A Modified Inhomogeneous Stochastic Simulation Algorithm to Model Reactive Boundary Conditions

The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.

Stochastic Simulation and Analysis of Geological Corrosion Defects in Dam Foundation

Uncertainty in geological structural modeling, especially geological corrosion(a kind of karst cave), is a bottleneck that restricts the development and application of geological computer modeling and effect estimation. To solve this issue, a stochastic modeling method based on the random field theory is proposed in comparison with the deterministic geometric modeling method. Then the constraint random field modeling method and the random field modeling method without constrained parameters are compared and analyzed. A case study shows that the novel stochastic simulation method is an effective tool to describe the distribution characteristics of corrosion parameters and reflect the updated geological prospecting information. The influence of geological corrosion on the dam behavior can also be better analyzed by using the stochastic simulation method. At the same time, the unconfined random field ignores the sample location information and may lead to higher variability. Therefore, the constraint random field modeling method can provide a useful reference for the numerical analysis under complex geological conditions.

Stochastic Simulation of Emission Spectra and Classical Photon Statistics of Quantum Dot Superluminescent Diodes

We present a stochastic procedure to investigate the correlation spectra of quantum dot superluminescent diodes. The classical electric field of a diode is formed by a polychromatic superposition of many independent stochastic oscillators. Assuming fields with individual carrier frequencies, Lorentzian linewidths and amplitudes we can form any relevant experimental spectrum using a least square fit. This is illustrated for Gaussian and Lorentzian spectra, Voigt profiles and box shapes. Eventually, the procedure is applied to an experimental spectrum of a quantum dot superluminescent diode which determines the first- and second-order temporal correlation functions of the emission. We find good agreement with the experimental data and a quantized treatment. Thus, a superposition of independent stochastic oscillators represents the first- and second-order correlation properties of broadband light emitted by quantum dot superluminescent diodes.

New Deterministic and Stochastic Simulation Models for UAV-MIMO Ricean Fading Channels

For the practical simulation and performance evaluation of unmanned aerial vehicle(UAV)multiple-input multiple-output(MIMO)Ricean fading channels,it is desirable to develop accurate UAV-MIMO channel simulation models for more realistic scenarios of non-isotropic scattering.In this study,using a twocylinder reference model to describe the distribution of scatterers,we propose new deterministic and stochastic simulation models.Analytical and numerical results indicate that both simulation models provide good approximations to the desired statistical properties of the reference model,and the stochastic simulation model results in a better performance under comparable computational complexity.

Stochastic Simulation of the Cell Cycle Model for Budding Yeast

We use the recently proposed Nested Stochastic Simulation Algorithm(Nested SSA)to simulate the cell cycle model for budding yeast.The results show that Nested SSA is able to significantly reduce the computational cost while capturing the essential dynamical features of the system.

An Algorithm for the Stochastic Simulation of Gene Expression and Heterogeneous Population Dynamics

We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics.The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations.To benchmark performance,we compare simulation results with steadystate and time-dependent analytical solutions for several scenarios,including steadystate and time-dependent gene expression,and the effects on population heterogeneity of cell growth,division,and DNA replication.This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression.We also use the algorithm to model gene expression dynamics within"bet-hedging"cell populations during their adaption to environmental stress.These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics,relevant physiological details and phenotypic variability.

Strong Convergence and Speed up of Nested Stochastic Simulation Algorithm

In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes,for which strong error estimates can also be obtained.Numerical experiments are presented to demonstrate the validity of our analysis.

Scheduling an Energy-Aware Parallel Machine System with Deteriorating and Learning Effects Considering Multiple Optimization Objectives and Stochastic Processing Time

Currently,energy conservation draws wide attention in industrial manufacturing systems.In recent years,many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as an effective approach.This paper puts forwards a multi-objective stochastic parallel machine scheduling problem with the consideration of deteriorating and learning effects.In it,the real processing time of jobs is calculated by using their processing speed and normal processing time.To describe this problem in a mathematical way,amultiobjective stochastic programming model aiming at realizing makespan and energy consumption minimization is formulated.Furthermore,we develop a multi-objective multi-verse optimization combined with a stochastic simulation method to deal with it.In this approach,the multi-verse optimization is adopted to find favorable solutions from the huge solution domain,while the stochastic simulation method is employed to assess them.By conducting comparison experiments on test problems,it can be verified that the developed approach has better performance in coping with the considered problem,compared to two classic multi-objective evolutionary algorithms.

