Effect Of Noise Correlation Research Articles

Effects of noise correlation and imperfect data sampling on indicators of critical slowing down

Effects of noise correlation and imperfect data sampling on indicators of critical slowing down

Filter Functions for Quantum Processes under Correlated Noise.

Many qubit implementations are afflicted by correlated noise not captured by standard theoretical tools that are based on Markov approximations. While independent gate operations are a key concept for quantum computing, it is actually not possible to fully describe noisy gates locally in time if noise is correlated on times longer than their duration. To address this issue, we develop a method based on the filter function formalism to perturbatively compute quantum processes in the presence of correlated classical noise. We derive a composition rule for the filter function of a sequence of gates in terms of those of the individual gates. The joint filter function allows us to efficiently compute the quantum process of the whole sequence. Moreover, we show that correlation terms arise which capture the effects of the concatenation and, thus, yield insight into the effect of noise correlations on gate sequences. Our generalization of the filter function formalism enables both qualitative and quantitative studies of algorithms and state-of-the-art tools widely used for the experimental verification of gate fidelities like randomized benchmarking, even in the presence of noise correlations.

Estimating Fisher discriminant error in a linear integrator model of neural population activity

Decoding approaches provide a useful means of estimating the information contained in neuronal circuits. In this work, we analyze the expected classification error of a decoder based on Fisher linear discriminant analysis. We provide expressions that relate decoding error to the specific parameters of a population model that performs linear integration of sensory input. Results show conditions that lead to beneficial and detrimental effects of noise correlation on decoding. Further, the proposed framework sheds light on the contribution of neuronal noise, highlighting cases where, counter-intuitively, increased noise may lead to improved decoding performance. Finally, we examined the impact of dynamical parameters, including neuronal leak and integration time constant, on decoding. Overall, this work presents a fruitful approach to the study of decoding using a comprehensive theoretical framework that merges dynamical parameters with estimates of readout error.

Optimizing and applying high-resolution, in-line laboratory phase-contrast X-ray imaging for low-density material samples.

In-line, or propagation-based phase-contrast X-ray imaging (PBI) is an attractive alternative to the attenuation-based modality for low-density, soft samples showing low attenuation contrast. With the growing availability of micro- and nano-focus X-ray tubes, the method is increasingly applied in the laboratory. Here, we discuss the technique and demonstrate its advantages for selected low-density, low attenuation material samples using a lab-based micro- and nano-computed tomography systems Easytom XL Ultra, providing micron and sub-micron range resolution PBI images. We demonstrate a multi-step optimization of the lab-based PBI technique on our scanner that includes choosing the optimal detector-source hardware combination available in the setup, then optimizing the imaging geometry and finally the phase retrieval process through a parametric study. We point out and elaborate on the effect of noise correlation and texturing due to phase retrieval. We demonstrate the overall benefits of using the phase image and the phase retrieval for the selected samples such as improved image quality, increased contrast-to-noise ratio while only marginally influencing the spatial resolution. The improvement in image quality also enables further image processing steps for detailed structural analysis of the samples, which would be much more complicated if not impossible based on the transmissionimage.

The covariance perceptron: A new paradigm for classification and processing of time series in recurrent neuronal networks.

Learning in neuronal networks has developed in many directions, in particular to reproduce cognitive tasks like image recognition and speech processing. Implementations have been inspired by stereotypical neuronal responses like tuning curves in the visual system, where, for example, ON/OFF cells fire or not depending on the contrast in their receptive fields. Classical models of neuronal networks therefore map a set of input signals to a set of activity levels in the output of the network. Each category of inputs is thereby predominantly characterized by its mean. In the case of time series, fluctuations around this mean constitute noise in this view. For this paradigm, the high variability exhibited by the cortical activity may thus imply limitations or constraints, which have been discussed for many years. For example, the need for averaging neuronal activity over long periods or large groups of cells to assess a robust mean and to diminish the effect of noise correlations. To reconcile robust computations with variable neuronal activity, we here propose a conceptual change of perspective by employing variability of activity as the basis for stimulus-related information to be learned by neurons, rather than merely being the noise that corrupts the mean signal. In this new paradigm both afferent and recurrent weights in a network are tuned to shape the input-output mapping for covariances, the second-order statistics of the fluctuating activity. When including time lags, covariance patterns define a natural metric for time series that capture their propagating nature. We develop the theory for classification of time series based on their spatio-temporal covariances, which reflect dynamical properties. We demonstrate that recurrent connectivity is able to transform information contained in the temporal structure of the signal into spatial covariances. Finally, we use the MNIST database to show how the covariance perceptron can capture specific second-order statistical patterns generated by moving digits.

