Stochastic Parameters Research Articles

Extrinsic fluctuations in the p53 cycle.

Fluctuations are inherent to biological systems, arising from the stochastic nature of molecular interactions, and influence various aspects of system behavior, stability, and robustness. These fluctuations can be categorized as intrinsic, stemming from the system's inherent structure and dynamics, and extrinsic, arising from external factors, such as temperature variations. Understanding the interplay between these fluctuations is crucial for obtaining a comprehensive understanding of biological phenomena. However, studying these effects poses significant computational challenges. In this study, we used an underexplored methodology to analyze the effect of extrinsic fluctuations in stochastic systems using ordinary differential equations instead of solving the master equation with stochastic parameters. By incorporating temperature fluctuations into reaction rates, we explored the impact of extrinsic factors on system dynamics. We constructed a master equation and calculated the equations for the dynamics of the first two moments, offering computational efficiency compared with directly solving the chemical master equation. We applied this approach to analyze a biological oscillator, focusing on the p53 model and its response to temperature-induced extrinsic fluctuations. Our findings underscore the impact of extrinsic fluctuations on the nature of oscillations in biological systems, with alterations in oscillatory behavior depending on the characteristics of extrinsic fluctuations. We observed an increased oscillation amplitude and frequency of the p53 concentration cycle. This study provides valuable insights into the effects of extrinsic fluctuations on biological oscillations and highlights the importance of considering them in more complex systems to prevent unwanted scenarios related to health issues.

A Study of Mixed Non-Motorized Traffic Flow Characteristics and Capacity Based on Multi-Source Video Data.

Mixed non-motorized traffic is largely unaffected by motor vehicle congestion, offering high accessibility and convenience, and thus serving as a primary mode of "last-mile" transportation in urban areas. To advance stochastic capacity estimation methods and provide reliable assessments of non-motorized roadway capacity, this study proposes a stochastic capacity estimation model based on power spectral analysis. The model treats discrete traffic flow data as a time-series signal and employs a stochastic signal parameter model to fit stochastic traffic flow patterns. Initially, UAVs and video cameras are used to capture videos of mixed non-motorized traffic flow. The video data were processed with an image detection algorithm based on the YOLO convolutional neural network and a video tracking algorithm using the DeepSORT multi-target tracking model, extracting data on traffic flow, density, speed, and rider characteristics. Then, the autocorrelation and partial autocorrelation functions of the signal are employed to distinguish among four classical stochastic signal parameter models. The model parameters are optimized by minimizing the AIC information criterion to identify the model with optimal fit. The fitted parametric models are analyzed by transforming them from the time domain to the frequency domain, and the power spectrum estimation model is then calculated. The experimental results show that the stochastic capacity model yields a pure EV capacity of 2060-3297 bikes/(h·m) and a pure bicycle capacity of 1538-2460 bikes/(h·m). The density-flow model calculates a pure EV capacity of 2349-2897 bikes/(h·m) and a pure bicycle capacity of 1753-2173 bikes/(h·m). The minimal difference between these estimates validates the effectiveness of the proposed model. These findings hold practical significance in addressing urban road congestion.

Fractional-Order Modeling and Stochastic Dynamics Analysis of a Nonlinear Rubbing Overhung Rotor System

To study the nonlinear dynamic behavior and system stability of a rubbing overhung rotor with viscoelastic and memory-effect damping and random uncertain parameters, this paper introduces a fractional-order modeling and stochastic dynamic analysis method for the nonlinear overhung rotor system with frictional impact faults. Firstly, the dynamic equations of the overhung rotor considering friction effect and fractional damping effect are established based on the transfer matrix method and fractional order derivative. Then, the time-domain response of the fractional-order dynamic equations is solved by combining the Runge–Kutta method and the continuous fractional expansion, and the steady-state response characteristics of different fractional damping are analyzed in the deterministic case. Finally, to analyze the response of the system under the effect of stochastic parameters, the sparse grid-based PCE metamodel of the system response is developed. Statistical moments, probability distributions, and sensitivity indices of the response of stochastic systems are revealed. The results of this paper provide a theoretical basis for efficient and accurate prediction of the stochastic response of nonlinear rubbing overhung rotor systems.

