Stochastic Calculations Research Articles

Spontaneous Stochasticity in the Presence of Intermittency.

Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain nondeterministic in the limit where the random input, namely, the thermal noise, vanishes. Here, we investigate the fate of spontaneous stochasticity in the presence of spatial intermittency, with multifractal scaling of the lognormal type, as usually encountered in turbulence studies. In principle, multifractality enhances the underlying roughness, and should also favor the spontaneous stochasticity. This letter exhibits a case with a less intuitive interplay between spontaneous stochasticity and spatial intermittency. We specifically address Lagrangian transport in unidimensional multifractal random flows, obtained by decorating rough Markovian monofractal Gaussian fields with frozen-in-time Gaussian multiplicative chaos. Combining systematic MonteCarlo simulations and formal stochastic calculations, we evidence a transition between spontaneously stochastic and deterministic behaviors when increasing the level of intermittency. While its key ingredient in the Gaussian setting, roughness here surprisingly conspires against the spontaneous stochasticity of trajectories.

Reform and innovation of saxophone teaching mode in colleges and universities based on Bayesian model

Abstract To improve the teaching level of saxophone performance in colleges and universities, this paper constructs a saxophone performance education optimization platform based on Bayesian theory. Bayesian clustering is used to informally cluster the saxophone performance education situation in colleges and universities, and the maximum likelihood algorithm is used to calculate the student behavior parameters. The Bayesian network tracking technique analyzes all learning behavior indicators to serve as a reference to obtain labels of learner motivation. To ensure the validity of the feedback metrics, the Bayesian stochastic calculation method was invoked to calculate the AUC (metric) mean ratio of the three feedback metrics. A practical teaching analysis was conducted to verify the platform’s timeliness. The results show that: The response time of login and resource search of the platform constructed in this paper is less than 2.5s and 1.2s, respectively, and the AUC mean ratio of three feedback metrics, namely, download rate, registration rate, and click rate, has improved by about 0.75%. Moreover, the positive attitude of university students towards learning has reached 88%. This shows the reliability of the educational platform constructed in this paper in optimizing higher education saxophone performance education, which can effectively improve the teaching level of saxophone performance education.

Revamping Biopharmaceutics-Pharmacokinetics with Scientific and Regulatory Implications for Oral Drug Absorption.

The Wagner-Nelson and Loo-Riegelman methods developed in the 1960s and used since for the construction of percent of drug absorbed as a function of time as well as in in vitro in vivo correlations are re-considered in the light of the physiologically sound Finite Absorption Time (F.A.T.) concept developed recently. The classical equations for the percentage of drug absorption as a function of time were modified by taking into account the termination of drug absorption at F.A.T., replacing the parameters associated with the assumption of infinite drug absorption. Mathematical analysis using the relevant Physiologically Based Pharmacokinetic Finite Time (PBFTK) models assuming one- or two-compartment drug disposition, revealed that the modified %absorbed versus time curves are of bilinear type with an ascending limb intersecting the horizontal line at F.A.T. A computer-based methodology is described for the estimation of F.A.T. from experimental data. More than one linear ascending limb is found when more than one absorption phase is operating. Experimental data were analyzed and the estimates for F.A.T were found to be similar to those derived from nonlinear regression analysis using PBFTPK models. These results place an end to the routinely reported exponential %absorbed versus time curves prevailing in biopharmaceutics-pharmacokinetics since their inception in the'60s. These findings point to the use of the F.A.T. concept in drug absorption research and regulatory guidelines such as deconvolution techniques for the assessment of drug input rate, stochastic mean absorption time calculations, population analyses, in vitro in vivo correlations and bioequivalence guidelines.

Research on fatigue reliability assessment of engine cylinder head based on neural network

Fatigue reliability (FR) evaluation is crucial for extending the service life and improving the reliability of automotive engines. This study proposed a general framework for assessing high cycle FR based on the back propagation neural network (BPNN). Using a diesel engine cylinder head (CH) as an example, the stochastic finite element analysis was implemented by considering the uncertainties of materials and loads. Subsequently, the stochastic finite element calculation process was replaced with the BPNN model to expedite fatigue life prediction. Ultimately, the reliability assessment of the CH was conducted, taking into account the influence of the load sequence. The research findings indicated that the reliable life t0.95 of the CH considering the load sequence was approximately 75 h, representing a 7.1% increase compared to the linear cumulative damage. During the service life of the CH, the failure probability sensitivity factor for the gas force load exceeded 0.9, offering an important reference for optimizing FR.

