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Journal articles on the topic 'Random noise theory'

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Author: Grafiati

Published: 4 June 2021

Last updated: 27 July 2024

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1

Veraart, Jelle, Els Fieremans, and Dmitry S. Novikov. "Diffusion MRI noise mapping using random matrix theory." Magnetic Resonance in Medicine 76, no. 5 (November 24, 2015): 1582–93. http://dx.doi.org/10.1002/mrm.26059.

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2

Hida, Takeyuki, and Si Si. "Innovations for Random Fields." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 04 (October 1998): 499–509. http://dx.doi.org/10.1142/s0219025798000272.

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There is a famous formula called Lévy's stochastic infinitesimal equation for a stochastic process X(t) expressed in the form [Formula: see text] We propose a generalization of this equation for a random field X(C) indexed by a contour C. Assume that the X(C) is homogeneous in a white noise x, say of degree n, we can then appeal to the classical theory of variational calculus and to the modern theory of white noise analysis in order to discuss the innovation for the X(C) and hence its probabilistic structure. Some of future directions are also mentioned.

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3

Hara, Hiroaki, Sang Don Choi, and Yeon Choon Chung. "A theory of noise based on generalized random walks." Physica A: Statistical Mechanics and its Applications 144, no. 2-3 (August 1987): 481–94. http://dx.doi.org/10.1016/0378-4371(87)90203-2.

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4

Thorarinsdottir, Thordis Linda. "BAYESIAN IMAGE RESTORATION, USING CONFIGURATIONS." Image Analysis & Stereology 25, no. 3 (May 3, 2011): 129. http://dx.doi.org/10.5566/ias.v25.p129-143.

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In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed in detail for 3 X 3 and 5 X 5 configurations and examples of the performance of the procedure are given.

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White, Benjamin S., Werner E. Kohler, and Leonard J. Srnka. "Random scattering in magnetotellurics." GEOPHYSICS 66, no. 1 (January 2001): 188–204. http://dx.doi.org/10.1190/1.1444894.

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Typical well logs show substantial variations of formation electrical resistivity over small spatial scales, down to the resolution of the logging tool. Using a plane stratified earth model, we examine the effects of this fine‐scale microstructure on scattering of the naturally occurring electromagnetic (EM) waves used in magnetotellurics. We show how 1-D magnetotelluric (MT) data may be viewed as arising statistically from a smoothed effective medium version of the resistivity‐depth profile. The difference between the data produced by the true medium and the effective medium is attributable to random scattering noise. This noise is fundamental to magnetotellurics and other diffusive‐wave EM exploration methods since it arises from the very small spatial scales that are usually ignored. The noise has unique statistical properties, which we characterize. We show that if scattering is the dominant noise source, a thin layer of increased resistivity at depth can be reliably detected only if the noise statistics are incorporated properly into the detection algorithm. This sets a new fundamental limit on the vertical detection capability of MT data. The theory agrees well with Monte Carlo simulations of MT responses from random resistivity microlayers.

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6

Miyoshi, Naoto. "A NOTE ON BOUNDS AND MONOTONICITY OF SPATIAL STATIONARY COX SHOT NOISES." Probability in the Engineering and Informational Sciences 18, no. 4 (October 2004): 561–71. http://dx.doi.org/10.1017/s026996480418409x.

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We consider shot-noise and max-shot-noise processes driven by spatial stationary Cox (doubly stochastic Poisson) processes. We derive their upper and lower bounds in terms of the increasing convex order, which is known as the order relation to compare the variability of random variables. Furthermore, under some regularity assumption of the random intensity fields of Cox processes, we show the monotonicity result which implies that more variable shot patterns lead to more variable shot noises. These are direct applications of the results obtained for so-called Ross-type conjectures in queuing theory.

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7

Duc, Luu Hoang. "Random attractors for dissipative systems with rough noises." Discrete & Continuous Dynamical Systems 42, no. 4 (2022): 1873. http://dx.doi.org/10.3934/dcds.2021176.

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<p style='text-indent:20px;'>We provide an analytic approach to study the asymptotic dynamics of rough differential equations, with the driving noises of Hölder continuity. Such systems can be solved with Lyons' theory of rough paths, in particular the rough integrals are understood in the Gubinelli sense for controlled rough paths. Using the framework of random dynamical systems and random attractors, we prove the existence and upper semi-continuity of the global pullback attractor for dissipative systems perturbed by bounded noises. Moreover, if the unperturbed system is strictly dissipative then the random attractor is a singleton for sufficiently small noise intensity.</p>

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8

Kuang, Z. F., and I. Pázsit. "The generalized theory of neutron noise in a random medium." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458, no. 2017 (January 8, 2002): 233–52. http://dx.doi.org/10.1098/rspa.2001.0856.

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9

Demers, Matthew, Herb Kunze, and Davide La Torre. "ON RANDOM ITERATED FUNCTION SYSTEMS WITH GREYSCALE MAPS." Image Analysis & Stereology 31, no. 2 (May 17, 2012): 109. http://dx.doi.org/10.5566/ias.v31.p109-120.

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In the theory of Iterated Function Systems (IFSs) it is known that one can find an IFS with greyscale maps (IFSM) to approximate any target signal or image with arbitrary precision, and a systematic approach for doing so was described. In this paper, we extend these ideas to the framework of random IFSM operators. We consider the situation where one has many noisy observations of a particular target signal and show that the greyscale map parameters for each individual observation inherit the noise distribution of the observation. We provide illustrative examples.

