Stochastic Calculations Research Articles

A stochastic approach to forecast project duration

For executives who track projects on a complete / failed basis, at each phase of the project, the project completion date may be adjusted using only stochastic calculations in closed form. The proposed method to predict the final project duration may be interpreted intuitively. The comparative analysis of the effectiveness of the proposed method shows a good computational accuracy of predictions in many cases surpassing the accuracy of existing methods.

Optimal Kalman-like filter for a class of nonlinear stochastic systems

This paper deals with an optimal Kalman-like filter for nonlinear discrete-time systems aided with auto and cross-correlated noises and stochastic parameter matrices involved in state and measurement equations, and random nonlinearity. The random variables are proposed by their statistical characteristics while the inquiry is focused on stochastic multivariate analysis and calculation. For the nonlinear system with the auto and cross-correlated noises and stochastic parameter matrices, an equivalent system is first reconstructed by decomposing stochastic parameter matrices and introducing uncorrelated pseudo-noises. Then a recursive filter that ensures unbiasedness and minimizes the error variance is designed for the newly transformed equivalent system. Finally, the filter is verified by applying it to some numerical simulations.

Dose-dependent strain localization and embrittlement in ferritic materials: A predictive approach based on sub-grain plasticity modelling

This paper presents a theoretical approach addressing plastic-strain spreading in post-irradiated BCC materials accounting for crucial sub-grain scale, dislocation-mediated plasticity mechanisms. The proposed model explicitly provides the number of shear-bands developed in irradiated ( N i r r ) versus non-irradiated ( N 00 d p a ) grain cases, for fixed amounts of plastic deformation. Calculations carried out under various irradiation defect size and number density cases, which helps it appraising important material properties, in particular the dose-dependent, grain-scale uniform elongation threshold. The model ability to handle macro-scale effects is then evaluated using a simple stochastic calculation procedure, taking advantage of actual grain size and orientation maps. The dose-dependent embrittlement amplitude appears to critically depend on the shear band thickness and spacing variations, existing near the fracture surface of failing specimens. That perception allows comparing our predictions with adapted test results, for validation.

Stochastic many-body calculations of moir\xe9 states in twisted bilayer graphene at high pressures

We introduce three developments within the stochastic many-body perturbation theory: efficient evaluation of off-diagonal self-energy terms, construction of Dyson orbitals, and stochastic constrained random phase approximation. The stochastic approaches readily handle systems with thousands of atoms. We use them to explore the electronic states of twisted bilayer graphene (tBLG) characterized by giant unit cells and correlated electronic states. We document the formation of electron localization under compression; weakly correlated states are merely shifted in energy. We demonstrate how to efficiently downfold the correlated subspace on a model Hamiltonian with a screened frequency-dependent two-body interaction. For the 6° tBLG system, the onsite interactions are between 200 and 300 meV under compression. The Dyson orbitals exhibit spatial distribution similar to the mean-field single-particle states. Under pressure, the electron-electron interactions increase in the localized states; however, the dynamical screening does not fully balance the dominant bare Coulomb interaction.

Stochastic Variational Approach to Small Atoms and Molecules Coupled to Quantum Field Modes in Cavity QED.

In this work, we present a stochastic variational calculation (SVM) of energies and wave functions of few particle systems coupled to quantum fields in cavity QED. The spatial wave function and the photon spaces are optimized by a random selection process. Using correlated basis functions, the SVM approach solves the problem accurately and opens the way to the same precision that is reached the nonlight coupled quantum systems. Examples for a two-dimensional trion and confined electrons as well as for the He atom and the H_{2} molecule are presented showing that the light-matter coupling drastically changes the electronic states.

Sensitivity Analysis of Stochastic Calculation of SCC Regarding Aggressive Environment.

