Noise Correlation Research Articles

Allelic correlation is a marker of trade-offs between barriers to transmission of expression variability and signal responsiveness in genetic networks.

Genetic networks should respond to signals but prevent the transmission of spontaneous fluctuations. Limited data from mammalian cells suggest that noise transmission is uncommon, but systematic claims about noise transmission have been limited by the inability to directly measure it. Here, we build a mathematical framework modeling allelic correlation and noise transmission, showing that allelic correlation and noise transmission correspond across model parameters and network architectures. Limiting noise transmission comes with the trade-off of being unresponsive to signals, and within responsive regimes, there is a further trade-off between response time and basal noise transmission. Analysis of allele-specific single-cell RNA-sequencing data revealed that genes encoding upstream factors in signaling pathways and cell-type-specific factors have higher allelic correlation than downstream factors, suggesting they are more subject to regulation. Overall, our findings suggest that some noise transmission must result from signal responsiveness, but it can be minimized by trading off for a slower response. A record of this paper's transparent peer review process is included in the supplemental information.

Numerical study on cavitation–vortex–noise correlation mechanism and dynamic mode decomposition of a hydrofoil

The large eddy simulation model coupled with the modified Schnerr–Sauer cavitation model has been used to numerically simulate the unsteady cavitation and noncavitation flow of the three-dimensional NACA66 (National Advisory Committee for Aeronautics) hydrofoil under different operating conditions. The results show that the magnitude of the cavitation number plays a decisive role in the hydrofoil cavitation quasiperiodic phenomenon. The cavitation number of 1.25 is used as a typical working condition for analysis. Using the Ffowcs Williams–Hawkings acoustic analogy approach accompanied by the vorticity transport equation splitting, the growth and shedding of cavitation also lead to the growth and shedding of the vortex structure. The cavitation–vortex interaction is mainly influenced by the vortex stretching term and vortex dilatation term and amplitude of them are larger than 500. The baroclinic torque term may be responsible for generating vorticity during the cloud cavitation collapse and has a lower amplitude about 200. The cavity volume acceleration is the main influencing factor of the low-frequency pressure fluctuation around the cavitating hydrofoil. Moreover, the NACA66 hydrofoil surface-pressure data are collected for dynamic mode decomposition to locate the hydrofoil surface noise sources. The alternate high and low amplitude regions in the mode results overlap highly with the cavitation transformation regions. The cavity transformation and pressure fluctuations are the main reason for the generation of periodic low-frequency noise source regions on the hydrofoil surface. Moreover, the corresponding frequencies of each order mode are linearly correlated with the cavitation shedding frequency of 5.70 Hz. Combined with the results of the multiple mode comparisons, it can be inferred that the hydrofoil suction surface under the cavitation effect will generate quasiperiodic waves starting from upstream and moving downstream.

Tipping points in spatial ecosystems driven by short-range correlated noise.

Complex spatial systems can experience critical transitions or tippings on crossing a threshold value in their response to stochastic perturbations. While previous studies have well characterized the impact of white noise on tipping, the effect of correlated noise in spatial ecosystems remains largely unexplored. Here, we investigate the effect of both multiplicative and additive Ornstein-Uhlenbeck (OU) correlated noise on the occurrence of critical transitions in spatial ecosystems. We find that decreasing the noise correlation time of OU (exponentially correlated) noise aggravates the chance of critical transitions in spatiotemporal ecological systems. Our results hold good and are supported by the analysis of three well-studied spatial ecological models of varying nonlinearity. We also compute spatial early warning indicators (e.g., spatial variance, spatial skewness, and spatial correlation) to determine their reliability in anticipating tipping points with variations in noise correlation. The indicators of critical transitions exhibit mixed success in forewarning the occurrence of a tipping point, as indicated by the distribution of Kendall's rank correlation.