Understanding multivariate brain activity: Evaluating the effect of voxelwise noise correlations on population codes in functional magnetic resonance imaging.

Previous studies in neurophysiology have shown that neurons exhibit trial-by-trial correlated activity and that such noise correlations (NCs) greatly impact the accuracy of population codes. Meanwhile, multivariate pattern analysis (MVPA) has become a mainstream approach in functional magnetic resonance imaging (fMRI), but it remains unclear how NCs between voxels influence MVPA performance. Here, we tackle this issue by combining voxel-encoding modeling and MVPA. We focus on a well-established form of NC, tuning-compatible noise correlation (TCNC), whose sign and magnitude are systematically related to the tuning similarity between two units. We show that this form of voxelwise NCs can improve MVPA performance if NCs are sufficiently strong. We also confirm these results using standard information-theoretic analyses in computational neuroscience. In the same theoretical framework, we further demonstrate that the effects of noise correlations at both the neuronal level and the voxel level may manifest differently in typical fMRI data, and their effects are modulated by tuning heterogeneity. Our results provide a theoretical foundation to understand the effect of correlated activity on population codes in macroscopic fMRI data. Our results also suggest that future fMRI research could benefit from a closer examination of the correlational structure of multivariate responses, which is not directly revealed by conventional MVPA approaches.

Vertical Correlation and Array Gain Analysis for Vertical Line Array in Deep Water

Array gain (AG) is significant in evaluating the detection performance of the vertical line array, which is directly determined by the correlation of signal and noise, respectively. In this paper, we analyze the vertical correlation for a 16-element vertical line array experimented in the deep ocean in 2016. The ray interference theory is utilized to interpret the mechanism of the vertical correlation of the sound field in different zones. In the direct-arrival zone, the direct rays and once-surface-reflected rays are two dominated components, whose arrival time difference for each element are nearly the same, and the vertical correlation is high. In the shadow zone, the sound field is mainly dominated by bottom-reflected rays and the vertical correlation decreases due to different grazing angles and arrival times of each ray. Different from the previous assumption of noise independence, the effect of noise correlation on the AG is analyzed through the measured marine environmental noise. Results indicate that the noise correlation coefficients in two zones are low but not 0. In the direct-arrival zone, AG is about 10 dB, very close to the ideal value of 10 log M . AG even exceeds it when NG is negative. Moreover, AG in the direct-arrival zone is higher than the one in the shadow zone.

Noise Correlation Effect on Detection: Signals in Equicorrelated or Autoregressive(1) Gaussian.

In this letter, we consider the effect of noise correlation on the error performance of binary hypothesis signal detection, when one of two deterministic signals is received in correlated Gaussian noise. For the likelihood ratio detection scheme, analytical performance results are derived for equicorrelated and autoregressive order one models. Although it is known previously that the best signal lies in the direction of eigenvector corresponding to the minimum eigenvalue of the noise covariance matrix, our investigation of the variation of mean signal-to-noise power ratio as a function of correlation parameter (i) shows how correlation leads to increased probability of error up to a point, beyond which monotonic decrease in error probability with increasing correlation is possible and (ii) provides a max-min signal design solution for the unknown correlation parameter case. Numerical results are also included for some specific signals.

Kramers problem for a dimer: Effect of noise correlations.

The Kramers problem for a dimer in a bistable piecewise linear potential is studied in the presence of correlated noise processes. The effect of such a correlation is to redistribute the thermal power between the dynamical degrees of freedom, and this leads to significant deviations in the dynamics of the system from the case of independent noise processes. The distribution of first passage times from one minima to the basin of attraction of the other minima is found to have exponentially decaying tails with the parameter dependent on the amount of correlation and the coupling between the particles. The strong coupling limit of the problem is analyzed using adiabatic elimination, where it is found that the initial probability density relaxes towards a stationary value on the same time scale as the mean escape time when the noise intensity of the system is low. For higher noise fluctuations, the relaxation towards the stationary state is slower in comparison to escape times. In the extreme limit of perfect anticorrelation, the random dynamical system behaves as a deterministic system in a steady state in which the center of mass starting from the unstable maxima moves down the hill and gets trapped in the potential minima. The implications for polymer dynamics in a potential are discussed.