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10

Liu, Xin, and Yanjiao Li. "Dynamics of Non-Autonomous Stochastic Semi-Linear Degenerate Parabolic Equations with Nonlinear Noise." Mathematics 11, no. 14 (July 18, 2023): 3158. http://dx.doi.org/10.3390/math11143158.

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In the present paper, we aim to study the long-time behavior of a stochastic semi-linear degenerate parabolic equation on a bounded or unbounded domain and driven by a nonlinear noise. Since the theory of pathwise random dynamical systems cannot be applied directly to the equation with nonlinear noise, we first establish the existence of weak pullback mean random attractors for the equation by applying the theory of mean-square random dynamical systems; then, we prove the existence of (pathwise) pullback random attractors for the Wong–Zakai approximate system of the equation. In addition, we establish the upper semicontinuity of pullback random attractors for the Wong–Zakai approximate system of the equation under consideration driven by a linear multiplicative noise.

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11

Khoolenjani, Nayereh Bagheri, and Mohammad Hossein Alamatsaz. "A DE BRUIJN'S IDENTITY FOR DEPENDENT RANDOM VARIABLES BASED ON COPULA THEORY." Probability in the Engineering and Informational Sciences 30, no. 1 (October 14, 2015): 125–40. http://dx.doi.org/10.1017/s0269964815000315.

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De Bruijn's identity shows a link between two fundamental concepts in information theory: entropy and Fisher information. In the literature, De Bruijn's identity has been stated under the assumption of independence between input signal and an additive noise. However, in the real world, the noise could be highly dependent on the main signal. The main aim of this paper is, firstly, to extend De bruijn's identity for signal-dependent noise channels and, secondly, to study how Stein and heat identities are related to De bruijn's identity. Thus, new versions of De Bruijn's identity are introduced in the case when input signal and additive noise are dependent and are jointly distributed according to Archimedean and Gaussian copulas. It is shown that in this generalized model, the derivatives of the differential entropy can be expressed in terms of a function of Fisher information. Our finding enfolds the conventional De Bruijn's identity as some remarks. Then, the equivalence among the new De Bruijn-type identity, Stein's identity and heat equation identity is established. The paper concludes with an application of the developed results in information theory.

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12

Stahl, Frederic, and Max Bramer. "Random Prism: a noise-tolerant alternative to Random Forests." Expert Systems 31, no. 5 (June 10, 2013): 411–20. http://dx.doi.org/10.1111/exsy.12032.

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13

Xiao, Kai, and Yonghui Zhou. "Insider Trading with Memory under Random Deadline." Journal of Mathematics 2021 (July 15, 2021): 1–7. http://dx.doi.org/10.1155/2021/2973361.

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In this paper, we study a model of continuous-time insider trading in which noise traders have some memories and the trading stops at a random deadline. By a filtering theory on fractional Brownian motion and the stochastic maximum principle, we obtain a necessary condition of the insider’s optimal strategy, an equation satisfied. It shows that when the volatility of noise traders is constant and the noise traders’ memories become weaker and weaker, the optimal trading intensity and the corresponding residual information tend to those, respectively, when noise traders have no any memory. And, numerical simulation illustrates that if both the trading intensity of the insider and the volatility of noise trades are independent of trading time, the insider’s expected profit is always lower than that when the asset value is disclosed at a finite fixed time; this is because the trading time ahead is a random deadline which yields the loss of the insider’s information.

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14

Li, Guofu, Jie Liu, and Shuang Zhang. "Enhancing cross correlations of ocean ambient noise in the time domain based on random matrix theory." Journal of the Acoustical Society of America 152, no. 5 (November 2022): 2849–58. http://dx.doi.org/10.1121/10.0015135.

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Cross correlations of diffuse noise can be utilized to recover the time domain Green's function (TDGF) between two points. This principle allows for a variety of practical applications, such as seismic tomography, ocean thermometry, passive localization, etc. However, in the real ocean environment, loud interference noise sources usually bias the travel time estimates of the TDGF or result in poor recovery quality. To deal with this issue, a diffuse noise reconstruction approach is proposed to eliminate the influence of the strong interference noise by utilizing the time domain statistical property of ocean ambient noise recorded on single hydrophones with the help of random matrix theory. Simulation and experimental data analysis indicate that this algorithm can effectively extract the diffuse noise component from the ocean ambient noise field and retrieve the TDGF with a higher signal-to-noise ratio when coherent accumulation of cross correlations of the reconstructed diffuse noise is performed.

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15

ZMARROU, HICHAM, and ALE JAN HOMBURG. "Bifurcations of stationary measures of random diffeomorphisms." Ergodic Theory and Dynamical Systems 27, no. 5 (October 2007): 1651–92. http://dx.doi.org/10.1017/s0143385707000077.

