Noise Regime Research Articles

Flux noise in disordered spin systems

Impurity spins randomly distributed at the surfaces and interfaces of superconducting wires are known to cause flux noise in Superconducting Quantum Interference Devices, providing a mechanism for decoherence in superconducting qubits. While flux noise is well characterised experimentally, the microscopic model underlying spin dynamics remains unknown. First-principles theories are too computationally expensive to capture spin diffusion over large length scales, third-principles approaches lump spin dynamics into a single phenomenological spin-diffusion operator that is not able to describe the quantum noise regime and connect to microscopic models and disorder scenarios. Here we propose an intermediate "second principles" method to describe general spin dissipation and flux noise in the quantum regime. It leads to the interpretation that flux noise arises from the density of paramagnon excitations at the edge of the wire, with paramagnon-paramagnon interactions leading to spin diffusion, and interactions between paramagnons and other degrees of freedom leading to spin energy relaxation. At high frequency we obtain an upper bound for flux noise, showing that the (super)Ohmic noise observed in experiments does not originate from interacting spin impurities. We apply the method to Heisenberg models in two dimensional square lattices with random distribution of vacancies and nearest-neighbour spins coupled by constant exchange. Numerical calculations of flux noise show that it follows the observed power law $A/\omega^{\alpha}$, with amplitude $A$ and exponent $\alpha$ depending on temperature and inhomogeneities. These results are compared to experiments in niobium and aluminium devices. The method establishes a connection between flux noise experiments and microscopic Hamiltonians identifying relevant microscopic mechanisms and guiding strategies for reducing flux noise.

Lejos de Veracruz

The urban landscape of Mexico City has been the main subject of many Mexican films throughout the years, transforming the city into a character itself. The movie Güeros (dir. Alonso Ruizpalacios, 2014) is no exception, telling the story of four young people navigating the metropolis at a time of political and social turmoil in late 1990s Mexico. This essay discusses the intersection between three elements that construct the utopia these characters are looking for: the city, its sounds, and a former rock star. The main intention is to foreground the sounds of the city not as an accessory to the moving image, but as an integral part of the construction of the plot, drawing from R. Murray Schafer’s concept of “soundscape” (1979), as well as on Josh Kun’s (2005) and Brandon LaBelle’s (2010) discussions around space and sound. The film is shot in black and white in an effort to tell a tale of dualism, one that insists on constructing otherness through opposition, primarily as it relates to the urban. By following the binary gesture first presented by the chiaroscuro, this essay argues that silence opens up a possibility for intimacy as opposed to a deafening environment that engulfs the inner worlds of its inhabitants. The search for a home is framed by aural elements that resist the regime of noise that characterizes the city. I propose a counterintuitive analysis that unpacks the symbolic charge of these narrative elements as they tell a parallel story that may not be portrayed in purely visual terms.

The effect of time regime in noise exposure on the auditory system and behavioural stress in the zebrafish

Anthropogenic noise of variable temporal patterns is increasing in aquatic environments, causing physiological stress and sensory impairment. However, scarce information exists on exposure effects to continuous versus intermittent disturbances, which is critical for noise sustainable management. We tested the effects of different noise regimes on the auditory system and behaviour in the zebrafish (Danio rerio). Adult zebrafish were exposed for 24 h to either white noise (150 ± 10 dB re 1 μPa) or silent control. Acoustic playbacks varied in temporal patterns—continuous, fast and slow regular intermittent, and irregular intermittent. Auditory sensitivity was assessed with Auditory Evoked Potential recordings, revealing hearing loss and increased response latency in all noise-treated groups. The highest mean threshold shifts (c. 13 dB) were registered in continuous and fast intermittent treatments, and no differences were found between regular and irregular regimes. Inner ear saccule did not reveal significant hair cell loss but showed a decrease in presynaptic Ribeye b protein especially after continuous exposure. Behavioural assessment using the standardized Novel Tank Diving assay showed that all noise-treated fish spent > 98% time in the bottom within the first minute compared to 82% in control, indicating noise-induced anxiety/stress. We provide first data on how different noise time regimes impact a reference fish model, suggesting that overall acoustic energy is more important than regularity when predicting noise effects.