Effect of noise correlations on randomized benchmarking

Among the most popular and well studied quantum characterization, verification and validation techniques is randomized benchmarking (RB), an important statistical tool used to characterize the performance of physical logic operations useful in quantum information processing. In this work we provide a detailed mathematical treatment of the effect of temporal noise correlations on the outcomes of RB protocols. We provide a fully analytic framework capturing the accumulation of error in RB expressed in terms of a three-dimensional random walk in "Pauli space." Using this framework we derive the probability density function describing RB outcomes (averaged over noise) for both Markovian and correlated errors, which we show is generally described by a gamma distribution with shape and scale parameters depending on the correlation structure. Long temporal correlations impart large nonvanishing variance and skew in the distribution towards high-fidelity outcomes -- consistent with existing experimental data -- highlighting potential finite-sampling pitfalls and the divergence of the mean RB outcome from worst-case errors in the presence of noise correlations. We use the Filter-transfer function formalism to reveal the underlying reason for these differences in terms of effective coherent averaging of correlated errors in certain random sequences. We conclude by commenting on the impact of these calculations on the utility of single-metric approaches to quantum characterization, verification, and validation.

Performance of linear minimum‐output energy receiver for self and alien crosstalk mitigation in upstream vectored very high‐speed digital subscriber line

Linear zero-forcing (ZF) canceller does not perform well in the presence of alien crosstalk (AXT) while the receivers based on minimum-mean-square-error (MMSE) criterion require perfect knowledge of the noise covariance matrices. In this study, the authors consider the use of a constrained linear minimum-output energy (MOE) receiver in the presence of self-crosstalk and AXT in upstream vectored very high-speed digital subscriber line systems, that does not require knowledge of the noise correlation matrices and can be trained using the received signals without the use of training sequences. They derive bounds on the performance of the MOE receiver in the digital subscriber line environment and show that it reaches the MMSE performance for self-crosstalk cancellation. They also show that the performance of the proposed receiver lies in between that of the ZF receiver and the non-linear ZF generalised decision feedback equaliser receiver. An adaptation of the canceller coefficients using MOE algorithm shows comparable performance to that of the least mean squares algorithm. The effect of noise correlation on the capacity has also been highlighted via the Cramer-Rao lower bound. Computer simulations are presented to verify the analytical results and demonstrate the performance of the proposed receiver.

Decentralized Estimation Under Correlated Noise

In this paper, we consider distributed estimation of an unknown random scalar by using wireless sensors and a fusion center (FC). We adopt a linear model for distributed estimation of a scalar source where both observation models and sensor operations are linear, and the multiple access channel (MAC) is coherent. We consider a fusion center with multiple antennas and single antenna. In order to estimate the source, best linear unbiased estimation (BLUE) is adopted. Two cases are considered: Minimization of the mean square error (MSE) of the BLUE estimator subject to network power constraint, and minimization of the network power subject to the quality of service (QOS). For a fusion center with multiple antennas, iterative solutions are provided and it is shown that the proposed algorithms always converge. For a fusion center with single antenna, closed-form solutions are provided, and it is shown that the iterative solutions will reduce to the closed-form solutions. Furthermore, the effect of noise correlation at the sensors and fusion center is investigated. It is shown that knowledge of noise correlation at the sensors will help to improve the system performance. Moreover, if correlation exists and not factored in, the system performance might improve depending on the correlation structure. We also show, by simulations, that when noise at the fusion center is correlated, even with knowing the correlation structure, the system performance degrades. Finally, simulations are provided to verify the analysis and present the performance of the proposed schemes.

How noise correlations impact the amount of information in superior colliculus: the analysis of a population with shared receptive fields