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AbstractRandom diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss the dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of random diffeomorphisms. A bifurcation theory is developed under mild regularity assumptions on the diffeomorphisms and the noise distribution (e.g. smooth diffeomorphisms with uniformly distributed additive noise are included). We distinguish bifurcations where the density function of a stationary measure varies discontinuously or where the support of a stationary measure varies discontinuously. We establish that generic random diffeomorphisms are stable. The densities of stable stationary measures are shown to be smooth and to depend smoothly on an auxiliary parameter, except at bifurcation values. The bifurcation theory explains the occurrence of transients and intermittency as the main bifurcation phenomena in random diffeomorphisms. Quantitative descriptions by means of average escape times from sets as functions of the parameter are provided. Further quantitative properties are described through the speed of decay of correlations as a function of the parameter. Random differentiable maps which are not necessarily injective are studied in one dimension; we show that stable one-dimensional random maps occur open and dense and that in one-parameter families bifurcations are typically isolated. We classify codimension-one bifurcations for one-dimensional random maps; we distinguish three possible kinds, the random saddle node, the random homoclinic and the random boundary bifurcation. The theory is illustrated on families of random circle diffeomorphisms and random unimodal maps.

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16

Srinivasan, R. S., and P. A. Krishnan. "Random Response of Thick Laminated Rectangular Plates." Journal of Vibration and Acoustics 113, no. 3 (July 1, 1991): 286–91. http://dx.doi.org/10.1115/1.2930183.

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The present paper deals with the random response analysis of clamped thick laminated rectangular plates subjected to white noise excitation. The refined plate theory postulated by Reddy has been used. The analysis has been done using an integral equation technique. The random response results obtained for istropic square plates based on different plate theories (viz.) classical theory, first order theory and refined theory, have been compared. A parametric study has been conducted for angle ply and cross ply plates by varying the lay up of layers and a/h ratios.

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17

GUZ, SERGEY A., and MICHAEL V. SVIRIDOV. "SPATIAL ROTATION DRIVEN BY RANDOM ANGULAR VELOCITY (COLORED NOISE)." Fluctuation and Noise Letters 05, no. 04 (December 2005): L499—L505. http://dx.doi.org/10.1142/s0219477505002938.

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We consider kinematics of a rigid body rotation about a fixed point. An angular velocity is considered to be a sum of deterministic and random vector-functions. We suppose that the components of the latter are statistically independent small stationary processes. The problem is, for example, important for the theory of a rotational Brownian motion or an error analysis of strapped-down inertial navigation systems. We construct a multiplicative perturbation theory so that the desired matrix is represented as a product of deterministic matrix by random perturbation one. The perturbation matrix is approximately found by the first terms of a matrizant. As example, we consider the constant deterministic velocity and the components of the colored random velocity to be white noises (the Brownian motion), the Ornstein-Uhlenbeck processes, or the time derivative of the Ornstein-Uhlenbeck processes ("green" noises). In the second case it is shown that a diffusion of an instanta-neous rotation angle appears only if the deterministic rotation is not zero.

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18

Hayase, Tomohiro. "Identifiability of parametric random matrix models." Infinite Dimensional Analysis, Quantum Probability and Related Topics 22, no. 03 (September 2019): 1950018. http://dx.doi.org/10.1142/s0219025719500188.

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We investigate parameter identifiability of spectral distributions of random matrices. In particular, we treat compound Wishart type and signal-plus-noise type. We show that each model is identifiable up to some kind of rotation of parameter space. Our method is based on free probability theory.

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19

Middleton, D. "S.O. Rice and the theory of random noise: some personal recollections." IEEE Transactions on Information Theory 34, no. 6 (1988): 1367–73. http://dx.doi.org/10.1109/18.21273.

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20

Hsueh, Keng D., and Roger P. Hamernik. "A generalized approach to random noise synthesis: Theory and computer simulation." Journal of the Acoustical Society of America 87, no. 3 (March 1990): 1207–17. http://dx.doi.org/10.1121/1.398795.

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21

Guo, Shiqin, and Jilin Xu. "Art Financial Risk Prediction Algorithm Based on Random Matrix." Mathematical Problems in Engineering 2022 (July 30, 2022): 1–10. http://dx.doi.org/10.1155/2022/8477065.

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Random matrix theory is applied in the financial field to study the correlation of the financial correlation coefficient matrix, which is a key factor in network construction. In this paper, the random matrix theory is combined with network construction to study the art financial risk prediction algorithm based on the random matrix. Based on the stochastic matrix theory and the key nodes of the network, the financial network and the “noise” network before and after the “denoising” are analyzed and compared. It is found that the key and important information of the original network is still retained after the “denoising” of the network, and the noise information corresponds to the information represented by the smaller nodes in the original network. Based on the stochastic matrix of artwork financial risk prediction, the topological properties of the financial network before and after denoising are analyzed and compared from the perspectives of minimum spanning tree, model, and community structure. Based on the random matrix theory, this paper discusses the financial correlation coefficient matrix and the statistical properties of the eigenvalues of the random matrix, and on this basis, the existing denoising methods are improved, the correlation coefficient matrix more suitable for constructing the financial network is established, and the art financial risk prediction algorithm is constructed. Then, based on the stochastic matrix theory and the key nodes of the network, the financial network and the noise network before and after denoising are analyzed and compared. It is found that the key and important information of the original network is still retained after denoising the network, and the noise information corresponds to the information represented by the relatively small nodes in the original network. Finally, based on the stochastic matrix of art financial risk prediction, analysis of the financial network topology, such as minimum spanning tree, model, and community structure, found that the improved financial network topology is more obvious and the structure is closer.