Shear wave velocities in the upper crust of the Quadrilátero Ferrífero, Minas Gerais: Rayleigh-wave tomography

We applied a combination of ambient seismic noise and classical earthquake-receiver techniques to characterize the shallow crustal shear-wave velocities in the Quadrilátero Ferrífero (QF), Minas Gerais state, SE Brazil, to a depth of about 4 km. Ambient seismic noise was recorded by up to 26 stations. To improve the signal of the extracted empirical Green's function (EGF), we correlated short time windows of 10 min with 70% overlapping before stacking. To test the accuracy of the retrieved EGF signals, we compared the results obtained from ambient seismic noise correlation with results from an earthquake occurred near FABR station. After measuring dispersion using frequency-time analysis (FTAN), we applied strict quality criteria (e.g., eliminating paths with residuals larger than two standard deviations, or lengths smaller than 3 wavelengths). The Fast Marching Surface wave Tomography (FMST) method was used to obtain group velocity maps. Then, the local dispersion curves were inverted to obtain a 3D Vs model. The resulting 3D model shows low velocity anomalies in the middle of the QF, compared with high velocities in the Archean part of the São Francisco Craton to the west. The low velocity metasedimentary layer in the QF is about 1.5 km thick.

Noise correlation and its impact on the performance of multi-material decomposition-based spectral imaging in photon-counting CT.

It has been known that noise correlation plays an important role in the determination of the performance of spectral imaging based on two-material decomposition (2-MD). To further understand the basics of spectral imaging in photon-counting CT toward optimal design and implementation, we study the noise correlation in multi-MD (m-MD) and its impact on the performance of spectral imaging. We derive the equations that characterize the noise and noise correlation in the material-specific (basis) images in m-MD, followed by a simulation study to verify the derived equations and study the noise correlation's impact on the performance of spectral imaging. Using a specially designed digital phantom, the study of noise correlation runs over the cases of two-, three-, and four-MD (2-MD, 3-MD, and 4-MD). Then, the noise correlation's impact on the performance of spectral imaging in photon-counting CT is investigated, using a modified Shepp-Logan phantom. The results in 2-MD show that, in-line with what has been reported in the literature, the noise correlation coefficient between the material-specific images corresponding to the basis materials approaches -1. The results in m-MD (m≥3) are more complicated and interesting, as the noise correlation coefficients between a pair of the material-specific images alternate between ±1, and so do in the case of 4-MD. The m-MD data show that the noise in virtual monochromatic imaging (a form of spectral imaging) is moderate even though the noises in material-specific (basis) images vary drastically. The observation of noise correlation in 3-MD, 4-MD, and beyond (i.e., m-MD) is informative to the community. The relationship between noise correlation and the performance of spectral imaging revealed in this work may help clinical medical physicists understand the fundamentals of spectral imaging based on MD and optimize the performance of spectral imaging in photon-counting CT and other X-ray imaging modalities.

Bistatic noise radar: Demonstration of correlation noise suppression

AbstractIn this study, spatial separation of the radar transmitter and receiver units is considered, as a means of reducing the masking effect in noise radars. A bistatic radar system is constructed, with emphasis on a lightweight transmitter unit that can be mounted on a commercial Unmanned Aerial Vehicle (UAV). The system uses pseudo‐random noise, generated digitally at the receiver and transmitter units. Correlation losses, due to non‐linearities in the transmitter and receiver units, are measured to 0.1 dB. This study shows that by separating the transmitter and receiver unit the masking effect is significantly reduced, compared to a monostatic setup. This reduction is enough for the system to detect a slow flying UAV. Thus, bistatic separation should be considered as a practical tool to reduce the masking effect. By processing clutter with an extended CLEAN algorithm, the correlation noise floor is further suppressed.

A cryogenic 14-channel 13 C receiver array for 3T human head imaging.

This article presents a novel 14-channel receive-only array for 13 C human head imaging at 3T that explores the SNR gain by operating at cryogenic temperature cooled by liquid nitrogen. Cryostats are developed to evaluate single-coil bench SNR performance and cool the 14-channel array with liquid nitrogen while having enough thermal insulation between the coils and the sample. The temperature distribution for the coil array is measured. Circuits are adapted to the -189°C environment and implemented in the 14-channel array. 13 C images are acquired with the array at cryogenic and room temperature in a 3T scanner. Compared with room temperature, the array at cryogenic temperature provides 27%-168% SNR improvement over all voxels and 47% SNR improvement near the image center. The measurements show a decrease of the element noise correlation at cryogenic temperature. It is demonstrated that higher SNR can be achieved by cryogenically cooling the 14-channel array. A cryogenic array suitable for clinical imaging can be further developed on the array proposed. The cryogenic coil array is most likely suited for scenarios in which high SNR deep in a head and decent SNR on the periphery are required.

