Amount Of White Noise Research Articles

A machine learning approach to identify stochastic resonance in human perceptual thresholds

BackgroundStochastic resonance (SR) is achieved when a faint signal is improved with the addition of the appropriate amount of white noise. Perceptual thresholds are expected to follow a characteristic performance improvement curve as a function of the white noise level added (i.e., thresholds are reduced with an optimal amount of added white noise, beyond which excessive white noise is no longer beneficial). Since SR exhibition in perceptual thresholds is defined by a shape rather than a statistical difference, the presence of SR is typically identified qualitatively. The current state-of-the-art is for blinded human judges to categorize the presence of SR by visually examining data. While categorizations are made with subject data intermixed within a balanced, simulated dataset, which accounts for false positives, this method is still subjective and prone to human error. New methodWe use a logistic regression (LR) trained on engineered features in order to quantitatively classify exhibition of SR. The LR was trained on datasets simulated from a model for SR performance enhancement. ResultsWe implemented the algorithmic classification process in 6 perceptual threshold test cases, informed by the literature and parameters were defined by experimental subject data.Comparison to Existing Method(s): We report algorithmic classifications of SR exhibition, considering the 6 test cases, that outperform existing subjective methods in accuracy (p < 0.05). ConclusionsWe demonstrate that algorithmic classification can effectively identify SR in perceptual thresholds, providing a rigorous, objective, and quantitative approach to identifying the presence of SR.

Weak form of self-testing

The concept of self-testing (or rigidity) refers to the fact that for certain Bell inequalities the maximal violation can be achieved in an essentially unique manner. In this work we present a family of Bell inequalities which are maximally violated by multiple inequivalent quantum realisations. We completely characterise the quantum realisations achieving the maximal violation and we show that each of them requires a maximally entangled state of two qubits. This implies the existence of a new, weak form of self-testing in which the maximal violation allows us to identify the state, but does not fully determine the measurements. From the geometric point of view the set of probability points that saturate the quantum bound is a line segment. We then focus on a particular member of the family and show that the self-testing statement is robust, i.e. that observing a non-maximal violation allows us to make a quantitative statement about the unknown state. To achieve this we present a new construction of extraction channels and analyse their performance. For completeness we provide two independent approaches: analytical and numerical. The noise robustness, i.e. the amount of white noise at which the bound becomes trivial, of the analytical bound is rather small (~0.06%), but the numerical method takes us into an experimentally-relevant regime (~5%). We conclude by investigating the amount of randomness that can be certified using these Bell violations. Perhaps surprisingly, we find that the qualitative behaviour resembles the behaviour of rigid inequalities like the Clauser-Horne-Shimony-Holt inequality. This shows that at least for some device-independent applications rigidity is not a necessary ingredient.

Entanglement Detection beyond Measuring Fidelities.

One of the most widespread methods to determine if a quantum state is entangled, or to quantify its entanglement dimensionality, is by measuring its fidelity with respect to a pure state. In this Letter, we find a large class of states whose entanglement cannot be detected in this manner; we call them unfaithful. Wefind that unfaithful states are ubiquitous in information theory. For small dimensions, we check numerically that most bipartite states are both entangled and unfaithful. Similarly, numerical searches in low dimensions show that most pure entangled states remain entangled but become unfaithful when a certain amount of white noise is added. We also find that faithfulness can be self-activated, i.e., there exist instances of unfaithful states whose tensor powers are faithful. To explore how the fidelity approach limits the quantification of entanglement dimensionality, we generalize the notion of an unfaithful state to that of a D unfaithful state, one that cannot be certified as D-dimensionally entangled by measuring its fidelity with respect to a pure state. For describing such states, we additionally introduce a hierarchy of semidefinite programming relaxations that fully characterizes the set of states of Schmidt rank at most D.

A Low-Complexity Robust Beamforming Using Diagonal Unloading for Acoustic Source Localization

In sensor array beamforming methods, a class of algorithms commonly used to estimate the position of a radiating source, the diagonal loading of the beamformer covariance matrix is generally used to improve computational accuracy and localization robustness. This paper proposes a diagonal unloading (DU) method which extends the conventional response power beamforming method by imposing an additional constraint to the covariance matrix of the array output vector. The regularization is obtained by subtracting a given amount of white noise from the main diagonal of the covariance matrix. Specifically, the DU beamformer aims at subtracting the signal subspace from the noisy signal space and it is computed by constraining the regularized covariance matrix to be negative definite. It is hence a data-dependent covariance matrix conditioning method. We show how to calculate precisely the unloading parameter, and we present an eigenvalue analysis for comparing the proposed DU beamforming, the minimum variance distortionless response (MVDR) filter and the multiple signal classification (MUSIC) method. Theoretical analysis and experiments with acoustic sources demonstrate that the DU beamformer localization performance is comparable to that of MVDR and MUSIC. Since the DU beamformer computational cost is comparable to that of a conventional beamformer, the proposed method can be attractive in array processing due to its simplicity, effectiveness and computational efficiency.

