Noisy Process Research Articles

Algorithms for Constructing a Model of the Noisy Process by Correcting the Law of its Distribution

The authors have constructed the algorithms for building a noisy process probabilistic model consisting of probabilistic models of useful component and noise. A set of such characteristics of noise and a useful component as mathematical expectations, variance, mean-square deviations, distribution density functions and their maxima as well as inflection points along x-axis and y-axis obtained at different periods of time has been formed. It has been demonstrated that the use of these sets in an automated control system allows us to determine a moment of routine maintenance to be performed and thereby to avoid a process shutdown required to carry out a comprehensive overhaul.

Entanglement and Decoherence in Two-Dimensional Coherent State Superpositions

A detailed investigation of entanglement in the generalized two-dimensional nonorthogonal states, which are expressed in the framework of superposed coherent states, is presented. In addition to quantifying entanglement of the generalized two-dimensional coherent states superposition, necessary and sufficient conditions for maximality of entanglement of these states are found. We show that a large class of maximally entangled coherent states can be constructed, and hence, some new maximally entangled coherent states are explicitly manipulated. The investigation is extended to the mixed system states and entanglement properties of such mixed states are investigated. It is shown that in some cases maximally entangled mixed states can be detected. Furthermore, the effect of decoherence, due to both cavity losses and noisy channel process, on such entangled states are studied and its features are discussed.

Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes.

Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in cell-division times generates additional intercellular variability in protein levels. Moreover, as many mRNA/protein species are expressed at low-copy numbers, errors incurred in partitioning of molecules between two daughter cells are significant. We derive analytical formulas for the total noise in protein levels when the cell-cycle duration follows a general class of probability distributions. Using a novel hybrid approach the total noise is decomposed into components arising from i) stochastic expression; ii) partitioning errors at the time of cell division and iii) random cell-division events. These formulas reveal that random cell-division times not only generate additional extrinsic noise, but also critically affect the mean protein copy numbers and intrinsic noise components. Counter intuitively, in some parameter regimes, noise in protein levels can decrease as cell-division times become more stochastic. Computations are extended to consider genome duplication, where transcription rate is increased at a random point in the cell cycle. We systematically investigate how the timing of genome duplication influences different protein noise components. Intriguingly, results show that noise contribution from stochastic expression is minimized at an optimal genome-duplication time. Our theoretical results motivate new experimental methods for decomposing protein noise levels from synchronized and asynchronized single-cell expression data. Characterizing the contributions of individual noise mechanisms will lead to precise estimates of gene expression parameters and techniques for altering stochasticity to change phenotype of individual cells.

Jump Variation Estimation with Noisy High Frequency Financial Data via Wavelets

This paper develops a method to improve the estimation of jump variation using high frequency data with the existence of market microstructure noises. Accurate estimation of jump variation is in high demand, as it is an important component of volatility in finance for portfolio allocation, derivative pricing and risk management. The method has a two-step procedure with detection and estimation. In Step 1, we detect the jump locations by performing wavelet transformation on the observed noisy price processes. Since wavelet coefficients are significantly larger at the jump locations than the others, we calibrate the wavelet coefficients through a threshold and declare jump points if the absolute wavelet coefficients exceed the threshold. In Step 2 we estimate the jump variation by averaging noisy price processes at each side of a declared jump point and then taking the difference between the two averages of the jump point. Specifically, for each jump location detected in Step 1, we get two averages from the observed noisy price processes, one before the detected jump location and one after it, and then take their difference to estimate the jump variation. Theoretically, we show that the two-step procedure based on average realized volatility processes can achieve a convergence rate close to O P ( n − 4 / 9 ) , which is better than the convergence rate O P ( n − 1 / 4 ) for the procedure based on the original noisy process, where n is the sample size. Numerically, the method based on average realized volatility processes indeed performs better than that based on the price processes. Empirically, we study the distribution of jump variation using Dow Jones Industrial Average stocks and compare the results using the original price process and the average realized volatility processes.

