Noise Model Research Articles

Periodicity search in the timing of the 25 millisecond pulsars from the second data release of the European pulsar timing array

Abstract In this work, we investigated the presence of strictly periodic, as well as quasi-periodic signals, in the timing of the 25 millisecond pulsars from the EPTA DR2 dataset. This is especially interesting in the context of the recent hints of a gravitational wave background in these data, and the necessary further study of red-noise timing processes, which are known to behave quasi-periodically in some normal pulsars. We used Bayesian timing models developed through the run_enterprise pipeline: a strict periodicity was modelled as the influence of a planetary companion on the pulsar, while a quasi-periodicity was represented as a Fourier-domain Gaussian process. We found that neither model would clearly improve the timing models of the 25 millisecond pulsars in this dataset. This implies that noise and parameter estimates are unlikely to be biased by the presence of a (quasi-)periodicity in the timing data. Nevertheless, the results for PSRs J1744−1134 and J1012+5307 suggest that the standard noise models for these pulsars may not be sufficient. We also measure upper limits for the projected masses of planetary companions around each of the 25 pulsars. The data of PSR J1909−3744 yielded the best mass limits, such that we constrained the 95-percentile to ∼2 × 10−4 M⊕ (roughly the mass of the dwarf planet Ceres) for orbital periods between 5 d–17 yr. These are the best pulsar planet mass limits to date.

Improving Threshold for Fault-Tolerant Color-Code Quantum Computing by Flagged Weight Optimization

Color codes are promising quantum error-correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, the thresholds of color codes under circuit-level noise are relatively low, mainly because measurements of their high-weight stabilizer generators cause an increase in the circuit depth and, thus, substantial errors are introduced. This makes color codes not the best candidate for fault-tolerant quantum computing. Here, we propose a method to suppress the impact of such errors by optimizing weights of decoders using conditional error probabilities conditioned on the measurement outcomes of flag qubits. In numerical simulations, we improve the threshold of the (4.8.8) color code under circuit-level noise from 0.14% to around 0.27%, which is calculated by using an integer programming decoder. Furthermore, in the (6.6.6) color code, we achieve a circuit-level threshold of around 0.36%, which is almost the same value as the highest value in the previous studies employing the same noise model. In both cases, the effective code distance is also improved compared to a conventional method that uses a single ancilla qubit for each stabilizer measurement. Thereby, the achieved logical error rates at low physical error rates are almost one order of magnitude lower than those of the conventional method with the same code distance. Even when compared to the single-ancilla method with a higher code distance, considering the increased number of qubits used in our method, we achieve lower logical error rates in most cases. This method can also be applied to other weight-based decoders, making the color codes more promising as candidates for the experimental implementation of QEC. Furthermore, one can utilize this approach to improve a threshold of wider classes of QEC codes, such as high-rate quantum low-density parity-check codes. Published by the American Physical Society 2024

Dynamic mode decomposition based on expectation–maximization algorithm for simultaneous system identification and denoising

The present study proposes a novel dynamic mode decomposition (DMD) that can simultaneously estimate the reduced-order model, the original signal, and the system/observation noise model only from the noisy data. An expectation–maximization (EM)-algorithm DMD (EMDMD) combines DMD and the parameter adjustment of the linear dynamical system (LDS) based on the EM algorithm. The initial parameters based on the linearity of the reduced-order data are set by using DMD. Subsequently, the log-likelihood of the complete data is maximized by adjusting the LDS parameters while separating the noise. The proposed algorithm is applied to the benchmark data of the short-fat and tall-skinny data matrices with different noise and the time-series velocity fields of the flow around a circular cylinder and the separated flow around an airfoil. The performance of EMDMD in terms of system identification and noise separation from the noisy data is evaluated, and the EMDMD shows the highest system identification and noise separation performance in all data.

Learning to quantify uncertainty in off-target activity for CRISPR guide RNAs.

