Additive Noise Term Research Articles

Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold

Abstract We report a theoretical and experimental study of phase noise in semiconductor lasers when the bias current is below the threshold value. The theoretical study is performed by using two types of rate equations, with additive and multiplicative noise terms. We find the conditions for which the evolution in those rate equations can be described by 1-dimensional and two dimensional Brownian motions, respectively. The main statistical differences between the additive and multiplicative noise models are then illustrated by using the simplified Brownian motion models. Additive and multiplicative noise models predictions are compared with measurements of the phase noise with a coherent receiver using a 90o optical hybrid. We develop a novel method to extract the phase noise directly from our measurements, that in contrast to the usual direct method is not based on the analysis of the phase noise difference. The method permits a direct visualization of the phase noise trajectories and a calculation of the averages and the distribution that is valid in the short-time limit. Our results are in very good agreement with the results obtained with the method based on the phase noise difference. Our experimental results show that the variance of the phase noise grows linearly in time and has Gaussian statistics, supporting the modelization of the phase noise statistics with the additive noise model.

Stability analysis of the stochastic Grey‐Scott model using spectral method

The Grey‐Scott model is a prominent reaction–diffusion system that has sustain consequential recent research about patterning creation in the reaction–diffusion systems. The present research work, explore the stability analysis of a proposed stochastic Grey‐Scott model, which recommend the randomness or unpredictability into the complex system. To take into account the different variations in reactant concentrations profiles, the stochasticity is modeled using the additive white noise terms. To investigate the stability characteristics of the stochastic Grey‐Scott model, we use the spectral collocation technique. Such mathematical perspective sheds light on the different system's behavior in the addition of white noise, and also it may have significance for comprehending processes in the real world that are controlled by comparable dynamics.

Data-driven dynamical coarse-graining for condensed matter systems.

Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in a solution, where the molecule(s) and the solvent dynamics need to be integrated, rendering the simulations computationally costly and often unfeasible for physically/biologically relevant time scales. Standard coarse graining approaches can reproduce equilibrium distributions and structural features but do not properly include the dynamics. In this work, we develop a general data-driven coarse-graining methodology inspired by the Mori-Zwanzig formalism, which shows that macroscopic systems with a large number of degrees of freedom can be described by a few relevant variables and additional noise and memory terms. Our coarse-graining method consists of numerical integrators for the distinguished components, where the noise and interaction terms with other system components are substituted by a random variable sampled from a data-driven model. The model is parameterized using data from multiple short-time full-system simulations, and then, it is used to run long-time simulations. Applying our methodology to three systems-a distinguished particle under a harmonic and a bistable potential and a dimer with two metastable configurations-the resulting coarse-grained models are capable of reproducing not only the equilibrium distributions but also the dynamic behavior due to temporal correlations and memory effects. Remarkably, our method even reproduces the transition dynamics between metastable states, which is challenging to capture correctly. Our approach is not constrained to specific dynamics and can be extended to systems beyond Langevin dynamics, and, in principle, even to non-equilibrium dynamics.

Optimum Performance Analysis and Receiver Design for OFDM-Based Frequency-Splitting SWIPT With Strong Nonlinear Effects

Multicarrier based frequency splitting simultaneous wireless information and power transmission (FS-SWIPT) signals are very prone to nonlinear effects due to the combination of high-power energy harvesting (EH) subcarriers with low-power data subcarriers. In this paper, we study the impact of nonlinear effects in FS-SWIPT signals, as well as ways to minimize these effects on the data transmission performance. We start by analytically characterizing the impact of nonlinear devices on the signals, showing that the nonlinear effects on data subcarriers are exacerbated by a factor close to the ratio between the power spectral densities of EH and data terms. This suggests that conventional receivers, that treat nonlinear distortion as an additional noise term, can have very poor performance. Then, we present an iterative receiver that iteratively estimates and cancels nonlinear distortion, and is able to have a performance close to the linear case. Finally, we study the optimum performance of FS-SWIPT signals with strong nonlinear distortion levels, showing that, by using optimum receivers, the nonlinear distortion term can be used to improve the performance of FS-SWIPT, even outperforming the linear case.

BER analysis of an optimum MIMO linear receiver in optical SDM systems with mode-dependent loss.