Superior colliculus (SC) visuomovement neurons recorded while monkeys perform two versions of visual search task with different difficulty levels have discriminating ability that exceeds the monkey’s discriminating ability [1]. This suggests that there is substantial noise added to this neuronal population. We investigated the effect of noise correlation as a possible limiting factor on the population’s overall discrimination ability. We simultaneously recorded from pairs of neurons during the simpler version of the task, and quantified the noise correlations for each pair. As expected noise correlations were mostly positive for pairs that shared the same receptive field (average= 0.14), and they mostly had the same sign as the signal correlations. Theoretically, this should reduce the amount of information that the pairs carry about the stimulus. The dependence of noise correlations on the stimuli (0.14 for target, 0.13 for distracters) was not statistically significant (p= 0.7); therefore, we didn’t expect that information be significantly added to most of pairs. We investigated the overall impact of noise correlations on the amount of information that each pair carried, by and quantifying the amount of information that the pair carried, when the noise correlations were ignored. The impacts were negligible for each pair. However, it is possible that at the level of population, the impact be different from what we observed for the pairs, due to accumulation of small amounts of correlation. To completely rule out the possibility of limiting effects of noise correlations on growth of information in the population, we investigated if the impacts would be similar in a larger population. We simulated a population of neurons with their responses sharing the basic discharge properties of our recorded neurons during each version of the task, and incorporated randomly assigned noise correlations drawn from a normal distribution with its mean and standard deviation taken from what we had obtained from the simultaneously recorded neurons. Our results so far show that at least for the simpler version of the task, where the signal-to-noise ratio is generally higher, the noise correlations do not have a significant effect, even when the population size grows large enough to saturate the mutual information between the signal and neural responses to its maximum possible amount. Therefore, it can be suggested that noise correlations do not play an important role in limiting the amount of information in a population of SC neurons during a feature visual search task.

A Causal Perspective on the Analysis of Signal and Noise Correlations and Their Role in Population Coding

The role of correlations between neuronal responses is crucial to understanding the neural code. A framework used to study this role comprises a breakdown of the mutual information between stimuli and responses into terms that aim to account for different coding modalities and the distinction between different notions of independence. Here we complete the list of types of independence and distinguish activity independence (related to total correlations), conditional independence (related to noise correlations), signal independence (related to signal correlations), coding independence (related to information transmission), and information independence (related to redundancy). For each type, we identify the probabilistic criterion that defines it, indicate the information-theoretic measure used as statistic to test for it, and provide a graphical criterion to recognize the causal configurations of stimuli and responses that lead to its existence. Using this causal analysis, we first provide sufficiency conditions relating these types. Second, we differentiate the use of the measures as statistics to test for the existence of independence from their use for quantification. We indicate that signal and noise correlation cannot be quantified separately. Third, we explicitly define alternative system configurations used to construct the measures, in which noise correlations or noise and signal correlations are eliminated. Accordingly, we examine which measures are meaningful only as a comparison across configurations and which ones provide a characterization of the actually observed responses without resorting to other configurations. Fourth, we compare the commonly used nonparametric approach to eliminate noise correlations with a functional (model-based) approach, showing that the former approach does not remove those effects of noise correlations captured by the tuning properties of the individual neurons, and implies nonlocal causal structure manipulations. These results improve the interpretation of the measures on the framework and help in understanding how to apply it to analyze the role of correlations.

Effect of Noise Correlation on Noise-Induced Oscillation Frequency in the Photosensitive Belousov–Zhabotinsky Reaction in a Continuous Stirred Tank Reactor

We report on the experimental study of noise-induced oscillations in the photosensitive Ru(bpy)3(2+)-catalyzed Belousov-Zhabotinsky reaction in a continuous stirred tank reactor (CSTR). In the absence of deterministic oscillations and any external periodic forcing, oscillations appear when the system is perturbed by stochastic fluctuations in light irradiation with sufficiently high amplitude in the vicinity of the bifurcation point. The frequency distribution of the noise-induced oscillations is strongly affected by noise correlation. There is a shift of the noise-induced oscillation frequency toward higher frequencies for an intermediate range of the noise correlation exponent, indicating the occurrence of coherence resonance. Our findings indicate that, in principle, noise correlation can be used to direct chemical reactions toward certain behavior.

How noise correlation impact population code in superior colliculus: an information theoretic approach