CRISPR-based genome editing technologies have revolutionised the field of molecular biology, offering unprecedented opportunities for precise genetic manipulation. However, off-target effects remain a significant challenge, potentially leading to unintended consequences and limiting the applicability of CRISPR-based genome editing technologies in clinical settings. Current literature predominantly focuses on point predictions for off-target activity, which may not fully capture the range of possible outcomes and associated risks. Here, we present crispAI, a neural network architecture-based approach for predicting uncertainty estimates for off-target cleavage activity, providing a more comprehensive risk assessment and facilitating improved decision-making in single guide RNA (sgRNA) design. Our approach makes use of the count noise model Zero Inflated Negative Binomial (ZINB) to model the uncertainty in the off-target cleavage activity data. In addition, we present the first-of-its-kind genome-wide sgRNA efficiency score, crispAI-aggregate, enabling prioritization among sgRNAs with similar point aggregate predictions by providing richer information compared to existing aggregate scores. We show that uncertainty estimates of our approach are calibrated and its predictive performance is superior to the state-of-the-art in silico off-target cleavage activity prediction methods. The tool and the trained models are available at https://github.com/furkanozdenn/crispr-offtarget-uncertainty.

Harnessing graph state resources for robust quantum magnetometry under noise

Precise measurement of magnetic fields is essential for various applications, such as fundamental physics, space exploration, and biophysics. Although recent progress in quantum engineering has assisted in creating advanced quantum magnetometers, there are still ongoing challenges in improving their efficiency and noise resistance. This study focuses on using symmetric graph state resources for quantum magnetometry to enhance measurement precision by analyzing the estimation theory under time-homogeneous and time-inhomogeneous noise models. The results show a significant improvement in estimating both single and multiple Larmor frequencies. In single Larmor frequency estimation, the quantum Fisher information spans a spectrum from the standard quantum limit to the Heisenberg limit within a periodic range of the Larmor frequency, and in the case of multiple Larmor frequencies, it can exceed the standard quantum limit for both noisy cases. This study highlights the potential of graph state-based methods for improving magnetic field measurements under noisy environments.

Generalized interacting multiple model Kalman filtering algorithm for maneuvering target tracking under non-Gaussian noises

The traditional interacting multiple model Kalman filtering algorithm (IMM-KF) can deal with the maneuvering target problem under Gaussian noise by soft switching among possible motion models. In practice, its performance is likely to degrade when handling non-Gaussian noise. We introduce the Gaussian mixture model (GMM) into the IMM-KF, and the GMM is utilized to model the non-Gaussian measurement noise as a mixture of multiple Gaussian probability densities with a certain probability. Then, a GIMM framework is proposed that enables accurate switching and fusion among multiple possible motion and noise models. And combined with Kalman filtering (KF), a GIMM-KF algorithm is proposed that enables accurate state estimation of maneuvering targets under non-Gaussian noise conditions. Subsequently, the provided simulations and experiments validate that the GIMM-KF algorithm outperforms existing methods in terms of accuracy, stability and robustness.

Global prediction and analysis for helicopter noise footprint based on acoustic modes.

Aiming to address the significant external noise produced by helicopter rotors, an integrated process based on acoustic modes has been developed for predicting the global noise footprint. The proposed method has the advantages of global prediction, analysis, and low computational costs. The key steps involve constructing an acoustic modal database and efficient prediction of noise footprint. First, the global noise model is utilized to map the time-domain sound pressure to amplitudes and coefficients in the acoustic modal domain. Acoustic mode coefficients representing various flight states are systematically cataloged in the database. Subsequently, the coefficients are extracted based on the characteristic parameters of trajectory elements, allowing for the evaluation of noise radiation in the acoustic modal domain. To investigate the impact of descent angle and advance ratio on the noise footprint, a simulation study is conducted in the forward and approach flight with an AS350 helicopter. Results indicated that, for a region with 1800 observers, the computational time of the developed approach requires only one-fifth of the time compared to the traditional Rotorcraft Noise Model method. This remarkable reduction in computation time, along with the global predictive capability, supports the practicality of efficient noise footprint assessment in both military and civilian contexts.

Toward a dynamic national transportation noise map: Modeling temporal variability of spectral traffic noise emission levels.