Enhancing cross correlations of ocean ambient noise in the time domain based on random matrix theory.

Cross correlations of diffuse noise can be utilized to recover the time domain Green's function (TDGF) between two points. This principle allows for a variety of practical applications, such as seismic tomography, ocean thermometry, passive localization, etc. However, in the real ocean environment, loud interference noise sources usually bias the travel time estimates of the TDGF or result in poor recovery quality. To deal with this issue, a diffuse noise reconstruction approach is proposed to eliminate the influence of the strong interference noise by utilizing the time domain statistical property of ocean ambient noise recorded on single hydrophones with the help of random matrix theory. Simulation and experimental data analysis indicate that this algorithm can effectively extract the diffuse noise component from the ocean ambient noise field and retrieve the TDGF with a higher signal-to-noise ratio when coherent accumulation of cross correlations of the reconstructed diffuse noise is performed.

Stochastic behaviors of an improved Gompertz tumor growth model with coupled two types noise

In this work, an improved Gompertz tumor growth model has been introduced. The expressions of steady probability distributions (SPD) of stochastic Gompertz tumor growth models are studied by using the technique of Fokker-Planck equation (FPE), and their dynamic behaviors are also further investigated. Moreover, the expressions for mean, variance, skewness, as well as the mean first-passage time (MFPT) also have been derived. And the influence of noise intensity, correlation coefficient, and noise correlation time of SPD are further analyzed. It is worthy noting that the colored noise intensity has an important impact on SPD. Furthermore, adjusting birth and death parameters also significantly impact SPD, MFPT, mean, variance as well as skewness.

Deep-Learning-Based Electrical Noise Removal Enables High Spectral Optoacoustic Contrast in Deep Tissue

Image contrast in multispectral optoacoustic tomography (MSOT) can be severely reduced by electrical noise and interference in the acquired optoacoustic signals. Previously employed signal processing techniques have proven insufficient to remove the effects of electrical noise because they typically rely on simplified models and fail to capture complex characteristics of signal and noise. Moreover, they often involve time-consuming processing steps that are unsuited for real-time imaging applications. In this work, we develop and demonstrate a discriminative deep learning approach to separate electrical noise from optoacoustic signals prior to image reconstruction. The proposed deep learning algorithm is based on two key features. First, it learns spatiotemporal correlations in both noise and signal by using the entire optoacoustic sinogram as input. Second, it employs training on a large dataset of experimentally acquired pure noise and synthetic optoacoustic signals. We validated the ability of the trained model to accurately remove electrical noise on synthetic data and on optoacoustic images of a phantom and the human breast. We demonstrate significant enhancements of morphological and spectral optoacoustic images reaching 19% higher blood vessel contrast and localized spectral contrast at depths of more than 2 cm for images acquired in vivo. We discuss how the proposed denoising framework is applicable to clinical multispectral optoacoustic tomography and suitable for real-time operation.

Anderson and many-body localization in the presence of spatially correlated classical noise

We study the effect of spatially correlated classical noise on both Anderson and many-body localization of a disordered fermionic chain. By analyzing the evolution of the particle density imbalance following a quench from an initial charge density wave state, we find prominent signatures of localization also in the presence of the time-dependent noise, even though the system eventually relaxes to the infinite temperature state. In particular, for sufficiently strong static disorder we observe the onset of metastability, which becomes more prominent the stronger the spatial correlations of the noise. In this regime we find that the imbalance decays as a stretched-exponential - a behavior characteristic of glassy systems. We identify a simple scaling behavior of the relevant relaxation times in terms of the static disorder and of the noise correlation length. We discuss how our results could be exploited to extract information about the localization length in experimental setups.