StochSD: A Full Potential CSS Language for Dynamic and Stochastic Modelling, Simulation and Statistical Analysis

It is vital that a well-defined conceptual model can be realized by a macro-model (e.g., a Continuous System Simulation (CSS) model) or a micro-model (e.g., an Agent-Based model or Discrete Event Simulation model) and still produce mutually consistent results. The Full Potential CSS concept provides the rules so that the results from macro-modelling become fully consistent with those from micro-modelling. This paper focuses on the simulation language StochSD (Stochastic System Dynamics), which is an extension of classical Continuous System Simulation that implements the Full Potential CSS concept. Thus, in addition to modelling and simulating continuous flows between compartments represented by “real” numbers, it can also handle transitions of discrete entities by integer numbers, enabling combined models to be constructed in a straight-forward way. However, transition events of discrete entities (e.g., arrivals, accidents, deaths) usually happen irregularly over time, so stochasticity often plays a crucial role in their modelling. Therefore, StochSD contains powerful random functions to model uncertainties of different kinds, together with devices to collect statistics during a simulation or from multiple replications of the same stochastic model. Also, tools for sensitivity analysis, optimisation and statistical analysis are included. In particular, StochSD includes features for stochastic modelling, post-analysis of multiple simulations, and presentation of the results in statistical form. In addition to making StochSD a Full Potential CSS language, a second purpose is to provide an open-source package intended for small and middle-sized models in education, self-studies and research. To make StochSD and its philosophy easy to comprehend and use, it is based on the System Dynamics approach, where a system is described in terms of stocks and flows. StochSD is available for Windows, macOS and Linux. On the StochSD homepage, there is extensive material for a course in Modelling and Simulation in form of PowerPoint lectures and laboratory exercises.

Ground-motion simulation for the MW6.1 Ludian earthquake on 3 August 2014 using the stochastic finite-fault method

The stochastic finite-fault simulation method was applied to synthesize the horizontal ground acceleration seismograms produced by the MW6.1 Ludian earthquake on August 3,2014.For this purpose,we produced first a total of 200 kinematic source models for the Ludian event,which are characterized by the heterogeneous slip on the conjugated ruptured fault and the slip-dependent spreading of the rupture front.The results indicated that the heterogeneous slip and the spatial extent of the ruptured fault play dominant roles in the spatial distribution of ground motions in the near-fault area.The peak ground accelerations(PGAs)and 5%-damped pseudospectral accelerations(PSAs)at periods shorter than 0.5 s estimated on the resulting synthetics generally match well with the observations at stations with Joyner-Boore distances(RJB)greater than 20 km.The synthetic PGVs and PSAs at periods of 0.5 s and 0.75 s are in good agreement with predicted medians by the Yu14 model(Yu et al.,2014).However,the synthetic results are generally much lower than the predicted medians by BSSA14 model(Boore et al.,2014).Moreover,the ground motion variability caused by the randomness in the source rupture process was evaluated by these synthetics.The standard deviations of PSAs on the base-10 logarithmic scale,Sigma[log10(PSA)],are closely dependent on either the spectral period or the RJB.The Sigma[log10(PSA)]remains a constant approximately 0.55 at periods shorter than 0.1 s,and then increase continuously up to^0.13 as the period increases from 0.1 to 2.0 s.The Sigma[log10(PSA)]values at periods of 0.1‒2.0 s show the downward tendency as the RJB values increase.However,the Sigma[log10(PSA)]​values at periods shorter than 0.1 s decrease as the RJB values increase up to^50 km,and then increase with the increasing RJB.Furthermore,we found that the ground-motion variability shows the significant dependence on the azimuth.

Reducing Stochastic Discrete Models of Biochemical Networks

Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactions. Many biological processes in a cell are inherently stochastic, due to the existence of some low molecular amounts. These stochastic fluctuations may have a great effect on the biochemical system’s behaviour. In such cases, stochastic models are necessary to accurately describe the system’s dynamics. Biochemical systems at the cellular level may entail many species or reactions and their mathematical models may be non-linear and with multiple scales in time. In this work, we provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved. The proposed technique employs sensitivity analysis and requires solving an optimization problem. The numerical tests on several models of practical interest show that our model reduction strategy performs very well.

Approximations of Quasi-Stationary Distributions of the Stochastic <i>SVIR</i>Model for the Measles

In this paper, we analyze the quasi-stationary distribution of the stochastic SVIR (Susceptible, Vaccinated, Infected, Recovered) model for the measles. The quasi-stationary distributions, as discussed by Danoch and Seneta, have been used in biology to describe the steady state behaviour of population models which exhibit discernible stationarity before to become extinct. The stochastic SVIR model is a stochastic SIR (Susceptible, Infected, Recovered) model with vaccination and recruitment where the disease-free equilibrium is reached, regardless of the magnitude of the basic reproduction number. But the mean time until the absorption (the disease-free) can be very long. If we assume the effective reproduction number Rp < 1 or , the quasi-stationary distribution can be closely approximated by geometric distribution. β and δ stands respectively, for the disease transmission coefficient and the natural rate.