Probabilistic procedures considering the durability with respect to corrosion of reinforcement caused by aggressive substances are widely applied; however, they are based on narrow assumptions. The aspects need to be evaluated both in terms of the search for suitable application of the various experimental results and in terms of their impact on the result of the stochastic assessment itself. In this article, sensitivity analysis was used as an ideal tool to prove how input parameters affect the results of the evaluation, with consideration of different types of concrete (ordinary or self-compacting with and without fibres). These concretes may be used in aggressive environments, as an industrial floor or as a part of the load-bearing bridge structure. An example of a reinforced concrete bridge deck was selected as the solved structure. The results show that in the case of a classic evaluation, a larger amount of fibre reports a lower resistance of concrete, which contradicts the assumptions. The sensitivity analysis then shows that self-compacting concrete is more sensitive to the values of the diffusion coefficient, and with the consideration of fibres, the effect is even greater.

Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface.

The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a cubic single-particle representative volume element (RVE) of such a composite and the finite element method solution. A reinforcing particle is spherical, located centrally in the RVE, surrounded by the thin interphase of constant thickness, and remains in an elastic reversible regime opposite to the matrix, which is hyper-elastic. The interphase defects are represented as semi-spherical voids, which are placed on the outer surface of this particle. The interphase is modeled as hyper-elastic and isotropic, whose effective stiffness is calculated by the spatial averaging of hyper-elastic parameters of the matrix and of the defects. A constitutive relation of the matrix is recovered experimentally by its uniaxial stretch. The 3D homogenization problem solution is based upon a numerical determination of strain energy density in the given RVE under specific uniaxial and biaxial stretches as well as under shear deformations. The analytical relation of the effective composite stiffness to the input uncertain parameter is recovered via the response function method, using a polynomial basis and an optimized order. Probabilistic calculations are completed using three concurrent approaches, namely the iterative stochastic finite element method (SFEM), Monte Carlo simulation and by the semi-analytical method. Previous papers consider the composite fully elastic, which limits the applicability of the resulting effective stiffness tensor computed therein. The current study voids this assumption and defines the composite as fully hyper-elastic, thus extending applicability of this tensor to strains up to 0.25. The most important research finding is that (1) the effective stiffness tensor is sensitive to random interface defects in its hyper-elastic range, (2) its resulting randomness is not close to Gaussian, (3) the semi-analytical method is not perfectly suited to stochastic calculations in this region of strains, as opposed to the linear elastic region, and (4) that the increase in random dispersion of defects volume fraction has a much higher effect on the stochastic characteristics of this stiffness tensor than fluctuation of the strain.

SOME QUESTIONS OF ESTIMATING SUSPENDED SEDIMENT IN WATERCOURSES OF NORTH-WEST RUSSIA

In the practice of water management for economic purposes, calculations of suspended sediment for various time scales – from per-second to annual, are important. The estimation of annual suspended sediment transport, as well as of the statistical parameters of turbidity and the reliability of the estimates, is extremely difficult because of irregular and insufficient light conditions in different phases of the water regime. At the same time, owing to the knowledge of the processes that shape the quality of natural waters and a sufficient toolkit of calculation methods, the main indicators of water quality with can be reproduced with acceptable accuracy. The capabilities of statistical analysis of water quality indicators can be expanded by an integrated approach to estimating the indicators by means of well-proven deterministic and stochastic calculation algorithms with arguments observed regularly and for a long time. In this case, a composite method can be used to estimate the parameters of the suspended sediment distribution or water turbidity, which permits finding the parameters of the distribution curve of the function from the parameters of the distribution curve of its arguments. The paper presents a deterministic-stochastic modeling system “weather-runoff-suspended sediments”, based on a stochastic weather model, a model of runoff formation in a catchment area, and a model of annual suspended sediment transport. The system can estimate the distribution parameters of daily suspended sediment load and turbidity values in the situation of observed data shortage or changes in runoff formation in the catchment resulting from natural causes or economic activities.

Validation of a 6-Dye Short Tandem Repeat System: A Dry Kit With Lyophilized Amplification Reagent.