The National Transportation Noise Map predicts time-averaged road traffic noise across the continental United States (CONUS) based on annual average daily traffic counts. However, traffic noise can vary greatly with time. This paper outlines a method for predicting nationwide hourly varying source traffic sound emissions called the Vehicular Reduced-Order Observation-based Model (VROOM). The method incorporates three models that predict temporal variability of traffic volume, predict temporal variability of different traffic classes, and use Traffic Noise Model (TNM) 3.0 equations to give traffic noise emission levels based on vehicle numbers and class mix. Location-specific features are used to predict average class mix across CONUS. VROOM then incorporates dynamic traffic class mix data to obtain dynamic traffic class mix. TNM 3.0 equations then give estimated equivalent sound level emission spectra near roads with up to hourly resolution. Important temporal traffic noise characteristics are modeled, including diurnal traffic patterns, rush hours in urban locations, and weekly and yearly variation. Examples of the temporal variability are depicted and possible types of uncertainties are identified. Altogether, VROOM can be used to map national transportation noise with temporal and spectral variability.

Cauchy noise removal using high-order total variation and overlapping group sparsity

Image denoising presents a significant challenge in computer vision, aiming to eliminate unwanted noise from images and restore their original quality. Cauchy noise, characterized by its heavy-tailed distribution, poses a unique hurdle among various types of noise. While several denoising models have been proposed, Total Variation (TV)-based methods, such as the Remove Cauchy Noise model, are widely used for their effectiveness. However, these approaches often suffer from issues such as oversmoothing, staircase artifacts, and the introduction of false details. To address these limitations, recent research has explored the combination of high-order TV with Overlapping Group Sparsity (OGS), showing promising results in noise removal. Inspired by this, our article introduces a novel Cauchy denoising model. Our approach leverages OGS and directional higher-order TV to effectively remove Cauchy noise while preserving image details and minimizing aliasing and smoothing artifacts. The Chambolle-Pock algorithm efficiently solves the underlying optimization problem. Through qualitative and quantitative evaluations, including visualization and parameter measurements, we demonstrate the competitiveness of our model compared to existing methods.

Models and methods for RZ-signals distinction in non-Gaussian noise for information-measurement systems

Abstract Polynomial Decision Rules (DR) for the problems of discrete RZ (Return-to-Zero) signal distinction in asymmetric-excess non-Gaussian noise are proposed. A new approach is proposed, which is based on the use of a modified moment quality criterion of statistical hypothesis testing and the application of higher-order statistics to describe the characteristics of non-Gaussian noise. Simulation of the DR with different parameters of the signal and noise was carried out. It is shown that taking into account the coefficients of skewness and kurtosis of the non-Gaussian noise the efficiency of signal distinction increases with non-linear processing DR compared to known results, which are optimal for the Gaussian noise model. The conducted studies demonstrate a reduction in false decisions in the processing of RZ signals when considering the coefficients of skewness and kurtosis of non-Gaussian noise. Such an increase in efficiency can exceed twofold, depending on the noise parameters. It is shown that the efficiency of the proposed approach is much higher for small SNR (Signal-to-Noise Ratio) values, for example, less than 1.

Quantum-classical separations in shallow-circuit-based learning with and without noises

An essential problem in quantum machine learning is to find quantum-classical separations between learning models. However, rigorous and unconditional separations are lacking for supervised learning. Here we construct a classification problem defined by a noiseless constant depth (i.e., shallow) quantum circuit and rigorously prove that any classical neural network with bounded connectivity requires logarithmic depth to output correctly with a larger-than-exponentially-small probability. This unconditional near-optimal quantum-classical representation power separation originates from the quantum nonlocality property that distinguishes quantum circuits from their classical counterparts. We further characterize the noise regimes for demonstrating such a separation on near-term quantum devices under the depolarization noise model. In addition, for quantum devices with constant noise strength, we prove that no super-polynomial classical-quantum separation exists for any classification task defined by Clifford circuits, independent of the structures of the circuits that specify the learning models.

Adversarial Missingness Attacks on Causal Structure Learning

Causality-informed machine learning has been proposed as an avenue for achieving many of the goals of modern machine learning, from ensuring generalization under domain shifts to attaining fairness, robustness, and interpretability. A key component of causal machine learning is the inference of causal structures from observational data; in practice, this data may be incompletely observed. Prior work has demonstrated that adversarial perturbations of completely observed training data may be used to force the learning of inaccurate causal structural models (SCMs). However, when the data can be audited for correctness (e.g., it is cryptographically signed by its source), this adversarial mechanism is invalidated. This work introduces a novel attack methodology wherein the adversary deceptively omits a portion of the true training data to bias the learned causal structures in a desired manner (under strong signed sample input validation, this behavior seems to be the only strategy available to the adversary). Under this model, theoretically sound attack mechanisms are derived for the case of arbitrary SCMs, and a sample-efficient learning-based heuristic is given. Experimental validation of these approaches on real and synthetic data sets, across a range of SCMs from the family of additive noise models (linear Gaussian, linear non-Gaussian, and non-linear Gaussian) demonstrates the effectiveness of adversarial missingness attacks at deceiving popular causal structure learning algorithms.