Multiple-input multiple-output (MIMO) receivers designed to optimize the minimum mean square error (MMSE) are a common choice in coherent optical communication systems based on spatial division multiplexing (SDM). This kind of receivers naturally integrate both MIMO equalization and matched filtering functions. However, when the optical channel exhibits significant mode-dependent loss (MDL) and/or mode-dependent gain (MDG), the impact of inter-symbol interference (ISI) and crosstalk that arise, even using an ideal MIMO MMSE linear receiver, is barely analyzed. Moreover, due to the random nature of the MDL/MDG model, the resulting ISI, crosstalk, and bit error rate (BER) also become random variables and, hence the system performance is more unpredictable. In this paper, we first evaluate the residual distortion (ISI and crosstalk) after the MIMO receiver and then we study the validity of assuming it as an additional Gaussian noise term independent of the channel noise. Next, the probability density distribution (PDF) of the BER is analyzed, from both an analytical perspective and numerical simulations. For the latter, we use a single-carrier 2-PAM (pulse amplitude modulation) system, with pulse shaping, and the MIMO MMSE receiver implementation by means of a MIMO fractionally-spaced equalizer (FSE). We carry out simulations of the system under different conditions of MDL/MDG level and signal to noise ratio (SNR), measured at the receiver input. Additionally, we address possible fits of the BER PDF to known closed-form distributions, among which the Generalized Extreme Value (GEV) family of distributions is selected, and polynomial functions are proposed that relate the system parameters with the GEV PDF parameters. Finally, we present contour maps of BER according to a giving target of system outage probability (OP) that depend on the MDL/MDG and SNR conditions.

Amplitude and phase noise in two-membrane cavity optomechanics

Cavity optomechanics is a suitable field to explore quantum effects on macroscopic objects and develop quantum technology applications. A perfect control of the laser noise is required to operate the system in such extreme conditions necessary to reach the quantum regime. In this paper, we consider a Fabry–Perót cavity, driven by two laser fields, with two partially reflective SiN membranes inside it. We describe the effects of amplitude and phase noise on the laser introducing two additional noise terms in the Langevin equations of the system’s dynamics. Experimentally, we add an artificial source of noise on the laser. We calibrate the intensity of the noise, inject it into the system, and check the validity of the theoretical model. This procedure provides an accurate description of the effects of a noisy laser in the optomechanical setup and allows for quantifying the amount of noise.

Constructive role of shot noise in the collective dynamics of neural networks.

Finite-size effects may significantly influence the collective dynamics of large populations of neurons. Recently, we have shown that in globally coupled networks these effects can be interpreted as additional common noise term, the so-called shot noise, to the macroscopic dynamics unfolding in the thermodynamic limit. Here, we continue to explore the role of the shot noise in the collective dynamics of globally coupled neural networks. Namely, we study the noise-induced switching between different macroscopic regimes. We show that shot noise can turn attractors of the infinitely large network into metastable states whose lifetimes smoothly depend on the system parameters. A surprising effect is that the shot noise modifies the region where a certain macroscopic regime exists compared to the thermodynamic limit. This may be interpreted as a constructive role of the shot noise since a certain macroscopic state appears in a parameter region where it does not exist in an infinite network.

Numerical Stabilities of Vasicek and Geometric Brownian Motion Models

Stochastic differential equations (SDEs) are very often used as models for a large number of phenomena in the physical, economic and management sciences. They generalize the notion of ordinary differential equations, taking into account a white additive and multiplicative noise term, to model random trajectories such as stock market prices or particles movements, on the quantum scale, subject to diffusion phenomena. In rare cases, it is generally impossible to have explicit solution to these equations. In this case, the numerical approach, presenting itself under various aspects, is the only favorable outcome. However, the stability of numerical schemes for stochastic differential equations solution is much more significant. In this paper, we establish and make a classical proof of the mean and mean-square stabilities of the numerical SDEs schemes for Vasicek and Geometric Brownian motion models.

UPPER SEMICONTINUITY OF UNIFORM RANDOM ATTRACTORS FOR DELAY PARABOLIC EQUATION

This paper concentrates on the upper semicontinuity of uniform random attractors for a class of delay parabolic equations with additive noise and nonautonomous external force terms. Firstly, through the uniform estimation of the solution, it is proved that the solution of the equation has a closed uniform pullback absorbing set with respect to the symbolic space. Then, by Arzela-Ascoli theorem, we prove uniformly pullback compactness of solutions as well as the existence and uniqueness of uniform random attractors. Finally, we prove the upper semicontinuity of the uniform random attractors when time delay approaches to zero.

Strategic trading with information acquisition and long-memory stochastic liquidity

This paper investigates the strategic interaction of information acquisition, information-based dynamic trading, and noise trading patterns, as well as its significant implications on market equilibrium outcomes. We consider a market where the strategic trader can dynamically acquire costly information about an asset’s payoff via private signals instead of endowing him with its full information. The noise trading, which provides necessary liquidity for the market, has the feature of long-range dependence. The risk-neutral market maker then sets the equilibrium price for the asset based on information gleaned from the market total order flow. We characterize the equilibria for both opaque and transparent markets depending on whether or not the trader’s order flow is disclosed. In particular, closed-form solutions are obtained for two special cases and associated financial interpretations are provided. We find that: (1) the endogenous information acquisition and information-based trading help improve the price informativeness over time, while the information efficiency could be decreasing; (2) long-memory stochastic liquidity leads to an excessive price volatility; and (3) in a transparent market, the trader should adopt a mixed strategy by adding an additional noise term to the trading strategy to prevent rapid information leakage.