The SureID®S6 system used a lyophilized pellet as the amplification reagent to enable multiplexing of sex-determining marker Amelogenin, 21 autosomal short tandem repeats (STRs), and one Y-STR. To assess the performance, reliability, and limitation of the dry amplification system, the validation studies including PCR condition, reproducibility, sizing and precision, analytical threshold calculation, sensitivity and stochastic threshold calculation, species specificity, stability, mixture, case sample, and population and concordance were conducted according to the Scientific Working Group on DNA Analysis Methods (SWGDAM) Validation Guidelines. Experimental data suggested that the optimal range of total input DNA was from 125 to 500 pg; the appropriate analytical threshold was 80 relative fluorescence units (RFUs) while the stochastic threshold was 260 RFUs; for the stability studies, SureID®S6 system could resist against less than 500 μmol/L of hematin, 100 ng/μl of humic acid, 4 mM of indigotin, 800 mM of tannic acid, and 800 mM of calcium ion. Population and concordance studies using 500 unrelated individuals showed that the combined probability of discrimination (CPD) and cumulative probability of exclusion (CPE) values were 0.999999999999 and 0.999999998416, respectively. The genotypes for the same sample were concordant with the previously validated HUAXIA™ Platinum kit. The validation results demonstrated that the SureID®S6 system could be used for forensic applifications.

Non-Gaussian Tail of the Curvature Perturbation in Stochastic Ultraslow-Roll Inflation: Implications for Primordial Black Hole Production.

We consider quantum diffusion in ultraslow-roll (USR) inflation. Using the ΔN formalism, we present the first stochastic calculation of the probability distribution P(R) of the curvature perturbation during USR. We capture the nonlinearity of the system, solving the coupled evolution of the coarse-grained background with random kicks from the short wavelength modes, simultaneously with the mode evolution around the stochastic background. This leads to a non-Markovian process from which we determine the highly non-Gaussian tail of P(R). Studying the production of primordial black holes in a viable model, we find that stochastic effects during USR increase their abundance by a factor of ∼10^{5} compared with the Gaussian approximation.

Implementation of skyrmion cellular automaton using Brownian motion and magnetic dipole interaction

In this study, we investigated the interaction between skyrmions in Brownian motion at room-temperature. Cells containing two skyrmions were implemented by controlling the magnetic anisotropy in the Ta/CoFeB/Ta/MgO/SiO2 structure. The interaction between skyrmions was investigated by fabricating a circuit with two cells in close proximity to each other. It was found that the minimum value of the correlation coefficient was −0.234. These results show that the Brownian motion of skyrmions can potentially realize unconventional computing such as stochastic calculations and ultra-low power computing.

Efficient treatment of molecular excitations in the liquid phase environment via stochastic many-body theory.

Accurate predictions of charge excitation energies of molecules in the disordered condensed phase are central to the chemical reactivity, stability, and optoelectronic properties of molecules and critically depend on the specific environment. Herein, we develop a stochastic GW method for calculating these charge excitation energies. The approach employs maximally localized electronic states to define the electronic subspace of a molecule and the rest of the system, both of which are randomly sampled. We test the method on three solute-solvent systems: phenol, thymine, and phenylalanine in water. The results are in excellent agreement with the previous high-level calculations and available experimental data. The stochastic calculations for supercells containing up to 1000 electrons representing the solvated systems are inexpensive and require ≤1000 central processing unit hrs. We find that the coupling with the environment accounts for ∼40% of the total correlation energy. The solvent-to-solute feedback mechanism incorporated in the molecular correlation term causes up to 0.6eV destabilization of the quasiparticle energy. Simulated photo-emission spectra exhibit red shifts, state-degeneracy lifting, and lifetime shortening. Our method provides an efficient approach for an accurate study of excitations of large molecules in realistic condensed phase environments.

A New Adaptive Sparse Pseudospectral Approximation Method and its Application for Stochastic Power Flow

With the increasing integration of various renewable energy resources into electric power systems, the stochastic power flow calculation, which falls into the uncertainty propagation (UP) problems, has attracted renewed interest recently. The adaptive sparse pseudospectral approximation method (A-SPAM) is highly efficient to solve UP problems. However, there still exist two major drawbacks: 1) its global error estimate is not accurate enough to evaluate the actual approximation error; and 2) it is intended for single-output systems and there is no efficient method for its application in multi-output systems. In order to overcome these two defects, in this study a new adaptive sparse pseudospectral approximation method (NA-SPAM) is proposed based on two improvements on A-SPAM. First, a new global error estimate is presented which features much higher estimation accuracy. Second, a revised version of error estimates is given based on unification of the index set, which apparently improves the calculation efficiency for multi-output problems. At last, the effectiveness of the two improvements and NA-SPAM is validated by mathematical and practical cases.