Effect of Mach number on the aeroacoustic feedback loop generating airfoil tonal noise

Airfoil tonal noise emission at low-to-moderate Reynolds number and flow conditions featuring a laminar separation bubble close to the trailing edge is often related to an aeroacoustic feedback mechanism and, therefore, the Mach number is a primary parameter for the flow field and noise generation. This study experimentally explores the effect of the Mach number on airfoil tonal noise generation in the nominally incompressible flow regime. Using airfoil profiles of different chord lengths, the Mach number is varied for a constant Reynolds number. Acoustic and flow field measurements for a range of combinations of Reynolds and Mach numbers were conducted. At zero incidence, the tonal noise regime in the Reynolds number domain is found to be sensitive to the Mach number. At non-zero angle of attack (2°), the noise generation is found to be dominated by vortex shedding over a separation bubble on the pressure side. The details of the separation bubble and shedding process depend on the Mach number. The frequencies of the dominant tones and the frequency intervals between tones increase with the Mach number. Moreover, the measured frequency interval can be collapsed using a relation based on the aeroacoustic feedback loop model. The relation is rewritten to separate the effects of the Reynolds and Mach numbers. As a result, the dependence on the Mach number is identified and tested. In contrast, the tonal noise level shows a more complex dependence on details of the laminar separation bubble and the vortex shedding process.

A Framework for Characterizing the Value of Information in Hidden Markov Models

In this paper, a general framework is formalised to characterise the value of information (VoI) in hidden Markov models. Specifically, the VoI is defined as the mutual information between the current, unobserved status at the source and a sequence of observed measurements at the receiver, which can be interpreted as the reduction in the uncertainty of the current status given that we have noisy past observations of a hidden Markov process. We explore the VoI in the context of the noisy Ornstein-Uhlenbeck process and derive its closed-form expressions. Moreover, we investigate the effect of different sampling policies on VoI, deriving simplified expressions in different noise regimes and analysing statistical properties of the VoI in the worst case. We also study the optimal sampling policy to maximise the average information value under the sampling rate constraint. In simulations, the validity of theoretical results is verified, and the performance of VoI in Markov and hidden Markov models is also analysed. Numerical results further illustrate that the proposed VoI framework can support timely transmission in status update systems, and it can also capture the correlation properties of the underlying random process and the noise in the transmission environment.

Robust boundary formation in a morphogen gradient via cell-cell signaling.

Establishing sharp and correctly positioned boundaries in spatial gene expression patterns is a central task in both developmental and synthetic biology. We consider situations where a global morphogen gradient provides positional information to cells but is insufficient to ensure the required boundary precision, due to different types of noise in the system. In a conceptual model, we quantitatively compare three mechanisms, which combine the global signal with local signaling between neighboring cells, to enhance the boundary formation process. These mechanisms differ with respect to the way in which they combine the signals by following either an AND, an OR, or a SUM rule. Within our model, we analyze the dynamics of the boundary formation process, and the fuzziness of the resulting boundary. Furthermore, we consider the tunability of the boundary position and its scaling with system size. We find that all three mechanisms produce less fuzzy boundaries than the purely gradient-based reference mechanism, even in the regime of high noise in the local signals relative to the noise in the global signal. Among the three mechanisms, the SUM rule produces the most accurate boundary. However, in contrast to the other two mechanisms, it requires noise to exit metastable states and rapidly reach the stable boundary pattern.

Dihedral Multi-Reference Alignment

We study the dihedral multi-reference alignment problem of estimating the orbit of a signal from multiple noisy observations of the signal, acted on by random elements of the dihedral group. We show that if the group elements are drawn from a generic distribution, the orbit of a generic signal is uniquely determined from the second moment of the observations. This implies that the optimal estimation rate in the high noise regime is proportional to the square of the variance of the noise. This is the first result of this type for multi-reference alignment over a non-abelian group with a non-uniform distribution of group elements. Based on tools from invariant theory and algebraic geometry, we also delineate conditions for unique orbit recovery for multi-reference alignment models over finite groups (namely, when the dihedral group is replaced by a general finite group) when the group elements are drawn from a generic distribution. Finally, we design and study numerically three computational frameworks for estimating the signal based on group synchronization, expectation-maximization, and the method of moments.

Single-pixel imaging with heralded single photons

Traditional remote sensing applications are often based on pulsed laser illumination with a narrow linewidth and characteristic repetition rate, which are not conducive to covert operation. Whatever methods are employed for covert sensing, a key requirement is for the probe light to be indistinguishable from background illumination. We present a method to perform single-pixel imaging that suppresses the effect of background light and hence improves the signal-to-noise ratio by using correlated photon-pairs produced via spontaneous parametric down conversion. One of the photons in the pair is used to illuminate the object whilst the other acts as a temporal reference, allowing the signal photons to be distinguished from background noise. Understanding the noise regime is key to producing higher contrast images using this heralding method.