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22

Svirskis, G. "Fast Response to Small Signals with Noise in Neurons." Nonlinear Analysis: Modelling and Control 8, no. 1 (January 25, 2003): 77–84. http://dx.doi.org/10.15388/na.2003.8.1.15179.

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Neurons in the brain receive synaptic inputs delivered as random trains. Mathematical theory was developed to relate the rate of threshold crossings with statistics of membrane fluctuations evoked by random point input process. Integrate-and-fire neuronal model was used to check validity of theoretical results. Mathematical theory approximated firing rate for low level of activity and showed that dependence of threshold crossings on mean rate of membrane potential change brings about very fast response to small signals.

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23

Alpay, Daniel, and Ariel Pinhas. "Stochastic Wiener filter in the white noise space." Opuscula Mathematica 40, no. 3 (2020): 323–39. http://dx.doi.org/10.7494/opmath.2020.40.3.323.

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In this paper we introduce a new approach to the study of filtering theory by allowing the system's parameters to have a random character. We use Hida's white noise space theory to give an alternative characterization and a proper generalization to the Wiener filter over a suitable space of stochastic distributions introduced by Kondratiev. The main idea throughout this paper is to use the nuclearity of this space in order to view the random variables as bounded multiplication operators (with respect to the Wick product) between Hilbert spaces of stochastic distributions. This allows us to use operator theory tools and properties of Wiener algebras over Banach spaces to proceed and characterize the Wiener filter equations under the underlying randomness assumptions.

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24

Alpert, Nathaniel M., W. Craig Barker, Andrew Gelman, Stephen Weise, Michio Senda, and John A. Correia. "The Precision of Positron Emission Tomography: Theory and Measurement." Journal of Cerebral Blood Flow & Metabolism 11, no. 1_suppl (March 1991): A26—A30. http://dx.doi.org/10.1038/jcbfm.1991.33.

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The limits of quantitation with positron emission tomography (PET) are examined with respect to the noise propagation resulting from radioactive decay and other sources of random error. Theoretical methods for evaluating the statistical error have been devised but seldom applied to experimental data obtained on human subjects. This paper extends the analysis in several ways: (1) A Monte Carlo method is described for tracking the propagation of statistical error through the analysis of in vivo measurements; (2) Experimental data, obtained in phantoms, validating the Monte Carlo method and other methods are presented; (3) A difference in activation paradigm, performed on regional CBF (rCBF) data from five human subjects, was analyzed on 1.6-cm diameter regions of interest to determine the mean fractional statistical error in PET tissue concentration and in rCBF before and after stereotactic transformation; and (4) A linear statistical model and calculations of the various statistical errors were used to estimate the magnitude of the subject-specific fluctuations under various conditions. In this specific example, the root mean squared (RMS) noise in flow measurements was about three times higher than the RMS noise in the concentration measurements. In addition, the total random error was almost equally partitioned between statistical error and random fluctuations due to all other sources.

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25

XU, YONG, WEI XU, and GAMAL M. MAHMOUD. "GENERATING CHAOTIC LIMIT CYCLES FOR A COMPLEX DUFFING–VAN DER POL SYSTEM USING A RANDOM PHASE." International Journal of Modern Physics C 16, no. 09 (September 2005): 1437–47. http://dx.doi.org/10.1142/s0129183105008023.

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Stochastic forces or random noises have been greatly used in studying the control of chaos of random real systems, but little is reported for random complex systems. Chaotic limit cycles of a complex Duffing–Van der Pol system with a random excitation is studied. Generating chaos via adjusting the intensity of random phase is investigated. We consider the positive top Lyapunov exponent as a criterion of chaos for random dynamical systems. It is computed based on the Khasminskii's formulation and the extension of Wedig's algorithm for linear stochastic systems. We demonstrate the stable behavior of deterministic system when noise intensity is zero by means of the top (local) Lyapunov exponent. Poincaré surface analysis and phase plot are used to confirm our results. Later, random noise is used to generate chaos by adjusting the noise intensity to make the top (local) Lyapunov exponent changes from a negative sign to a positive one, and the Poincaré surface analysis is also applied to verify the obtained results and excellent agreement between these results is found.

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26

Song, Di, Qi Feng, Shengyao Chen, Feng Xi, and Zhong Liu. "Random Matrix Theory-Based Reduced-Dimension Space-Time Adaptive Processing under Finite Training Samples." Remote Sensing 14, no. 16 (August 15, 2022): 3959. http://dx.doi.org/10.3390/rs14163959.

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Space-time adaptive processing (STAP) is a fundamental topic in airborne radar applications due to its clutter suppression ability. Reduced-dimension (RD)-STAP can release the requirement of the number of training samples and reduce the computational load from traditional STAP, which attracts much attention. However, under the situation that training samples are severely deficient, RD-STAP will become poor like the traditional STAP. To enhance RD-STAP performance in such cases, this paper develops a novel RD-STAP algorithm using random matrix theory (RMT), RMT-RD-STAP. By minimizing the output clutter-plus-noise power, the estimate of the inversion of clutter plus noise covariance matrix (CNCM) can be obtained through optimally manipulating its eigenvalues, thus producing the optimal STAP weight vector. Specifically, the clutter-related eigenvalues are estimated according to the clutter-related sample eigenvalues via RMT, and the noise-related eigenvalue is optimally selected from the noise-related sample eigenvalues. It is found that RMT-RD-STAP significantly outperforms the RD-STAP algorithm when the RMB rule cannot be satisfied. Theoretical analyses and numerical results demonstrate the effectiveness and the performance advantages of the proposed RMT-RD-STAP algorithm.

