array project, including those predicted to be the most susceptible to calibration errors. We employ measurement equation template matching (METM) for instrumental calibration and matrix template matching (MTM) for arrival time estimation, resulting in significantly improved timing residuals with up to a sixfold reduction in white noise compared to arrival times estimated using scalar template matching and conventional calibration based on the ideal feed assumption. The median relative reduction in white noise is 33%, and the maximum absolute reduction is 4.5 μs. For PSR J0437−4715, METM and MTM reduce the best-fit power-law amplitude (2.7σ) and spectral index (1.7σ) of the red noise in the arrival time residuals, which can be tentatively interpreted as mitigation of 1/f noise due to otherwise unmodeled steps in polarimetric response. These findings demonstrate the potential to directly enhance the sensitivity of pulsar timing array experiments through more accurate methods of instrumental calibration and arrival time estimation.

Information Criteria for Signal Extraction Using Singular Spectrum Analysis: White and Red Noise

In singular spectrum analysis, which is applied to signal extraction, it is of critical importance to select the number of components correctly in order to accurately estimate the signal. In the case of a low-rank signal, there is a challenge in estimating the signal rank, which is equivalent to selecting the model order. Information criteria are commonly employed to address these issues. However, singular spectrum analysis is not aimed at the exact low-rank approximation of the signal. This makes it an adaptive, fast, and flexible approach. Conventional information criteria are not directly applicable in this context. The paper examines both subspace-based and information criteria, proposing modifications suited to the Hankel structure of trajectory matrices employed in singular spectrum analysis. These modifications are initially developed for white noise, and a version for red noise is also proposed. In the numerical comparisons, a number of scenarios are considered, including the case of signals that are approximated by low-rank signals. This is the most similar to the case of real-world time series. The criteria are compared with each other and with the optimal rank choice that minimizes the signal estimation error. The results of numerical experiments demonstrate that for low-rank signals and noise levels within a region of stable rank detection, the proposed modifications yield accurate estimates of the optimal rank for both white and red noise cases. The method that considers the Hankel structure of the trajectory matrices appears to be a superior approach in many instances. Reasonable model orders are obtained for real-world time series. It is recommended that a transformation be applied to stabilize the variance before estimating the rank.

Patterns in the Chaos: The Moving Hurst Indicator and Its Role in Indian Market Volatility

Estimating the impact of volatility in financial markets is challenging due to complex dynamics, including random fluctuations involving white noise and trend components involving brown noise. In this study, we explore the potential of leveraging the chaotic properties of time series data for improved accuracy. Specifically, we introduce a novel trading strategy based on a technical indicator, Moving Hurst (MH). MH utilizes the Hurst exponent which characterizes the chaotic properties of time series. We hypothesize and then prove empirically that MH outperforms traditional indicators like Moving Averages (MA) in analyzing Indian equity indices and capturing profitable trading opportunities while mitigating the impact of volatility.

Identifying chaotic dynamics in noisy time series through multimodal deep neural networks

Abstract Chaos detection is the problem of identifying whether a series of measurements is being sampled from an underlying set of chaotic dynamics. The unavoidable presence of measurement noise significantly affects the performance of chaos detectors, as discerning chaotic dynamics from stochastic signals becomes more challenging. This paper presents a computationally efficient multi-modal deep neural network tailored for chaos detection by combining information coming from the analysis of time series, recurrence plots and spectrograms. The proposed approach is the first one suitable for multi-class classification of chaotic systems while being robust with respect to measurement noise, and is validated on a dataset of 15 different chaotic and non-chaotic dynamics subject to white, pink or brown coloured noise.

Estimating and Analyzing The Stability of Brazilian Gnss Stations for Tectonic Studies

The detailed study of stresses and strains is fundamental for geophysical and geodetic studies, enabling the development of plate motion models, geodynamic processes and several proposals. GNSS positioning has been used to estimate these stresses and strains. However, for the accuracy required, it is necessary a rigorous assessment of the behavior of GNSS stations and their position time series. This paper aims to analyze the influence of the different types of geodetic monuments present in the Brazilian GNSS Continuous Monitoring Network by estimating and characterizing noise in the time series and investigating variables that can affect the stability of the stations to establish criteria for using this data in tectonic and geodynamic studies. The evaluation of 119 GNSS stations throughout Brazil indicates the significant presence of random walk noise in some of these stations, detected by analyzing the magnitude of the noise and the spectral index. It was found that the stations with unstable monuments have been observed for at least eight years and are mostly in coastal areas or under the influence of large watercourses.