Early detection of the combustion instabilities by quantifying diagonal-wise measurements of joint recurrence plots of pressure and radiant energy fluctuations

This article presents a study of the early detection of combustion instabilities of a 250 kW liquid rapid premixed oil swirled burner. The main objective was the calculation of indexes, based on a chaotic analysis, able to detect in advance the combustion instabilities. In the combustor, the air mass flow rate was kept constant, and in order to induce the combustion instabilities, the fuel mass flow rate was adjusted during the experiments in which pressure and radiant energy fluctuations were simultaneously measured from the combustion chamber. In this chaotic analysis, joint recurrence plots were calculated in order to analyze the dependence between the pressure and radiant energy fluctuations. Hence, a diagonal-wise quantification was applied to the joint recurrence plots to calculate four indexes: the τ-recurrence rate index RRτ, the τ-determinism index DETτ, the τ-average diagonal line length index Lτ, and the τ-entropy index sτ. The results show that all four indexes were capable of sorting all cases under analysis into two groups: the “combustion noise regime” due to the low-amplitude aperiodic oscillations and the “combustion instability regime” due to the high-amplitude periodic oscillations. In addition, early detection of the transitions were also detected. Therefore, the results presented in this research showed that the four indexes were effective precursors in order to detect in advance the combustion instabilities.

Combining electron spin resonance spectroscopy with scanning tunneling microscopy at high magnetic fields.

The continuous increase in storage densities and the desire for quantum memories and computers push the limits of magnetic characterization techniques. Ultimately, a tool that is capable of coherently manipulating and detecting individual quantum spins is needed. Scanning tunneling microscopy (STM) is the only technique that unites the prerequisites of high spatial and energy resolution, low temperature, and high magnetic fields to achieve this goal. Limitations in the available frequency range for electron spin resonance STM (ESR-STM) mean that many instruments operate in the thermal noise regime. We resolve challenges in signal delivery to extend the operational frequency range of ESR-STM by more than a factor of two and up to 100 GHz, making the Zeeman energy the dominant energy scale at achievable cryogenic temperatures of a few hundred millikelvin. We present a general method for augmenting existing instruments into ESR-STM to investigate spin dynamics in the high-field limit. We demonstrate the performance of the instrument by analyzing inelastic tunneling in a junction driven by a microwave signal and provide proof of principle measurements for ESR-STM.

Pathway-resolved decomposition demonstrates correlation and noise dependencies of redundant information processing in recurrent feed-forward topologies.

In a biochemical assay that converts fan-in networks into feed-forward loops (FFLs), we show that the inter-regulator redundant information about the output gene product can be decomposed into finer components, mediated by the constituent pathways. Variance-based information within the linear noise regime facilitates quantifying these submodular redundancies. Contrary to the conventional wisdom on information decomposition, we report that information redundancy depends nontrivially on inter-regulator correlation. For the type-1 coherent (C1) and incoherent (I1) FFLs, the direct regulatory path-mediated redundancy is certainly correlation independent. However, components induced by the indirect regulatory path and interpathway interference are correlation dependent in (non)linear fashion. The trade-off between information redundancy and similarly decomposable extrinsic noise from input to output node has been demonstrated for the pathways and full motifs. Our analyses suggest that the interpathway cross redundancy positively and negatively influences the superposition of elementary redundancies in the C1- and I1-FFLs, respectively. Their corresponding total extrinsic noise is produced by the weighted sum and difference of the pathway-specific components. We find that the I1-FFL is able to manufacture more varied redundancy and extrinsic noise responses compared to the C1-FFL. Underlying the differing characteristics of the composite metrics across FFL variants, there exist uniformly behaving pathway-dependent elements. The decomposition framework has been meticulously explored in biologically rational parametric realizations through analytical estimates and stochastic simulations.

Interplay of vibration- and environment-assisted energy transfer

We study the interplay between two environmental influences on excited state energy transfer in photosynthetic light harvesting complexes, namely, vibrationally assisted energy transfer (VAET) and environment-assisted quantum transport (ENAQT), considering a dimeric chromophore donor–acceptor model as a prototype for larger systems. We demonstrate how the basic features of the excitonic energy transfer are influenced by these two environments, both separately and together, with the environment being fully quantum in the case of VAET and treated in the Haken–Strobl–Reineker classical limit in the case of ENAQT. Our results reveal that in the weak noise regime, the presence of a classical noise source is detrimental to the energy transfer that is resonantly assisted by the exciton-vibration interactions intrinsic to VAET. In the strong noise regime we reproduce all the features of ENAQT, including the turnover into a Zeno regime where energy transfer is suppressed, and VAET is insignificant.