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27

Ashok, K., A. Kalaiselvi, and V. R. Vijaykumar. "Adaptive impulse detection based selective window median filter for removal of random-valued impulse noise in digital images." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 35, no. 5 (September 5, 2016): 1604–16. http://dx.doi.org/10.1108/compel-04-2016-0140.

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Purpose One of the fundamental tasks in the field of image processing is image denoising. Images are often corrupted by different types of noise and the restoration of images degraded with random-valued impulse noise is still a challenging task. The paper aims to discuss these issues. Design/methodology/approach This paper presents an adaptive threshold-based impulse noise detection following by a novel selective window median filter for restoration of RVIN pixels. Findings The proposed method emphasis a local image statistics using an exponential nonlinear function with an adaptive threshold is derived from the rank-ordered trimmed median absolute difference (ROTMAD) are deliberated to detect the noisy pixels. In the filtering stage, a selective 3×3 moving window median filter is applied to restore the detected noisy pixel. Originality/value Experimental result shows that the proposed algorithm outperforms the existing state-of-art techniques in terms of noise removal and quantitative metrics such as peak signal to noise ratio (PSNR), mean absolute error (MAE), structural similarity index metric (SSIM) and miss and false detection rate.

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Anantharam, Venkat, and François Baccelli. "Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements." Advances in Applied Probability 47, no. 1 (March 2015): 1–26. http://dx.doi.org/10.1239/aap/1427814578.

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Consider a real-valued discrete-time stationary and ergodic stochastic process, called the noise process. For each dimension n, we can choose a stationary point process in ℝn and a translation invariant tessellation of ℝn. Each point is randomly displaced, with a displacement vector being a section of length n of the noise process, independent from point to point. The aim is to find a point process and a tessellation that minimizes the probability of decoding error, defined as the probability that the displaced version of the typical point does not belong to the cell of this point. We consider the Shannon regime, in which the dimension n tends to ∞, while the logarithm of the intensity of the point processes, normalized by dimension, tends to a constant. We first show that this problem exhibits a sharp threshold: if the sum of the asymptotic normalized logarithmic intensity and of the differential entropy rate of the noise process is positive, then the probability of error tends to 1 with n for all point processes and all tessellations. If it is negative then there exist point processes and tessellations for which this probability tends to 0. The error exponent function, which denotes how quickly the probability of error goes to 0 in n, is then derived using large deviations theory. If the entropy spectrum of the noise satisfies a large deviations principle, then, below the threshold, the error probability goes exponentially fast to 0 with an exponent that is given in closed form in terms of the rate function of the noise entropy spectrum. This is obtained for two classes of point processes: the Poisson process and a Matérn hard-core point process. New lower bounds on error exponents are derived from this for Shannon's additive noise channel in the high signal-to-noise ratio limit that hold for all stationary and ergodic noises with the above properties and that match the best known bounds in the white Gaussian noise case.

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Anantharam, Venkat, and François Baccelli. "Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements." Advances in Applied Probability 47, no. 01 (March 2015): 1–26. http://dx.doi.org/10.1017/s0001867800007679.

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Consider a real-valued discrete-time stationary and ergodic stochastic process, called the noise process. For each dimension n, we can choose a stationary point process in ℝ n and a translation invariant tessellation of ℝ n . Each point is randomly displaced, with a displacement vector being a section of length n of the noise process, independent from point to point. The aim is to find a point process and a tessellation that minimizes the probability of decoding error, defined as the probability that the displaced version of the typical point does not belong to the cell of this point. We consider the Shannon regime, in which the dimension n tends to ∞, while the logarithm of the intensity of the point processes, normalized by dimension, tends to a constant. We first show that this problem exhibits a sharp threshold: if the sum of the asymptotic normalized logarithmic intensity and of the differential entropy rate of the noise process is positive, then the probability of error tends to 1 with n for all point processes and all tessellations. If it is negative then there exist point processes and tessellations for which this probability tends to 0. The error exponent function, which denotes how quickly the probability of error goes to 0 in n, is then derived using large deviations theory. If the entropy spectrum of the noise satisfies a large deviations principle, then, below the threshold, the error probability goes exponentially fast to 0 with an exponent that is given in closed form in terms of the rate function of the noise entropy spectrum. This is obtained for two classes of point processes: the Poisson process and a Matérn hard-core point process. New lower bounds on error exponents are derived from this for Shannon's additive noise channel in the high signal-to-noise ratio limit that hold for all stationary and ergodic noises with the above properties and that match the best known bounds in the white Gaussian noise case.

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30

Balan, Raluca M. "SPDEs with α-Stable Lévy Noise: A Random Field Approach." International Journal of Stochastic Analysis 2014 (February 4, 2014): 1–22. http://dx.doi.org/10.1155/2014/793275.