Intelligent robust controllers for tribotronic conical fluid film bearings

The article presents the results of the development of means for intelligent robust control of the parameters of a tribotronic rotor-support system with a tapered bearing with a removable bush. The proposed controller is implemented on the basis of deep Q-network reinforcement learning (DQN) synthesized on the basis of a numerical model of a rotor support system. The control strategy involved simultaneous control of the shaft position and friction in the lubrication layer. Methods for control synthesis are presented for both a deterministic system and a system with stochastic parameters. In the latter case, a controller synthesis technique is proposed that takes into account uncertainties in the system at the training stage. Testing of the resulting controllers shows the better ability of a controller trained to take into account uncertainties to cope with variable loads, as well as predict possible changes in the system and proactively transfer the system to more advantageous states.

Stochastic Parameterization of Moist Physics Using Probabilistic Diffusion Model

Deep-learning-based convection schemes have garnered significant attention for their notable improvements in simulating precipitation distribution and tropical convection in Earth system models. However, these schemes struggle to capture the stochastic nature of moist physics, which can degrade the simulation of large-scale circulations, climate means, and variability. To address this issue, a stochastic parameterization scheme called DIFF-MP, based on a probabilistic diffusion model, is developed. Cloud-resolving data are coarse-grained into resolved-scale variables and subgrid contributions, which serve as conditional inputs and outputs for DIFF-MP. The performance of DIFF-MP is compared with that of generative adversarial networks and variational autoencoders. The results demonstrate that DIFF-MP consistently outperforms these models in terms of prediction error, coverage ratio, and spread–skill correlation. Furthermore, the standard deviation, skewness, and kurtosis of the subgrid contributions generated by DIFF-MP more closely match the test data than those produced by the other models. Interpretability experiments confirm that DIFF-MP’s parameterization of moist physics is physically consistent.

Impact of stochastic physics on the representation of atmospheric blocking in EC-Earth3

Abstract. Atmospheric blocking is a synoptic-scale phenomenon that consists in an obstruction of the normal easterly progression of weather patterns in the midlatitudes, leading to persistent atmospheric conditions sometimes associated with extreme weather. State-of-the-art climate models systematically underestimate winter atmospheric-blocking frequency, especially over Europe. This is often attributed to a poor representation of small-scale processes that are fundamental for the onset and maintenance of blocking events. Here, we explore how the implementation of two stochastic parameterizations, namely the stochastically perturbed parameterization tendencies (SPPTs) and the stochastic kinetic energy backscatter (SKEB) schemes, influences the representation of Northern Hemisphere winter blocking in EC-Earth3. We show that the activation of the two stochastic schemes has moderate detrimental effects on blocking representation, when assessed through a gradient reversal index. Using a zonal–blocked flow linear decomposition, we attribute such modification to changes in the mean winter atmospheric circulation, primarily manifested in a strengthening of the midlatitude jet stream and an intensification of the Hadley cell. Ultimately, an analysis of the meridional transport of zonal momentum by stationary and transient eddies reveals that these circulation differences arise from changes in tropical stationary-eddy activity. Our findings reconnect with earlier literature on similar experiments and suggest that the activation of stochastic parameterizations may require a retuning of the model to account for the resulting significant changes in the mean atmospheric circulation.

The renormalization group for large-scale structure: origin of galaxy stochasticity

The renormalization group equations for large-scale structure (RG-LSS) describe how the bias and stochastic (noise) parameters — both of matter and biased tracers such as galaxies — evolve as a function of the cutoff Λ of the effective field theory. In previous work, we derived the RG-LSS equations for the bias parameters using the Wilson-Polchinski framework. Here, we extend these results to include stochastic contributions, corresponding to terms in the effective action that are higher order in the current J. We derive the general local interaction terms that describe stochasticity at all orders in perturbations,and a closed set of nonlinear RG equations for their coefficients. These imply thata single nonlinear bias term generates all stochastic moments through RG evolution. Further, theevolution is controlled by a different, lower scale than the nonlinear scale. This has implications for the optimal choice of the renormalization scale when comparing the theory with data to obtain cosmological constraints.