Study on Dynamic Interval Power Flow Calculation of Microgrid Based on Monte Carlo Algorithm

In order to effectively monitor the stability of the microgrid, based on the advantages of the Monte Carlo algorithm, a dynamic interval power flow calculation method for microgrid is designed. First, based on the multilayer complex structure of the microgrid, the hierarchical topology of its interval structure is analyzed. Then, the micropower flow model is designed, the affine algorithm is used to accurately describe the relationship between the variables in the microgrid structure, and the dynamic interval affine calculation is completed. Therefore, in the dynamic interval of the microgrid, the Monte Carlo probability method is applied to obtain more random data. Based on this, a model is established for the probability of wind power generation and photovoltaic power generation to simulate the output characteristics of the microgrid. Finally, the voltage variable, active power variable, and reactive power variable are calculated and embedded in the iterative algorithm to realize the stochastic power flow calculation of the microgrid. After experimental verification, the voltage amplitude calculated using the method proposed in this article has a small error value compared to the actual voltage, with a minimum error value of 0.2, close to 0. Under the condition of convergence accuracy of 10−6, the minimum convergence frequency is 3 times, and the power flow calculation process time does not exceed 38 seconds. This proves that the algorithm has high calculation accuracy, good convergence performance and timeliness, and can provide certain technical support for the stable operation of microgrids.

Frequency-domain adaptive MIMO filter with fractional oversampling using stochastic gradient descent for long-haul transmission over coupled 4-core fibers.

We propose a fractionally spaced frequency-domain adaptive multi-input multi-output (MIMO) filter architecture in which the sampling rate of input signals is below 2× oversampling with a non-integer oversampling factor for mode demultiplexing in long-haul transmission over coupled multi-core fibers. The frequency-domain sampling rate conversion to the symbol rate, i.e., 1× sampling, is placed after the fractionally spaced frequency-domain MIMO filter. The filter coefficients are adaptively controlled by stochastic gradient descent and gradient calculation with back propagation through the sampling rate conversion from the output signals on the basis of deep unfolding. We evaluated the proposed filter through a long-haul transmission experiment of 16-channel wavelength-division multiplexed and 4-core space-division multiplexed 32-Gbaud polarization-division-multiplexed quadrature phase shift keying signals over coupled 4-core fibers. The fractional oversampling frequency-domain adaptive 8×8 filter with 9/8× oversampling provided little performance penalty after 6240-km transmission compared to the conventional 2× oversampling frequency-domain adaptive 8×8 filter. The computational complexity in terms of the required number of complex-valued multiplications was reduced by 40.7%.

Phase transitions in de Sitter spacetimes: Quantum Corrections

We investigate the decay rate of a false vacuum state in de Sitter space at high Hubble rates, using two methods: the Hawking-Moss instanton method which is fully quantum mechanical but relies on the saddle-point approximation, and the Starobinsky-Yokoyama stochastic approach which is nonperturbative but does not include quantum effects. We use the flux over population method to compute the Hawking-Moss decay rate at one-loop order, and demonstrate that in its domain of validity, it is reproduced by the stochastic calculation using the one-loop constraint effective potential. This suggests that the stochastic approach together with the constraint effective potential can be used to accurately describe vacuum decay beyond the saddle-point approximation.

Design and performance evaluation of a slit-slat camera for 2D prompt gamma imaging in proton therapy monitoring: A Monte Carlo simulation study.

We investigated the design of a prompt gamma camera for real-time dose delivery verification and the partial mitigation of range uncertainties. A slit slat (SS) camera was optimized using the trade-off between the signal-to-noise ratio and spatial resolution. Then, using the GATE Monte Carlo package, the camera performances were estimated by means of target shifts, beam position quantification, changing the camera distance from the beam, and air cavity inserting. A homogeneous PMMA phantom and the air gaps induced PMMA phantom were used. The air gaps ranged from 5mm to 30mm by 5mm increments were positioned in the middle of the beam range. To reduce the simulation time, phase space scoring was used. The batch method with five realizations was used for stochastic error calculations. The system's detection efficiency was PGs/proton) for a 10 × 20 cm2 detector (source-to-collimator distance=15.0cm). Axial and transaxial resolutions were 23mm and 18mm, respectively. The SS camera estimated the range as 69.0±3.4 (relative stochastic error 1-sigma is 5%) and 67.6±1.8mm (2.6%) for the real range of 67.0mm for 107 and 108 protons of 100 MeV, respectively. Considering 160 MeV, these values are 155.5±3.1 (2%) and 152.2±2.0mm (1.3%) for the real range of 152.0mm for 107 and 108 protons, respectively. Considering phantom shift, for a 100 MeV beam, the precision of the quantification (1-sigma) in the axial and lateral phantom shift estimation is 2.6mm and 1mm, respectively. Accordingly, the axial and lateral quantification precisions were 1.3mm and 1mm for a 160 MeV beam, respectively. Furthermore, the quantification of an air gap formulated as , where and gapreal are the estimated and real air gap, respectively. The precision of the air gap quantification is 1.6mm (1 sigma). Moreover, 2D PG images show the trajectory of the proton beam through the phantom. The proposed slit-slat imaging systems can potentially provide a real-time, in-vivo, and non-invasive treatment monitoring method for proton therapy.