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This paper is dedicated to the study of a nonlinear SPDE on a bounded domain in Rd, with zero initial conditions and Dirichlet boundary, driven by an α-stable Lévy noise Z with α∈(0,2), α≠1, and possibly nonsymmetric tails. To give a meaning to the concept of solution, we develop a theory of stochastic integration with respect to this noise. The idea is to first solve the equation with “truncated” noise (obtained by removing from Z the jumps which exceed a fixed value K), yielding a solution uK, and then show that the solutions uL,L>K coincide on the event t≤τK, for some stopping times τK converging to infinity. A similar idea was used in the setting of Hilbert-space valued processes. A major step is to show that the stochastic integral with respect to ZK satisfies a pth moment inequality. This inequality plays the same role as the Burkholder-Davis-Gundy inequality in the theory of integration with respect to continuous martingales.

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31

Honkonen, Juha. "Fractional Stochastic Field Theory." EPJ Web of Conferences 173 (2018): 01005. http://dx.doi.org/10.1051/epjconf/201817301005.

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Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

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Czerwinski, Artur. "Entanglement characterization by single-photon counting with random noise." Quantum Information and Computation 22, no. 1&2 (January 2022): 1–16. http://dx.doi.org/10.26421/qic22.1-2-1.

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In this article, we investigate the problem of entanglement characterization by polarization measurements combined with maximum likelihood estimation (MLE). A realistic scenario is considered with measurement results distorted by random experimental errors. In particular, by imposing unitary rotations acting on the measurement operators, we can test the performance of the tomographic technique versus the amount of noise. Then, dark counts are introduced to explore the efficiency of the framework in a multi-dimensional noise scenario. The concurrence is used as a figure of merit to quantify how well entanglement is preserved through noisy measurements. Quantum fidelity is computed to quantify the accuracy of state reconstruction. The results of numerical simulations are depicted on graphs and discussed.

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Cederbaum, G. "Random Vibrations of Viscoelastic Laminated Plates." Journal of Applied Mechanics 57, no. 3 (September 1, 1990): 688–93. http://dx.doi.org/10.1115/1.2897078.

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The response of viscoelastic laminated plates subjected to random excitation is investigated. The Fourier transform of the Boltzmann representation of the viscoelastic phases is incorporated into a micromechanical analysis, which establish the five frequency-dependent functions, characterizing the effective behavior of unidirectional fiber composites. This enables to express the governing equation, using the first-order shear deformation theory, in the frequency domain. The inversion of the response function into the time domain is performed by the Fast Fourier Transform algorithm. Two stationary random fields are considered: (i) ideal white noise, and (ii) band-limited white noise. In both cases analytical expressions for the mean squares are derived. Furthermore, the complex eigenvalues are investigated and the ratio between the imaginary part and the real one, η, is shown to relate to the damping ratio. The influence of the temperature, length-to-thickness ratio, and the fibers’ orientation on η is studied.

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VITIELLO, GIUSEPPE. "CLASSICAL CHAOTIC TRAJECTORIES IN QUANTUM FIELD THEORY." International Journal of Modern Physics B 18, no. 04n05 (February 20, 2004): 785–92. http://dx.doi.org/10.1142/s0217979204024409.

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Trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations are shown to be classical trajectories. Under convenient conditions, they may exhibit properties typical of chaotic behavior in classical nonlinear dynamics. Quantum noise in fluctuating random force in the system–environment coupling and system–environment entanglement is also discussed.

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Jittawiriyanukoon, Chanintorn. "Estimation of regression-based model with bulk noisy data." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 5 (October 1, 2019): 3649. http://dx.doi.org/10.11591/ijece.v9i5.pp3649-3656.

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<span>The bulk noise has been provoking a contributed data due to a communication network with a tremendously low signal to noise ratio. An appreciated method for revising massive noise of individuals through information theory is widely discussed. One of the practical applications of this approach for bulk noise estimation is analyzed using intelligent automation and machine learning tools, dealing the case of bulk noise existence or nonexistence. A regression-based model is employed for the investigation and experiment. Estimation for the practical case with bulk noisy datasets is proposed. The proposed method applies slice-and-dice technique to partition a body of datasets down into slighter portions so that it can be carried out. The average error, correlation, absolute error and mean square error are computed to validate the estimation. Results from massive online analysis will be verified with data collected in the following period. In many cases, the prediction with bulk noisy data through MOA simulation reveals Random Imputation minimizes the average error.</span>

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Omar, M. A., Khaled T. Ramadan, and Allam A. Allam. "Tsunami Generation and Propagation by a Curvilinear Stochastic Spreading Seismic Faulting in Linearized Water Wave Theory." Journal of Earthquake and Tsunami 11, no. 03 (August 14, 2017): 1750005. http://dx.doi.org/10.1142/s1793431117500051.

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The generation and propagation of tsunami caused by a curvilinear stochastic seismic faulting driven by two Gaussian white noise processes in the [Formula: see text]- and [Formula: see text]-directions are investigated. This model is used to study the tsunami build up and propagation during and after a realistic curvilinear source model represented by a random spreading slip-fault model. The amplification of tsunami amplitudes builds up progressively as time increases during the generation process due to wave focusing while the maximum wave amplitude decreases with time during the propagation process due to geometric spreading and dispersion. The increase of the normalized noise intensities on the random bottom leads to an increase in oscillations and amplitude of the free surface elevation. Tsunami waveforms using linearized shallow water theory for constant water depth are analyzed analytically by transform methods. The mean and variance of the random tsunami waves are derived and analyzed as a function of the noise intensities, propagated uplift length and the average depth of the ocean along the generation and propagation path.