We previously showed that superior colliculus (SC) visuomovement neurons recorded while monkeys perform visual search tasks have discriminating ability that exceeds the monkey's discriminating ability, suggesting that there is substantial noise added to this neuronal population [1]. We recently began to investigate the latter issue with modeling. First, we examined the effect of noise correlation as a limiting factor on the population's overall discrimination ability. To do so, we simulated a population of singly recorded neurons while manipulating noise correlation within the range of our estimates made from simultaneously recorded pairs of neurons with overlapping receptive fields. Positive noise correlation did decrease the performance of our simulated neuronal population. Based on these results, we sought to further investigate the effect of noise correlation on the discriminating ability of simultaneously recorded pairs of neurons. Here, we examine the effects of noise correlations on ability of simultaneously recorded pairs of neurons in SC to discriminate between two types of stimuli, the target and distractors. We use different time intervals of these recorded responses, to quantify the amount of transmitted information in two conditions: once with the cross-correlations among cells taken into consideration, and another time, considering the cell responses being independent. By comparing the amount of information between the two conditions, we can determine if the noise correlations have a role in limiting the performance of subjects compared to that of the single neurons. If the amount of information with regard to discrimination of the stimuli is larger in the joint population responses than in the sum of information in responses of individual neurons, then the noise correlations have an enhancing effect on discrimination. On the other hand, less information for the joint neuronal activity compared to the independent responses, can indicate that noise correlations are indeed one of the limiting factors that decrease the efficiency of SC in a visual search task. We explore different time windows during the trial for this analysis, since the effects are expected to be larger, and therefore, more tractable, in time intervals that are further from saccade point, when the amounts of noise are larger.

Eigenvalue-Based Sensing and SNR Estimation for Cognitive Radio in Presence of Noise Correlation

Herein, we present a detailed analysis of an eigenvalue-based sensing technique in the presence of correlated noise in the context of a cognitive radio (CR). We use standard-condition-number (SCN)-based decision statistics based on asymptotic random matrix theory (RMT) for the decision process. First, the effect of noise correlation on eigenvalue-based spectrum sensing (SS) is analytically studied under both the noise-only and signal-plus-noise hypotheses. Second, new bounds for the SCN are proposed to achieve improved sensing in correlated noise scenarios. Third, the performance of fractional-sampling (FS)-based SS is studied, and a method to determine the operating point for the FS rate in terms of sensing performance and complexity is suggested. Finally, a signal-to-noise ratio (SNR) estimation technique based on the maximum eigenvalue of the covariance matrix of the received signal is proposed. It is shown that the proposed SCN-based threshold improves sensing performance in correlated noise scenarios, and SNRs up to 0 dB can be reliably estimated with a normalized mean square error (MSE) of less than <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{1}\%$</tex></formula> in the presence of correlated noise without the knowledge of noise variance.

Investigation of the Effect of Noise Correlations on Diversity Gains and Capacities of Multiport Antennas Using Reverberation Chamber

Most of previous studies on diversity gains and capacities of multiantenna systems assumed independent and identically distributed (i.i.d.) Gaussian noises. There are a few studies about the noise correlation effects on diversity gains or MIMO capacities, however, by simulations only. In this paper, the maximum ratio combining (MRC) diversity gain and multiple-input multiple-output (MIMO) capacity including correlated noises are presented. Based on the derived formulas, measurements in a reverberation chamber are performed for the first time to observe the effect of noise correlations on diversity gains and MIMO capacities.

EFFECTS OF NOISE CORRELATION AND TIME DELAY ON TRANSIENT PROPERTIES OF A CANCER GROWTH SYSTEM WITH IMMUNIZATION

The effects of noise correlation and time delay on the transient properties of a cancer growth system are studied in terms of the mean first-passage time (MFPT), which provides a measure of the mean extinction time of the tumor cell population. The results indicate that the additive and multiplicative noises can induce the noise-enhanced stability (NES) effect. The increasing of the delay time weakens the NES effect in the presence of two noise sources and induces a shift of the maximum of the MFPT towards smaller values of the noise intensities. The increasing of cross-correlation strength between noises can only restrain the NES effect induced by the multiplicative noise and can induce a shift of the peak of the MFPT towards larger values of the noise intensities.

The Effect of Noise Correlations in Populations of Diversely Tuned Neurons

The amount of information encoded by networks of neurons critically depends on the correlation structure of their activity. Neurons with similar stimulus preferences tend to have higher noise correlations than others. In homogeneous populations of neurons, this limited range correlation structure is highly detrimental to the accuracy of a population code. Therefore, reduced spike count correlations under attention, after adaptation, or after learning have been interpreted as evidence for a more efficient population code. Here, we analyze the role of limited range correlations in more realistic, heterogeneous population models. We use Fisher information and maximum-likelihood decoding to show that reduced correlations do not necessarily improve encoding accuracy. In fact, in populations with more than a few hundred neurons, increasing the level of limited range correlations can substantially improve encoding accuracy. We found that this improvement results from a decrease in noise entropy that is associated with increasing correlations if the marginal distributions are unchanged. Surprisingly, for constant noise entropy and in the limit of large populations, the encoding accuracy is independent of both structure and magnitude of noise correlations.