Distilling Importance Sampling for Likelihood Free Inference

Likelihood-free inference involves inferring parameter values given observed data and a simulator model. The simulator is computer code which takes parameters, performs stochastic calculations, and outputs simulated data. In this work, we view the simulator as a function whose inputs are (1) the parameters and (2) a vector of pseudo-random draws. We attempt to infer all these inputs conditional on the observations. This is challenging as the resulting posterior can be high dimensional and involves strong dependence. We approximate the posterior using normalizing flows, a flexible parametric family of densities. Training data is generated by likelihood-free importance sampling with a large bandwidth value ϵ , which makes the target similar to the prior. The training data is “distilled” by using it to train an updated normalizing flow. The process is iterated, using the updated flow as the importance sampling proposal, and slowly reducing ϵ so the target becomes closer to the posterior. Unlike most other likelihood-free methods, we avoid the need to reduce data to low-dimensional summary statistics, and hence can achieve more accurate results. We illustrate our method in two challenging examples, on queuing and epidemiology. Supplementary materials for this article are available online.

Deep learning-aided joint DG-substation siting and sizing in distribution network stochastic expansion planning

The rapid growth of distributed generation (DG) and load has highlighted the necessity of optimizing their ways of integration, as their siting and sizing significantly impact distribution networks. However, little attention has been paid to the siting and sizing of new substations which are to be installed. This paper proposes deep learning-aided joint DG-substation siting and sizing in distribution network stochastic expansion planning. First, as the model depends on an accurate forecast, Long Short-Term Memory (LSTM) deep neural network is used to forecast DG output and load, where electricity growth rate, bidding capacity of the electric expansion, and industrial difference are all considered. Then, a two-stage stochastic mixed integer bilinear programming model was established for joint DG-substation siting and sizing under uncertainties, where multiple objective functions are comprehensively addressed. By using the Fortuny-Amat McCarl Linearization, the resultant bilinear model is equivalently transformed into a mixed integer linear program, which can be efficiently solved. Finally, stochastic power flow calculation in the IEEE 69-node system is conducted to analyze the influence of electric expansion and DG integration on the node voltage and power flow distribution of the power system. The effectiveness of the proposed method is also verified by simulation tests.

Seismic Deformation Evaluation of High Concrete Face Rockfill Dam Based on Stochastic Dynamic Analysis Method

Most of the existing studies on high dams under seismic action use stable ground motions, which cannot simulate the non-stationary process of practical ground motions well. Although many scholars have studied the special characteristics of ground motion frequency and intensity lately, relatively few systematic studies have been carried out for the residual deformation of practical high dam projects. In this paper, considering the special characteristics of ground motions, 144 non-stationary stochastic seismic acceleration time histories are generated by the spectral expression-random function method, and stochastic dynamic calculations are carried out for four three-dimensional models of Gushui, Lava, Dashixia, and Ciha Gorge, respectively. We analyze the acceleration and residual deformation laws of four concrete face rockfill dams (CFRDs) based on the generalized probability density evolution method (GPDEM) and extreme value distribution theory. According to the results, the reference value of the dam body deformation of the 250 m panel under different seismic intensities is given, and the settlement at the dam crest is proposed. When the safety control standard is 1.0~1.1%, the ultimate seismic capacity of the 250 m face rockfill dam is 0.7~0.8 g.

Risk assessment of a layered slope considering spatial variabilities of interlayer and intralayer

While many studies have analyzed the effects of spatial variabilities of intralayer soil parameters on the probability of failure and risk of layered slopes, there is a paucity of research on the effects of interlayer variability. This paper is intended to investigate the influence of interlayer variability on the mechanical responses of a layered slope, as well as the effects of spatial variabilities of strength parameters of intralayer soils. To characterize the uncertainty of intralayer and interlayer spatial variabilities of layered geologic profiles, an integrated random field is developed using the program of FLAC based on both the two-dimensional random field theory and one-dimensional random process theory. Particularly, the random field for the interlayer transition zone is generated by a linear interpolation technique. Within the framework of Monte-Carlo simulation, a large number of stochastic calculations for a two-layered slope are conducted to evaluate the influences of spatial variabilities of both interlayer and intralayer on the stability and risk of the slope. The results show the failure mode of a two-layered slope changes greatly due to the stochastic layered boundary. It is also noted that the probability and risk of slope failure might be underestimated if ignoring the uncertainty arising from layered boundary and layered transition zone. The proposed equations can provide helpful information when investigating the probability and risk associated with layered slopes.

Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime

We introduce a second-order stochastic effective theory for light scalar fields in de Sitter spacetime, extending the validity of the stochastic approach beyond the massless limit and demonstrating how it can be used to compute long-distance correlation functions nonperturbatively. The parameters of the second-order stochastic theory are determined from quantum field theory through a perturbative calculation, which is valid if the self-interaction parameter $\ensuremath{\lambda}$ satisfies $\ensuremath{\lambda}\ensuremath{\ll}{m}^{2}/{H}^{2}$, where $m$ is the scalar and $H$ is the Hubble rate. Therefore, it allows stronger self-interactions than conventional perturbation theory, which is limited to $\ensuremath{\lambda}\ensuremath{\ll}{m}^{4}/{H}^{4}$ by infrared divergences. We demonstrate the applicability of the second-order stochastic theory by comparing its results with perturbative quantum field theory and overdamped stochastic calculations, and discuss the prospects of improving its accuracy with a full one-loop calculation of its parameters.

Optimizing inland container logistics through dry ports: A two-stage stochastic mixed-integer programming approach considering volume discounts and consolidation in rail transport

It is essential for container shipping companies to plan for the optimum number and locations of dry ports as well as efficient inland container logistics operations to reduce costs and environmental impacts while improving customer service. The plan for optimum inland container transportation network design must account for demand uncertainty to eliminate financial difficulty due to redundant investment. In this regard, this study proposed a two-stage stochastic mixed-integer programming model for optimizing inland container logistics through dry ports. The model contributes to the state of the art in current research by including a piecewise-linear cost function for railway transportation to account for volume discounts, integrating full container scheduling with transport mode selection and empty container relocation for consolidation, and reflecting the fact that the amount of import and export full containers transported between customers (consignees and consignors) and seaports are exogenously decided. The solution results demonstrated the definite performance superiority of the progressive hedging algorithm over the extensive form solution. Additionally, the value of stochastic solution calculation showed that the application of stochastic solution might result in significant cost savings compared to the application of mean value deterministic solution. The proposed model can be applied for practical necessities to design robust optimum inland container logistics operations using intermodal rail transport with the progressive hedging algorithm as an efficient solution approach.

Economic perspectives on blanket and selective dry cow therapy

Dry cow therapy (DCT) is an efficient measure to control intramammary infections (IMI) in dairy herds. In a blanket-DCT practice (BDCT), all cows receive antibiotics at dry-off. In a selective-DCT practice (SDCT), treatments are targeted only at infected cows. Our objective was to compare the economy of SDCT and BDCT under Finnish production conditions. Economic analysis is needed to show numerically whether the farms currently applying BDCT can switch to SDCT without the dairy farmer’s economic losses. We applied a partial budgeting approach and built a stochastic calculation model to show the margin for costs that are equal in both DCT policies. Data for modeling were generated by running 100,000 Monte Carlo simulations. The parameters for the model were extracted from the literature and from official statistics. SDCT is a competitive management practice, especially with herds succeeding in keeping their IMI risk low. Therefore, the focus in farm-level decision-making should be on the herd’s udder health status. In those herds with high IMI prevalence, the problem must be tackled primarily by means other than BDCT, which does not support the goal of reducing the use of antibiotics and which, when used routinely, is also contrary to existing EU legislation.

MODELING THE SPATIAL RESOLUTION AND FLIGHT ALTITUDE DEPENDENCE OF THE RESPONSE IN RADIOMETRIC MONITORING USING UAV.

The result interpretation of a terrain airborne radiometric monitoring depends, among others, on the spatial resolution of the measurement (i.e. the area from which the value of the measured quantity is averaged) and on the altitude dependence of the response of the measuring device. For the needs of monitoring using unmanned aerial vehicles, the approximate values of these parameters were determined by stochastic calculations for selected model conditions. Calculations were of natural background components (K, U and Th) and the surface contamination with radionuclides emitting energies was in the range of 0.3-3MeV. The dependence on the source radius was modeled in the range of 2-450 m and flight altitude dependence was modeled in the range of 1-30 m. The modeled dependencies are used to refine the interpretation of experimental data, or to optimize the planning of monitoring the flight routes, according to specified monitoring objectives.