A Stochastic SVIR Model for Measles

In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average of the stochastic solution in the case of small population size. The choice of this model takes into account the random fluctuations inherent to the epidemiological characteristics of rural populations of Niger, notably a high prevalence of measles in children under 5, coupled with a very low immunization coverage.

Effective Finite-Difference Techniques for Estimating Sensitivities for Stochastic Biochemical Systems

Cellular environments are in essence stochastic, owing to the random character of the biochemical reaction events in a single cell. Stochastic fluctuations may substantially contribute to the dynamics of systems with small copy numbers of some biochemical species. Then, stochastic models are indispensable for properly portraying the behaviour of the system. Sensitivity analysis is one of the central tools for studying stochastic models of cellular dynamics. Here, we propose some finite-difference strategies for estimating parametric sensitivities of higher-order moments of the system state for stochastic discrete biochemical kinetic models. To reduce the variance of the sensitivity estimator, we employ various coupling techniques. The advantages of the proposed methods are illustrated in several models of biochemical systems of practical relevance.

Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

Simulating the strong ground motion of the 2022 MS6.8 Luding,Sichuan,China Earthquake

Stochastic finite-fault simulations are effective for simulating ground motions and are widely used in engineering to determine the impacts of ground motion and develop relevant predictive equations.In this study,the source,path,and site amplification coefficient of western Sichuan Province,China,and stochastic finite-fault simulations were used to simulate the acceleration time series,Fourier amplitude spectra,and 5%damped response spectra of 28 strong-motion stations with rupture distances within 300 km of the 2022 MS6.8 Luding earthquake.The simulation results of 14 stations at rupture distances of 45-185 km match the observation.However,the simulation results of 3 near-and 6 far-field stations at rupture distances of 12-36 km and 222-286 km,respectively,were obviously deviated from the observations.Simulation results of the near-field stations are larger than the observations at high frequencies(>6 Hz).The discrepancy likely comes from the nonlinear site effect of near-field stations,which reduced the site amplification at high frequencies.Simulation result of the far-field stations is smaller than the observation at frequencies above 1 Hz.As these stations are located close to the Longmenshan Fault Zone(LFZ),thus,we obtained a new quality factor(Q)from data of historical events and stations located around LFZ.Using the new Q value,the discrepancies of the high-frequency simulation results of the far-field stations were corrected.This result indicated that the laterally varying Q values can be used to address the impact of strong crustal lateral heterogeneity on simulation.

How to compare market efficiency? The Sharpe ratio based on the ARMA-GARCH forecast

This paper derives a new method for comparing the weak-form efficiency of markets.The author derives the formula of the Sharpe ratio from the ARMA-GARCH model and finds that the Sharpe ratio just depends on the coefficients of the AR and MA terms and is not affected by the GARCH process.For empirical purposes,the Sharpe ratio can be formulated with a monotonic increasing function of R-squared if the sample size is large enough.One can utilize the Sharpe ratio to compare weak-form efficiency among different markets.The results of stochastic simulation demonstrate the validity of the proposed method.The author also constructs empirical AR-GARCH models and computes the Sharpe ratio for S&P 500 Index and the SSE Composite Index.

Robotic Unicycle Intelligent Robust Control Pt I: Soft Computational Intelligence Toolkit

The concept of an intelligent control system for a complex nonlinear biomechanical system of an extension cableless robotic unicycle discussed.A thermodynamic approach to study optimal control processes in complex nonlinear dynamic systems applied.The results of stochastic simulation of a fuzzy intelligent control system for various types of external/internal excitations for a dynamic,globally unstable control object-extension cableless robotic unicycle based on Soft Computing(Computational Intelligence Toolkit-SCOptKBTM)technology presented.A new approach to design an intelligent control system based on the principle of the minimum entropy production(minimum of useful resource losses)determination in the movement of the control object and the control system is developed.This determination as a fitness function in the genetic algorithm is used to achieve robust control of a robotic unicycle.An algorithm for entropy production computing and representation of their relationship with the Lyapunov function(a measure of stochastic robust stability)described.

Bayesian Analysis of Simple Random Densities

A tractable nonparametric prior over densities is introduced which is closed under sampling and exhibits proper posterior asymptotics.