Cross-evaluation of a parallel operating SVM – CNN classifier for reliable internal decision-making processes in composite inspection

In the aerospace industry, automated fibre laying processes are often applied for economical composite part fabrication. Unfortunately, the current mandatory visual quality assurance process takes up to 50% of the entire manufacturing time. An automised classification of manufacturing deviations using Neural Networks potentially improves the inspection's effectiveness. Unfortunately, the automated decision-making procedures of machine learning approaches are challenging to trace. Therefore, we introduce an approach for evaluating the classifiers response for this use case.For this purpose, we present a parallel classification approach of Convolutional Neural Network (CNN) and Support Vector Machine (SVM) with suitable intermediate checking stages between both classification processes. The particular novelty of this study is this intermediate comparison to trace the behaviour of the two classifiers along their image processing chains and to project the results back to the input image.With respect to the SVM, we analyse their extracted input features via t-Distributed Stochastic Neighbor Embedding calculations and parallel coordinates plots. Moreover, the classification score of the SVM as well as the feature vector distances within the SVM are investigated. For the CNN, the outputs of its first joined convolutional layer are correlated with the raw input images of different classes using Structural Similarity Index Measure metrics. Additionally, also the CNN's classification rates are analysed. Accordingly, a suitable uncertainty confidence interval for the CNN is determined on the bases of its neural activations. Finally, the relevance of individual pixels for the CNN decision is determined through Smooth Integrated Gradients and linked to the manually extracted image features for the SVM Classifier.The results of this paper are particularly valuable for developers and users of visual inspection systems in safety-critical domains.

Hydroxyl radical yields in the heavy ion radiolysis of water

The yields of hydroxyl radicals in the radiolysis of water with protons and carbon ions have been examined using experimental scavenging techniques coupled with Monte Carlo track simulations. Combined with previous results using helium ions, this set of data gives valuable information on the potential for radiation induced damage to biological systems for light ions with very different track structures. Carbon dioxide production from aerated formic acid solutions in concentrations ranging from 10−3 to 1 M was used as a probe of hydroxyl radical yields from about 6 ns to 818 ns. Numerical interpolation of the results at slightly different ion energies in combination with data from gamma radiolysis allows for a systematic analysis of both track average and track segment yields. As expected, considerable track chemistry is found to occur on the nanosecond to microsecond time scales. Monte Carlo track simulations employing stochastic diffusion-kinetic calculations of product yields are found to reproduce experimental observations satisfactorily. The track simulations are used to extract hydroxyl radical kinetics in pure water at neutral conditions.

Productive efficiency of the pelagic trawl fisheries in the Southern Black Sea

This study aimed to reveal the need for efficient catching activity by comparing the efficiency of pelagic trawl fisheries in Turkey with Stochastic frontier analysis (SFA). For this purpose, data were obtained through face-to-face interviews with 19 vessels randomly selected among 82 fishing vessels during the period. Variables used for technical inefficiency (ui) were determined as professional trawling experience, the total crew, pelagic trawling subsidy rates, and the use of pelagic trawling credits. It was used the FRONTIER 4.1. for Stochastic efficiency frontier calculations developed by Coelli (2007). As a result of the study, it was revealed that an improvement of 26% was required for trawlers to become efficient. Technical efficiency in the sampled vessels ranged from 0.413 to 0.998, with an average of 0.739. According to the results, it was concluded that the efficiency of pelagic trawl fisheries could be increased due to the improvements in the existing structural conditions and the revisions to be made in the policies implemented and the subsidies provided. However, the factors affecting inefficiency seem to be influenced by internal factors such as experience in pelagic trawling, the total crew, and the most critical issue to eliminate inefficiency seems to be increasing the subsidy rate in pelagic trawlers.In this study, it was found that the effects of engine power, total length, fuel consumption and active fishing day reduce the effect of fish catching pressure to a low level. However, other factors affecting this pressure were also included in the model. Especially when it was considered that the use of credit did not affect the efficiency, it was revealed that the increase in the subsidy rates rather than the fuel subsidy would make the trawlers more efficient.

