Noisy Process Research Articles

Linear–quadratic mean-field game for stochastic systems with partial observation

This paper is concerned with a class of linear–quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each agent follows a linear stochastic differential equation driven by the individual noise, and all agents are coupled together via the control average term. By studying the associated mean-field game and using the backward separation principle with a state decomposition technique, the decentralized optimal control can be obtained in the open-loop form through a forward–backward stochastic differential equation with the conditional expectation. The optimal filtering equation is also provided. Thanks to the decoupling method, the decentralized optimal control can also be further presented as the feedback of state filtering via the Riccati equation. The explicit solution of the control average limit is given, and the consistency condition system is discussed. Moreover, the related ɛ-Nash equilibrium property is verified. To illustrate the good performance of theoretical results, an example in finance is studied.

Stable developmental patterns of gene expression without morphogen gradients.

Gene expression patterns in developing organisms are established by groups of cross-regulating target genes that are driven by morphogen gradients. As development progresses, morphogen activity is reduced, leaving the emergent pattern without stabilizing positional cues and at risk of rapid deterioration due to the inherently noisy biochemical processes at the cellular level. But remarkably, gene expression patterns remain spatially stable and reproducible over long developmental time spans in many biological systems. Here we combine spatial-stochastic simulations with an enhanced sampling method (Non-Stationary Forward Flux Sampling) and a recently developed stability theory to address how spatiotemporal integrity of a gene expression pattern is maintained in developing tissue lacking morphogen gradients. Using a minimal embryo model consisting of spatially coupled biochemical reactor volumes, we study a prototypical stripe pattern in which weak cross-repression between nearest neighbor expression domains alternates with strong repression between next-nearest neighbor domains, inspired by the gap gene system in the Drosophila embryo. We find that tuning of the weak repressive interactions to an optimal level can prolong stability of the expression patterns by orders of magnitude, enabling stable patterns over developmentally relevant times in the absence of morphogen gradients. The optimal parameter regime found in simulations of the embryo model closely agrees with the predictions of our coarse-grained stability theory. To elucidate the origin of stability, we analyze a reduced phase space defined by two measures of pattern asymmetry. We find that in the optimal regime, intact patterns are protected via restoring forces that counteract random perturbations and give rise to a metastable basin. Together, our results demonstrate that metastable attractors can emerge as a property of stochastic gene expression patterns even without system-wide positional cues, provided that the gene regulatory interactions shaping the pattern are optimally tuned.

Plausible, robust biological oscillations through allelic buffering

Biological oscillators can specify time- and dose-dependent functions via dedicated control of their oscillatory dynamics. However, how biological oscillators, which recurrently activate noisy biochemical processes, achieve robust oscillations remains unclear. Here, we characterize the long-term oscillations of p53 and its negative feedback regulator Mdm2 in single cells after DNA damage. Whereas p53 oscillates regularly, Mdm2 from a single MDM2 allele exhibits random unresponsiveness to ∼9% of p53 pulses. Using allelic-specific imaging of MDM2 activity, we show that MDM2 alleles buffer each other to maintain p53 pulse amplitude. Removal of MDM2 allelic buffering cripples the robustness of p53 amplitude, thereby elevating p21 levels and cell-cycle arrest. In silico simulations support that allelic buffering enhances the robustness of biological oscillators and broadens their plausible biochemical space. Our findings show how allelic buffering ensures robust p53 oscillations, highlighting the potential importance of allelic buffering for the emergence of robust biological oscillators during evolution. A record of this paper's transparent peer review process is included in the supplemental information.

Stress-Induced Constraint on Expression Noise of Essential Genes in E. coli

Gene expression is an inherently noisy process that is constrained by natural selection. Yet the condition dependence of constraint on expression noise remains unclear. Here, we address this problem by studying constraint on expression noise of E. coli genes in eight diverse growth conditions. In particular, we use variation in expression noise as an analog for constraint, examining its relationships to expression level and to the number of regulatory inputs from transcription factors across and within conditions. We show that variation in expression noise is negatively associated with expression level, implicating constraint to minimize expression noise of highly expressed genes. However, this relationship is condition dependent, with the strongest constraint observed when E. coli are grown in the presence of glycerol or ciprofloxacin, which result in carbon or antibiotic stress, respectively. In contrast, we do not observe evidence of constraint on expression noise of highly regulated genes, suggesting that highly expressed and highly regulated genes represent distinct classes of genes. Indeed, we find that essential genes are often highly expressed but not highly regulated, with elevated expression noise in glycerol and ciprofloxacin conditions. Thus, our findings support the hypothesis that selective constraint on expression noise is condition dependent in E. coli, illustrating how it may play a critical role in ensuring expression stability of essential genes in unstable environments.