Bandit online optimization over the permutahedron

The permutahedron is the convex polytope with vertex set consisting of the vectors (π(1),…,π(n)) for all permutations (bijections) π over {1,…,n}. We study a bandit game in which, at each step t, an adversary chooses a hidden weight vector st, a player chooses a vertex πt of the permutahedron and suffers an observed instantaneous loss of ∑i=1nπt(i)st(i).We study the problem in two different approaches. In the two approaches, we assume that st is a point in the polytope dual to the permutahedron. Algorithm CombBand of Cesa-Bianchi et al. (2012) guarantees a regret of O(nTlog⁡n) after T steps. Unfortunately, CombBand requires at each step an n-by-n matrix permanent computation, a #P-hard problem. Approximating the permanent is possible in the impractical running time of O(n10), with an additional heavy inverse-polynomial dependence on the sought accuracy. In the first approach, we provide an algorithm of slightly worse regret O(n3/2T) but with more realistic time complexity O(n3) per step. The technical contribution is a bound on the variance of the Plackett–Luce noisy sorting process's ‘pseudo loss’, obtained by establishing positive semi-definiteness of a family of 3-by-3 matrices of rational functions in exponents of 3 parameters.In the second approach, we present and analyze an algorithm based on Bubeck et al.'s (2012) OSMD approach with a novel projection and decomposition technique for the permutahedron. The second algorithm's running time and regret guarantees are similar to our first algorithm, modulo a numerical line search procedure the running time of which we have not been able to analyze. It is interesting that the two approaches are totally different.The main open problem from this work is whether there exists a bandit algorithm for this problem with both optimal regret of O(nT) and running time of O(n3) for either regime, or there is an inherent tradeoff between the two performance measures.

Individual cell heterogeneity in Predictive Food Microbiology: Challenges in predicting a “noisy” world

Gene expression is a fundamentally noisy process giving rise to a significant cell to cell variability at the phenotype level. The phenotypic noise is manifested in a wide range of microbial traits. Heterogeneous behavior of individual cells is observed at the growth, survival and inactivation responses and should be taken into account in the context of Predictive Food Microbiology (PMF). Recent methodological advances can be employed for the study and modeling of single cell dynamics leading to a new generation of mechanistic models which can provide insight into the link between phenotype, gene-expression, protein and metabolic functional units at the single cell level. Such models however, need to deal with an enormous amount of interactions and processes that influence each other, forming an extremely complex system. In this review paper, we discuss the importance of noise and present the future challenges in predicting the “noisy” microbial responses in foods.

Estimation of mean first passage time for bursty gene expression

Gene expression is an intrinsically noisy process, typically, producing mRNAs and proteins in bursts. An important description of such stochastic processes can be done in terms of the mean first passage time (MFPT), i.e., the time taken by mRNAs/proteins to reach a particular threshold. We study the role of burstiness on MFPT and obtain an analytical expression for different models of transcriptional and translational bursts. Our analytical results and numerical simulations confirm that MFPT monotonically decreases with burstiness.

On the Noise Robustness of Simultaneous Orthogonal Matching Pursuit

In this paper, the joint support recovery of several sparse signals whose supports present similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the dimension of the sparse signals. The measurement noise is assumed additive, Gaussian, and admits different variances for each sparse signal that is measured. Using the theory of compressed sensing, the performance of simultaneous orthogonal matching pursuit (SOMP) is analysed for the envisioned signal model. The cornerstone of this paper is a novel analysis method upper bounding the probability that SOMP recovers at least one incorrect entry of the joint support during a prescribed number of iterations. Furthermore, the probability of SOMP failing is investigated whenever the number of sparse signals being recovered simultaneously increases and tends to infinity. In particular, convincing observations and theoretical results suggest that SOMP committing no mistake in the noiseless case does not guarantee the absence of error in the noisy case whenever the number of acquired sparse signals scales to infinity. Finally, simulation results confirm the validity of the theoretical results.