Comparison of three artificial intelligence methods for predicting 90% quantile interval of future insulin sensitivity of intensive care patients

Insulin dosing of hyperglycemic patients in the intensive care unit (ICU) is a complex and nonlinear clinical control problem. Recent model-based glycemic control protocols predict a patient-specific and time-specific future insulin sensitivity distribution, which defines the future patient state in response to insulin and nutrition inputs. The prediction methods provide a 90% confidence interval for a future insulin sensitivity distribution for a given time horizon, making the prediction problem more specific compared to common prediction problems where the aim is to predict the expected value of the given stochastic parameter. This study proposes three alternative artificial intelligence-based insulin sensitivity prediction methods to improve the prediction accuracy and make prediction parameters better fit the clinical requirements. The proposed prediction methods use different neural network models: a classification deep neural network model, a Mixture Density Network model, and a Quantile Regression-based model. A large patient data set was used to create the neural network models, including 2357 patients and 92646 blood glucose measurements from three clinical sites (Christchurch, New Zealand, Gyula, Hungary, and Liege, Belgium). Prediction accuracy was assessed by statistical metrics expressing clinical requirements, as well as via validated in-silico virtual patient simulations comparing the clinical performance of a proven glycaemic control protocol using the alternative prediction methods to assess impact on glycemic control performance and thus the need for these alternative models.

Stochastic LPV MPC-based path following control for bevel-tip flexible needle with probabilistic constraints

This paper addresses the path-tracking problem for flexible needle control systems using a stochastic linear parameter varying (LPV) and model predictive control (MPC) strategy. Flexible needles operating in dynamic environments with non-uniform tissue density often deviate from ideal assumptions, resulting in non-standard models. The bicycle kinematics model for flexible needle motion control is transformed into an LPV model, improving accuracy and enabling more efficient control. The proposed stochastic LPV MPC approach aims to mitigate uncertainties arising from modelling errors and dynamic environmental factors, ensuring accurate trajectory tracking for the flexible needle. The sample and removal method is utilized to reformulate the probabilistic-constrained optimization problem for implementation. The contributions of this work lie in the application of stochastic LPV MPC to address the trajectory tracking problem in the presence of uncertainties. The simulation results illustrate the superior robustness of the stochastic LPV MPC approach, as evidenced by significantly smaller tracking errors across various scenarios.

A Deep Learning-Enhanced Compartmental Model and Its Application in Modeling Omicron in China.

The mainstream compartmental models require stochastic parameterization to estimate the transmission parameters between compartments, whose calculation depend upon detailed statistics on epidemiological characteristics, which are expensive, economically and resource-wise, to collect. In addition, infectious diseases spread in three dimensions: temporal, spatial, and mobile, i.e., they affect a population through not only the time progression of infection, but also the geographic distribution and physical mobility of the population. However, the parameterization process for the mainstream compartmental models does not effectively capture the spatial and mobile dimensions. As an alternative, deep learning techniques are utilized in estimating these stochastic parameters with greatly reduced dependency on data particularity and with a built-in temporal-spatial-mobile process that models the geographic distribution and physical mobility of the population. In particular, we apply DNN (Deep Neural Network) and LSTM (Long-Short Term Memory) techniques to estimate the transmission parameters in a customized compartmental model, then feed the estimated transmission parameters to the compartmental model to predict the development of the Omicron epidemic in China over the 28 days for the period between 4 June and 1 July 2022. The average levels of predication accuracy of the model are 98% and 92% for the number of infections and deaths, respectively. We establish that deep learning techniques provide an alternative to the prevalent compartmental modes and demonstrate the efficacy and potential of applying deep learning methodologies in predicting the dynamics of infectious diseases.

Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification

We present a novel physics-constrained polynomial chaos expansion as a surrogate modeling method capable of performing both scientific machine learning (SciML) and uncertainty quantification (UQ) tasks. The proposed method possesses a unique capability: it seamlessly integrates SciML into UQ and vice versa, which allows it to quantify the uncertainties in SciML tasks effectively and leverage SciML for improved uncertainty assessment during UQ-related tasks. The proposed surrogate model can effectively incorporate a variety of physical constraints, such as governing partial differential equations (PDEs) with associated initial and boundary conditions constraints, inequality-type constraints (e.g., monotonicity, convexity, non-negativity, among others), and additional a priori information in the training process to supplement limited data. This ensures physically realistic predictions and significantly reduces the need for expensive computational model evaluations to train the surrogate model. Furthermore, the proposed method has a built-in uncertainty quantification (UQ) feature to efficiently estimate output uncertainties. To demonstrate the effectiveness of the proposed method, we apply it to a diverse set of problems, including linear/non-linear PDEs with deterministic and stochastic parameters, data-driven surrogate modeling of a complex physical system, and UQ of a stochastic system with parameters modeled as random fields.

Spectral incremental dynamic methodology for nonlinear structural systems endowed with fractional derivative elements subjected to fully non-stationary stochastic excitation

A novel spectral incremental dynamic analysis methodology for analysing structural response in nonlinear systems with fractional derivative elements is presented, aligning with modern seismic design codes, like Eurocode 8. Drawing inspiration from the concept of fully non-stationary stochastic processes, the vector of the imposed seismic excitations is characterised by time and frequency evolving power spectra stochastically compatible with elastic response spectra of specified damping ratio and ground acceleration. The proposed method efficiently determines the nonlinear system time-dependent probability density functions for the non-stationary system response amplitude by employing potent nonlinear stochastic dynamics concepts, such as stochastic averaging and statistical linearisation. Unlike traditional incremental dynamic analysis curves found in the literature, the herein proposed method introduces a three-dimensional alternative counterpart, that of stochastic engineering demand parameter surfaces, providing with higher-order statistics of the system response. An additional noteworthy aspect involves the derivation of response evolutionary power spectra as function of spectral acceleration, offering a deeper insight into the underlying system dynamics. Besides its capabilities, the method maintains the coveted element of a particularly low associated computational cost, increasing its attractiveness and practicality among diverse applications of engineering interest. Numerical examples comprising the bilinear hysteretic model endowed with fractional derivative elements subject to an Eurocode 8 elastic design spectrum demonstrate the capabilities and reliability of the proposed methodology. Its accuracy is assessed by juxtaposing the derived results with germane Monte Carlo Simulation data.

Myobolica: a stochastic approach to estimate physiological muscle control variability.

The inherent redundancy of the musculoskeletal systems is traditionally solved by optimizing a cost function. This approach may not be correct to model non-adult or pathological populations likely to adopt a "non-optimal" motor control strategy. Over the years, various methods have been developed to address this limitation, such as the stochastic approach. A well-known implementation of this approach, Metabolica, samples a wide number of plausible solutions instead of searching for a single one, leveraging Bayesian statistics and Markov Chain Monte Carlo algorithm, yet allowing muscles to abruptly change their activation levels. To overcome this and other limitations, we developed a new implementation of the stochastic approach (Myobolica), adding constraints and parameters to ensure the identification of physiological solutions. The aim of this study was to evaluate Myobolica, and quantify the differences in terms of width of the solution band (muscle control variability) compared to Metabolica. To this end, both muscle forces and knee joint force solutions bands estimated by the two approaches were compared to one another, and against (i) the solution identified by static optimization and (ii) experimentally measured knee joint forces. The use of Myobolica led to a marked narrowing of the solution band compared to Metabolica. Furthermore, the Myobolica solutions well correlated with the experimental data (R2 = 0.92, RMSE = 0.3 BW), but not as much with the optimal solution (R2 = 0.82, RMSE = 0.63 BW). Additional analyses are required to confirm the findings and further improve this implementation.

Dynamic reliability and seismic fragility analysis for high concrete-faced rockfill dam slopes subjected to stochastic earthquake and parameter excitation via PDEM