Asynchronous magnetic resonance elastography: Shear wave speed reconstruction using noise correlation ofincoherent waves.

The noninvasive measurement of biological tissue elasticity is an evolving technology that enables the robust characterization of soft tissue mechanics for a wide array of biomedical engineering and clinical applications. We propose, design, and implement here a new MRI technique termed asynchronous magnetic resonance elastography (aMRE) that pushes the measurement technology toward a driverless implementation. This technique can be added to clinical MRI scanners without any additional specialized hardware. Asynchronous MRE is founded on the theory of diffuse wavefields and noise correlation previously developed in ultrasound to reconstruct shear wave speeds using seemingly incoherent wavefields. Unlike conventional elastography methods that solve an inverse problem, aMRE directly reconstructs a pixel-wise mapping of wave speed using the spatial-temporal statistics of the measured wavefield. Incoherent finger tapping served as the wave-generating source for all aMRE measurements. Asynchronous MRE was performed on a phantom using a Siemens Prismafit as an experimental validation of the theory. It was further performed on thigh muscles as a proof-of-concept implementation of in vivo imaging using a Siemens Skyra scanner. Numerical and phantom experiments show an accurate reconstruction of wave speeds from seemingly noisy wavefields. The proof-of-concept thigh experiments also show that the aMRE protocol can reconstruct a pixel-wise mapping of wave speeds. Asynchronous MRE is shown to accurately reconstruct shear wave speeds in phantom experiments and remains at the proof-of-concept stage for in vivo imaging. After further validation and improvements, it has the potential to lower both the technical and monetary barriers of entry to measuring tissue elasticity.

Decreased Modulation of Population Correlations in Auditory Cortex Is Associated with Decreased Auditory Detection Performance in Old Mice.

Age-related hearing loss (presbycusis) affects one-third of the world's population. One hallmark of presbycusis is difficulty hearing in noisy environments. Presbycusis can be separated into two components: the aging ear and the aging brain. To date, the role of the aging brain in presbycusis is not well understood. Activity in the primary auditory cortex (A1) during a behavioral task is because of a combination of responses representing the acoustic stimuli, attentional gain, and behavioral choice. Disruptions in any of these aspects can lead to decreased auditory processing. To investigate how these distinct components are disrupted in aging, we performed in vivo 2-photon Ca2+ imaging in both male and female mice (Thy1-GCaMP6s × CBA/CaJ mice) that retain peripheral hearing into old age. We imaged A1 neurons of young adult (2-6 months) and old mice (16-24 months) during a tone detection task in broadband noise. While young mice performed well, old mice performed worse at low signal-to-noise ratios. Calcium imaging showed that old animals have increased prestimulus activity, reduced attentional gain, and increased noise correlations. Increased correlations in old animals exist regardless of cell tuning and behavioral outcome, and these correlated networks exist over a much larger portion of cortical space. Neural decoding techniques suggest that this prestimulus activity is predictive of old animals making early responses. Together, our results suggest a model in which old animals have higher and more correlated prestimulus activity and cannot fully suppress this activity, leading to the decreased representation of targets among distracting stimuli.SIGNIFICANCE STATEMENT Aging inhibits the ability to hear clearly in noisy environments. We show that the aging auditory cortex is unable to fully suppress its responses to background noise. During an auditory behavior, fewer neurons were suppressed in the old relative to young animals, which leads to higher prestimulus activity and more false alarms. We show that this excess activity additionally leads to increased correlations between neurons, reducing the amount of relevant stimulus information in the auditory cortex. Future work identifying the lost circuits that are responsible for proper background suppression could provide new targets for therapeutic strategies to preserve auditory processing ability into old age.

Coding of latent variables in sensory, parietal, and frontal cortices during closed-loop virtual navigation.