Weight-Reduced Stabilizer Codes with Lower Overhead

Stabilizer codes are the most widely studied class of quantum error-correcting codes and form the basis of most proposals for a fault-tolerant quantum computer. A stabilizer code is defined by a set of parity-check operators, which are measured in order to infer information about errors that may have occurred. In typical settings, measuring these operators is itself a noisy process and the noise strength scales with the number of qubits involved in a given parity check, or its weight. Hastings has proposed a method for reducing the weights of the parity checks of a stabilizer code, though it has previously only been studied in the asymptotic regime. Here, we instead focus on the regime of small to medium-size codes suitable for quantum computing hardware. We both provide a fully explicit description of Hastings’s method and propose a substantially simplified weight-reduction method that is applicable to the class of quantum product codes. Our simplified method allows us to reduce the check weights of hypergraph- and lifted-product codes to at most six, while preserving the number of logical qubits and at least retaining (in fact, often increasing) the code distance. The price we pay is an increase in the number of physical qubits by a constant factor but we find that our method is much more efficient than Hastings’s method in this regard. We benchmark the performance of our codes on a simulated photonic quantum computing architecture based on Gottesman-Kitaev-Preskill qubits and passive linear optics, finding that our weight-reduction method substantially improves code performance. Published by the American Physical Society 2024

Noise control at the receiver: Promoting hearing conservation in society

Noise Control Engineering traditionally employs a Source/Path/Receiver model to mitigate the generation of noise in all sorts of activities. The industrial hygiene hierarchy of controls seeks to eliminate noisy processes, to identify substitute processes, or to develop engineering solutions that reduce noise at the Source or along the Path. Administrative controls and personal protective equipment (PPE) are the last resort to reduce noise at the receiver, our ears. The first three decades of my career were as an officer of the Commissioned Corps of the United States Public Health Service and I was assigned to the Centers for Disease Control, National Institute for Occupational Safety and Health. My research focused on developing rating and testing methods for hearing protection devices, standards to evaluate occupational noise exposures, and methods to measure impulse noise exposures. This talk will describe how I transitioned from graduate student in physics to a noise researcher focused on the protection of the receiver's ears.

Enhancing fault detection in multivariate industrial processes: Kolmogorov–Smirnov non-parametric statistical approach

The accurate detection of abnormal events in modern process plants is extremely important. The detection of faults of small magnitude and in a noisy process environment is still a challenge that many industries face. In this paper, a Kolmogorov–Smirnov (KS) based non-parametric statistical fault indicator is proposed to identify a variety of sensor faults in process plants. The data collected from most modern process plants are randomly varying and non-Gaussian, due to which the multivariate scheme based on Independent Component Analysis (ICA) is considered. The KS-based indicator is amalgamated with the ICA multivariate model, which yields a novel ICA-KS-based fault detection (FD) scheme. The KS statistical indicator compares any two distributions and checks if they are similar or dissimilar. The potential of the KS indicator is extended in the FD domain, where the residuals of training and testing data are compared in a sliding window. The ability of the proposed ICA-KS-based FD strategy is validated on a simulated Distillation column (DC) process and the benchmark Tennessee Eastman (TE) process to identify a variety of sensor faults. The simulation results demonstrate the effectiveness of the detection performance of the ICA-KS scheme, which outperforms conventional FD-based methods with a high detection rate.

Evidence for widespread translation of 5' untranslated regions.

Ribosome profiling experiments support the translation of a range of novel human open reading frames. By contrast, most peptides from large-scale proteomics experiments derive from just one source, 5' untranslated regions. Across the human genome we find evidence for 192 translated upstream regions, most of which would produce protein isoforms with extended N-terminal ends. Almost all of these N-terminal extensions are from highly abundant genes, which suggests that the novel regions we detect are just the tip of the iceberg. These upstream regions have characteristics that are not typical of coding exons. Their GC-content is remarkably high, even higher than 5' regions in other genes, and a large majority have non-canonical start codons. Although some novel upstream regions have cross-species conservation - five have orthologues in invertebrates for example - the reading frames of two thirds are not conserved beyond simians. These non-conserved regions also have no evidence of purifying selection, which suggests that much of this translation is not functional. In addition, non-conserved upstream regions have significantly more peptides in cancer cell lines than would be expected, a strong indication that an aberrant or noisy translation initiation process may play an important role in translation from upstream regions.

