Coloured-noise-induced transport in a model of the thermochemical reactor

In this paper, effects of coloured noise on the stochastic excitement in a model of the thermochemical flow reactor are studied. Transport phenomena associated with noise-induced generation of large-amplitude oscillations are investigated depending on the correlation time of coloured noise. We study how probability of the noise-induced excitement is related to the stochastic sensitivity of the system to coloured noise with certain correlation characteristics. Parameter zones of the high stochastic sensitivity are found and discussed in connection with occurrence of resonance. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Small head movements increase and colour noise in data from five video-based P–CR eye trackers

We empirically investigate the role of small, almost imperceptible balance and breathing movements of the head on the level and colour of noise in data from five commercial video-based P-CR eye trackers. By comparing noise from recordings with completely static artificial eyes to noise from recordings where the artificial eyes are worn by humans, we show that very small head movements increase levels and colouring of the noise in data recorded from all five eye trackers in this study. This increase of noise levels is seen not only in the gaze signal, but also in the P and CR signals of the eye trackers that provide these camera image features. The P and CR signals of the SMI eye trackers correlate strongly during small head movements, but less so or not at all when the head is completely still, indicating that head movements are registered by the P and CR images in the eye camera. By recording with artificial eyes, we can also show that the pupil size artefact has no major role in increasing and colouring noise. Our findings add to and replicate the observation by Niehorster et al., (2021) that lowpass filters in video-based P–CR eye trackers colour the data. Irrespective of source, filters or head movements, coloured noise can be confused for oculomotor drift. We also find that usage of the default head restriction in the EyeLink 1000+, the EyeLink II and the HiSpeed240 result in noisier data compared to less head restriction. Researchers investigating data quality in eye trackers should consider not using the Gen 2 artificial eye from SR Research / EyeLink. Data recorded with this artificial eye are much noisier than data recorded with other artificial eyes, on average 2.2–14.5 times worse for the five eye trackers.

Hyperspectral image analysis using a simultaneous denoising and intrinsic order selection (DIOS) approach

Recent hyperspectral applications demand for higher accuracy and speed. This thesis develops a hyperspectral application analysis solution to address challenges in the different steps of denoising, order selection and unmixing of hyperspectral application data. Currently, all these steps process the data in cascade to achieve the optimum results. While in existing approaches the desired criterion is different in these steps, the proposed simultaneous Denoising and Intrinsic Order Selection (DIOS) method unifies these criteria. This property not only makes more sense for the desired optimization problem, but also leads to a faster processing algorithm. Consequently, DIOS avoids possible error propagation from the denoising stage to the dimension estimation stage, leading to more accurate results. The proposed method is based on minimizing the estimated Mean Square Error (MSE). The success rate of existing dimension estimation methods declines with the increase of image dimension and the decrease of Signal-to-Noise Ratio (SNR). The most competitive method fails to detect the correct dimension in 30% of cases around 2dB. However, in simulation results DIOS is shown to be successful with a failure rate of about 5%. The proposed unmixing method, based on a simple least square estimation, improves the speed performance least 10 times for an average-sized data cube of 2MB. Compared to some well known existing approaches, the unmixing method improves the estimated MSE up to 60% for SNR<10dB. A new whitening process for hyperspectral applications with coloured noise is also proposed. Since the proposed method avoids the inversion of large matrices, computational complexity is substantially decreased. In the presence of coloured noise, simulation results show that the proposed whitening method lowers the MSE of unmixing and outperforms the existing whitening methods particularly when the noise correction factors increase.