Heteroscedastic Gaussian Process Regression for material structure–property relationship modeling

Uncertainty quantification is a critical aspect of machine learning models for material property predictions. Gaussian Process Regression (GPR) is a popular technique for capturing uncertainties, but most existing models assume homoscedastic aleatoric uncertainty (noise), which may not adequately represent the heteroscedastic behavior observed in real-world datasets. Heteroscedasticity arises from various factors, such as measurement errors and inherent variability in material properties. Ignoring heteroscedasticity can lead to lower model performance, biased uncertainty estimates, and inaccurate predictions. Existing Heteroscedastic Gaussian Process Regression (HGPR) models often employ complicated structures to capture input-dependent noise but may lack interpretability. In this paper, we propose an HGPR approach that combines GPR with polynomial regression-based noise modeling to capture and quantify uncertainties in material property predictions while providing interpretable noise models. We demonstrate the effectiveness of our approach on both synthetic and physics-based simulation datasets, including mechanical properties (effective stress) of porous materials. We also introduce an approximated expected log predictive density method for model selection, which eliminates the need for retraining the model during leave-one-out cross-validation, allowing for efficient hyperparameter tuning and model evaluation. By capturing heteroscedastic behavior, enhancing interpretability, and improving model selection, our approach contributes to the development of more robust and reliable machine learning models for material property predictions, enabling informed decision-making in material design and optimization.

Tensor network noise characterization for near-term quantum computers

Characterization of noise in current near-term quantum devices is of paramount importance to fully use their computational power. However, direct quantum process tomography becomes unfeasible for systems composed of tens of qubits. A promising alternative method based on tensor networks was recently proposed []. In this paper, we adapt it for the characterization of noise channels on near-term quantum computers and investigate its performance thoroughly. In particular, we show how experimentally feasible tomographic samples are sufficient to accurately characterize realistic correlated noise models affecting individual layers of quantum circuits, and study its performance on systems composed of up to 20 qubits. Furthermore, we combine this noise characterization method with a recently proposed noise-aware tensor network error mitigation protocol for correcting outcomes in noisy circuits, resulting accurate estimations even on deep circuit instances. This positions the tensor-network-based noise characterization protocol as a valuable tool for practical error characterization and mitigation in the near-term quantum computing era. Published by the American Physical Society 2024

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.

A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits

Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits, even in the presence of certain noise models. Our results allow us to understand under one framework all aforementioned sources of BPs. This theoretical leap resolves a standing conjecture about a connection between loss concentration and the dimension of the Lie algebra of the circuit’s generators.

Disentangling signal and noise in neural responses through generative modeling.

Measurements of neural responses to identically repeated experimental events often exhibit large amounts of variability. This noise is distinct from signal , operationally defined as the average expected response across repeated trials for each given event. Accurately distinguishing signal from noise is important, as each is a target that is worthy of study (many believe noise reflects important aspects of brain function) and it is important not to confuse one for the other. Here, we describe a principled modeling approach in which response measurements are explicitly modeled as the sum of samples from multivariate signal and noise distributions. In our proposed method-termed Generative Modeling of Signal and Noise (GSN)-the signal distribution is estimated by subtracting the estimated noise distribution from the estimated data distribution. Importantly, GSN improves estimates of the signal distribution, but does not provide improved estimates of responses to individual events. We validate GSN using ground-truth simulations and show that it compares favorably with related methods. We also demonstrate the application of GSN to empirical fMRI data to illustrate a simple consequence of GSN: by disentangling signal and noise components in neural responses, GSN denoises principal components analysis and improves estimates of dimensionality. We end by discussing other situations that may benefit from GSN's characterization of signal and noise, such as estimation of noise ceilings for computational models of neural activity. A code toolbox for GSN is provided with both MATLAB and Python implementations.