Spectral Reflectance Estimation with Smoothness Constraint

We consider the problem of estimating surface-spectral reflectance with a smoothness constraint from image data. The total variation of a spectral reflectance over the visible wavelength range is defined as the measure of smoothness. A penalty on roughness, equivalent to smoothness, is added to the performance index to estimate the spectral reflectance functions. The optimal estimates of the spectral reflectance functions are determined to minimize a total cost function consisting of the estimation error and the roughness of the spectral functions. An RGB camera and multiple LED light sources are used to construct the multispectral image acquisition system. We model the observed images using spectral sensitivities, illuminant spectrum, unknown spectral reflectance, a gain parameter, and an additive noise term. The estimation algorithms are developed for the two estimation methods of PCA and LMMSE. The optimal estimators are derived based on the least-square criterion for PCA and the mean squared error minimization criterion for LMMSE. The feasibility of the proposed method is shown in an experiment using three mobile phone cameras. It is confirmed that the optimal estimators improve the accuracy for both original PCA and LMMS estimators.

Nonuniqueness in law for stochastic hypodissipative Navier–Stokes equations

We study the incompressible hypodissipative Navier–Stokes equations with dissipation exponent 0<α<12 on the three-dimensional torus perturbed by an additive Wiener noise term and prove the existence of an initial condition for which distinct probabilistic weak solutions exist. To this end, we employ convex integration methods to construct a pathwise probabilistically strong solution, which violates a pathwise energy inequality up to a suitable stopping time. This paper seems to be the first in which such solutions are constructed via Beltrami waves instead of intermittent jets or flows in a stochastic setting.

Blind Restoration of Atmospheric Turbulence-Degraded Images Based on Curriculum Learning

Atmospheric turbulence-degraded images in typical practical application scenarios are always disturbed by severe additive noise. Severe additive noise corrupts the prior assumptions of most baseline deconvolution methods. Existing methods either ignore the additive noise term during optimization or perform denoising and deblurring completely independently. However, their performances are not high because they do not conform to the prior that multiple degradation factors are tightly coupled. This paper proposes a Noise Suppression-based Restoration Network (NSRN) for turbulence-degraded images, in which the noise suppression module is designed to learn low-rank subspaces from turbulence-degraded images, the attention-based asymmetric U-NET module is designed for blurred-image deconvolution, and the Fine Deep Back-Projection (FDBP) module is used for multi-level feature fusion to reconstruct a sharp image. Furthermore, an improved curriculum learning strategy is proposed, which trains the network gradually to achieve superior performance through a local-to-global, easy-to-difficult learning method. Based on NSRN, we achieve state-of-the-art performance with PSNR of 30.1 dB and SSIM of 0.9 on the simulated dataset and better visual results on the real images.

Channel Estimation and Secret Key Rate Analysis of MIMO Terahertz Quantum Key Distribution

We study the secret key rate (SKR) of a multiple-input multiple-output (MIMO) continuous variable quantum key distribution (CVQKD) system operating at terahertz (THz) frequencies, accounting for the effects of channel estimation. We propose a practical channel estimation scheme for the THz MIMO CVQKD system which is necessary to realize transmit-receive beamforming between Alice and Bob. We characterize the input-output relation between Alice and Bob during the key generation phase, by incorporating the effects of additional noise terms arising due to the channel estimation error and detector noise. Furthermore, we analyze the SKR of the system and study the effect of channel estimation error and overhead. Our simulation results reveal that the SKR may degrade significantly as compared to the SKR upper bound that assumes perfect channel state information, particularly at large transmission distances.

Benefits of quasi-continuous symbol rate tunability in links constrained by ROADM filtering

As modern optical networks continue evolving toward higher symbol rates while supporting tight channel spacing, penalties due to optical filtering incurred by transmission through reconfigurable optical add-drop multiplexers (ROADMs) can become significant within the overall link budget. For this reason, filtering impairments must be realistically assessed and accurately modeled, particularly in terrestrial networks where signals may traverse many ROADMs. Given that modern transceivers can provide flexible modulation options and most ROADMs in use today support flexible grid operation, there remains the challenge of optimizing performance and/or capacity while managing these multiple degrees of freedom. In this work, we use real-time transceivers with a tunable symbol rate up to 72 GBaud and variable modulation up to 64QAM to experimentally investigate the impact of ROADM filtering on the optimum operating condition required to maximize channel capacity or margin. We also present a simplified model for considering the filtering impairment as an additive noise term and use it to predict performance in other scenarios. It is shown that symbol rate tunability in steps below 5 GBd is required to maximize the margin for a given link passband. Finally, we explore the difference in performance for filtering conditions with passband narrowing on both sides of the signal, assuming individual wavelength routing, or only on one side of the signal, assuming multi-carrier routing.