The NANOGrav 15 yr Data Set: Chromatic Gaussian Process Noise Models for Six Pulsars

Abstract Pulsar timing arrays (PTAs) are designed to detect low-frequency gravitational waves (GWs). GWs induce achromatic signals in PTA data, meaning that the timing delays do not depend on radio frequency. However, pulse arrival times are also affected by radio-frequency-dependent “chromatic” noise from sources such as dispersion measure (DM) and scattering delay variations. Furthermore, the characterization of GW signals may be influenced by the choice of chromatic noise model for each pulsar. To better understand this effect, we assess if and how different chromatic noise models affect the achromatic noise properties in each pulsar. The models we compare include existing DM models used by the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and noise models used for the European PTA Data Release 2 (EPTA DR2). We perform this comparison using a subsample of six pulsars from the NANOGrav 15 yr data set, selecting the same six pulsars as from the EPTA DR2 six-pulsar data set. We find that the choice of chromatic noise model noticeably affects the achromatic noise properties of several pulsars. This is most dramatic for PSR J1713+0747, where the amplitude of its achromatic red noise lowers from log 10 A RN = − 14.1 − 0.1 + 0.1 to − 14.7 − 0.5 + 0.3 , and the spectral index broadens from γ RN = 2.6 − 0.4 + 0.5 to γ RN = 3.5 − 0.9 + 1.2 . We also compare each pulsar's noise properties with those inferred from the EPTA DR2, using the same models. From the discrepancies, we identify potential areas where the noise models could be improved. These results highlight the potential for custom chromatic noise models to improve PTA sensitivity to GWs.

Large deviation principle for pseudo-monotone evolutionary equation

. In this article, we explore Freidlin-Wentzell’s large deviation principle for a stochastic partial differential equation with the nonlinear diffusion-convection operator in divergence form satisfying p-type growth, involving coercivity assumptions, perturbed by small multiplicative Brownian noise. We use the weak convergence method to prove the Laplace principle, which is equivalent to the large deviation principle in our framework.

Significance testing for cross correlation: A critical examination of correlations between ENSO and GRACE-derived terrestrial water storage variabilities

The cross correlation has a wide range of applications in geophysical fields for measuring linear connections or relationships among physical quantities. Nonetheless, there remains a dearth of comprehensive discourse regarding its statistical significance testing, which is crucial for differentiating meaningful outcomes from those merely stemming from fortuity or pure randomness. Conventional theoretical methods for significance testing, commonly used in statistical analysis tools such as SPSS and MATLAB, are only applicable when dealing with idealized circumstances such as white noise. In discretionary application of these methods to analyze geophysical signals with, say, red noise may result in potentially unjustified conclusions. This study aims to develop a comprehensive approach based on the t-distribution within a rigorous statistical context, aiming to facilitate significance tests of cross correlation for general signals with specified time shifts or ranges. Extensive Monte Carlo experiments substantiate its robustness, thereby paving the way for accurate and expeditious identification of statistically (hence potentially physically) meaningful correlations in general. As an example, we examine critically the previously purported significant correlations between ENSO (El Niño Southern Oscillation) and global terrestrial water storage variations derived from the GRACE (Gravity Recovery and Climate Experiment) satellite mission, demonstrating that they are subject to questioning in the absence of complete significance testing.

Diffraction by gratings: from the C-method to the stochastic C-method

The Chandezon, or C-method, is an efficient and versatile numerical method for modeling diffraction problems involving smooth surface relief gratings. For some grating profiles, the C-method is limited when the height-to-period ratio exceeds a factor of three. This is due to the formation of ill-conditioned matrices for inversion. Here, the stochastic C-method (SCM) is introduced as a solution that leverages stochastic differential equations to overcome these numerical difficulties. The SCM is developed by altering the physical model of the grating profile function to include an additive Brownian noise component. The inclusion of noise dramatically expands the applicability of the C-method and enriches the physical model. Numerical experiments show that the SCM achieves a precision on the order of 10−5 for diffracted/transmitted amplitudes on sinusoidal profiles with height-to-period ratios as high as 72. These results are in agreement with those obtained using multi-precision and the rigorous coupled wave analysis (RCWA).