Acoustic sensor structural configuration study.

This work examines the configuration requirements for a sensor being developed to provide information about the location of an acoustic source. The continuous sensor’s vibrational response, caused by a traveling acoustic wave, is used in an inverse method to reconstruct the forces in that wave. A finite‐length beam supported on an elastic foundation is the candidate structure. The impact of changing various structural parameters on the beam’s vibration response is examined analytically using finite element methods. A goal in configuring the beam sensor is to obtain a response with enough dynamic information to accommodate a successful force reconstruction. Some of the configuration parameters of interest include the beam material, geometry, thickness, and the elastic foundation properties. The excitations used in the study consist of transient waves with differing numbers of sinusoidal half‐cycles. Because background noise has the potential to impact the force reconstruction, various amounts of white noise are added to the simulated response values prior to performing the traveling wave reconstruction. Tikhonov regularization and the L‐curve method are used. Results obtained from the simulations show that this sensor model is effective in identifying moving wave loads. [Work supported by NSF Sensor Innovation and Systems.]

Violation of equalities in bipartite qutrits systems

We have recently shown that for the special case of a bipartite system with binary inputs and outputs there exist equalities in local theories which are violated by quantum theory. The amount of white noise tolerated by these equalities are twice that of inequalities. In this paper we will first introduce an inequality in bipartite qutrits systems which, if non-maximally entangled state is used instead of maximally entangled state, is violated more strongly by quantum theory. Hence reproducing the results obtained in the literature. We will then prove that our equalities in this case are violated by quantum theory too, and they tolerate much more white noise than inequalities.

Bell’s inequalities for three-qubit entangled states with white noise

We consider three-qubit entangled states classified by Acin et al. and evaluate Bell’s inequalities for them when the white noise exists, which may be a real situation for the experiment of the Bells inequality to three-qubit entangled states. We obtain the maximum violation for the Bell inequality in each case and find the condition for exceeding the classical limit. And we observe that even when there would exist quite amount of white noise, some of three-qubit entangled states(for example 2b, 3a, 3b-I, 3b-II and 3b-III types) might show the violation of the Bell inequality.

Changes in the structure of children’s isometric force variability with practice

This study examined the effect of age and practice on the structure of children’s force variability to test the information processing hypothesis that a reduction of sensorimotor system noise accounts in large part for age-related reductions in perceptual-motor performance variability. In the study, 6-year-olds, 10-year-olds, and young adults practiced on 5 consecutive days (15 trials/day), maintaining for 15-s trials a constant level of force (5 or 25% of maximum voluntary contraction) against an object using a pinch grip (thumb and index finger). With increasing age, the amount of force error and variability decreased, but the sequential structure of variability increased in irregularity. With practice, children reduced the amount of variability by changing the structure of the force output so as to be more similar to that of their older counterparts. The findings provide further evidence that practice-driven changes in the structure of force output, rather than a decline in the amount of white noise, largely account for age-related reductions in the amount of force variability.

Real-time estimations of multi-modal frequencies for smart structures

In this paper, various methods for the real-time estimation of multi-modal frequencies are realized in real time and compared through numerical and experimental tests. These parameter-based frequency estimation methods can be applied to various engineering fields such as communications, radar and adaptive vibration and noise control. Well-known frequency estimation methods are introduced and explained. The Bairstow method is introduced to find the roots of a characteristic equation for estimations of multi-modal frequencies, and the computational efficiency of the Bairstow method is shown quantitatively. For a simple numerical test, we consider two sinusoids of the same amplitudes mixed with various amounts of white noise. The test results show that the auto regressive (AR) and auto regressive and moving average (ARMA) methods are unsuitable in noisy environments. The other methods apart from the AR method have fast tracking capability. From the point of view of computational efficiency, the results reveal that the ARMA method is inefficient, while the cascade notch filter method is very effective. The linearized adaptive notch filter and recursive maximum likelihood methods have average performances. Experimental tests are devised to confirm the feasibility of real-time computations and to impose the severe conditions of drastically different amplitudes and of considerable changes of natural frequencies. We have performed experiments to extract the natural frequencies from the vibration signal of wing-like composite plates in real time. The natural frequencies of the specimen are changed by added masses. Especially, the AR method exhibits a remarkable performance in spite of the severe conditions. This study will be helpful to anyone who needs a frequency estimation algorithm for real-time applications.