Improved method for spectral reflectance estimation and application to mobile phone cameras.

We propose an improved method for estimating surface-spectral reflectance from the image data acquired by an RGB digital camera. We suppose a multispectral image acquisition system in the visible range, where a camera captures multiple images for the scene of an object under multiple light sources. First, the observed image data are described using the camera spectral sensitivities, the surface-spectral reflectance, the illuminant spectral power distributions, an additive noise term, and a gain parameter. Then, the optimal reflectance estimate is determined to minimize the mean-square error between the estimate and the original surface-spectral reflectance. We attempt to further improve the estimation accuracy and develop a novel linear estimator in a more general form than the Wiener estimator. Furthermore, we calibrate the imaging system using a reference standard sample. Finally, experiments are performed to validate the proposed method for estimating the surface-spectral reflectance using different mobile phone cameras.

A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression

Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is nonlinearly integrated into the corresponding evolution term, typically termed as random ordinary differential equations (RODEs). The classical averaging methods fail to treat such RODEs. Therefore, we introduce a novel averaging method appropriate to be applied to a specific class of RODEs. To exemplify the importance of our method, we apply it to an important biomedical problem, in particular, we implement the method to the assessment of intratumoral heterogeneity impact on tumor dynamics. Precisely, we model gliomas according to a well-known Go or Grow (GoG) model, and tumor heterogeneity is modeled as a stochastic process. It has been shown that the corresponding deterministic GoG model exhibits an emerging Allee effect (bistability). In contrast, we analytically and computationally show that the introduction of white noise, as a model of intratumoral heterogeneity, leads to monostable tumor growth. This monostability behavior is also derived even when spatial cell diffusion is taken into account.

Delay induced dynamical behaviors in a stochastic insect outbreak model in presence of Michaelis-Menten type harvesting

In this paper, we have considered stochastic insect outbreak model in presence of Michaelis-Menten type of harvesting. The growth of the insect species is taken as delayed logistic type together with a multiplicative noise term. The impact of internal environmental disturbances on the insect population is taken into account by adding an additive noise term in the model. The effects of the noises, cross correlation strength of the noises and time delay on the insect population are investigated and observed very rich dynamical behaviors. It is ascertained that multiplicative noise reduces population size greatly than additive noise. As usual, increase of harvesting of insect species reduces the population size at faster rate. Regime shift is possible depending on multiplicative noise only in contrast it is not possible via only additive noise. One of the key finding is the noise-delayed switching phenomenon for negatively correlated noises.

Numerical approximation of the stochastic Cahn\u2013Hilliard equation near the sharp interface limit

We consider the stochastic Cahn–Hilliard equation with additive noise term varepsilon ^gamma g, {dot{W}} (gamma >0) that scales with the interfacial width parameter varepsilon . We verify strong error estimates for a gradient flow structure-inheriting time-implicit discretization, where varepsilon ^{-1} only enters polynomially; the proof is based on higher-moment estimates for iterates, and a (discrete) spectral estimate for its deterministic counterpart. For gamma sufficiently large, convergence in probability of iterates towards the deterministic Hele–Shaw/Mullins–Sekerka problem in the sharp-interface limit varepsilon rightarrow 0 is shown. These convergence results are partly generalized to a fully discrete finite element based discretization. We complement the theoretical results by computational studies to provide practical evidence concerning the effect of noise (depending on its ’strength’ gamma ) on the geometric evolution in the sharp-interface limit. For this purpose we compare the simulations with those from a fully discrete finite element numerical scheme for the (stochastic) Mullins–Sekerka problem. The computational results indicate that the limit for gamma ge 1 is the deterministic problem, and for gamma =0 we obtain agreement with a (new) stochastic version of the Mullins–Sekerka problem.

Well-posedness of renormalized solutions for a stochastic p -Laplace equation with L^1 -initial data

We consider a $ p $-Laplace evolution problem with stochastic forcing on a bounded domain $ D\subset\mathbb{R}^d $ with homogeneous Dirichlet boundary conditions for $ 1&lt;p&lt;\infty $. The additive noise term is given by a stochastic integral in the sense of Itô. The technical difficulties arise from the merely integrable random initial data $ u_0 $ under consideration. Due to the poor regularity of the initial data, estimates in $ W^{1,p}_0(D) $ are available with respect to truncations of the solution only and therefore well-posedness results have to be formulated in the sense of generalized solutions. We extend the notion of renormalized solution for this type of SPDEs, show well-posedness in this setting and study the Markov properties of solutions.