Experimental measurements and mathematical modeling of biological noise arising from transcriptional and translational regulation of basic synthetic gene circuits

The small number of molecules, unevenly distributed within an isogenic cell population, makes gene expression a noisy process, and strategies have evolved to deal with this variability in protein concentration and to limit its impact on cellular behaviors. As translational efficiency has a major impact on biological noise, a possible strategy to control noise is to regulate gene expression processes at the post-transcriptional level. In this study, fluctuations in the concentration of a green fluorescent protein were compared, at the single cell level, upon transformation of an isogenic bacterial cell population with synthetic gene circuits implementing either a transcriptional or a post-transcriptional control of gene expression. Experimental measurements showed that protein variability is lower under post-transcriptional control, when the same average protein concentrations are compared. This effect is well reproduced by stochastic simulations, supporting the hypothesis that noise reduction is due to the control mechanism acting on the efficiency of translation. Similar strategies are likely to play a role in noise reduction in natural systems and to be useful for controlling noise in synthetic biology applications.

Fundamental Limits to Cellular Sensing

In recent years experiments have demonstrated that living cells can measure low chemical concentrations with high precision, and much progress has been made in understanding what sets the fundamental limit to the precision of chemical sensing. Chemical concentration measurements start with the binding of ligand molecules to receptor proteins, which is an inherently noisy process, especially at low concentrations. The signaling networks that transmit the information on the ligand concentration from the receptors into the cell have to filter this noise extrinsic to the cell as much as possible. These networks, however, are also stochastic in nature, which means that they will also add noise to the transmitted signal. In this review, we will first discuss how the diffusive transport and binding of ligand to the receptor sets the receptor correlation time, and then how downstream signaling pathways integrate the noise in the receptor state; we will discuss how the number of receptors, the receptor correlation time, and the effective integration time together set a fundamental limit on the precision of sensing. We then discuss how cells can remove the receptor noise while simultaneously suppressing the intrinsic noise in the signaling network. We describe why this mechanism of time integration requires three classes of resources---receptors and their integration time, readout molecules, energy---and how each resource class sets a fundamental sensing limit. We also briefly discuss the scheme of maximum-likelihood estimation, the role of receptor cooperativity, and how cellular copy protocols differ from canonical copy protocols typically considered in the computational literature, explaining why cellular sensing systems can never reach the Landauer limit on the optimal trade-off between accuracy and energetic cost.

Technology for Calculating the Parameters of the Density Function of the Normal Distribution of the Useful Component in a Noisy Process

Technology for Calculating the Parameters of the Density Function of the Normal Distribution of the Useful Component in a Noisy Process

A necessary condition for mean-field type stochastic differential equations with correlated state and observation noises

This paper is concerned with a mean-field type optimal control problem, whose new features are that the state $x^v_t$ is partially observed by a noisy process $y(t)$, and the control problem is time inconsistent in the sense that Bellman optimality principle does not work. A necessary condition for optimality is derived by convex variation, dual technique and backward stochastic differential equations (BSDEs). A linear-quadratic (LQ) optimal control example is studied, and the optimal solution is obtained by the optimal filtering for BSDEs and the necessary condition.

Generalized Method of Integrated Moments for High-Frequency Data

We propose a semiparametric two-step inference procedure for a finite-dimensional parameter based on moment conditions constructed from high-frequency data. The population moment conditions take the form of temporally integrated functionals of state-variable processes that include the latent stochastic volatility process of an asset. In the first step, we nonparametrically recover the volatility path from high-frequency asset returns. The nonparametric volatility estimator is then used to form sample moment functions in the second-step GMM estimation, which requires the correction of a high-order nonlinearity bias from the first step. We show that the proposed estimator is consistent and asymptotically mixed Gaussian and propose a consistent estimator for the conditional asymptotic variance. We also construct a Bierens-type consistent specification test. These infill asymptotic results are based on a novel empirical-process-type theory for general integrated functionals of noisy semimartingale processes.

A Multiresolution Wavelet based Subspace Identification

Abstract This paper presents multiresolution subspace identification as an extension of classical subspace modeling, thus inheriting features of robust subspace identification with added advantages of wavelet based modeling enabling multiresolution state-space model development. Identification of a noisy process in presence of mild nonlinearity can be approximated by estimating multiple multiresolution time invariant models. Parameter estimation in projection space at appropriate scales is achieved using least squares method. The efficacy of the proposed approach has been demonstrated by modeling nuclear reactor in prediction as well as simulation environment. It is shown that root mean squared error reduces significantly as compared to their single scale counterparts providing better modeling performances.