Error analysis for denoising smooth modulo signals on a graph

In many applications, we are given access to noisy modulo samples of a smooth function with the goal being to robustly unwrap the samples, i.e., to estimate the original samples of the function. In a recent work, Cucuringu and Tyagi [11] proposed denoising the modulo samples by first representing them on the unit complex circle and then solving a smoothness regularized least squares problem – the smoothness measured w.r.t. the Laplacian of a suitable proximity graph G – on the product manifold of unit circles. This problem is a quadratically constrained quadratic program (QCQP) which is nonconvex, hence they proposed solving its sphere-relaxation leading to a trust region subproblem (TRS). In terms of theoretical guarantees, ℓ 2 error bounds were derived for (TRS). These bounds are however weak in general and do not really demonstrate the denoising performed by (TRS). In this work, we analyse the (TRS) as well as an unconstrained relaxation of (QCQP). For both these estimators we provide a refined analysis in the setting of Gaussian noise and derive noise regimes where they provably denoise the modulo observations w.r.t. the ℓ 2 norm. The analysis is performed in a general setting where G is any connected graph.

Regret-Optimal Filtering for Prediction and Estimation

The filtering problem of causally estimating a desired signal from a related observation signal is investigated through the lens of regret optimization. Classical filter designs, such as $\mathcal H_2$ (Kalman) and $\mathcal H_\infty$, minimize the average and worst-case estimation errors, respectively. As a result $\mathcal H_2$ filters are sensitive to inaccuracies in the underlying statistical model, and $\mathcal H_\infty$ filters are overly conservative since they safeguard against the worst-case scenario. We propose instead to minimize the \emph{regret} in order to design filters that perform well in different noise regimes by comparing their performance with that of a clairvoyant filter. More explicitly, we minimize the largest deviation of the squared estimation error of a causal filter from that of a non-causal filter that has access to future observations. In this sense, the regret-optimal filter will have the best competitive performance with respect to the non-causal benchmark filter no matter what the true signal and the observation process are. For the important case of signals that can be described with a time-invariant state-space, we provide an explicit construction for the regret optimal filter in the estimation (causal) and the prediction (strictly-causal) regimes. These solutions are obtained by reducing the regret filtering problem to a Nehari problem, i.e., approximating a non-causal operator by a causal one in spectral norm. The regret-optimal filters bear some resemblance to Kalman and $H_\infty$ filters: they are expressed as state-space models, inherit the finite dimension of the original state-space, and their solutions require solving algebraic Riccati equations. Numerical simulations demonstrate that regret minimization inherently interpolates between the performances of the $H_2$ and $H_\infty$ filters and is thus a viable approach for filter design.

Robust Localization With Bounded Noise: Creating a Superset of the Possible Target Positions via Linear-Fractional Representations

Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable, applications require localization methods that assume minimal knowledge on the noise distribution. We present a scalable algorithm delimiting a tight superset of all possible target locations, assuming range measurements to known landmarks, contaminated with bounded noise and unknown distributions. This superset is of primary interest in robust statistics since it is a tight majorizer of the set of Maximum-Likelihood (ML) estimates parametrized by noise densities respecting two main assumptions: (1) the noise distribution is supported on a ellipsoidal uncertainty region and (2) the measurements are non-negative with probability one. We create the superset through convex relaxations that use Linear Fractional Representations (LFRs), a well-known technique in robust control. For low noise regimes the supersets created by our method double the accuracy of a standard semidefinite relaxation. For moderate to high noise regimes our method still improves the benchmark but the benefit tends to be less significant, as both supersets tend to have the same size (area).

An approximate expectation-maximization for two-dimensional multi-target detection.

We consider the two-dimensional multi-target detection (MTD) problem of estimating a target image from a noisy measurement that contains multiple copies of the image, each randomly rotated and translated. The MTD model serves as a mathematical abstraction of the structure reconstruction problem in single-particle cryo-electron microscopy, the chief motivation of this study. We focus on high noise regimes, where accurate detection of image occurrences within a measurement is impossible. To estimate the image, we develop an expectation-maximization framework that aims to maximize an approximation of the likelihood function. We demonstrate image recovery in highly noisy environments, and show that our framework outperforms the previously studied autocorrelation analysis in a wide range of parameters.