DISPO 4.0 | Simulation-Based Optimization of Stochastic Demand Calculation in Consumption-Based Material Planning in the Capital Goods Industry

This paper presents a digital material planning approach, utilizing simulation-based optimization to select and parametrize article specific demand forecasting methods. Demand forecasts are the basis of material requirements planning in consumption-based material planning, and are an essential lever for efficient inventory and order calculation. Despite their acknowledged potential, digital tools for optimized demand calculation are still lacking in practice. Thus, the goal of the presented approach to provide an applicationoriented method to optimally select and parametrize state-of-the-art forecasting methods, based on product-specific demand data. In this approach, a rule-based selection heuristic is combined with static simulation of demand time-series and a metaheuristics-based optimization of forecasting parameters, to provide automatically optimized article-specific demand forecasts. Case studies for two companies in the capital goods industry evaluate and quantify the application potential. The results point to significantly improved, itemspecific demand planning

McCARD/MIG stochastic sampling calculations for nuclear cross section sensitivity and uncertainty analysis

In this study, a cross section stochastic sampling (S.S.) capability is implemented into both the McCARD continuous energy Monte Carlo code and MIG multiple-correlated data sampling code. The ENDF/B-VII.1 covariance data based 30 group cross section sets and the SCALE6 covariance data based 44 group cross section sets are sampled by the MIG code. Through various uncertainty quantification (UQ) benchmark calculations, the McCARD/MIG results are verified to be consistent with the McCARD stand-alone sensitivity/uncertainty (S/U) results and the XSUSA S.S. results. UQ analyses for Three Mile Island Unit 1, Peach Bottom Unit 2, and Kozloduy-6 fuel pin problems are conducted to provide the uncertainties of keff and microscopic and macroscopic cross sections by the McCARD/MIG code system. Moreover, the SNU S/U formulations for uncertainty propagation in a MC depletion analysis are validated through a comparison with the McCARD/MIG S.S. results for the UAM Exercise I-1b burnup benchmark. It is therefore concluded that the SNU formulation based on the S/U method has the capability to accurately estimate the uncertainty propagation in a MC depletion analysis.

A fully adaptive method for structural stochastic response analysis based on direct probability integral method

This paper proposes a fully adaptive method to estimate the probability density function (PDF) of the responses for stochastic structures under static and dynamic loads. The PDF is described by a recently published direct probability integral method (DPIM). In DPIM, the key smoothing parameter σ and the number of samples Ns, which have significant impacts on the determination of PDF and the efficiency of stochastic response calculation, are still difficult to determine in a completely adaptive manner. To this end, we derive a weighted kernel density estimation (weighted-KDE) method to adaptively obtain the σ by minimizing the mean integrated squared error between the estimated PDF and the real PDF. In addition, a new iterative sampling strategy is proposed to adaptively determine the Ns, in which a candidate sample pool is generated firstly, then the samples are gradually selected from the pool. This strategy ensures that the used samples in each iteration can fill the probability space in a ‘highly uniform’ manner. Based on the standard deviation calculated by the estimated PDF, a stopping criterion is presented to stop the iterative process. Moreover, the detailed steps of the proposed fully adaptive method is given by combining the weighted-KDE method and the sampling strategy. Four engineering examples validate the adaptive ability, efficiency and accuracy of the proposed method.

The Mini Labyrinth Benchmark for Radiation Protection and Shielding Analysis

The Mini Labyrinth experiment is a neutron and gamma shielding experiment currently being developed at the Slovak University of Technology, Bratislava (STU). The STU Mini Labyrinth consists of NEUTRONSTOP shielding blocks, water tank, PuBe neutron source, and graphite prism. This article describes the second construction version of the Mini Labyrinth experiment and presents the newest results of the neutron and gamma fields’ simulation and measurement. The PuBe neutron source with the emission rate of 1.06E7 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{n}\cdot \text{s}^{-1}$ </tex-math></inline-formula> was used in the experiment. The measurement of gamma ambient dose equivalent H*(10) and neutron count rates is performed by the Thermo Scientific RadEye portable survey meter and the SNM-11 BF3-filled corona detector. The simulation part was carried out using the state-of-the-art MCNP6 and SCALE6 MONACO stochastic calculation tools, considering the detailed geometry of the Mini Labyrinth and a combined neutron and gamma source of particles. The comparisons were performed between codes and the experiment. The propagation of cross-sectional uncertainties was investigated through the shielding analysis. Almost perfect agreements between simulation codes were achieved. The comparison with measurement suggests the further needs of room effect assessment.