Overdispersion in gate tomography: Experiments and continuous, two-scale random walk model on the Bloch sphere

Noisy intermediate-scale quantum computers (NISQ) are computing hardware in their childhood, but they are showing high promise and growing quickly. They are based on so-called qubits, which are the quantum equivalents of bits. Any given qubit state results in a given probability of observing a value of zero or one in the readout process. One of the main concerns for NISQ machines is the inherent noisiness of qubits, i.e. the observable frequencies of zeros and ones do not correspond to the theoretically expected probability, as the qubit states are subject to random disturbances over time and with each additional algorithmic operation applied to them. Models to describe the influence of this noise exist. In this study, we conduct extensive experiments on quantum noise. Based on our data, we show that existing noise models lack important aspects. Specifically, they fail to properly capture the aggregation of noise effects over time (or over an algorithm’s runtime), and they are underdispersed. With underdispersion, we refer to the fact that observable frequencies scatter much more between repeated experiments than what the standard assumptions of the binomial distribution would allow for. Based on these shortcomings, we develop an extended noise model for the probability distribution of observable frequencies as a function of the number of gate operations. The model roots back to a known continuous random walk on the (Bloch) sphere, where the angular diffusion coefficient can be used to characterize the standard noisiness of gate operations. Here, we superimpose a second random walk at the scale of multiple readouts to account for overdispersion. Further, our model has known, explicit components for noise during state preparation and measurement (SPAM). The interaction of these two random walks predicts theoretical, runtime-dependent bounds for probabilities. Overall, it is a three-parameter distributional model that fits the data much better than the corresponding one-scale model (without overdispersion), and we demonstrate the better fit and the plausibility of the predicted bounds via Bayesian data-model analysis.

Analysis of Channel Current Noise in Small Nanoscale Metal Oxide Semiconductor Field Effect Transistors.

The shrinkage of metal oxide semiconductor field effect transistor (MOSFET) to the small size of the nanoscale results in changes in their channel current noise composition. This paper determines the channel current noise composition of 90nm MOSFET through experiments, and according to the device material and noise characteristics analysis, the channel current noise of 90nm and below is obtained, which not only contains thermal noise and suppressed channel shot noise, but also adds suppressed gate tunneling shot noise and cross-correlation noise. Then, Monte Carlo simulation of 10nm MOSFET noise is further used to determine the channel current composition of small size nanoscale devices. Subsequently, based on the device structure and fundamental characteristics of channel current noise, the channel current noise model is established. Finally, this model is employed to analyze the relationship between thermal noise, suppressed shot noise, cross-correlation noise, and channel current noise in relation to bias parameters and device characteristics. The theoretical results are basically consistent with the experimental and the simulated results, and the channel noise increases with the increase of bias voltage. This achievement holds promise for enhancing the operational efficiency, reliability, and lifetime of nanoscale small-sized MOSFET devices.

Synchrophasing control of multiple propellers based on hardware in the loop experimental platform

A hardware in the loop experimental platform is established to evaluate the optimal noise reduction prediction and maintenance capability of multiple propellers under high-precision synchrophasing control. This platform incorporates an online propeller noise model and a digital turboprop engine model into a novel integrated measurement system. Firstly, an improved propeller signature theory using CFD simulation's sound pressure signals is proposed to predict the online propeller noise efficiently. It achieves acceptable noise prediction accuracy using a subset of synchrophase angles to predict noise for all synchrophase angles at all receivers. Secondly, a high-priority interrupt method is proposed for the novel integrated measurement system to guarantee precise measurement and ultimate high-precision synchrophasing control. Thirdly, a turboprop engine model based on a component level model and propeller performance maps' CFD data is also established. To enhance the simulation confidence of the system, we compare the dynamic synchrophasing control effects between systems with and without the integration of a turboprop engine mode. The experimental results demonstrate that the high-priority interrupt method effectively reduces the synchrophase angle(θ) error. These approaches reduce noise by 3.62dB at SPL, exhibit a noise variation within ±0.13dB/°, and effectively manage thrust fluctuation within 4.14%. These results indicate that the method meets the control accuracy and noise reduction requirements in a twin-engined turboprop aircraft.