Enhanced Signal-Associated Noise in a φ-OTDR System

Owing to their high sensitivity with respect to external measurands, Rayleigh-based distributed optical fiber sensors (DOFS) find their way into applications in many industrial and academic sectors. To further transcend the limit of these sensors in terms of sensing range, low spatial resolution, speed and accuracy of the measurement, improving the signal-to-noise ratio (SNR) of the system plays a pivotal role. Out of the several existing techniques for enhancing the SNR, one such method, solely dedicated to the Rayleigh-based sensors, is through intrinsically increasing the backreflected signal of the fibers. The enhanced backreflected signal provided by such fibers, generally known as reflection-enhanced fibers (REF), is rigorously analysed in the present work. It is inferred from the analysis that the enhanced signal is essentially accompanied by enhanced signal-dependent noises, which can adversely affect their performance. For instance, when a performance comparison is carried out between the REF and a standard single-mode fiber (SMF) under identical experimental conditions, due to their different intrinsic backreflected signal levels, the two fibers experience dissimilar noise regimes leading to an erroneous estimation of the performance of the former. This necessitates the optimisation of the interrogation system and the experimental parameters while employing such fibers for specific sensing applications. Additionally, a distributed temperature measurement is presented by taking advantage of the enhanced SNR of a 100 m long REF exhibiting a sub-mK temperature uncertainty of 0.5 mK at metric spatial resolution yielding a sixfold improvement compared to the 3 mK uncertainty of an SMF.

Two-Dimensional Multi-Target Detection: An Autocorrelation Analysis Approach

We consider thetwo-dimensional multi-target detection problem of recovering a target image from a noisy measurement that contains multiple copies of the image, each randomly rotated and translated. Motivated by the structure reconstruction problem in single-particle cryo-electron microscopy, we focus on the high noise regime, where the noise hampers accurate detection of the image occurrences. We develop an autocorrelation analysis framework to estimate the image directly from a measurement with an arbitrary spacing distribution of image occurrences, bypassing the estimation of individual locations and rotations. We conduct extensive numerical experiments, and demonstrate image recovery in highly noisy environments. <xref ref-type="fn" rid="fn1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¹</xref>

Synchronized measurements of noise characteristics and flow regimes near the thermal expansion valve using R134a refrigerant

• Quantitative flow-induced noise prediction model. • Synchronized measurements of flow-induced noise and flow regimes. • Comparison between noise modeling and experimental measurements. • Distinguished flow-induced noise waveforms for different flow regimes. Flow-induced noise in the expansion device can be very disturbing. The thermal expansion valve is usually positioned near the occupants, often resulting in flow-induced noise that can be perceived as annoying. Current studies lack a quantitative relationship between flow characteristics and flow-induced noise. Therefore, in this paper, a noise prediction model is proposed to predict the sound pressure level of flow-induced noise. The study utilizes a pumped R134a loop for synchronized measurements between flow-induced noise and flow regimes. Synchronized high-speed measurements obtained from a microphone and a high-speed camera enable simultaneous investigation of flow-induced noise and flow regimes. In this case, the experimental results find a gurgling noise distributing near 9 kHz. Using the TXV inlet pressure for calculating thermodynamic properties, the gurgling noise sound pressure level prediction error is less than 15%. A hissing noise distributing at around 15 kHz is not as noticeable as the gurgling noise. The error of sound pressure level prediction for hissing noise is less than 40%. Both the experimental results and the modeling results show that the sound pressure level of gurgling noise increases as the vapor mass fraction increases or the system mass flux increases. From the experimental results, the noise waveforms are distinguished. The model can correctly outline the shape of noise waveforms for different flow regimes with the help of visualizations. The model introduced in this paper shows the proper prediction for flow-induced noise except for the annular flow entering the valve.

Optimal Passive Source Localization for Acoustic Emissions.

Acoustic emission is a non-destructive testing method where sensors monitor an area of a structure to detect and localize passive sources of elastic waves such as expanding cracks. Passive source localization methods based on times of arrival (TOAs) use TOAs estimated from the noisy signals received by the sensors to estimate the source position. In this work, we derive the probability distribution of TOAs assuming they were obtained by the fixed threshold technique—a popular low-complexity TOA estimation technique—and show that, if the sampling rate is high enough, TOAs can be approximated by a random variable distributed according to a mixture of Gaussian distributions, which reduces to a Gaussian in the low noise regime. The optimal source position estimator is derived assuming the parameters of the mixture are known, in which case its MSE matches the Cramér–Rao lower bound, and an algorithm to estimate the mixture parameters from noisy signals is presented. We also show that the fixed threshold technique produces biased time differences of arrival (TDOAs) and propose a modification of this method to remove the bias. The proposed source position estimator is validated in simulation using biased and unbiased TDOAs, performing better than other TOA-based passive source localization methods in most scenarios.