Zero-phasing the zero-phase source

This paradoxical title is in fact a tribute to the classic paper by Gibson and Larner, “Predictive deconvolution and the zero-phase source” (Geophysics, 1984). Their work was originally presented at the 1982 SEG Annual Meeting, which means that it has been almost 20 years since they exposed the problems associated with controlling the phase of vibroseis records, and we are still struggling with them. The main issue is not related to the zero-phase Klauder wavelet itself but rather with the rest of the recording chain which contains a series of minimum-phase filters (such as the geophone response and possibly the coupling conditions). The resulting seismic wavelet is therefore mixed phase, thus making it virtually impossible to process correctly and obtain final zero-phase records with standard deconvolution processing. To circumvent this problem, Gib-son and Larner recommended transforming the vibroseis data into minimum-phase records by applying a deterministic filter based on the known Klauder wavelet. The resulting records can then be processed within a controlled-phase sequence similar to that used for dynamite data. However, there is no clear minimum-phase equivalent for the vibroseis wavelet, and Gibson and Larner suggested that such a “beast” might not even exist. Figure 1, taken from their paper, shows four different minimum-phase equivalents of a Klauder wavelet, corresponding to four values of an obscure parameter in the minimum-phase transform. If the minimum-phase equivalent of the vibroseis source is nonunique, how can we guarantee a final zero-phase result? Figure 1. Klauder wavelet (top) and four minimum-phase equivalent wavelets generated using the indicated amounts of white-noise. (From Gibson and Larner.) This paper follows up the aforementioned classic. I will show that although a unique minimum-phase equivalent exists, it is neither practical nor necessary to compute. In-stead, I will show a simple and effective method to process vibroseis data …

Stochastic Resonance in Cochlear Signal Transduction

The use of a stochastic resonance model contributes crucially to our comprehension of the intensity resolution characteristics of the mammalian cochlea. In guinea pigs, as demonstrated by different statistical methods, the temporal distribution of the interspike intervals of the spontaneous activity reflects an intrinsic cochlear white noise process, demanded as basic requirement for manifest stochastic resonance phenomena. Brownian motion of cochlear fluids is discussed as the underlying white noise motor. Following our model, the amount of white noise, adjusted at the level of the stereocilia of the inner hair cells, determines the threshold, dynamic range and intensity discrimination limen of an individual afferent neuron of the mammalian cochlea.

Predictive deconvolution and the zero‐phase source

Predictive deconvolution is commonly applied to seismic data generated with a Vibroseisr® source. Unfortunately, when this process invokes a minimum‐phase assumption, the phase of the resulting trace will not be correct. Nonetheless, spiking deconvolution is an attractive process because it restores attenuated higher frequencies, thus increasing resolution. For detailed stratigraphic analyses, however, it is desirable that the phase of the data be treated properly as well. The most common solution is to apply a phase‐shifting filter that corrects for errors attributable to a zero‐phase source. The phase correction is given by the minimum‐phase spectrum of the correlated Vibroseis wavelet. Because no minimum‐phase spectrum truly exists for this bandlimited wavelet, white noise is added to its amplitude spectrum in order to design the phase‐correction filter. Different levels of white noise, however, produce markedly different results when field data sections are filtered. A simple argument suggests that the amount of white noise used should match that added in designing the (minimum‐phase) spiking deconvolution operator. This choice, however, also produces inconsistent results; field data again show that the phase treatment is sensitive to the amount of added white noise. Synthetic data tests show that the standard phase‐correction procedure breaks down when earth attenuation is severe. Deterministically reducing the earth‐filter effects before deconvolution improved the resulting phase treatment for the synthetic data. After application of the inverse attenuation filter to the field data, however, phase differences again remain for different levels of added white noise. These inconsistencies are attributable to the phase action of spiking deconvolution. This action is dependent upon the shape of the signal spectrum as well as the spectral shape and level of contaminating noise. Thus, in practice the proper treatment of phase in data-dependent processing requires extensive knowledge of the spectral characteristics of both signal and noise. With such knowledge, one could apply deterministic techniques that either eliminate the need for statistical deconvolution or condition the data so as to satisfy better the statistical model assumed in data‐dependent processing.