Direct characterization of quantum dynamics with noisy ancilla

We present methods for the direct characterization of quantum dynamics in which both the principal and ancilla systems undergo noisy processes. Using a concatenated error detection code, we discriminate between located and unlocated errors on the principal system in what amounts to filtering of ancilla noise. The example of composite noise involving amplitude damping and depolarizing channels is used to demonstrate the method, while we find the rate of noise filtering is more generally dependent on code distance. Our results indicate the accuracy of quantum process characterization can be greatly improved while remaining within reach of current experimental capabilities.

Estimating the coherence of noise

Noise mechanisms in quantum systems can be broadly characterized as either coherent (i.e., unitary) or incoherent. For a given fixed average error rate, coherent noise mechanisms will generally lead to a larger worst-case error than incoherent noise. We show that the coherence of a noise source can be quantified by the unitarity, which we relate to the average change in purity averaged over input pure states. We then show that the unitarity can be efficiently estimated using a protocol based on randomized benchmarking that is efficient and robust to state-preparation and measurement errors. We also show that the unitarity provides a lower bound on the optimal achievable gate infidelity under a given noisy process.

Nonlinear Gaussian Belief Network based fault diagnosis for industrial processes

A Nonlinear Gaussian Belief Network (NLGBN) based fault diagnosis technique is proposed for industrial processes. In this study, a three-layer NLGBN is constructed and trained to extract useful features from noisy process data. The nonlinear relationships between the process variables and the latent variables are modelled by a set of sigmoidal functions. To take into account the noisy nature of the data, model variances are also introduced to both the process variables and the latent variables. The three-layer NLGBN is first trained with normal process data using a variational Expectation and Maximization algorithm. During real-time monitoring, the online process data samples are used to update the posterior mean of the top-layer latent variable. The absolute gradient denoted as G-index to update the posterior mean is monitored for fault detection. A multivariate contribution plot is also generated based on the G-index for fault diagnosis. The NLGBN-based technique is verified using two case studies. The results demonstrate that the proposed technique outperforms the conventional nonlinear techniques such as KPCA, KICA, SPA, and Moving Window KPCA.

Artificial Neural Networks and Advanced Fuzzy Techniques for Predicting Noise Level in the Industrial Embroidery Workrooms

Noise prediction techniques are considered to be an important tool for evaluating cost-effective noise control measures in industrial workrooms. One of the most important issues in this regard is the development of accurate methods for analysis of the complex relationships among acoustic features affecting noise level in workrooms. In this study, artificial neural networks and advanced fuzzy techniques were employed to develop a relatively accurate model for noise prediction in the noisy process of industrial embroidery. The data were collected from 60 embroidery workrooms. Some acoustical descriptors of workrooms were selected as input features based on International Organization for Standardization (ISO) 11690-3. Prediction errors of all structures associated with neural networks and fuzzy models were approximately similar and lower than 1 dB. However, neurofuzzy models could slightly improve the accuracy of noise prediction compared with neural networks. These results confirmed that these techniques can be regarded as useful tools for occupational health professionals in order to design, implement, and evaluate various noise control measures in noisy workrooms.

Secret sharing of a known arbitrary quantum state with noisy environment

We study quantum state sharing (QSTS) with noisy environment in this paper. As an example, we present a QSTS scheme of a known state whose information is hold by the dealer and then investigate the noisy influence process of the scheme. Taking the amplitude-damping noise and the phase-damping noise as typical noisy channels, we show that the secret state can be shared among agents with some information lost. Our research connects the areas of quantum state sharing and remote state preparation.

Quantifying effects of stochasticity in reference frame transformations on posterior distributions.

Reference frame transformations are usually considered to be deterministic. However, translations, scaling or rotation angles could be stochastic. Indeed, variability of these entities often originates from noisy estimation processes. The impact of transformation noise on the statistics of the transformed signals is unknown and a quantification of these effects is the goal of this study. We first quantify analytically and numerically how stochastic reference frame transformations (SRFT) alter the posterior distribution of the transformed signals. We then propose an new empirical measure to quantify deviations from a given distribution when only limited data is available. We apply this empirical measure to an example in sensory-motor neuroscience to quantify how different head roll angles change the distribution of reach endpoints away from the normal distribution.