A residual autoencoder-based transformer for fault detection of multivariate processes

The complexity of high-dimensional and noisy process signals reduces the effectiveness of conventional fault detection methods in industrial processes. Based on the hypothesis that data collected from normal and faulty processes has different characteristics, unsupervised deep neural networks, e.g., autoencoders, have been widely applied in process fault detection and achieved good performance. Many variants have been proposed to improve feature learning by combining different network structures. In this paper, a new transformer model, residual autoencoder-based transformer, is proposed for process fault detection. Firstly, autoencoder and transformer are integrated for better unsupervised feature learning of process signals. Secondly, linear embedding and attention mechanisms with bias are proposed to generate effective features from process signals. Finally, residual connections are constructed between the encoder and decoder of RATransformer to address overfitting in training. Four industrial cases are used to test the performance of RATransformer for process fault detection. The results show that the fault detection rate of RATransformer is at least 1 % higher than other comparison methods. Moreover, the testing results show that the model structure improves the fault detection performance of RATransformer. The complex models like RATransformer can be used in the industrial process when sufficient normal process data is available. An end-to-end training method can be further developed to improve the applicability of RATransformer in process fault detection in the future.

Insensitive Investors

ABSTRACTWe experimentally study the transmission of subjective expectations into actions. Subjects in our experiment report valuations that are far too insensitive to their expectations, relative to the prediction from a frictionless model. We propose that the insensitivity is driven by a noisy cognitive process that prevents subjects from precisely computing asset valuations. The empirical link between subjective expectations and actions becomes stronger as subjective expectations approach rational expectations. Our results highlight the importance of incorporating weak transmission into belief‐based asset pricing models. Finally, we discuss how cognitive noise can provide a microfoundation for inelastic demand in the stock market.

Stochastic intervention control of mean-field jump system with noisy observation via L-derivatives with application to finance

In this paper, we investigate stochastic optimal intervention control of mean-field nonlinear random Poisson-jump-system with related noisy process. We derive the necessary conditions of optimality for partially observed optimal intervention control problems of mean-field type. The coefficients depend on the state of the solution process as well as of its probability distribution and the control variable. The proof of our main result is obtained by applying L-derivatives in the sense of Lions. In our control model, there are two models of jumps for the state process, the inaccessible ones which come from the random Poission process and the predictable ones which come from the intervention control. Finally, we apply our result to study conditional mean-variance portfolio selection problem with interventions, where the foreign exchange interventions are intended to contain excessive fluctuations in foreign exchange rates and to stabilize them.

Improved likelihood estimation for noisy gamma degradation processes via sequential Monte Carlo

The use of Gamma processes for modeling various degradation phenomena has recently gained extensive attention. In many cases, the degradation data contain measurement errors and an intractable likelihood phenomenon comes into sight. Therefore, in order to perform efficient statistical inference, one must obtain high-quality estimates of the corresponding likelihood. Our findings indicate that the crude Monte Carlo method, which is the de facto state-of-the-art method, is not adequate in practice for efficient likelihood estimation. To cope with this problem, we propose to employ the sequential Monte Carlo approach, which shows promise for improved reliability compared to the current state of the art. Our approach leads to efficient variance minimization and opens the way for effective and scalable inference procedures.

Two-dimensional LSTM soft sensor using noisy process data

Establishing a reliable data-based soft sensor still faces a series of challenges, particularly the presence of outliers and different kinds of noise which are non-negligible in process data. To address these challenges, a correntropy-based two-dimensional long short-term memory (TLSTM) model is developed to handle noisy process data. First, the multidimensional time series samples are reconstructed into numerous two-dimensional input matrices in the feature and time directions. Then, the convolution and pooling operations are used to extract useful information in the process variables related to the quality variable. Meanwhile, a gating mechanism is employed to learn the internal representation of time series. Finally, a correntropy-based strategy is utilized to assign relatively small weights to outliers automatically, enabling reliable prediction. Two cases illustrate the reliability and advantages of TLSTM in effectively extracting quality-related features for prediction.