Hyperspectral image analysis using a simultaneous denoising and intrinsic order selection (DIOS) approach

Recent hyperspectral applications demand for higher accuracy and speed. This thesis develops a hyperspectral application analysis solution to address challenges in the different steps of denoising, order selection and unmixing of hyperspectral application data. Currently, all these steps process the data in cascade to achieve the optimum results. While in existing approaches the desired criterion is different in these steps, the proposed simultaneous Denoising and Intrinsic Order Selection (DIOS) method unifies these criteria. This property not only makes more sense for the desired optimization problem, but also leads to a faster processing algorithm. Consequently, DIOS avoids possible error propagation from the denoising stage to the dimension estimation stage, leading to more accurate results. The proposed method is based on minimizing the estimated Mean Square Error (MSE). The success rate of existing dimension estimation methods declines with the increase of image dimension and the decrease of Signal-to-Noise Ratio (SNR). The most competitive method fails to detect the correct dimension in 30% of cases around 2dB. However, in simulation results DIOS is shown to be successful with a failure rate of about 5%. The proposed unmixing method, based on a simple least square estimation, improves the speed performance least 10 times for an average-sized data cube of 2MB. Compared to some well known existing approaches, the unmixing method improves the estimated MSE up to 60% for SNR<10dB. A new whitening process for hyperspectral applications with coloured noise is also proposed. Since the proposed method avoids the inversion of large matrices, computational complexity is substantially decreased. In the presence of coloured noise, simulation results show that the proposed whitening method lowers the MSE of unmixing and outperforms the existing whitening methods particularly when the noise correction factors increase.

All order effective action for charge diffusion from Schwinger-Keldysh holography

An effective action for diffusion of a conserved U(1) charge is derived to all orders in the derivative expansion within a holographic model dual to the Schwinger-Keldysh closed time path. A systematic approach to solution of the 5D Maxwell equations in a doubled Schwarzschild-AdS5 black brane geometry is developed. Constitutive relation for the stochastic charge current is shown to have a term induced by thermal fluctuations (coloured noise). All transport coefficient functions parameterising the effective action and constitutive relations are computed analytically in the hydrodynamic expansion, and then numerically for finite momenta.

Prediction of Ship Motions in Irregular Waves Based on Response Amplitude Operators Evaluated Experimentally in Noise Waves

The most common methods for predicting ship roll motions in a specified sea state are direct measurements of motions in a representative irregular wave realisation (time domain) or calculations of motions from response amplitude operators (RAOs) in the frequency domain. The result of the first method is valid only for the tested sea state, whilst the second method is more flexible but less accurate. RAO-based predictions are calculated assuming a linear model of ship motions in waves. RAO functions are usually evaluated by means of tests in regular waves for a limited number of frequencies and a constant wave amplitude. This approach is time-consuming and the discrete form of the RAO functions obtained for a limited number of frequencies may lead to discrepancies in the prediction of seakeeping and often does not allow the actual amplitude of the response in resonant frequency to be determined. Another challenge is the appropriate selection of wave amplitude for tests due to the considerable influence of viscous damping on roll response in irregular sea waves. There are alternative methods for the experimental determination of RAO functions and one of them is presented in this study. The presented approach allows RAO functions to be evaluated in one run by the generation of irregular waves characterised by a white or coloured noise spectrum. This method reduces the experiment duration, with almost continuous RAO characteristics obtained. The flat (white noise) and linear (coloured noise) wave spectral energy characteristics are considered in the experiment and the obtained predictions are compared with the results of accurate measurements in irregular waves.

Statistics of an Appealing Class of Random Processes

The white noise process, the Ornstein-Uhlenbeck process, and coloured noise process are salient noise processes to model the effect of random perturbations. In this chapter, the statistical properties, the master's equations for the Brownian noise process, coloured noise process, and the OU process are summarized. The results associated with the white noise process would be derived as the special cases of the Brownian and the OU noise processes. This chapter also formalizes stochastic differential rules for the Brownian motion and the OU process-driven vector stochastic differential systems in detail. Moreover, the master equations, especially for the coloured noise-driven stochastic differential system as well as the OU noise process-driven, are recast in the operator form involving the drift and modified diffusion operators involving an additional correction term to the standard diffusion operator. The results summarized in this chapter will be useful for modelling a random walk in stochastic systems.