Perovskite-Doped Modulated Color-Selective Photosynaptic Transistors for Target Object Recognition.

The processing of multicolor noisy images in visual neuromorphic devices requires selective absorption at specific wavelengths; however, it is difficult to achieve this because the spectral absorption range of the device is affected by the type of material. Surprisingly, the absorption range of perovskite materials can be adjusted by doping. Herein, a CdCl2 co-doped CsPbBr3 nanocrystal-based photosensitive synaptic transistor (PST) is reported. By decreasing the doping concentration, the response of the PST to short-wavelength light is gradually enhanced, and even weak light of 40 μW·cm-2 can be detected. Benefiting from the excellent color selectivity of the PST device, the device array is applied to feature extraction of target blue items and removal of red and green noise, which results in the recognition accuracy of 95% for the noisy MNIST data set. This work provides new ideas for the application of novel transistors integrating sensors and storage computing.

X-raying the ζ Tau binary system

Context. The Be star ζ Tau was recently reported to be a γ Cas analog; that is, it displays an atypical (bright and hard) X-ray emission. The origin of these X-rays remains debated. Aims. The first X-ray observations indicated a very large absorption of the hot plasma component (NH ~ 1023 cm−2). This is most probably related to the edge-on configuration of the ζ Tau disk. If the X-ray emission arises close to the companion, an orbital modulation of the absorption could be detected as the disk comes in and out of the line of sight. Methods. New XMM-Newton data were obtained to characterize the high-energy properties of ζ Tau in more detail. They are complemented by previous Chandra and SRG/eROSITA observations as well as by optical spectroscopy and TESS photometry. Results. The high-quality XMM-Newton data reveal the presence of a faint soft X-ray emission, which appears in line with that recorded for non-γ Cas Be stars. In addition, ζ Tau exhibits significant short-term variability at all energies, with larger amplitudes at lower frequencies (“red noise”), as is found in X-ray data of other γ Cas stars. Transient variability (softness dip, low-frequency signal) may also be detected at some epochs. In addition, between X-ray exposures, large variations in the spectra are detected in the 1.5–4 keV energy band. They are due to large changes in absorption toward the hottest (9 keV) plasma. These changes are not correlated with either the orbital phase or the depth of the shell absorption of the Hα line. These observed properties are examined in the light of proposed γ Cas models.

Kelvin-Helmholtz instability and heating in oscillating loops perturbed by power-law transverse wave drivers

Context. Instabilities in oscillating loops are believed to be essential for dissipating the wave energy and heating the solar coronal plasma. Aims. Our aim is to study the development of the Kelvin-Helmholtz (KH) instability in an oscillating loop that is driven by random footpoint motions. Methods. Using the PLUTO code, we performed 3D simulations of a straight gravitationally stratified flux tube. The loop footpoints are embedded in chromospheric plasma, in the presence of thermal conduction and an artificially broadened transition region. Using drivers with a power-law spectrum, one with a red noise spectrum and one with the low-frequency part subtracted, we excited standing oscillations and the KH instability in our loops, after one-and-a-half periods of the oscillation. Results. We see that our broadband drivers lead to fully deformed, turbulent loop cross-sections over the entire coronal part of the loop due to the spatially extended KH instability. The low RMS velocity of our driver without the low-frequency components supports the working hypothesis that the KH instability can easily manifest in oscillating coronal loops. We report for the first time in driven transverse oscillations of loops the apparent propagation of density perturbations due to the onset of the KH instability, from the apex towards the footpoints. Both drivers input sufficient energy to drive enthalpy and mass flux fluctuations along the loop, while also causing heating near the driven footpoint of the oscillating loop, which becomes more prominent when a low-frequency component is included in the velocity driver. Finally, our power-law driver with the low-frequency component provides a RMS input Poynting flux of the same order as the radiative losses of the quiet-Sun corona, giving us promising prospects for the contribution of decayless oscillations in coronal heating.