EZ-CDM: Fast, simple, robust, and accurate estimation of circular diffusion model parameters.

The investigation of cognitive processes that form the basis of decision-making in paradigms involving continuous outcomes has gained the interest of modeling researchers who aim to develop a dynamic decision theory that accounts for both speed and accuracy. One of the most important of these continuous models is the circular diffusion model (CDM, Smith. Psychological Review, 123(4), 425. 2016), which posits a noisy accumulation process mathematically described as a stochastic two-dimensional Wiener process inside a disk. Despite the considerable benefits of this model, its mathematical intricacy has limited its utilization among scholars. Here, we propose a straightforward and user-friendly method for estimating the CDM parameters and fitting the model to continuous-scale data using simple formulas that can be readily computed and do not require theoretical knowledge of model fitting or extensive programming. Notwithstanding its simplicity, we demonstrate that the aforementioned method performs with a level of accuracy that is comparable to that of the maximum likelihood estimation method. Furthermore, a robust version of the method is presented, which maintains its simplicity while exhibiting a high degree of resistance to contaminant responses. Additionally, we show that the approach is capable of reliably measuring the key parameters of the CDM, even when these values are subject to across-trial variability. Finally, we demonstrate the practical application of the method on experimental data. Specifically, an illustrative example is presented wherein the method is employed along with estimating the probability of guessing. It is hoped that the straightforward methodology presented here will, on the one hand, help narrow the divide between theoretical constructs and empirical observations on continuous response tasks and, on the other hand, inspire cognitive psychology researchers to shift their laboratory investigations towards continuous response paradigms.

Efficient DNA-based data storage using shortmer combinatorial encoding

Data storage in DNA has recently emerged as a promising archival solution, offering space-efficient and long-lasting digital storage solutions. Recent studies suggest leveraging the inherent redundancy of synthesis and sequencing technologies by using composite DNA alphabets. A major challenge of this approach involves the noisy inference process, obstructing large composite alphabets. This paper introduces a novel approach for DNA-based data storage, offering, in some implementations, a 6.5-fold increase in logical density over standard DNA-based storage systems, with near-zero reconstruction error. Combinatorial DNA encoding uses a set of clearly distinguishable DNA shortmers to construct large combinatorial alphabets, where each letter consists of a subset of shortmers. We formally define various combinatorial encoding schemes and investigate their theoretical properties. These include information density and reconstruction probabilities, as well as required synthesis and sequencing multiplicities. We then propose an end-to-end design for a combinatorial DNA-based data storage system, including encoding schemes, two-dimensional (2D) error correction codes, and reconstruction algorithms, under different error regimes. We performed simulations and show, for example, that the use of 2D Reed-Solomon error correction has significantly improved reconstruction rates. We validated our approach by constructing two combinatorial sequences using Gibson assembly, imitating a 4-cycle combinatorial synthesis process. We confirmed the successful reconstruction, and established the robustness of our approach for different error types. Subsampling experiments supported the important role of sampling rate and its effect on the overall performance. Our work demonstrates the potential of combinatorial shortmer encoding for DNA-based data storage and describes some theoretical research questions and technical challenges. Combining combinatorial principles with error-correcting strategies, and investing in the development of DNA synthesis technologies that efficiently support combinatorial synthesis, can pave the way to efficient, error-resilient DNA-based storage solutions.

Uncertainty assessment of aquifer hydraulic parameters from pumping test data

Data from pumping tests is a noisy process, and therefore, performing the pumping test numerous times will not get the same drawdown values. As a consequence, various pumping experiments lead to different values for aquifer parameter estimates. The data of pumping tests are usually analyzed using traditional methods (aquifer tests and AQtesolv software), which depend on trial and error technique. During these methods, non-unique values of hydraulic parameters are selected, which usually have a high level of uncertainty. Uncertainty must be taken into account in determining aquifer parameters, especially when using groundwater models for decision makers. The main goal of this study is to build a comprehensive tool for quantifying uncertainty associated with hydraulic parameter estimation from different pumping test conditions for fully penetrating wells in confined and semi-confined aquifers. To achieve the previous objective, a FORTRAN code was developed to apply the Markov Chain Monte Carlo (MCMC) algorithm using different likelihood functions (exponential, inverse, and log). This developed tool can be used to detect the most probable range of aquifer parameters that are consistent with pumping test data with a high degree of confidence. The tool was successfully used to several hypothetical cases to demonstrate the uncertainty in the quantification of aquifer parameters and compare the findings to the standard method's results. Also, the concept was verified numerically (using Modflow program) with satisfactory results using a hypothetical case with well-known aquifer parameters. Finally, the tool was applied for actual pumping test data with good results.