We do not understand how neural nodes operate and coordinate within the recurrent action-perception loops that characterize naturalistic self-environment interactions. Here, we record single-unit spiking activity and local field potentials (LFPs) simultaneously from the dorsomedial superior temporal area (MSTd), parietal area 7a, and dorsolateral prefrontal cortex (dlPFC) as monkeys navigate in virtual reality to 'catch fireflies'. This task requires animals to actively sample from a closed-loop virtual environment while concurrently computing continuous latent variables: (i) the distance and angle travelled (i.e., path integration) and (ii) the distance and angle to a memorized firefly location (i.e., a hidden spatial goal). We observed a patterned mixed selectivity, with the prefrontal cortex most prominently coding for latent variables, parietal cortex coding for sensorimotor variables, and MSTd most often coding for eye movements. However, even the traditionally considered sensory area (i.e., MSTd) tracked latent variables, demonstrating path integration and vector coding of hidden spatial goals. Further, global encoding profiles and unit-to-unit coupling (i.e., noise correlations) suggested a functional subnetwork composed by MSTd and dlPFC, and not between these and 7a, as anatomy would suggest. We show that the greater the unit-to-unit coupling between MSTd and dlPFC, the more the animals' gaze position was indicative of the ongoing location of the hidden spatial goal. We suggest this MSTd-dlPFC subnetwork reflects the monkeys' natural and adaptive task strategy wherein they continuously gaze toward the location of the (invisible) target. Together, these results highlight the distributed nature of neural coding during closed action-perception loops and suggest that fine-grain functional subnetworks may be dynamically established to subserve (embodied) task strategies.

Ambient energy harvesting from colored multiplicative noise

The present study examines the effect of multiplicative Gaussian noise on the conversion of vibration energy into electrical energy. Nonlinear oscillators are considered in the present model. The results demonstrate that similar to additive noise case, the harvesting of the vibration energy to electricity could be good if the voltage can closely track the advancement of the amplitude of the oscillator. Another observation is that the power of the micro-electromechanical systems (MEMS) goes through a maximum as with inverse of noise correlation time. Further, the position of the maxima in power generation occurs for higher noise correlation time due to the space dependency associated with the multiplicative Gaussian noise. Along with these, we have investigated how the power generation is dependent on the environment, properties of the oscillating systems and the piezoelectric dynamics.

Plasma noise in TianQin time-delay interferometry

TianQin is a proposed geocentric space-based gravitational wave observatory mission, which requires time-delay interferometry (TDI) to cancel laser frequency noise. With high demands for precision, solar-wind plasma environment at $\sim 10^5$ km above the Earth may constitute a non-negligible noise source to laser interferometric measurements between satellites, as charged particles perturb the refractivity along light paths. In this paper, we first assess the plasma noises along single links from space-weather models and numerical orbits, and analyze the time and frequency domain characteristics. Particularly, to capture the plasma noise in the entire measurement band of $10^{-4} - 1$ Hz, we have performed additional space-weather magnetohydrodynamic simulations in finer spatial and temporal resolutions and utilized Kolmogorov spectra in high-frequency data generation. Then we evaluate the residual plasma noises of the first- and second-generation TDI combinations. Both analytical and numerical estimations have shown that under normal solar conditions the plasma noise after TDI is less than the secondary noise requirement. Moreover, TDI is shown to exhibit moderate suppression on the plasma noise below $\sim 10^{-2}$ Hz due to noise correlation between different arms, when compared with the secondary noise before and after TDI.

Unconventional pairing in few-fermion systems at finite temperature

Attractively interacting two-component mixtures of fermionic particles confined in a one-dimensional harmonic trap are investigated. Properties of balanced and imbalanced systems are systematically explored with the exact diagonalization approach, focusing on the finite-temperature effects. Using single- and two-particle density distributions, specific non-classical pairing correlations are analyzed in terms of the noise correlations—quantity directly accessible in state-of-the-art experiments with ultra-cold atoms. It is shown that along with increasing temperature, any imbalanced system hosting Fulde–Ferrel–Larkin–Ovchinnikov pairs crossovers to a standard Bardeen-Cooper-Schrieffer one characterized by zero net momentum of resulting pairs. By performing calculations for systems with different imbalances, the approximate boundary between the two phases on a phase diagram is determined.