Hybrid Model for Multistep-Ahead Rainfall Forecast in Northeast India: A Comparative Study

Abstract Among all hydrometeorological parameters, rainfall strongly correlates with hydrometeorological disasters. The rainfall forecast process remains challenging due to the nonlinear, nonstationary nature and multiscale variability of rainfall. Moreover, the unique microclimate in different regions further complicates the forecasting process. This study proposes a hybrid model employing multivariate singular spectrum analysis (MSSA) and long short-term memory (LSTM) for multistep-ahead hourly rainfall forecasting in urban areas of northeast India. The model is trained and evaluated using high-resolution (12 km) hourly meteorological data from the Indian Monsoon Data Assimilation and Analysis (IMDAA) dataset for Guwahati (plain) and Aizawl (hilly) regions from 2015 to 2019. The hybrid model outperforms the single LSTM model in both plain and hilly regions, with an average percentage gain of 47.99% and 43.88% for symmetric mean absolute percentage error (SMAPE) and root-mean-square error (RMSE) in the case of the Guwahati dataset and 84.59% and 82.27% in the case of the Aizawl dataset, respectively. The performance of the LSTM model significantly improves as the zero values in the observed data are eliminated after reconstruction by MSSA. This enables the model to discern essential patterns and relationships in the data, which leads to more accurate forecasts. However, the hybrid model underestimates the rainfall, which can be tackled by hypertuning the parameters. The study highlights the importance of considering the interplay between rainfall and meteorological parameters for accurate rainfall forecasting in urban areas. The proposed MSSA–LSTM model can be used as a decision support tool for urban planning and disaster management. Significance Statement This study addresses a critical need in multistep-ahead hourly rainfall forecasting in urban areas, with a focus on the unique conditions of northeast India. Our research has identified the presence of red noise in the rainfall data, shedding light on the complexities of the underlying rainfall patterns. Furthermore, we delve into the intricate interplay between rainfall and meteorological parameters, providing valuable insights into the factors influencing rainfall dynamics. Notably, our study underscores the region-specific challenges in rainfall forecasting. While the hybrid model demonstrates reasonable accuracy in the plains, its performance in the hilly region falls short of expectations. This highlights the nuanced nature of rainfall prediction in areas with varying topography and emphasizes the need for tailored forecasting approaches.

The second data release from the European Pulsar Timing Array V. Search for continuous gravitational wave signals

We present the results of a search for continuous gravitational wave signals (CGWs) in the second data release (DR2) of the European Pulsar Timing Array (EPTA) collaboration. The most significant candidate event from this search has a gravitational wave frequency of 4-5 nHz. Such a signal could be generated by a supermassive black hole binary (SMBHB) in the local Universe. We present the results of a follow-up analysis of this candidate using both Bayesian and frequentist methods. The Bayesian analysis gives a Bayes factor of 4 in favour of the presence of the CGW over a common uncorrelated noise process. In contrast, the frequentist analysis estimates the p-value of the candidate to be $< 1<!PCT!>$, also assuming the presence of common uncorrelated red noise. However, comparing a model that includes both a CGW and a gravitational wave background (GWB) to a GWB only, the Bayes factor in favour of the CGW model is only $0.7$. Therefore, we cannot conclusively determine the origin of the observed feature, nor can we rule it out as a CGW source. We present results of simulations that demonstrate that data containing a weak gravitational wave background can be misinterpreted as data including a CGW and vice versa, providing two plausible explanations for the EPTA DR2 data. Further investigations combining data from all PTA collaborations will be needed to reveal the true origin of this feature.

Brownian thermal birefringent noise due to the nondiagonal anisotropic photoelastic effect in multilayer coated mirrors

Brownian thermal birefringent noise due to the nondiagonal anisotropic photoelastic effect in multilayer coated mirrors

Flow and rheology of suspensions of two-dimensional cylindrical or anisotropic particles with Navier slip

Through boundary integral simulations, we investigate, in the creeping flow limit and in the absence of Brownian noise, the effects of Navier slip on the orientational dynamics and effective shear viscosity of a semidilute suspension of two-dimensional particles with either circular or elongated (platelike) shape, interacting only via hydrodynamic and contact forces. We have recently shown that it is theoretically possible for a dilute system of slip platelike particles to display an effective shear viscosity smaller than the viscosity of the suspending fluid. This large viscosity reduction is primarily due to the suppression of the tumbling motion predicted for a no-slip particle and the attainment of a stable orientation. In this paper, we show that the effect of particle-particle interaction at semidilute concentrations is to cause the particles to fluctuate about the stable orientation and, above a threshold solid fraction ccrt, to tumble. As a consequence, a sharp increase in the effective shear viscosity with solid fraction c occurs for c>ccrt. Our results suggest that, for a given particle aspect ratio, there is a value of c that maximizes the reduction in the effective shear viscosity of the suspension. Published by the American Physical Society 2024