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Bertola, V., and E. Cafaro. "Deterministic–stochastic approach to compartment fire modelling." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2104 (December 9, 2008): 1029–41. http://dx.doi.org/10.1098/rspa.2008.0382.

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A generalized Semenov model is proposed to describe the dynamics of compartment fires. It is shown that the transitions to flashover or to extinction can be described in the context of the catastrophe theory (or the theory of dynamical systems) by introducing a suitable potential function of the smoke layer temperature. The effect on the fire dynamics of random perturbations is then studied by introducing a random noise term accounting for internal and external perturbations with an arbitrary degree of correlation. While purely Gaussian perturbations (white noise) do not change the behaviour of the fire with respect to the deterministic model, perturbations depending on the model variable (‘coloured’ noise) may drive the system to different states. This suggests that the compartment fires can be controlled or driven to extinction by introducing appropriate external perturbations.

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Pacheco, Carlos G. "Green kernel for a random Schrödinger operator." Communications in Contemporary Mathematics 18, no. 05 (July 18, 2016): 1550082. http://dx.doi.org/10.1142/s0219199715500820.

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We find explicitly the Green kernel of a random Schrödinger operator with Brownian white noise. To do this, we first handle the random operator by defining it weakly using the inner product of a Hilbert space. Then, using classic Sturm–Liouville theory, we can build the Green kernel with linearly independent solutions of a homogeneous problem. As a corollary, we have that the random operator has a discrete spectra.

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Faranda, Davide, Jorge Milhazes Freitas, Pierre Guiraud, and Sandro Vaienti. "Extreme value theory for piecewise contracting maps with randomly applied stochastic perturbations." Stochastics and Dynamics 16, no. 03 (March 8, 2016): 1660015. http://dx.doi.org/10.1142/s0219493716600157.

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We consider globally invertible and piecewise contracting maps in higher dimensions and perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process: in this framework we develop an extreme value theory for a few classes of observables and we show how to get the (usual) limiting distributions together with an extremal index depending on the strength of the noise.

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Chen, I.-Te. "Random Numbers Generated from Audio and Video Sources." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/285373.

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Random numbers are very useful in simulation, chaos theory, game theory, information theory, pattern recognition, probability theory, quantum mechanics, statistics, and statistical mechanics. The random numbers are especially helpful in cryptography. In this work, the proposed random number generators come from white noise of audio and video (A/V) sources which are extracted from high-resolution IPCAM, WEBCAM, and MPEG-1 video files. The proposed generator applied on video sources from IPCAM and WEBCAM with microphone would be the true random number generator and the pseudorandom number generator when applied on video sources from MPEG-1 video file. In addition, when applying NIST SP 800-22 Rev.1a 15 statistics tests on the random numbers generated from the proposed generator, around 98% random numbers can pass 15 statistical tests. Furthermore, the audio and video sources can be found easily; hence, the proposed generator is a qualified, convenient, and efficient random number generator.

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Ndagijimana, Protais, Fulgence Nahayo, Marc Kokou Assogba, Adoté François-Xavier Ametepe, and Juma Shabani. "Towards Post-Quantum Cryptography Using Thermal Noise Theory and True Random Numbers Generation." Journal of Information Security 11, no. 03 (2020): 149–60. http://dx.doi.org/10.4236/jis.2020.113010.

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Hulbert, Christopher, and Kathleen E. Wage. "Random matrix theory analysis of the dominant mode rejection beamformer white noise gain." Journal of the Acoustical Society of America 148, no. 4 (October 2020): 2477. http://dx.doi.org/10.1121/1.5146863.

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Yamaguchi, Shizuma, Yuichi Kato, Kensei Oimatsu, and Tetsuro Saeki. "A psychological evaluation method for fluctuating random noise based on fuzzy set theory." Applied Acoustics 45, no. 2 (1995): 139–54. http://dx.doi.org/10.1016/0003-682x(94)00042-t.

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Deon, Aleksei F., Oleg K. Karaduta, and Yulian A. Menyaev. "Phase Congruential White Noise Generator." Algorithms 14, no. 4 (April 5, 2021): 118. http://dx.doi.org/10.3390/a14040118.

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White noise generators can use uniform random sequences as a basis. However, such a technology may lead to deficient results if the original sequences have insufficient uniformity or omissions of random variables. This article offers a new approach for creating a phase signal generator with an improved matrix of autocorrelation coefficients. As a result, the generated signals of the white noise process have absolutely uniform intensities at the eigen Fourier frequencies. The simulation results confirm that the received signals have an adequate approximation of uniform white noise.

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Xu, Wei Chang, Tao Tang, Ji Fang Liu, and Wei Huang. "The Research to the De-Noising Method for the Vibration Signals Based on EEMD." Applied Mechanics and Materials 687-691 (November 2014): 3806–8. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.3806.

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Dynamical properties of mechanical systems can be obtained with the vibration signals from the systems. However, for the influence of noises, it is difficult to accurately acquire the features. Therefore, de-noising operation is significant for vibration signal in the practical engineering. In order to resolve this problem, the Ensemble Empirical Mode Decomposition (EEMD) method is introduced to try to eliminate noises from the analyzed signal. At first, the theory of the method is illustrated, which included adding white noises, EMD for the signal and calculating the mean of the intrinsic mode function. On this base, the signal which contains several harmonic components with white noise is processed by EEMD. As the result shown, the random noise can be effectively removed; moreover, the harmonic components can be accurately separated. And these improve that the EEMD is an effective method for the de-noising.