A dynamic spike threshold with correlated noise predicts observed patterns of negative interval correlations in neuronal spike trains

Negative correlations in the sequential evolution of interspike intervals (ISIs) are a signature of memory in neuronal spike-trains. They provide coding benefits including firing-rate stabilization, improved detectability of weak sensory signals, and enhanced transmission of information by improving signal-to-noise ratio. Primary electrosensory afferent spike-trains in weakly electric fish fall into two categories based on the pattern of ISI correlations: non-bursting units have negative correlations which remain negative but decay to zero with increasing lags (Type I ISI correlations), and bursting units have oscillatory (alternating sign) correlation which damp to zero with increasing lags (Type II ISI correlations). Here, we predict and match observed ISI correlations in these afferents using a stochastic dynamic threshold model. We determine the ISI correlation function as a function of an arbitrary discrete noise correlation function {{,mathrm{mathbf {R}},}}_k, where k is a multiple of the mean ISI. The function permits forward and inverse calculations of the correlation function. Both types of correlation functions can be generated by adding colored noise to the spike threshold with Type I correlations generated with slow noise and Type II correlations generated with fast noise. A first-order autoregressive (AR) process with a single parameter is sufficient to predict and accurately match both types of afferent ISI correlation functions, with the type being determined by the sign of the AR parameter. The predicted and experimentally observed correlations are in geometric progression. The theory predicts that the limiting sum of ISI correlations is -0.5 yielding a perfect DC-block in the power spectrum of the spike train. Observed ISI correlations from afferents have a limiting sum that is slightly larger at -0.475 pm 0.04 (text {mean} pm text {s.d.}). We conclude that the underlying process for generating ISIs may be a simple combination of low-order AR and moving average processes and discuss the results from the perspective of optimal coding.

Imaging with seismic noise: improving extraction of body wave phases from the deep Earth through selective stacking based on H/V ratios

SUMMARY Generating high-resolution images of the deep Earth remains a challenge. Body waves extracted from noise correlations hold high promise to complement earthquake-based studies, but data processing and interpretation are still under development. We develop a methodology to improve signal-to-noise ratio (SNR) of P410P and P660P, waves reflected at the top and bottom of the mantle transition zone, using data from the greater Alpine area and focussing on the second microseismic peak (2.5–10 s period). Rather than stacking all available data, we only stack correlations for days with a low ratio of amplitudes between the horizontal plane and vertical direction (H/V). Due to an improved SNR we can stack over fewer correlation pairs, with the result that horizontal resolution is significantly improved. We propose a systematic approach to determine at each study point the optimal combination of station pairs and the H/V threshold. We observe that the optimal choice of parameters is location dependent and that it is generally different for P410P and P660P. Additionally, we show that in our study area the maximum interstation distance needs to be reduced to ∼150 km for P410P to avoid that this arrival is contaminated by surface waves. Applied to the greater Alpine area we demonstrate a significant improvement of signal extraction: while P410P and P660P were only sporadically identified in standard stacks, with the new processing scheme these arrivals are clearly identified with coherent phases across large distances. We also show that amplitudes of P660P decrease drastically around longitude ∼11°E to ∼12°E, indicating that the lower discontinuity of the transition zone in that area is too broad to have a significant reflexion coefficient for P waves in the second microseismic peak.

Dynamics of a colloidal particle coupled to a Gaussian field: from a confinement-dependent to a non-linear memory

The effective dynamics of a colloidal particle immersed in a complex medium is often described in terms of an overdamped linear Langevin equation for its velocity with a memory kernel which determines the effective (time-dependent) friction and the correlations of fluctuations. Recently, it has been shown in experiments and numerical simulations that this memory may depend on the possible optical confinement the particle is subject to, suggesting that this description does not capture faithfully the actual dynamics of the colloid, even at equilibrium. Here, we propose a different approach in which we model the medium as a Gaussian field linearly coupled to the colloid. The resulting effective evolution equation of the colloidal particle features a non-linear memory term which extends previous models and which explains qualitatively the experimental and numerical evidence in the presence of confinement. This non-linear term is related to the correlations of the effective noise via a novel fluctuation-dissipation relation which we derive.