The randomness of material parameters and earthquake excitation greatly impacts the seismic stability of high concrete-faced rockfill dam (CFRD) slopes. However, no research has comprehensively analyzed the impacts of stochastic earthquake excitations, random parameters and their coupled effects on seismic stability of CFRD slopes and selected a multi-indicator evaluation criterion to carry out performance-based safety assessment. This paper develops a novel and comprehensive framework for evaluating the seismic stability of CFRD slopes based on the generalized probability density evolution method (GPDEM) with high efficiency and accuracy. The effects of three kinds of randomness on seismic stability of CFRD slopes were comprehensively compared and analyzed on the basis of multi-indices (safety factor (FS), cumulative slip displacement and cumulative time with FS < 1.0). Firstly, the nonlinear shear strength parameters of 40 high CFRDs were statistically collected to obtain the statistical characteristics of rockfill material strength parameters of actual CFRD projects. Secondly, three kinds of random samples were generated using generalized F-discrepancy (GF-discrepancy) method and Spectral expression-Random function (SERF) method. Then, the GPDEM was introduced to combine with three indices to perform the stochastic analysis and reliability evaluation. Finally, the fragility analysis of the CFRD slope was conducted. The results reveal that FS is more sensitive to the ground motions randomness, while cumulative slip displacement and cumulative time with FS < 1.0 are more sensitive to the material parameters randomness. The seismic safety evaluation of CFRD slopes based on multiple indices with full consideration of coupled randomness effects is necessary.

Hybrid uncertainty propagation for mechanical dynamics problems via polynomial chaos expansion and Legendre interval inclusion function

This paper investigates a non-intrusive hybrid uncertainty propagation framework in mechanical dynamic systems, utilizing polynomial chaos expansion (PCE) and Legendre inclusion function. Uncertainties with substantial knowledge and information are conceptualized as stochastic parameters and described using PCE, while Legendre polynomials are employed to represent uncertain, bounded parameters, specifically interval uncertainties. During the computation, the PCE model for each time step is developed through Galerkin projection and sparse grid numerical integration. Consequently, the statistical moments of the dynamic responses relative to the stochastic parameters are derived from the orthogonality of the PCE and transformed into functions reflecting the interval parameters. The interval bounds for these statistical moments are further determined using the Legendre inclusion function, which is obtained through optimal Latin hypercube sampling and collocation methods. Three dynamics examples, respectively, modeled by differential–algebraic equations, finite element method, and commercial software proves its applicability and superiority. Detailed assessment demonstrates that this method offers high computational efficiency and accuracy. As a non-intrusive approach, it poses no particular limitations on numerical methods for solving differential equations, making it universally applicable.

Bayesian image segmentation under varying blur with triplet Markov random field

Abstract In this paper, we place ourselves in the context of the Bayesian framework for image segmentation in the presence of varying blur. The proposed approach is based on Triplet Markov Random Fields (TMRF). This method takes into account, during segmentation, peculiarities of an image such as noise, blur, and texture. We present an unsupervised TMRF method, which jointly deals with the problem of segmentation, and that of depth estimation in order to process fluorescence microscopy images. In addition to the estimation of the depth maps using the Metropolis-Hasting and the Stochastic Parameter Estimation (SPE) algorithms, we also estimate the model parameters using the SPE algorithm. We compare our TMRF method to other MRF models on simulated images, and to an unsupervised method from the state of art on real fluorescence microscopy images. Our method offers improved results, especially when blur is important.

On the multi‐parameters identification of concrete dams: A novel stochastic inverse approach

AbstractThis paper introduces a novel stochastic inverse method that utilizes perturbation theory and advanced intelligence techniques to solve the multi‐parameter identification problem of concrete dams using displacement field monitoring data. The proposed method considers the uncertainties associated with the dam displacement monitoring data, which are comprised of two distinct sources: the first is related to stochastic mechanical properties of the dam, and the second is due to observation errors. The displacements at different measuring points generated by dam mechanical properties exhibit spatial correlation, while the observation errors at different points can be considered statistically random. In this context, the inversion formulas are derived for unknown stochastic parameters of the dam by combining perturbation equations and Taylor expansion methods. An improved meta‐heuristic optimization method is employed to identify the mean of stochastic parameters, while mathematical and statistical methods are used to determine the variance of stochastic parameters. The feasibility of the proposed method is verified through numerical examples of a typical dam section under different conditions. Additionally, the paper discusses and demonstrates the applicability of this method in a practical dam project. Results indicate that this method can effectively capture the uncertainty of dam's mechanical properties and separates them from observation errors.