Pareto optimality of stochastic cooperative differential game with general delays in finite horizon

The Pareto optimality of stochastic cooperative differential game with a discrete delay, a moving-average delay and a noisy memory process is studied. We establish two sets of equivalent necessary and sufficient conditions for Pareto efficient strategies. The first set comes from reduction to a discrete delayed Pareto optimality, while the second set given by Malliavin derivative is derived by the decomposition of the adjoint equation and the relationship between two Hamiltonian functions. As applications, we use the theoretical results to an indefinite linear quadratic (LQ) Pareto game with general delays.

An online low-dimension fuzzy modeling method for time-varying processes

Many industrial processes are full of nonlinearity and noise. Fuzzy modeling often leads to issues with dimension disaster and poor robustness for such processes. To address these issues, an online low-dimension fuzzy method (OLDF) is proposed here. First, an explicit mapping-based low-dimension fuzzy method (EMLF) is proposed to handle intricate nonlinear and noisy processes. In this method, similar fuzzy sets are combined into larger ones using a novel similarity criterion to reduce the fuzzy rules. Then, an explicit mapping strategy is developed to represent the local nonlinearities in each enlarged fuzzy set through an explicit mapping function. Subsequently, a robust objective function is constructed to improve the robustness of EMLF model. This objective function minimizes both the mean and variance of the modeling error, ensuring robust performance even in scenarios featuring non-Gaussian noise or outliers. After that, an online update strategy is designed to account for time-varying dynamics. It designs an adaptive detection mechanism to identify changes in dynamic behaviors. Following detection, global and local updating strategies are developed to dynamically update model parameters. Further analysis and proof highlight the effectiveness of the proposed method. Experiments with time-varying processes also confirm its success.

Noisy Delay Denoises Biochemical Oscillators.

Genetic oscillations are generated by delayed transcriptional negative feedback loops, wherein repressor proteins inhibit their own synthesis after a temporal production delay. This delay is distributed because it arises from a sequence of noisy processes, including transcription, translocation, translation, and folding. Because the delay determines repression timing and, therefore, oscillation period, it has been commonly believed that delay noise weakens oscillatory dynamics. Here, we demonstrate that noisy delay can surprisingly denoise genetic oscillators. Specifically, moderate delay noise improves the signal-to-noise ratio and sharpens oscillation peaks, all without impacting period and amplitude. We show that this denoising phenomenon occurs in a variety of well-studied genetic oscillators, and we use queueing theory to uncover the universal mechanisms that produce it.

Enhancing Semi Supervised Semantic Segmentation Through Cycle-Consistent Label Propagation in Video

To perform semantic image segmentation using deep learning models, a significant quantity of data and meticulous manual annotation is necessary (Mani in: Research anthology on improving medical imaging techniques for analysis and intervention. IGI Global, pp. 107–125, 2023), and the process consumes a lot of resources, including time and money. To resolve such issues, we introduce a unique label propagation method (Qin et al. in IEEE/CAA J Autom Sinica 10(5):1192–1208, 2023) that utilizes cycle consistency across time to propagate labels over longer time horizons with higher accuracy. Additionally, we acknowledge that dense pixel annotation is a noisy process (Das et al. in: Proceedings of the IEEE/CVF winter conference on applications of computer vision, pp. 5978–5987, 2023), whether performed manually or automatically. To address this, we present a principled approach that accounts for label uncertainty when training with labels from multiple noisy labeling processes. We introduce two new approaches; Warp-Refine Propagation and Uncertainty-Aware Training, for improving label propagation and handling noisy labels, respectively, and support the process with quantitative and qualitative evaluations and theoretical justification. Our contributions are validated on the Cityscapes and ApolloScape datasets, where we achieve encouraging results. In later endeavors, the aim should be to expand such approaches to include other noisy augmentation processes like image-based rendering methods (Laraqui et al. in Int J Comput Aid Eng Technol 18(5):141–151, 2023), thanks to the noisy label learning approach.