Volatilized and Condensed Sb- and As-Bearing Phases Produced During Roasting of Cu-Rich Complex Concentrate in Nitrogen Atmosphere with Oxygen in Traces

A Cu-rich complex sulpfide concentrate (containing Sb as sulphosalts and gudmundite, and As as arsenopyrite) is roasted in Nitrogen atmosphere carrying traces of oxygen ({text{p}}^{{text{O}}_{2}} approx {10}^{-5.3}text{ bar)}. In situ measurements through QMS indicated that the volatilized species are mainly elemental sulfur, S2(g), and gaseous sulfur oxides. Sb- and As-bearing volatilized species could not be detected, owing to their low concentrations in the gas phase. Characterization studies through XRD and SEM-EDS confirmed that the condensates collected at room temperature during the roasting experiments comprised of (1) cyclo-octa sulfur, S8(s) and polysulfur oxides, Sn−xOx(s); (2) amorphous trisulfides of Sb and As; (3) and cubic crystalline trioxides of Sb and As. The solid phases in the condensate were found to be fine-sized (sub-micronic) and widely intermixed. Consequently, quantification of the solid phases in the condensates through direct measurement techniques like QEMSCAN was not possible. A novel approach of partial quantification of solid phases in the condensate through a stochastic model-based calculation approach is also presented. The model results suggested the occurrence of vapor-phase complexation of sulfides of Sb and As in the gas phase. Additional attributes of the volatilized species could be determined through a thermodynamic equilibrium calculation showing that the formation of the complex oxides, As4−nSbnO6(g), would be negligible compared to that of the complex sulfides, As4−nSbnS6(g).

Accelerate stochastic calculation of random-phase approximation correlation energy difference with an atom-based correlated sampling

A kernel polynomial method is developed to calculate the random phase approximation (RPA) correlation energy. In the method, the RPA correlation energy is formulated in terms of the matrix that is the product of the Coulomb potential and the density linear response functions. The integration over the matrix’s eigenvalues is calculated by expanding the density of states of the matrix in terms of the Chebyshev polynomials. The coefficients in the expansion are obtained through stochastic sampling. Since it is often the energy difference between two systems that is of much interest in practice, another focus of this work is to develop a correlated sampling scheme to accelerate the convergence of the stochastic calculations of the RPA correlation energy difference between two similar systems. The scheme is termed the atom-based correlated sampling (ACS). The performance of ACS is examined by calculating the isomerization energy of acetone to 2-propenol and the energy of the water–gas shift reaction. Using ACS, the convergences of these two examples are accelerated by 3.6 and 4.5 times, respectively. The methods developed in this work are expected to be useful for calculating RPA-level reaction energies for the reactions that take place in local regions, such as calculating the adsorption energies of molecules on transition metal surfaces for modeling surface catalysis.

Non-equilibrium Berezinskii-Kosterlitz-Thouless transition in driven-dissipative condensates (a) (a)Contribution to the Focus Issue Turbulent Regimes in Bose-Einstein Condensates edited by Alessandra Lanotte, Iacopo Carusotto and Alberto Bramati.

We study the two-dimensional phase transition of a driven-dissipative system of exciton-polaritons under non-resonant pumping. Stochastic calculations are used to investigate the Berezinskii-Kosterlitz-Thouless–like phase diagram for experimentally realistic parameters, with a special attention to the non-equilibrium features.

Bernoulli's Number One Solution for Stochastic Equilibrium

The present research studies the numerical methods for resolving Bernoulli’s divisive statistical stability, because it is difficult to find analytical solutions for the largest number of stochastic divisive calculations. We found a new way for Bernoulli by adding white noise. Price measurement was achieved with a variety of selected models, and we realized through the solutions that the larger the (n) we find, the more we find the direct solution that approaches zero, and the error rate that approaches zero. The difference between a numerical solution and a direct solution has been observed.