Exploring chaos and ergodic behavior of an inductorless circuit driven by stochastic parameters

There exist extensive studies on periodic and random perturbations of various smooth maps investigating their dynamics. Unlike smooth maps, non-smooth maps are yet to be studied extensively under a stochastic regime. This paper presents a stochastic piecewise-smooth map derived from a simple inductorless switching circuit. The stochasticity is introduced in parameter values. The distribution of the parameter values is bounded and randomly selected from uniform and triangular distributions and ranges between high and low bifurcation parameter values of the deterministic map. Due to this inherent stochasticity in parameter values, the time evolution of the state variable cannot be predicted at a specific time instant. We observe that the state variable exhibits completely ergodic behavior when the minimum value of the parameter is the same as the minimum bifurcation parameter of the deterministic system. However, the ensemble average of the state variable converges to a fixed value. The system demonstrates nonchaotic behavior for a particular range of parameter values but the deterministic map in that bifurcation range shows interplay between chaos and periodic orbits. The values of Lyapunov exponents decrease monotonically with increased asymmetry of the distribution from which the bifurcation parameter values are chosen. We determine the probability density function of the stochastic map and verify its invariance under initial conditions. The most noteworthy result is the disappearance of chaotic behavior when the lower range of the distribution is varied while maintaining a fixed upper threshold for a particular distribution, even though the deterministic map exhibits an array of periodic and chaotic behaviors within the range. As the period-incrementing cascade with chaotic inclusion only occurs in nonsmooth maps, this paper numerically shows the stochasticity of a piecewise-smooth map obtained from a practical system for the first time where randomness is introduced in the parameter space.

A Reliability-Based Design Approach for the Flexural Resistance of Compression Yielded Fibre-Reinforced Polymer (FRP)-Reinforced Concrete Beams

Fibre-reinforced polymer (FRP) reinforcement has been employed as an alternative to conventional steel reinforcement in concrete structures, which is attributed to its excellent strength and corrosion resistance. However, one drawback is that FRP reinforcements are brittle and affect the ductility of concrete structures. One of the recent effective techniques proposed to overcome ductility issues is the compression yielding (CY) concept. The CY mechanism allows the structure to fail differently than the conventional FRP-reinforced concrete structure. Thus, the existing design recommendations as per the current codes for FRP-reinforced concrete structures are not appropriate. Hence, reliability studies are crucial for the development of a functional CY beam design in order to emphasise the structure’s lifetime performance and to guarantee safety requirements. In this study, a reliability-based design approach is developed for a compression-yielded FRP-reinforced concrete beam (CY beam) using load and resistance factor design (LRFD). Firstly, the flexural failure modes of CY beams are discussed. The uncertainties involved in the development of the probabilistic model for the CY beam are defined. A case study is consequently conducted for a CY beam with random variables that are associated with the statistical characteristics of material properties and load. The reliability analysis method employed in this research is the Hasofer–Lind method. The results suggest the importance of choosing appropriate design variables and stochastic parameters for CY blocks that contribute to a higher level of reliability. The reliability index and resistance factors of a CY beam are then evaluated using the Monte Carlo Simulation computational method. The reliability index value of 3.336 is obtained from the simulation, which indicates that the CY beam demonstrates ductile behaviour. The results not only demonstrate ductile behaviour but also contribute to a possible reduction in material costs and a substantial safety margin. When compared to conventional FRP-reinforced concrete beams, for different load ratios, CY beams showed higher resistance and better reliability levels.

The renormalization group for large-scale structure: primordial non-Gaussianities

The renormalization group for large-scale structure (RG-LSS) describes the evolution of galaxy bias and stochastic parameters as a function of the cutoff Λ. In this work, we introduce interaction vertices that describe primordial non-Gaussianity into the Wilson-Polchinski framework, thereby extending the free theory to the interacting case.The presence of these interactions forces us to include new operators and bias coefficients to the bias expansion to ensure closure under renormalization.We recover the previously-derived “scale-dependent bias” contributions, as well as a new (subdominant) stochastic contribution.We derive the renormalization group equations governing the RG-LSS for a large class of interactions which account for vertices at linear order in f NL that parametrize interacting scalar and massive spinning fields during inflation.Solving the RG equations, we show the evolution of the non-Gaussian contributions to galaxy clustering as a function of scale.