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Zhou, Zi Ping, Yu Zhu, and Tian Hao Wang. "The Application of Cross-Correlation Algorithm in CSAMT Received Data Processing." Advanced Materials Research 989-994 (July 2014): 2278–82. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.2278.

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Controlled source audio-frequency magnetotelluric method (CSAMT) is an effective frequency domain detecting method in metallic ore exploration. In view of the weak response of a deep target signal and the serious measuring environmental noise,this paper proposes a method to deal with the noise of the CSAMT data based on the theory of cross-correlation algorithm. Emission signal current waveform recorder is designed to record signal parameters.According to cross-correlation technology, this paper uses the characteristics that correlation between emission and received signals is strong, yet the correlation between emission signals and random noise is weak, to deal with emission signals and received signals by cross-correlation ,in order to filter out random noise and other jamming signals.Field exploration test data processing contrast results show that the method can suppress noise signal, and improve the CSAMT measuring accuracy.

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Liu, Wansu, and Zhenggao Pan. "Construction and Application of Automatic Attendance Prediction System for Classroom Education Teaching Based on Random Matrix Theory." Mathematical Problems in Engineering 2022 (July 20, 2022): 1–11. http://dx.doi.org/10.1155/2022/6888526.

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Random matrix theory, as a theoretical tool for statistical processing of complex systems and high-dimensional data, has been more and more combined with big data technology and applied to automatic attendance prediction analysis of classroom education. Firstly, the basic definition of the random matrix is introduced. Secondly, the single ring theorem of the random matrix is introduced. Based on this, the random matrix model of data is established. However, few undergraduate or graduate students in physics have been exposed to this theory. By introducing the basic concept of random matrix theory, this paper analyzes the necessity and feasibility of introducing random matrix theory into automatic attendance prediction teaching in classroom education. As a biometrics technology, random matrix theory technology has been widely used in various fields of the identity verification system, and classroom attendance system is an important field of random matrix theory technology application. The traditional random matrix theory class attendance has the problem of slow recognition speed and low accuracy. With the popularity of deep learning, the random matrix theory based on deep learning has gradually replaced the traditional random matrix theory. In this paper, the SSD target detection algorithm, NB algorithm, and RF algorithm based on deep learning are used to improve and optimize the traditional random matrix theory class attendance system, which effectively improves the efficiency and accuracy of random matrix theory attendance. Then, aiming at the low recall rate and recognition rate of random matrix theory in low-pixel images, we try to apply the random matrix theory of single image resolution reconstruction method to face detection and random matrix theory and give a calculation method to deal with outliers and noise.

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Cheng, Feng Qin, and Yao Wu Shi. "Random Phase Weak Sine Signal Detection Based on Autocorrelation and Chaos Theory." Applied Mechanics and Materials 397-400 (September 2013): 2129–33. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.2129.

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The paper expounds the basic principle of the weak signal detection on chaotic system at first , according to the actual situation that the signal phase is unknown Received in the communication and radar systems, a new chaos detection model is presented based on traditional chaos system, combined with autocorrelation detection technology , completed the random phase weak sinusoidal signal detection. The simulation analysis indicates that the proposed method succeeds in detecting Random Phase weak sinusoidal signal, and furthermore the signal-to-noise threshold is lower than either autocorrelation or chaotic oscillator.

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Berthelot, A., C. Voisin, C. Delalande, Ph Roussignol, R. Ferreira, and G. Cassabois. "From Random Telegraph to Gaussian Stochastic Noises: Decoherence and Spectral Diffusion in a Semiconductor Quantum Dot." Advances in Mathematical Physics 2010 (2010): 1–13. http://dx.doi.org/10.1155/2010/494738.

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We present a general theoretical description of the extrinsic dephasing mechanism of spectral diffusion that dominates the decoherence dynamics in semiconductor quantum dots at low temperature. We discuss the limits of random telegraph and Gaussian stochastic noises and show that the combination of both approaches in the framework of the pre-Gaussian noise theory allows a quantitative interpretation of high-resolution experiments in single semiconductor quantum dots. We emphasize the generality and the versatility of our model where the inclusion of asymmetric jump processes appears as an essential extension for the understanding of semiconductor quantum dot physics.

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Loreto, V., M. Serva, and A. Vulpiani. "On the Concept of Complexity of Random Dynamical Systems." International Journal of Modern Physics B 12, no. 03 (January 30, 1998): 225–43. http://dx.doi.org/10.1142/s0217979298000181.

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We show how to introduce a characterization the "complexity" of random dynamical systems. More precisely we propose a suitable indicator of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by these systems. This indicator of complexity, which can be extracted from real experimental data, turns out to be very natural in the context of information theory. For dynamical systems with random perturbations, it coincides with the rate K of divergence of nearby trajectories evolving under two different noise realizations. In presence of strong dynamical intermittency, the value of K is very different from the standard Lyapunov exponent λσ computed through the consideration of two nearby trajectories evolving under the same realization of the random perturbation. However, the former is much more relevant than the latter from a physical point of view as illustrated by some numerical examples of noisy and random maps.

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